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Sample records for reservoir flow equations

  1. Production of Natural Gas and Fluid Flow in Tight Sand Reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Maria Cecilia Bravo

    2006-06-30

    This document reports progress of this research effort in identifying relationships and defining dependencies between macroscopic reservoir parameters strongly affected by microscopic flow dynamics and production well performance in tight gas sand reservoirs. These dependencies are investigated by identifying the main transport mechanisms at the pore scale that should affect fluids flow at the reservoir scale. A critical review of commercial reservoir simulators, used to predict tight sand gas reservoir, revealed that many are poor when used to model fluid flow through tight reservoirs. Conventional simulators ignore altogether or model incorrectly certain phenomena such as, Knudsen diffusion, electro-kinetic effects, ordinary diffusion mechanisms and water vaporization. We studied the effect of Knudsen's number in Klinkenberg's equation and evaluated the effect of different flow regimes on Klinkenberg's parameter b. We developed a model capable of explaining the pressure dependence of this parameter that has been experimentally observed, but not explained in the conventional formalisms. We demonstrated the relevance of this, so far ignored effect, in tight sands reservoir modeling. A 2-D numerical simulator based on equations that capture the above mentioned phenomena was developed. Dynamic implications of new equations are comprehensively discussed in our work and their relative contribution to the flow rate is evaluated. We performed several simulation sensitivity studies that evidenced that, in general terms, our formalism should be implemented in order to get more reliable tight sands gas reservoirs' predictions.

  2. Investigation of seasonal thermal flow in a real dam reservoir using 3-D numerical modeling

    Directory of Open Access Journals (Sweden)

    Üneş Fatih

    2015-03-01

    Full Text Available Investigations indicate that correct estimation of seasonal thermal stratification in a dam reservoir is very important for the dam reservoir water quality modeling and water management problems. The main aim of this study is to develop a hydrodynamics model of an actual dam reservoir in three dimensions for simulating a real dam reservoir flows for different seasons. The model is developed using nonlinear and unsteady continuity, momentum, energy and k-ε turbulence model equations. In order to include the Coriolis force effect on the flow in a dam reservoir, Coriolis force parameter is also added the model equations. Those equations are constructed using actual dimensions, shape, boundary and initial conditions of the dam and reservoir. Temperature profiles and flow visualizations are used to evaluate flow conditions in the reservoir. Reservoir flow’s process and parameters are determined all over the reservoir. The mathematical model developed is capable of simulating the flow and thermal characteristics of the reservoir system for seasonal heat exchanges. Model simulations results obtained are compared with field measurements obtained from gauging stations for flows in different seasons. The results show a good agreement with the field measurements.

  3. Gravity Effect on Two-Phase Immiscible Flows in Communicating Layered Reservoirs

    DEFF Research Database (Denmark)

    Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan

    2012-01-01

    An upscaling method is developed for two-phase immiscible incompressible flows in layered reservoirs with good communication between the layers. It takes the effect of gravity into consideration. Waterflooding of petroleum reservoirs is used as a basic example for application of this method....... An asymptotic analysis is applied to a system of 2D flow equations for incompressible fluids at high-anisotropy ratios, but low to moderate gravity ratios, which corresponds to the most often found reservoir conditions. The 2D Buckley–Leverett problem is reduced to a system of 1D parabolic equations...

  4. Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

    Science.gov (United States)

    Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

    2018-01-01

    This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

  5. The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

    Energy Technology Data Exchange (ETDEWEB)

    Nielsen, Bjoern Fredrik

    1997-12-31

    The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

  6. The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

    Energy Technology Data Exchange (ETDEWEB)

    Nielsen, Bjoern Fredrik

    1998-12-31

    The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

  7. HESS Opinions: Linking Darcy's equation to the linear reservoir

    Science.gov (United States)

    Savenije, Hubert H. G.

    2018-03-01

    In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological timescales. This drainage network provides equally distributed resistance for water to access the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the timescale of the linear reservoir appears to be inversely proportional to Darcy's conductance, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

  8. An overview of iterative coupling between geomechanical deformation and reservoir flow

    International Nuclear Information System (INIS)

    Tran, D.; Nghiem, L.; Buchanan, L.

    2005-01-01

    The coupling of a reservoir simulator to a geomechanics module has been widely applied in the petroleum industry. In a traditional reservoir simulator, subsidence can be estimated by a relatively simple formula. In a coupled simulator, flow is strongly affected by stresses and strains through porosity. Stress-dependence is ignored completely in conventional simulators, and solutions obtained from them cannot give accurate results if a stress sensitive reservoir is under consideration. In addition, thermal stresses cannot be accounted for. An iterative coupling method was presented. The basic equations for fluid flow in a porous medium consist of the equation of mass conservation, the equation of energy conservation, Darcy's law and equations of state depicting fluid characteristics. A continuum approach was used to develop the conservative equations. Material was assumed to be homogenous, isotropic and symmetric. Three test examples were used to illustrate the validity of geomechanics in reservoir simulation. The first example illustrated the difference in heave when a linear thermo-elastic constitutive model and a thermo-elastoplastic model were used. In the second example, a plastic cap model and a no-cap model were used to illustrate differences in porosity calculations. The 2 examples demonstrated that displacements and porosity calculations depend on the stress response and on the constitutive law of a material. In the third example a pseudo dilation-recompaction model showed a displacement calculation that was comparable with calculations obtained with 2-way coupling. The example illustrated the application of one-way coupling in scenarios where rigorous geomechanics calculations of subsidence are performed without the constraint of feeding back the information to a reservoir simulator. 22 refs., 13 figs

  9. Modelling and simulation of compressible fluid flow in oil reservoir: a case study of the Jubilee Field, Tano Basin (Ghana)

    International Nuclear Information System (INIS)

    Gawusu, S.

    2015-07-01

    Oil extraction represents an important investment and the control of a rational exploitation of a field means mastering various scientific techniques including the understanding of the dynamics of fluids in place. This thesis presents a theoretical investigation of the dynamic behaviour of an oil reservoir during its exploitation. The study investigated the dynamics of fluid flow patterns in a homogeneous oil reservoir using the Radial Diffusivity Equation (RDE) as well as two phase oil-water flow equations. The RDE model was solved analytically and numerically for pressure using the Constant Terminal Rate Solution (CTRS) and the fully implicit Finite Difference Method (FDM) respectively. The mathematical derivations of the models and their solution procedures were presented to allow for easy utilization of the techniques for reservoir and engineering applications. The study predicted that the initial oil reservoir pressure will be able to do the extraction for a very long time before any other recovery method will be used to aid in the extraction process depending on the rate of production. Reservoir simulation describing a one dimensional radial flow of a compressible fluid in porous media may be adequately performed using ordinary laptop computers as revealed by the study. For the simulation of MATLAB, the case of the Jubilee Fields, Tano Basin was studied, an algorithm was developed for the simulation of pressure in the reservoir. It ensues from the analysis of the plots of pressure vrs time and space that the Pressure Transient Analysis (PTA) was duly followed. The approximate solutions of the analytical and numerical solutions to the Radial Diffusivity Equation (RDE) were in excellent agreement, thus the reservoir simulation model developed can be used to describe typical pressure-time relationships that are used in conventional Pressure Transient Analysis (PTA). The study was extended to two phase oil-water flow in reservoirs. The flow of fluids in multi

  10. Application of the Fokker-Plank-Kolmogorov equation for affluence forecast to hydropower reservoirs (Betania Case)

    International Nuclear Information System (INIS)

    Dominguez Calle, Efrain Antonio

    2004-01-01

    This paper shows a modeling technique to forecast probability density curves for the flows that represent the monthly affluence to hydropower reservoirs. Briefly, the factors that require affluence forecast in terms of probabilities, the ranges of existing forecast methods as well as the contradiction between those techniques and the real requirements of decision-making procedures are pointed out. The mentioned contradiction is resolved applying the Fokker-Planck-Kolmogorov equation that describes the time evolution of a stochastic process that can be considered as markovian. We show the numerical scheme for this equation, its initial and boundary conditions, and its application results in the case of Betania's reservoir

  11. Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs

    KAUST Repository

    Negara, Ardiansyah

    2015-11-09

    Shale gas resources have received great attention in the last decade due to the decline of the conventional gas resources. Unlike conventional gas reservoirs, the gas flow in shale formations involves complex processes with many mechanisms such as Knudsen diffusion, slip flow (Klinkenberg effect), gas adsorption and desorption, strong rock-fluid interaction, etc. Shale formations are characterized by the tiny porosity and extremely low-permeability such that the Darcy equation may no longer be valid. Therefore, the Darcy equation needs to be revised through the permeability factor by introducing the apparent permeability. With respect to the rock formations, several studies have shown the existence of anisotropy in shale reservoirs, which is an essential feature that has been established as a consequence of the different geological processes over long period of time. Anisotropy of hydraulic properties of subsurface rock formations plays a significant role in dictating the direction of fluid flow. The direction of fluid flow is not only dependent on the direction of pressure gradient, but it also depends on the principal directions of anisotropy. Therefore, it is very important to take into consideration anisotropy when modeling gas flow in shale reservoirs. In this work, the gas flow mechanisms as mentioned earlier together with anisotropy are incorporated into the dual-porosity dual-permeability model through the full-tensor apparent permeability. We employ the multipoint flux approximation (MPFA) method to handle the full-tensor apparent permeability. We combine MPFA method with the experimenting pressure field approach, i.e., a newly developed technique that enables us to solve the global problem by breaking it into a multitude of local problems. This approach generates a set of predefined pressure fields in the solution domain in such a way that the undetermined coefficients are calculated from these pressure fields. In other words, the matrix of coefficients

  12. Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs

    KAUST Repository

    Negara, Ardiansyah; Salama, Amgad; Sun, Shuyu; Elgassier, Mokhtar; Wu, Yu-Shu

    2015-01-01

    Shale gas resources have received great attention in the last decade due to the decline of the conventional gas resources. Unlike conventional gas reservoirs, the gas flow in shale formations involves complex processes with many mechanisms such as Knudsen diffusion, slip flow (Klinkenberg effect), gas adsorption and desorption, strong rock-fluid interaction, etc. Shale formations are characterized by the tiny porosity and extremely low-permeability such that the Darcy equation may no longer be valid. Therefore, the Darcy equation needs to be revised through the permeability factor by introducing the apparent permeability. With respect to the rock formations, several studies have shown the existence of anisotropy in shale reservoirs, which is an essential feature that has been established as a consequence of the different geological processes over long period of time. Anisotropy of hydraulic properties of subsurface rock formations plays a significant role in dictating the direction of fluid flow. The direction of fluid flow is not only dependent on the direction of pressure gradient, but it also depends on the principal directions of anisotropy. Therefore, it is very important to take into consideration anisotropy when modeling gas flow in shale reservoirs. In this work, the gas flow mechanisms as mentioned earlier together with anisotropy are incorporated into the dual-porosity dual-permeability model through the full-tensor apparent permeability. We employ the multipoint flux approximation (MPFA) method to handle the full-tensor apparent permeability. We combine MPFA method with the experimenting pressure field approach, i.e., a newly developed technique that enables us to solve the global problem by breaking it into a multitude of local problems. This approach generates a set of predefined pressure fields in the solution domain in such a way that the undetermined coefficients are calculated from these pressure fields. In other words, the matrix of coefficients

  13. AUTOMATED TECHNIQUE FOR FLOW MEASUREMENTS FROM MARIOTTE RESERVOIRS.

    Science.gov (United States)

    Constantz, Jim; Murphy, Fred

    1987-01-01

    The mariotte reservoir supplies water at a constant hydraulic pressure by self-regulation of its internal gas pressure. Automated outflow measurements from mariotte reservoirs are generally difficult because of the reservoir's self-regulation mechanism. This paper describes an automated flow meter specifically designed for use with mariotte reservoirs. The flow meter monitors changes in the mariotte reservoir's gas pressure during outflow to determine changes in the reservoir's water level. The flow measurement is performed by attaching a pressure transducer to the top of a mariotte reservoir and monitoring gas pressure changes during outflow with a programmable data logger. The advantages of the new automated flow measurement techniques include: (i) the ability to rapidly record a large range of fluxes without restricting outflow, and (ii) the ability to accurately average the pulsing flow, which commonly occurs during outflow from the mariotte reservoir.

  14. The reservoir model: a differential equation model of psychological regulation.

    Science.gov (United States)

    Deboeck, Pascal R; Bergeman, C S

    2013-06-01

    Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

  15. A fully-coupled discontinuous Galerkin spectral element method for two-phase flow in petroleum reservoirs

    Science.gov (United States)

    Taneja, Ankur; Higdon, Jonathan

    2018-01-01

    A high-order spectral element discontinuous Galerkin method is presented for simulating immiscible two-phase flow in petroleum reservoirs. The governing equations involve a coupled system of strongly nonlinear partial differential equations for the pressure and fluid saturation in the reservoir. A fully implicit method is used with a high-order accurate time integration using an implicit Rosenbrock method. Numerical tests give the first demonstration of high order hp spatial convergence results for multiphase flow in petroleum reservoirs with industry standard relative permeability models. High order convergence is shown formally for spectral elements with up to 8th order polynomials for both homogeneous and heterogeneous permeability fields. Numerical results are presented for multiphase fluid flow in heterogeneous reservoirs with complex geometric or geologic features using up to 11th order polynomials. Robust, stable simulations are presented for heterogeneous geologic features, including globally heterogeneous permeability fields, anisotropic permeability tensors, broad regions of low-permeability, high-permeability channels, thin shale barriers and thin high-permeability fractures. A major result of this paper is the demonstration that the resolution of the high order spectral element method may be exploited to achieve accurate results utilizing a simple cartesian mesh for non-conforming geological features. Eliminating the need to mesh to the boundaries of geological features greatly simplifies the workflow for petroleum engineers testing multiple scenarios in the face of uncertainty in the subsurface geology.

  16. Electrokinetic Flow in Microchannels with Finite Reservoir Size Effects

    International Nuclear Information System (INIS)

    Yan, D; Yang, C; Nguyen, N-T; Huang, X

    2006-01-01

    In electrokinetically-driven microfluidic applications, reservoirs are indispensable and have finite sizes. During operation processes, as the liquid level difference in reservoirs keeps changing as time elapses, the flow characteristics in a microchannel exhibit a combination of the electroosmotic flow and the time-dependent induced backpressure-driven flow. In this work, an assessment of the finite reservoir size effect on electroosmotic flows is presented theoretically and experimentally. A model is developed to describe the timedependent electrokinetic flow with finite reservoir size effects. The theoretical analysis shows that under certain conditions the finite reservoir size effect is significant. The important parameters that describe the effect of finite reservoir size on the flow characteristics are discussed. A new concept denoted as 'effective pumping period' is introduced to characterize the reservoir size effect. The proposed model clearly identifies the mechanisms of the finitereservoir size effects and is further confirmed by using micro-PIV technique. The results of this study can be used for facilitating the design of microfluidic devices

  17. Triple-porosity/permeability flow in faulted geothermal reservoirs: Two-dimensional effects

    Energy Technology Data Exchange (ETDEWEB)

    Cesar Suarez Arriaga, M. [Michoacan Univ. & CFE, Mich. (Mexico); Samaniego Verduzco, F. [National Autonomous Univ. of Mexico, Coyoacan (Mexico)

    1995-03-01

    An essential characteristic of some fractured geothermal reservoirs is noticeable when the drilled wells intersect an open fault or macrofracture. Several evidences observed, suggest that the fluid transport into this type of systems, occurs at least in three stages: flow between rock matrix and microfractures, flow between fractures and faults and flow between faults and wells. This pattern flow could define, by analogy to the classical double-porosity model, a triple-porosity, triple-permeability concept. From a mathematical modeling point of view, the non-linearity of the heterogeneous transport processes, occurring with abrupt changes on the petrophysical properties of the rock, makes impossible their exact or analytic solution. To simulate this phenomenon, a detailed two-dimensional geometric model was developed representing the matrix-fracture-fault system. The model was solved numerically using MULKOM with a H{sub 2}O=CO{sub 2} equation of state module. This approach helps to understand some real processes involved. Results obtained from this study, exhibit the importance of considering the triple porosity/permeability concept as a dominant mechanism producing, for example, strong pressure gradients between the reservoir and the bottom hole of some wells.

  18. Upscaling of Two-Phase Immiscible Flows in Communicating Stratified Reservoirs

    DEFF Research Database (Denmark)

    Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan

    2011-01-01

    A semi-analytical method for upscaling two-phase immiscible flows in heterogeneous porous media is described. This method is developed for stratified reservoirs with perfect communication between layers (the case of vertical equilibrium), in a viscous dominant regime, where the effects of capillary...... forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure...... and piston-like displacement, and it presumes non-zero exchange between layers. The method generalizes also the study of Yortsos (Transp Porous Media 18:107–129, 1995), taking into account in a more consistent way the interactions between the layers....

  19. The model coupling fluid flow in reservoir with flow in horizontal wellbore

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Xiangping; Jiang, Zhixiang [RIPED-TEXACO Horizontal Well Technology Laboratory (United States)

    1998-12-31

    Three-dimensional pressure distributions of oil flow in a reservoir with horizontal well were derived, and a new formula to calculate pressure drop along the horizontal wellbore was developed based on the principle of conservation of matter and momentum. The formula considers the effect of influx into the horizontal wellbore from the reservoir on pressure drop in the wellbore. A mathematical model to couple fluid flow in the reservoir with flow in the horizontal wellbore is presented. Model results and experimental data showed good correspondence. Results showed the influence of pressure drop on well performance. 13 refs., 2 tabs., 7 figs.

  20. Development and linearization of generalized material balance equation for coal bed methane reservoirs

    International Nuclear Information System (INIS)

    Penuela, G; Ordonez R, A; Bejarano, A

    1998-01-01

    A generalized material balance equation was presented at the Escuela de Petroleos de la Universidad Industrial de Santander for coal seam gas reservoirs based on Walsh's method, who worked in an analogous approach for oil and gas conventional reservoirs (Walsh, 1995). Our equation was based on twelve similar assumptions itemized by Walsh for his generalized expression for conventional reservoirs it was started from the same volume balance consideration and was finally reorganized like Walsh (1994) did. Because it is not expressed in terms of traditional (P/Z) plots, as proposed by King (1990), it allows to perform a lot of quantitative and qualitative analyses. It was also demonstrated that the existent equations are only particular cases of the generalized expression evaluated under certain restrictions. This equation is applicable to coal seam gas reservoirs in saturated, equilibrium and under saturated conditions, and to any type of coal beds without restriction on especial values of the constant diffusion

  1. Enhanced Recovery in Tight Gas Reservoirs using Maxwell-Stefan Equations

    Science.gov (United States)

    Santiago, C. J. S.; Kantzas, A.

    2017-12-01

    Due to the steep production decline in unconventional gas reservoirs, enhanced recovery (ER) methods are receiving great attention from the industry. Wet gas or liquid rich reservoirs are the preferred ER candidates due to higher added value from natural gas liquids (NGL) production. ER in these reservoirs has the potential to add reserves by improving desorption and displacement of hydrocarbons through the medium. Nevertheless, analysis of gas transport at length scales of tight reservoirs is complicated because concomitant mechanisms are in place as pressure declines. In addition to viscous and Knudsen diffusion, multicomponent gas modeling includes competitive adsorption and molecular diffusion effects. Most models developed to address these mechanisms involve single component or binary mixtures. In this study, ER by gas injection is investigated in multicomponent (C1, C2, C3 and C4+, CO2 and N2) wet gas reservoirs. The competing effects of Knudsen and molecular diffusion are incorporated by using Maxwell-Stefan equations and the Dusty-Gas approach. This model was selected due to its superior properties on representing the physics of multicomponent gas flow, as demonstrated during the presented model validation. Sensitivity studies to evaluate adsorption, reservoir permeability and gas type effects are performed. The importance of competitive adsorption on production and displacement times is demonstrated. In the absence of adsorption, chromatographic separation is negligible. Production is merely dictated by competing effects between molecular and Knudsen diffusion. Displacement fronts travel rapidly across the medium. When adsorption effects are included, molecules with lower affinity to the adsorption sites will be produced faster. If the injected gas is inert (N2), an increase in heavier fraction composition occurs in the medium. During injection of adsorbing gases (CH4 and CO2), competitive adsorption effects will contribute to improved recovery of heavier

  2. Structural characterization and numerical simulations of flow properties of standard and reservoir carbonate rocks using micro-tomography

    Science.gov (United States)

    Islam, Amina; Chevalier, Sylvie; Sassi, Mohamed

    2018-04-01

    With advances in imaging techniques and computational power, Digital Rock Physics (DRP) is becoming an increasingly popular tool to characterize reservoir samples and determine their internal structure and flow properties. In this work, we present the details for imaging, segmentation, as well as numerical simulation of single-phase flow through a standard homogenous Silurian dolomite core plug sample as well as a heterogeneous sample from a carbonate reservoir. We develop a procedure that integrates experimental results into the segmentation step to calibrate the porosity. We also look into using two different numerical tools for the simulation; namely Avizo Fire Xlab Hydro that solves the Stokes' equations via the finite volume method and Palabos that solves the same equations using the Lattice Boltzmann Method. Representative Elementary Volume (REV) and isotropy studies are conducted on the two samples and we show how DRP can be a useful tool to characterize rock properties that are time consuming and costly to obtain experimentally.

  3. Master equation and two heat reservoirs.

    Science.gov (United States)

    Trimper, Steffen

    2006-11-01

    A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma-sigma and TT'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.

  4. Modeling Highly Buoyant Flows in the Castel Giorgio: Torre Alfina Deep Geothermal Reservoir

    Directory of Open Access Journals (Sweden)

    Giorgio Volpi

    2018-01-01

    Full Text Available The Castel Giorgio-Torre Alfina (CG-TA, central Italy is a geothermal reservoir whose fluids are hosted in a carbonate formation at temperatures ranging between 120°C and 210°C. Data from deep wells suggest the existence of convective flow. We present the 3D numerical model of the CG-TA to simulate the undisturbed natural geothermal field and investigate the impacts of the exploitation process. The open source finite-element code OpenGeoSys is applied to solve the coupled systems of partial differential equations. The commercial software FEFLOW® is also used as additional numerical constraint. Calculated pressure and temperature have been calibrated against data from geothermal wells. The flow field displays multicellular convective patterns that cover the entire geothermal reservoir. The resulting thermal plumes protrude vertically over 3 km at Darcy velocity of about 7⁎10-8 m/s. The analysis of the exploitation process demonstrated the sustainability of a geothermal doublet for the development of a 5 MW pilot plant. The buoyant circulation within the geothermal system allows the reservoir to sustain a 50-year production at a flow rate of 1050 t/h. The distance of 2 km, between the production and reinjection wells, is sufficient to prevent any thermal breakthrough within the estimated operational lifetime. OGS and FELFOW results are qualitatively very similar with differences in peak velocities and temperatures. The case study provides valuable guidelines for future exploitation of the CG-TA deep geothermal reservoir.

  5. The impact of hydraulic flow unit & reservoir quality index on pressure profile and productivity index in multi-segments reservoirs

    Directory of Open Access Journals (Sweden)

    Salam Al-Rbeawi

    2017-12-01

    Full Text Available The objective of this paper is studying the impact of the hydraulic flow unit and reservoir quality index (RQI on pressure profile and productivity index of horizontal wells acting in finite reservoirs. Several mathematical models have been developed to investigate this impact. These models have been built based on the pressure distribution in porous media, depleted by a horizontal well, consist of multi hydraulic flow units and different reservoir quality index. The porous media are assumed to be finite rectangular reservoirs having different configurations and the wellbores may have different lengths. Several analytical models describing flow regimes have been derived wherein hydraulic flow units and reservoir quality index have been included in addition to rock and fluid properties. The impact of these two parameters on reservoir performance has also been studied using steady state productivity index.It has been found that both pressure responses and flow regimes are highly affected by the existence of multiple hydraulic flow units in the porous media and the change in reservoir quality index for these units. Positive change in the RQI could lead to positive change in both pressure drop required for reservoir fluids to move towards the wellbore and hence the productivity index.

  6. Design of a lube oil reservoir by using flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Rinkinen, J; Alfthan, A. [Institute of Hydraulics and Automation IHA, Tampere University of Technology, Tampere (Finland)] Suominen, J. [Institute of Energy and Process Engineering, Tampere University of Technology, Tampere (Finland); Airaksinen, A; Antila, K [R and D Engineer Safematic Oy, Muurame (Finland)

    1998-12-31

    The volume of usual oil reservoir for lubrication oil systems is designed by the traditional rule of thumb so that the total oil volume is theoretically changed in every 30 minutes by rated pumping capacity. This is commonly used settling time for air, water and particles to separate by gravity from the oil returning of the bearings. This leads to rather big volumes of lube oil reservoirs, which are sometimes difficult to situate in different applications. In this presentation traditionally sized lube oil reservoir (8 m{sup 3}) is modelled in rectangular coordinates and laminar oil flow is calculated by using FLUENT software that is based on finite difference method. The results of calculation are velocity and temperature fields inside the reservoir. The velocity field is used to visualize different particle paths through the reservoir. Particles that are studied by the model are air bubbles and water droplets. The interest of the study has been to define the size of the air bubbles that are released and the size of the water droplets that are separated in the reservoir. The velocity field is also used to calculate the modelled circulating time of the oil volume which is then compared with the theoretical circulating time that is obtained from the rated pump flow. These results have been used for designing a new lube oil reservoir. This reservoir has also been modelled and optimized by the aid of flow calculations. The best shape of the designed reservoir is constructed in real size for empirical measurements. Some results of the oil flow measurements are shown. (orig.) 7 refs.

  7. Design of a lube oil reservoir by using flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Rinkinen, J.; Alfthan, A. [Institute of Hydraulics and Automation IHA, Tampere University of Technology, Tampere (Finland)] Suominen, J. [Institute of Energy and Process Engineering, Tampere University of Technology, Tampere (Finland); Airaksinen, A.; Antila, K. [R and D Engineer Safematic Oy, Muurame (Finland)

    1997-12-31

    The volume of usual oil reservoir for lubrication oil systems is designed by the traditional rule of thumb so that the total oil volume is theoretically changed in every 30 minutes by rated pumping capacity. This is commonly used settling time for air, water and particles to separate by gravity from the oil returning of the bearings. This leads to rather big volumes of lube oil reservoirs, which are sometimes difficult to situate in different applications. In this presentation traditionally sized lube oil reservoir (8 m{sup 3}) is modelled in rectangular coordinates and laminar oil flow is calculated by using FLUENT software that is based on finite difference method. The results of calculation are velocity and temperature fields inside the reservoir. The velocity field is used to visualize different particle paths through the reservoir. Particles that are studied by the model are air bubbles and water droplets. The interest of the study has been to define the size of the air bubbles that are released and the size of the water droplets that are separated in the reservoir. The velocity field is also used to calculate the modelled circulating time of the oil volume which is then compared with the theoretical circulating time that is obtained from the rated pump flow. These results have been used for designing a new lube oil reservoir. This reservoir has also been modelled and optimized by the aid of flow calculations. The best shape of the designed reservoir is constructed in real size for empirical measurements. Some results of the oil flow measurements are shown. (orig.) 7 refs.

  8. Analytical Solution for 2D Inter-Well Porous Flow in a Rectangular Reservoir

    Directory of Open Access Journals (Sweden)

    Junfeng Ding

    2018-04-01

    Full Text Available Inter-well fluid flows through porous media are commonly encountered in the production of groundwater, oil, and geothermal energy. In this paper, inter-well porous flow inside a rectangular reservoir is solved based on the complex variable function theory combined with the method of mirror images. In order to derive the solution analytically, the inter-well flow is modeled as a 2D flow in a homogenous and isotropic porous medium. The resulted exact analytical solution takes the form of an infinite series, but it can be truncated to give high accuracy approximation. In terms of nine cases of inter-well porous flow associated with enhanced geothermal systems, the applications of the obtained analytical solution are demonstrated, and the convergence properties of the truncated series are investigated. It is shown that the convergent rate of the truncated series increases with the symmetric level of well distribution inside the reservoir, and the adoption of Euler transform significantly accelerates the convergence of alternating series cases associated with asymmetric well distribution. In principle, the analytical solution proposed in this paper can be applied to other scientific and engineering fields, as long as the involved problem is governed by 2D Laplace equation in a rectangular domain and subject to similar source/sink and boundary conditions, i.e., isolated point sources/sinks and uniform Dirichlet or homogeneous Neumann boundary conditions.

  9. Reservoir simulation with MUFITS code: Extension for double porosity reservoirs and flows in horizontal wells

    Science.gov (United States)

    Afanasyev, Andrey

    2017-04-01

    Numerical modelling of multiphase flows in porous medium is necessary in many applications concerning subsurface utilization. An incomplete list of those applications includes oil and gas fields exploration, underground carbon dioxide storage and geothermal energy production. The numerical simulations are conducted using complicated computer programs called reservoir simulators. A robust simulator should include a wide range of modelling options covering various exploration techniques, rock and fluid properties, and geological settings. In this work we present a recent development of new options in MUFITS code [1]. The first option concerns modelling of multiphase flows in double-porosity double-permeability reservoirs. We describe internal representation of reservoir models in MUFITS, which are constructed as a 3D graph of grid blocks, pipe segments, interfaces, etc. In case of double porosity reservoir, two linked nodes of the graph correspond to a grid cell. We simulate the 6th SPE comparative problem [2] and a five-spot geothermal production problem to validate the option. The second option concerns modelling of flows in porous medium coupled with flows in horizontal wells that are represented in the 3D graph as a sequence of pipe segments linked with pipe junctions. The well completions link the pipe segments with reservoir. The hydraulics in the wellbore, i.e. the frictional pressure drop, is calculated in accordance with Haaland's formula. We validate the option against the 7th SPE comparative problem [3]. We acknowledge financial support by the Russian Foundation for Basic Research (project No RFBR-15-31-20585). References [1] Afanasyev, A. MUFITS Reservoir Simulation Software (www.mufits.imec.msu.ru). [2] Firoozabadi A. et al. Sixth SPE Comparative Solution Project: Dual-Porosity Simulators // J. Petrol. Tech. 1990. V.42. N.6. P.710-715. [3] Nghiem L., et al. Seventh SPE Comparative Solution Project: Modelling of Horizontal Wells in Reservoir Simulation

  10. Cross-flow analysis of injection wells in a multilayered reservoir

    Directory of Open Access Journals (Sweden)

    Mohammadreza Jalali

    2016-09-01

    Natural and forced cross-flow is modeled for some injection wells in an oil reservoir located at North Sea. The solution uses a transient implicit finite difference approach for multiple sand layers with different permeabilities separated by impermeable shale layers. Natural and forced cross-flow rates for each reservoir layer during shut-in are calculated and compared with different production logging tool (PLT measurements. It appears that forced cross-flow is usually more prolonged and subject to a higher flow rate when compared with natural cross-flow, and is thus worthy of more detailed analysis.

  11. Gauge-invariant flow equation

    Science.gov (United States)

    Wetterich, C.

    2018-06-01

    We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

  12. Interaction between Proppant Packing, Reservoir Depletion, and Fluid Flow in Pore Space

    Science.gov (United States)

    Fan, M.; McClure, J. E.; Han, Y.; Chen, C.

    2016-12-01

    In the oil and gas industry, the performance of proppant pack in hydraulically created fractures has a significant influence on fracture conductivity. A better understanding of proppant transport and deposition pattern in a hydraulic fracture is vital for effective and economical production within oil and gas reservoirs. In this research, a numerical modeling approach, combining Particle Flow Code (PFC) and GPU-enhanced lattice Boltzmann simulator (GELBS), is adopted to advance the understanding of the interaction between proppant particle packing, depletion of reservoir formation, and transport of reservoir flow through the pore space. In this numerical work flow, PFC is used to simulate effective stress increase and proppant particle movement and rearrangement under increasing mechanical loading. The pore structure of the proppant pack evolves subsequently and the geometrical data are output for lattice Boltzmann (LB) simulation of proppant pack permeability. Three different proppant packs with fixed particle concentration and 12/18, 16/30, and 20/40 mesh sizes are generated. These proppant packs are compressed with specified loading stress and their subsequent geometries are used for fluid flow simulations. The simulation results are in good agreement with experimental observations, e.g., the conductivity of proppant packs decreases with increasing effective stress. Three proppant packs with the same average diameter were generated using different coefficients of variation (COVs) for the proppant diameter (namely cov5%, cov20%, and cov30%). By using the coupled PFC-LBM work flow, the proppant pack permeability as functions of effective stress and porosity is investigated. The results show that the proppant pack with a higher proppant diameter COV has lower permeability and porosity under the same effective stress, because smaller particles fill in the pore space between bigger particles. The relationship between porosity and permeability is also consistent with

  13. Tracing fluid flow in geothermal reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Rose, P.E.; Adams, M.C. [Univ. of Utah, Salt Lake City, UT (United States)

    1997-12-31

    A family of fluorescent compounds, the polycyclic aromatic sulfonates, were evaluated for application in intermediate- and high-temperature geothermal reservoirs. Whereas the naphthalene sulfonates were found to be very thermally stable and reasonably detectable, the amino-substituted naphthalene sulfonates were found to be somewhat less thermally stable, but much more detectable. A tracer test was conducted at the Dixie Valley, Nevada, geothermal reservoir using one of the substituted naphthalene sulfonates, amino G, and fluorescein. Four of 9 production wells showed tracer breakthrough during the first 200 days of the test. Reconstructed tracer return curves are presented that correct for the thermal decay of tracer assuming an average reservoir temperature of 227{degrees}C. In order to examine the feasibility of using numerical simulation to model tracer flow, we developed simple, two-dimensional models of the geothermal reservoir using the numerical simulation programs TETRAD and TOUGH2. By fitting model outputs to measured return curves, we show that numerical reservoir simulations can be calibrated with the tracer data. Both models predict the same order of elution, approximate tracer concentrations, and return curve shapes. Using these results, we propose a method for using numerical models to design a tracer test.

  14. Flow of a stream through a reservoir

    International Nuclear Information System (INIS)

    Sauerwein, K.

    1967-01-01

    If a reservoir is fed from a single source, which may not always be pure, the extent to which the inflowing stream mixes with the water in the reservoir is important for the quality of the water supplied by the reservoir. This question was investigated at the Lingese Reservoir, containing between one and two million cubic metres of water, in the Bergisches Land (North Rhine-Westphalia). The investigation was carried out at four different seasons so that the varying effects of the stream-water temperatures could be studied in relation to the temperature of the reservoir water. The stream was radioactively labelled at the point of inflow into the reservoir, and its flow through the reservoir was measured in length and depth from boats, by means of 1-m-long Geiger counters. In two cases the radioactivity of the outflowing water was also measured at fixed points. A considerable variety of intermixing phenomena were observed; these were mainly of limnological interest. The results of four experiments corresponding to the four different seasons are described in detail. They were as follows: (1) The mid-October experiment where the stream, with a temperature of 8.0 deg. C, was a good 5 deg. C colder than the water of the reservoir, whose temperature was almost uniform, ranging from 13.2 deg. C at the bed to 13.6 deg. C at the surface. (2) The spring experiment (second half of March), when the stream temperature was only 0.3 deg. C below that of the reservoir surface (7.8 deg. C), while the temperature of the bed was 5.8 deg. C. (3) The winter experiment (early December) where at first the temperature of the stream was approximately the same as that of the surface so that, once again, the stream at first flowed 1/2 - 1 m below the surface. During the almost wind-free night a sudden fall in temperature occurred, and the air temperature dropped from 0 deg. C to -12 deg. C. (4) The summer experiment (end of July to mid-August) when the stream was nearly 1 deg. C colder than

  15. Quantifying the clay content with borehole depth and impact on reservoir flow

    Science.gov (United States)

    Sarath Kumar, Aaraellu D.; Chattopadhyay, Pallavi B.

    2017-04-01

    This study focuses on the application of reservoir well log data and 3D transient numerical model for proper optimization of flow dynamics and hydrocarbon potential. Fluid flow through porous media depends on clay content that controls porosity, permeability and pore pressure. The pressure dependence of permeability is more pronounced in tight formations. Therefore, preliminary clay concentration analysis and geo-mechanical characterizations have been done by using wells logs. The assumption of a constant permeability for a reservoir is inappropriate and therefore the study deals with impact of permeability variation for pressure-sensitive formation. The study started with obtaining field data from available well logs. Then, the mathematical models are developed to understand the efficient extraction of oil in terms of reservoir architecture, porosity and permeability. The fluid flow simulations have been done using COMSOL Multiphysics Software by choosing time dependent subsurface flow module that is governed by Darcy's law. This study suggests that the reservoir should not be treated as a single homogeneous structure with unique porosity and permeability. The reservoir parameters change with varying clay content and it should be considered for effective planning and extraction of oil. There is an optimum drawdown for maximum production with varying permeability in a reservoir.

  16. An efficient permeability scaling-up technique applied to the discretized flow equations

    Energy Technology Data Exchange (ETDEWEB)

    Urgelli, D.; Ding, Yu [Institut Francais du Petrole, Rueil Malmaison (France)

    1997-08-01

    Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale. However, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions; (2) discretization of flow equations with a full permeability tensor is not straightforward and little work has been done on this subject. In this paper, we propose a new method, which allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. So, in the proposed method, the permeability up-scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite-volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented. Some numerical examples are tested for flow simulation. This new method is compared with some published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.

  17. Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

    Science.gov (United States)

    Franz, Delbert D.; Melching, Charles S.

    1997-01-01

    The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

  18. Efficient Reservoir Simulation with Cubic Plus Association and Cross-Association Equation of State for Multicomponent Three-Phase Compressible Flow with Applications in CO2 Storage and Methane Leakage

    Science.gov (United States)

    Moortgat, J.

    2017-12-01

    We present novel simulation tools to model multiphase multicomponent flow and transport in porous media for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2 and H2S. Such mixtures often occur when CO2 is injected and stored in saline aquifers, or when methane is leaking into groundwater. To accurately predict the species transfer between aqueous, gaseous and oleic phases, and the subsequent change in phase properties, the self- and cross-associating behavior of molecules needs to be taken into account, particularly at the typical temperatures and pressures in deep formations. The Cubic-Plus-Association equation-of-state (EOS) has been demonstrated to be highly accurate for such problems but its excessive computational cost has prevented widespread use in reservoir simulators. We discuss the thermodynamical framework and develop sophisticated numerical algorithms that allow reservoir simulations with efficiencies comparable to a simple cubic EOS. This approach improves our predictive powers for highly nonlinear fluid behavior related to geological carbon sequestration, such as density driven flow and natural convection (solubility trapping), evaporation of water into the CO2-rich gas phase, and competitive dissolution-evaporation when CO2 is injected in, e.g., methane saturated aquifers. Several examples demonstrate the accuracy and robustness of this EOS framework for complex applications.

  19. Numerical simulation of single-phase and multiphase non-Darcy flowin porous and fractured reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yu-Shu

    2000-06-02

    A numerical method as well as a theoretical study of non-Darcy fluid flow of through porous and fractured reservoirs is described. The non-Darcy flow is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in geothermal reservoirs.

  20. Effect of wettability on scale-up of multiphase flow from core-scale to reservoir fine-grid-scale

    Energy Technology Data Exchange (ETDEWEB)

    Chang, Y.C.; Mani, V.; Mohanty, K.K. [Univ. of Houston, TX (United States)

    1997-08-01

    Typical field simulation grid-blocks are internally heterogeneous. The objective of this work is to study how the wettability of the rock affects its scale-up of multiphase flow properties from core-scale to fine-grid reservoir simulation scale ({approximately} 10{prime} x 10{prime} x 5{prime}). Reservoir models need another level of upscaling to coarse-grid simulation scale, which is not addressed here. Heterogeneity is modeled here as a correlated random field parameterized in terms of its variance and two-point variogram. Variogram models of both finite (spherical) and infinite (fractal) correlation length are included as special cases. Local core-scale porosity, permeability, capillary pressure function, relative permeability functions, and initial water saturation are assumed to be correlated. Water injection is simulated and effective flow properties and flow equations are calculated. For strongly water-wet media, capillarity has a stabilizing/homogenizing effect on multiphase flow. For small variance in permeability, and for small correlation length, effective relative permeability can be described by capillary equilibrium models. At higher variance and moderate correlation length, the average flow can be described by a dynamic relative permeability. As the oil wettability increases, the capillary stabilizing effect decreases and the deviation from this average flow increases. For fractal fields with large variance in permeability, effective relative permeability is not adequate in describing the flow.

  1. A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

    International Nuclear Information System (INIS)

    Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming

    2013-01-01

    Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)

  2. Nuclear stimulation of oil-reservoirs

    International Nuclear Information System (INIS)

    Delort, F.; Supiot, F.

    1970-01-01

    Underground nuclear explosions in the Hoggar nuclear test site have shown that the geological effects may increase the production of oil or gas reservoirs. By studying the permanent liquid flow-rate with approximate DUPUIT's equation, or with a computer code, it is shown that the conventional well flow-rate may be increased by a factor between 3 and 50, depending on the medium and explosion conditions. (author)

  3. Nuclear stimulation of oil-reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Delort, F; Supiot, F [Commissariat a l' Energie Atomique, Centre d' Etudes de Bruyere-le-Chatel (France)

    1970-05-01

    Underground nuclear explosions in the Hoggar nuclear test site have shown that the geological effects may increase the production of oil or gas reservoirs. By studying the permanent liquid flow-rate with approximate DUPUIT's equation, or with a computer code, it is shown that the conventional well flow-rate may be increased by a factor between 3 and 50, depending on the medium and explosion conditions. (author)

  4. Numerical optimization using flow equations

    Science.gov (United States)

    Punk, Matthias

    2014-12-01

    We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

  5. Fluid flow in gas condensate reservoirs. The interplay of forces and their relative strengths

    Energy Technology Data Exchange (ETDEWEB)

    Ursin, Jann-Rune [Stavanger University College, Department of Petroleum Engineering, PO Box 8002, Stavanger, 4068 (Norway)

    2004-02-01

    Natural production from gas condensate reservoirs is characterized by gas condensation and liquid dropout in the reservoir, first in the near wellbore volume, then as a cylindrical shaped region, dynamically developing into the reservoir volume. The effects of liquid condensation are reduced productivity and loss of production. Successful forecast of well productivity and reservoir production depends on detailed understanding of the effect of various forces acting on fluid flow in time and space. The production form gas condensate reservoirs is thus indirectly related to the interplay of fundamental forces, such as the viscosity, the capillary, the gravitational and the inertial force and their relative strengths, demonstrated by various dimensionless numbers. Dimensionless numbers are defined and calculated for all pressure and space coordinates in a test reservoir. Various regions are identified where certain forces are more important than others. Based on reservoir pressure development, liquid condensation and the numerical representation of dimensionless numbers, a conceptual understanding of a varying reservoir permeability has been reached.The material balance, the reservoir fluid flow and the wellbore flow calculations are performed on a cylindrical reservoir model. The ratios between fundamental forces are calculated and dimensionless numbers defined. The interplay of forces, demonstrated by these numbers, are calculated as function of radial dimension and reservoir pressure.

  6. Symmetries of the Euler compressible flow equations for general equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-10-15

    The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

  7. Radiant heating of petroleum reservoirs; Aquecimento radiante de reservatorios petroliferos

    Energy Technology Data Exchange (ETDEWEB)

    Sidrim, Fernando A.C.

    1990-12-31

    This work presents a proposal of a simplified model for the enhanced oil recovery process through radiant heating of oil reservoirs. The resulting continuity, energy and motion equations were solved analytically for the prediction of the increase in well flow rates. The heat loss to adjacent formations and the necessary for the establishment of the temperature profile,which are transient terms of energy equation, have been neglected. Also, no temperature gradient in the axial direction has been modelled as a cylindrical wave propagating in a loss medium. It is concluded that: the inclusion of a radial conduction term in the energy equation led to higher flow rates than the ones predicted by the literature existing solution; if the absorption coefficient is too large, it is profitable to dry the reservoir around the well bore; the transient terms in the energy equation are significant for extended periods of well production. 47 refs., 18 figs., 4 tabs.

  8. Multigrid methods for fully implicit oil reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Molenaar, J.

    1995-12-31

    In this paper, the authors consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations the material balance or continuity equations, and the equation of motion (Darcy`s law). For the numerical solution of this system of nonlinear partial differential equations, there are two approaches: the fully implicit or simultaneous solution method, and the sequential solution method. In this paper, the authors consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations.

  9. The flow equation approach to many-particle systems

    CERN Document Server

    Kehrein, Stefan; Fujimori, A; Varma, C; Steiner, F

    2006-01-01

    This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate- level solid-state theory.

  10. Modelling of fluid flow in fractured porous media by the singular integral equations method

    International Nuclear Information System (INIS)

    Vu, M.N.

    2012-01-01

    This thesis aims to develop a method for numerical modelling of fluid flow through fractured porous media and for determination of their effective permeability by taking advantage of recent results based on formulation of the problem by Singular Integral Equations. In parallel, it was also an occasion to continue on the theoretical development and to obtain new results in this area. The governing equations for flow in such materials are reviewed first and mass conservation at the fracture intersections is expressed explicitly. Using the theory of potential, the general potential solutions are proposed in the form of a singular integral equation that describes the steady-state flow in and around several fractures embedded in an infinite porous matrix under a far-field pressure condition. These solutions represent the pressure field in the whole body as functions of the infiltration in the fractures, which fully take into account the fracture interaction and intersections. Closed-form solutions for the fundamental problem of fluid flow around a single fracture are derived, which are considered as the benchmark problems to validate the numerical solutions. In particular, the solution obtained for the case of an elliptical disc-shaped crack obeying to the Poiseuille law has been compared to that obtained for ellipsoidal inclusions with Darcy law.The numerical programs have been developed based on the singular integral equations method to resolve the general potential equations. These allow modeling the fluid flow through a porous medium containing a great number of fractures. Besides, this formulation of the problem also allows obtaining a semi-analytical infiltration solution over a single fracture depending on the matrice permeability, the fracture conductivity and the fracture geometry. This result is the important key to up-scaling the effective permeability of a fractured porous medium by using different homogenisation schemes. The results obtained by the self

  11. Reservoir simulation with the cubic plus (cross-) association equation of state for water, CO2, hydrocarbons, and tracers

    Science.gov (United States)

    Moortgat, Joachim

    2018-04-01

    This work presents an efficient reservoir simulation framework for multicomponent, multiphase, compressible flow, based on the cubic-plus-association (CPA) equation of state (EOS). CPA is an accurate EOS for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2, and H2S. While CPA is accurate, its mathematical formulation is highly non-linear, resulting in excessive computational costs that have made the EOS unfeasible for large scale reservoir simulations. This work presents algorithms that overcome these bottlenecks and achieve an efficiency comparable to the much simpler cubic EOS approach. The main applications that require such accurate phase behavior modeling are 1) the study of methane leakage from high-pressure production wells and its potential impact on groundwater resources, 2) modeling of geological CO2 sequestration in brine aquifers when one is interested in more than the CO2 and H2O components, e.g. methane, other light hydrocarbons, and various tracers, and 3) enhanced oil recovery by CO2 injection in reservoirs that have previously been waterflooded or contain connate water. We present numerical examples of all those scenarios, extensive validation of the CPA EOS with experimental data, and analyses of the efficiency of our proposed numerical schemes. The accuracy, efficiency, and robustness of the presented phase split computations pave the way to more widespread adoption of CPA in reservoir simulators.

  12. Macroscopic balance equations for two-phase flow models

    International Nuclear Information System (INIS)

    Hughes, E.D.

    1979-01-01

    The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

  13. Effect of flow forecasting quality on benefits of reservoir operation - a case study for the Geheyan reservoir (China)

    NARCIS (Netherlands)

    Dong, Xiaohua; Dohmen-Janssen, Catarine M.; Booij, Martijn J.; Hulscher, Suzanne J.M.H.

    2006-01-01

    This paper presents a methodology to determine the effect of flow forecasting quality on the benefits of reservoir operation. The benefits are calculated in terms of the electricity generated, and the quality of the flow forecasting is defined in terms of lead time and accuracy of the forecasts. In

  14. A Novel Method for Performance Analysis of Compartmentalized Reservoirs

    Directory of Open Access Journals (Sweden)

    Shahamat Mohammad Sadeq

    2016-05-01

    Full Text Available This paper presents a simple analytical model for performance analysis of compartmentalized reservoirs producing under Constant Terminal Rate (CTR and Constant Terminal Pressure (CTP. The model is based on the well-known material balance and boundary dominated flow equations and is written in terms of capacitance and resistance of a production and a support compartment. These capacitance and resistance terms account for a combination of reservoir parameters which enable the developed model to be used for characterizing such systems. In addition to considering the properties contrast between the two reservoir compartments, the model takes into account existence of transmissibility barriers with the use of resistance terms. The model is used to analyze production performance of unconventional reservoirs, where the multistage fracturing of horizontal wells effectively creates a Stimulated Reservoir Volume (SRV with an enhanced permeability surrounded by a non-stimulated region. It can also be used for analysis of compartmentalized conventional reservoirs. The analytical solutions provide type curves through which the controlling reservoirs parameters of a compartmentalized system can be estimated. The contribution of the supporting compartment is modeled based on a boundary dominated flow assumption. The transient behaviour of the support compartment is captured by application of “distance of investigation” concept. The model shows that depletion of the production and support compartments exhibit two unit slopes on a log-log plot of pressure versus time for CTR. For CTP, however, the depletions display two exponential declines. The depletion signatures are separated by transition periods, which depend on the contribution of the support compartment (i.e. transient or boundary dominated flow. The developed equations can be implemented easily in a spreadsheet application, and are corroborated with the use of a numerical simulation. The study

  15. Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

    KAUST Repository

    Potsepaev, R.

    2010-09-06

    Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

  16. Modeling flow in naturally fractured reservoirs : effect of fracture aperture distribution on dominant sub-network for flow

    NARCIS (Netherlands)

    Gong, J.; Rossen, W.R.

    2017-01-01

    Fracture network connectivity and aperture (or conductivity) distribution are two crucial features controlling flow behavior of naturally fractured reservoirs. The effect of connectivity on flow properties is well documented. In this paper, however, we focus here on the influence of fracture

  17. Special considerations for electric submersible pump applications in underpressured reservoirs

    International Nuclear Information System (INIS)

    Powers, M.L.

    1991-01-01

    This paper investigates the effect of electric submersible pump performance tolerances and minor speed variations on the producing rate of wells completed in underpressured reservoirs, and presents ESP design considerations which are unique for this class of wells. These wells require considerable head to initiate flow and have relatively flat well-load curves. Pumps that operate near their maximum recommended rate have steep performance curves. it is shown that this minimizes the effect of an underperforming pump on producing rate. Equations are developed for calculating the effects of pump performance and speed. Application requires evaluating the slopes of the pump performance curve and well-load curve at design rate. Utility of these equations is demonstrated by practical examples. It is also demonstrated that flow-stall can easily occur in underpressured reservoir applications when pumps designed to operate near their minimum recommended rate are installed

  18. CO2 interfacial properties: application to multiphase flow at reservoir conditions

    International Nuclear Information System (INIS)

    Chalbaud, C.

    2007-07-01

    In this work we deal with the interfacial properties of CO 2 at reservoir conditions with a special interest on deep saline aquifers. Each chapter of this dissertation represents a different physical scale studied with different experimental devices and simulation tools. The results obtained in the first part of this study represent a complete data set of brine-CO 2 interfacial tension at reservoir conditions. A semi-analytical equation is proposed in order to facilitate the work of reservoir engineers. The second deals with the interfacial properties at the pore scale using glass micro-models at different wettability conditions. This part shows the wetting behavior of CO 2 on hydrophobic or oil-wet solid surfaces. A pore network model was used for the interpretation and exploitation of these results. The third part corresponds to two different experimental approaches at the core scale at different wettability conditions associated to a modelling at flue Darcy scale. This part is a significant contribution to the validation of COORES compositional reservoir simulator developed by IFP. It has also allow us to estimate multiphase properties, Pc and kr, for brine-CO 2 systems at reservoir conditions. This study presents the necessary scales to model CO 2 storage in deep saline aquifers. (author)

  19. Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow

    International Nuclear Information System (INIS)

    Baransky, Y.A.

    1987-01-01

    The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)

  20. A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs

    Science.gov (United States)

    Dana, Saumik; Ganis, Benjamin; Wheeler, Mary F.

    2018-01-01

    In coupled flow and poromechanics phenomena representing hydrocarbon production or CO2 sequestration in deep subsurface reservoirs, the spatial domain in which fluid flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a coupled problem domain or to model flow on a huge domain with zero permeability cells to mimic the no flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. In order to address these challenges, we augment the fixed-stress split iterative scheme with upscaling and downscaling operators to enable modeling flow and mechanics on overlapping nonmatching hexahedral grids. Flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming Galerkin method. The multiscale operators are constructed using a procedure that involves singular value decompositions, a surface intersections algorithm and Delaunay triangulations. We numerically demonstrate the convergence of the augmented scheme using the classical Mandel's problem solution.

  1. Optimization of fracture length in gas/condensate reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Mohan, J.; Sharma, M.M.; Pope, G.A. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)

    2006-07-01

    A common practice that improves the productivity of gas-condensate reservoirs is hydraulic fracturing. Two important variables that determine the effectiveness of hydraulic fractures are fracture length and fracture conductivity. Although there are no simple guidelines for the optimization of fracture length and the factors that affect it, it is preferable to have an optimum fracture length for a given proppant volume in order to maximize productivity. An optimization study was presented in which fracture length was estimated at wells where productivity was maximized. An analytical expression that takes into account non-Darcy flow and condensate banking was derived. This paper also reviewed the hydraulic fracturing process and discussed previous simulation studies that investigated the effects of well spacing and fracture length on well productivity in low permeability gas reservoirs. The compositional simulation study and results and discussion were also presented. The analytical expression for optimum fracture length, analytical expression with condensate dropout, and equations for the optimum fracture length with non-Darcy flow in the fracture were included in an appendix. The Computer Modeling Group's GEM simulator, an equation-of-state compositional simulator, was used in this study. It was concluded that for cases with non-Darcy flow, the optimum fracture lengths are lower than those obtained with Darcy flow. 18 refs., 5 tabs., 22 figs., 1 appendix.

  2. STRUCTURAL HETEROGENEITIES AND PALEO FLUID FLOW IN AN ANALOG SANDSTONE RESERVOIR 2001-2004

    International Nuclear Information System (INIS)

    Pollard, David; Aydin, Atilla

    2005-01-01

    Fractures and faults are brittle structural heterogeneities that can act both as conduits and barriers with respect to fluid flow in rock. This range in the hydraulic effects of fractures and faults greatly complicates the challenges faced by geoscientists working on important problems: from groundwater aquifer and hydrocarbon reservoir management, to subsurface contaminant fate and transport, to underground nuclear waste isolation, to the subsurface sequestration of CO2 produced during fossil-fuel combustion. The research performed under DOE grant DE-FG03-94ER14462 aimed to address these challenges by laying a solid foundation, based on detailed geological mapping, laboratory experiments, and physical process modeling, on which to build our interpretive and predictive capabilities regarding the structure, patterns, and fluid flow properties of fractures and faults in sandstone reservoirs. The material in this final technical report focuses on the period of the investigation from July 1, 2001 to October 31, 2004. The Aztec Sandstone at the Valley of Fire, Nevada, provides an unusually rich natural laboratory in which exposures of joints, shear deformation bands, compaction bands and faults at scales ranging from centimeters to kilometers can be studied in an analog for sandstone aquifers and reservoirs. The suite of structures there has been documented and studied in detail using a combination of low-altitude aerial photography, outcrop-scale mapping and advanced computational analysis. In addition, chemical alteration patterns indicative of multiple paleo fluid flow events have been mapped at outcrop, local and regional scales. The Valley of Fire region has experienced multiple episodes of fluid flow and this is readily evident in the vibrant patterns of chemical alteration from which the Valley of Fire derives its name. We have successfully integrated detailed field and petrographic observation and analysis, process-based mechanical modeling, and numerical

  3. Hazard Assessment of Debris Flows in the Reservoir Region of Wudongde Hydropower Station in China

    Directory of Open Access Journals (Sweden)

    Cencen Niu

    2015-11-01

    Full Text Available The outbreak of debris flows in a reservoir region can affect the stability of hydropower stations and threaten the lives of the people living downstream of dams. Therefore, determining the hazard degree of debris flows in a reservoir region is of great importance. SPOT5 remote sensing images and digital elevation models are introduced to determine the characteristics of debris-flow catchments. The information is acquired through comprehensive manual investigation and satellite image interpretation. Ten factors that influence debris flow are extracted for the hazard assessment. The weight of these factors is determined using the analytic hierarchy process method. As a multi-criterion decision analysis method, fuzzy synthetic evaluation is applied for hazard assessment.

  4. Large Dam Effects on Flow Regime and Hydraulic Parameters of river (Case study: Karkheh River, Downstream of Reservoir Dam

    Directory of Open Access Journals (Sweden)

    Farhang Azarang

    2017-06-01

    Full Text Available Introduction: The critical role of the rivers in supplying water for various needs of life has led to engineering identification of the hydraulic regime and flow condition of the rivers. Hydraulic structures such dams have inevitable effects on their downstream that should be well investigated. The reservoir dams are the most important hydraulic structures which are the cause of great changes in river flow conditions. Materials and Methods: In this research, an accurate assessment was performed to study the flow regime of Karkheh river at downstream of Karkheh Reservoir Dam as the largest dam in Middle East. Karkheh River is the third waterful river of Iran after Karun and Dez and the third longest river after the Karun and Sefidrud. The Karkheh Dam is a large reservoir dam built in Iran on the Karkheh River in 2000. The Karkheh Reservoir Dam is on the Karkheh River in the Northwestern Khouzestan Province, the closest city being Andimeshk to the east. The part of Karkheh River, which was studied in this research is located at downstream of Karkheh Reservoir Dam. This interval is approximately 94 km, which is located between PayePol and Abdolkhan hydrometric stations. In this research, 138 cross sections were used along Karkheh River. Distance of cross sections from each other was 680m in average. The efficient model of HEC-RAS has been utilized to simulate the Karkheh flow conditions before and after the reservoir dam construction using of hydrometric stations data included annually and monthly mean discharges, instantaneous maximum discharges, water surface profiles and etc. Three defined discharges had been chosen to simulate the Karkheh River flow; maximum defined discharge, mean defined discharge and minimum defined discharge. For each of these discharges values, HEC-RAS model was implemented as a steady flow of the Karkheh River at river reach of study. Water surface profiles of flow, hydraulic parameters and other results of flow regime in

  5. Simulation of a multistage fractured horizontal well in a water-bearing tight fractured gas reservoir under non-Darcy flow

    Science.gov (United States)

    Zhang, Rui-Han; Zhang, Lie-Hui; Wang, Rui-He; Zhao, Yu-Long; Huang, Rui

    2018-06-01

    Reservoir development for unconventional resources such as tight gas reservoirs is in increasing demand due to the rapid decline of production in conventional reserves. Compared with conventional reservoirs, fluid flow in water-bearing tight gas reservoirs is subject to more nonlinear multiphase flow and gas slippage in nano/micro matrix pores because of the strong collisions between rock and gas molecules. Economic gas production from tight gas reservoirs depends on extensive application of water-based hydraulic fracturing of horizontal wells, associated with non-Darcy flow at a high flow rate, geomechanical stress sensitivity of un-propped natural fractures, complex flow geometry and multiscale heterogeneity. How to efficiently and accurately predict the production performance of a multistage fractured horizontal well (MFHW) is challenging. In this paper, a novel multicontinuum, multimechanism, two-phase simulator is established based on unstructured meshes and the control volume finite element method to analyze the production performance of MFHWs. The multiple interacting continua model and discrete fracture model are coupled to integrate the unstimulated fractured reservoir, induced fracture networks (stimulated reservoir volumes, SRVs) and irregular discrete hydraulic fractures. Several simulations and sensitivity analyses are performed with the developed simulator for determining the key factors affecting the production performance of MFHWs. Two widely applied fracturing models, classic hydraulic fracturing which generates long double-wing fractures and the volumetric fracturing aimed at creating large SRVs, are compared to identify which of them can make better use of tight gas reserves.

  6. Two-phase flow in volatile oil reservoir using two-phase pseudo-pressure well test method

    Energy Technology Data Exchange (ETDEWEB)

    Sharifi, M.; Ahmadi, M. [Calgary Univ., AB (Canada)

    2009-09-15

    A study was conducted to better understand the behaviour of volatile oil reservoirs. Retrograde condensation occurs in gas-condensate reservoirs when the flowing bottomhole pressure (BHP) lowers below the dewpoint pressure, thus creating 4 regions in the reservoir with different liquid saturations. Similarly, when the BHP of volatile oil reservoirs falls below the bubblepoint pressure, two phases are created in the region around the wellbore, and a single phase (oil) appears in regions away from the well. In turn, higher gas saturation causes the oil relative permeability to decrease towards the near-wellbore region. Reservoir compositional simulations were used in this study to predict the fluid behaviour below the bubblepoint. The flowing bottomhole pressure was then exported to a well test package to diagnose the occurrence of different mobility regions. The study also investigated the use of a two-phase pseudo-pressure method on volatile and highly volatile oil reservoirs. It was concluded that this method can successfully predict the true permeability and mechanical skin. It can also distinguish between mechanical skin and condensate bank skin. As such, the two-phase pseudo-pressure method is particularly useful for developing after-drilling well treatment and enhanced oil recovery process designs. However, accurate relative permeability and PVT data must be available for reliable interpretation of the well test in volatile oil reservoirs. 18 refs., 3 tabs., 9 figs.

  7. Map of fluid flow in fractal porous medium into fractal continuum flow.

    Science.gov (United States)

    Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

    2012-05-01

    This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

  8. Poiseuille equation for steady flow of fractal fluid

    Science.gov (United States)

    Tarasov, Vasily E.

    2016-07-01

    Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

  9. Carbon flow dynamics in the pelagic community of the Sau Reservoir (Catalonia, NE Spain)

    Czech Academy of Sciences Publication Activity Database

    Comerma, M.; García, J. C.; Romero, M.; Armengol, J.; Šimek, Karel

    2003-01-01

    Roč. 504, - (2003), s. 87-98 ISSN 0018-8158. [Reservoir Limnology and Water Quality /4./. České Budějovice, 12.08.2002-16.08.2002] Institutional research plan: CEZ:AV0Z6017912 Keywords : reservoir * longitudinal plankton succession * carbon flow through microbial food webs Subject RIV: EE - Microbiology, Virology Impact factor: 0.720, year: 2003

  10. Vapor-droplet flow equations

    International Nuclear Information System (INIS)

    Crowe, C.T.

    1975-01-01

    General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources

  11. Improving reservoir history matching of EM heated heavy oil reservoirs via cross-well seismic tomography

    KAUST Repository

    Katterbauer, Klemens

    2014-01-01

    Enhanced recovery methods have become significant in the industry\\'s drive to increase recovery rates from oil and gas reservoirs. For heavy oil reservoirs, the immobility of the oil at reservoir temperatures, caused by its high viscosity, limits the recovery rates and strains the economic viability of these fields. While thermal recovery methods, such as steam injection or THAI, have extensively been applied in the field, their success has so far been limited due to prohibitive heat losses and the difficulty in controlling the combustion process. Electromagnetic (EM) heating via high-frequency EM radiation has attracted attention due to its wide applicability in different environments, its efficiency, and the improved controllability of the heating process. While becoming a promising technology for heavy oil recovery, its effect on overall reservoir production and fluid displacements are poorly understood. Reservoir history matching has become a vital tool for the oil & gas industry to increase recovery rates. Limited research has been undertaken so far to capture the nonlinear reservoir dynamics and significantly varying flow rates for thermally heated heavy oil reservoir that may notably change production rates and render conventional history matching frameworks more challenging. We present a new history matching framework for EM heated heavy oil reservoirs incorporating cross-well seismic imaging. Interfacing an EM heating solver to a reservoir simulator via Andrade’s equation, we couple the system to an ensemble Kalman filter based history matching framework incorporating a cross-well seismic survey module. With increasing power levels and heating applied to the heavy oil reservoirs, reservoir dynamics change considerably and may lead to widely differing production forecasts and increased uncertainty. We have shown that the incorporation of seismic observations into the EnKF framework can significantly enhance reservoir simulations, decrease forecasting

  12. Reservoir resistivity characterization incorporating flow dynamics

    KAUST Repository

    Arango, Santiago

    2016-04-07

    Systems and methods for reservoir resistivity characterization are provided, in various aspects, an integrated framework for the estimation of Archie\\'s parameters for a strongly heterogeneous reservoir utilizing the dynamics of the reservoir are provided. The framework can encompass a Bayesian estimation/inversion method for estimating the reservoir parameters, integrating production and time lapse formation conductivity data to achieve a better understanding of the subsurface rock conductivity properties and hence improve water saturation imaging.

  13. Reservoir resistivity characterization incorporating flow dynamics

    KAUST Repository

    Arango, Santiago; Sun, Shuyu; Hoteit, Ibrahim; Katterbauer, Klemens

    2016-01-01

    Systems and methods for reservoir resistivity characterization are provided, in various aspects, an integrated framework for the estimation of Archie's parameters for a strongly heterogeneous reservoir utilizing the dynamics of the reservoir are provided. The framework can encompass a Bayesian estimation/inversion method for estimating the reservoir parameters, integrating production and time lapse formation conductivity data to achieve a better understanding of the subsurface rock conductivity properties and hence improve water saturation imaging.

  14. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu

    2017-01-01

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  15. Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media

    KAUST Repository

    El-Amin, Mohamed

    2017-07-06

    In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.

  16. Explicit flow equations and recursion operator of the ncKP hierarchy

    International Nuclear Information System (INIS)

    He, Jingsong; Wang, Lihong; Tu, Junyi; Li, Xiaodong

    2011-01-01

    The explicit expression of the flow equations of the noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy is derived. Compared with the flow equations of the KP hierarchy, our result shows that the additional terms in the flow equations of the ncKP hierarchy indeed consist of commutators of dynamical coordinates {u i }. The recursion operator for the flow equations under n-reduction is presented. Further, under 2-reduction, we calculate a nonlocal recursion operator Φ(2) of the noncommutative Korteweg–de Vries(ncKdV) hierarchy, which generates a hierarchy of local, higher-order flows. Thus we solve the open problem proposed by Olver and Sokolov (1998 Commun. Math. Phys. 193 245–68)

  17. Estimating reservoir permeability from gravity current modeling of CO2 flow at Sleipner storage project, North Sea

    Science.gov (United States)

    Cowton, L. R.; Neufeld, J. A.; Bickle, M.; White, N.; White, J.; Chadwick, A.

    2017-12-01

    Vertically-integrated gravity current models enable computationally efficient simulations of CO2 flow in sub-surface reservoirs. These simulations can be used to investigate the properties of reservoirs by minimizing differences between observed and modeled CO2 distributions. At the Sleipner project, about 1 Mt yr-1 of supercritical CO2 is injected at a depth of 1 km into a pristine saline aquifer with a thick shale caprock. Analysis of time-lapse seismic reflection surveys shows that CO2 is distributed within 9 discrete layers. The trapping mechanism comprises a stacked series of 1 m thick, impermeable shale horizons that are spaced at 30 m intervals through the reservoir. Within the stratigraphically highest reservoir layer, Layer 9, a submarine channel deposit has been mapped on the pre-injection seismic survey. Detailed measurements of the three-dimensional CO2 distribution within Layer 9 have been made using seven time-lapse surveys, providing a useful benchmark against which numerical flow simulations can be tested. Previous simulations have, in general, been largely unsuccessful in matching the migration rate of CO2 in this layer. Here, CO2 flow within Layer 9 is modeled as a vertically-integrated gravity current that spreads beneath a structurally complex caprock using a two-dimensional grid, considerably increasing computational efficiency compared to conventional three-dimensional simulators. This flow model is inverted to find the optimal reservoir permeability in Layer 9 by minimizing the difference between observed and predicted distributions of CO2 as a function of space and time. A three parameter inverse model, comprising reservoir permeability, channel permeability and channel width, is investigated by grid search. The best-fitting reservoir permeability is 3 Darcys, which is consistent with measurements made on core material from the reservoir. Best-fitting channel permeability is 26 Darcys. Finally, the ability of this simplified numerical model

  18. Reservoir characterization of Pennsylvanian sandstone reservoirs. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Kelkar, M.

    1995-02-01

    This final report summarizes the progress during the three years of a project on Reservoir Characterization of Pennsylvanian Sandstone Reservoirs. The report is divided into three sections: (i) reservoir description; (ii) scale-up procedures; (iii) outcrop investigation. The first section describes the methods by which a reservoir can be described in three dimensions. The next step in reservoir description is to scale up reservoir properties for flow simulation. The second section addresses the issue of scale-up of reservoir properties once the spatial descriptions of properties are created. The last section describes the investigation of an outcrop.

  19. A complementary conventional analysis for channelized reservoirs

    International Nuclear Information System (INIS)

    Escobar Freddy Humberto; Montealegre M, Matilde

    2007-01-01

    Many well pressure data coming from long and narrow reservoirs which result from either fluvial deposition of faulting connote be completely interpreted by conventional analysis since some flow regimes are not conventionally recognized yet in the oil literature. This narrow geometry allows for the simultaneous development of two linear flow regimes coming from each one of the lateral sides of the system towards the well. This has been called dual linear flow regime. If the well is off-centered with regards to the two lateral boundaries, then, and of the linear flow regimes vanishes and, than, two possibilities con be presented. Firstly, if the closer lateral boundary is close to flow the unique linear flow persists along the longer lateral boundary. It has been called single linear flow. Following this, either steady or pseudo-steady states will develop. Secondly, if a constant - pressure closer lateral boundary is dealt with, then parabolic flow develops along the longer lateral boundary. Steady state has to be developed once the disturbance reaches the farther boundary. This study presents new equations for conventional analysis for the dual linear, linear and parabolic flow regimes recently introduced to the oil literature. The equations were validated by applying them to field and simulated examples

  20. Computerized X-ray Microtomography Observations and Fluid Flow Measurements of the Effect of Effective Stress on Fractured Reservoir Seal Shale

    Science.gov (United States)

    Welch, N.; Crawshaw, J.; Boek, E.

    2014-12-01

    The successful storage of carbon dioxide in geologic formations requires an in-depth understanding of all reservoir characteristics and morphologies. An intact and substantial seal formation above a storage reservoir is required for a significant portion of the initial sealing mechanisms believed to occur during carbon dioxide storage operations. Shales are a common seal formation rock types found above numerous hydrocarbon reservoirs, as well as potential saline aquifer storage locations. Shales commonly have very low permeability, however they also have the tendency to be quite fissile, and the formation of fractures within these seals can have a significant detrimental effect on the sealing potential of a reservoir and amount to large areas of high permeability and low capillary pressures compared to the surrounding intact rock. Fractured shales also have an increased current interest due to the increasing development of shale gas reservoirs using hydraulic fracturing techniques. This work shows the observed changes that occur within fractured pieces of reservoir seal shale samples, along with quarry analogues, using an in-situ micro-CT fluid flow imaging apparatus with a Hassler type core holder. Changes within the preferential flow path under different stress regimes as well as physical changes to the fracture geometry are reported. Lattice Boltzmann flow simulations were then performed on the extracted flow paths and compared to experiment permeability measurements. The preferential flow path of carbon dioxide through the fracture network is also observed and compared to the results two-phase Lattice Boltzmann fluid flow simulations.

  1. Navier-Stokes-like equations for traffic flow.

    Science.gov (United States)

    Velasco, R M; Marques, W

    2005-10-01

    The macroscopic traffic flow equations derived from the reduced Paveri-Fontana equation are closed starting with the maximization of the informational entropy. The homogeneous steady state taken as a reference is obtained for a specific model of the desired velocity and a kind of Chapman-Enskog method is developed to calculate the traffic pressure at the Navier-Stokes level. Numerical solution of the macroscopic traffic equations is obtained and its characteristics are analyzed.

  2. Diagonalizing quadratic bosonic operators by non-autonomous flow equations

    CERN Document Server

    Bach, Volker

    2016-01-01

    The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

  3. Analysis of Flow Behavior for Acid Fracturing Wells in Fractured-Vuggy Carbonate Reservoirs

    Directory of Open Access Journals (Sweden)

    Mingxian Wang

    2018-01-01

    Full Text Available This study develops a mathematical model for transient flow analysis of acid fracturing wells in fractured-vuggy carbonate reservoirs. This model considers a composite system with the inner region containing finite number of artificial fractures and wormholes and the outer region showing a triple-porosity medium. Both analytical and numerical solutions are derived in this work, and the comparison between two solutions verifies the model accurately. Flow behavior is analyzed thoroughly by examining the standard log-log type curves. Flow in this composite system can be divided into six or eight main flow regimes comprehensively. Three or two characteristic V-shaped segments can be observed on pressure derivative curves. Each V-shaped segment corresponds to a specific flow regime. One or two of the V-shaped segments may be absent in particular cases. Effects of interregional diffusivity ratio and interregional conductivity ratio on transient responses are strong in the early-flow period. The shape and position of type curves are also influenced by interporosity coefficients, storativity ratios, and reservoir radius significantly. Finally, we show the differences between our model and the similar model with single fracture or without acid fracturing and further investigate the pseudo-skin factor caused by acid fracturing.

  4. An Analysis of Vehicular Traffic Flow Using Langevin Equation

    Directory of Open Access Journals (Sweden)

    Çağlar Koşun

    2015-08-01

    Full Text Available Traffic flow data are stochastic in nature, and an abundance of literature exists thereof. One way to express stochastic data is the Langevin equation. Langevin equation consists of two parts. The first part is known as the deterministic drift term, the other as the stochastic diffusion term. Langevin equation does not only help derive the deterministic and random terms of the selected portion of the city of Istanbul traffic empirically, but also sheds light on the underlying dynamics of the flow. Drift diagrams have shown that slow lane tends to get congested faster when vehicle speeds attain a value of 25 km/h, and it is 20 km/h for the fast lane. Three or four distinct regimes may be discriminated again from the drift diagrams; congested, intermediate, and free-flow regimes. At places, even the intermediate regime may be divided in two, often with readiness to congestion. This has revealed the fact that for the selected portion of the highway, there are two main states of flow, namely, congestion and free-flow, with an intermediate state where the noise-driven traffic flow forces the flow into either of the distinct regimes.

  5. River Stream-Flow and Zayanderoud Reservoir Operation Modeling Using the Fuzzy Inference System

    Directory of Open Access Journals (Sweden)

    Saeed Jamali

    2007-12-01

    Full Text Available The Zayanderoud basin is located in the central plateau of Iran. As a result of population increase and agricultural and industrial developments, water demand on this basin has increased extensively. Given the importance of reservoir operation in water resource and management studies, the performance of fuzzy inference system (FIS for Zayanderoud reservoir operation is investigated in this paper. The model of operation consists of two parts. In the first part, the seasonal river stream-flow is forecasted using the fuzzy rule-based system. The southern oscillated index, rain, snow, and discharge are inputs of the model and the seasonal river stream-flow its output. In the second part, the operation model is constructed. The amount of releases is first optimized by a nonlinear optimization model and then the rule curves are extracted using the fuzzy inference system. This model operates on an "if-then" principle, where the "if" is a vector of fuzzy permits and "then" is the fuzzy result. The reservoir storage capacity, inflow, demand, and year condition factor are used as permits. Monthly release is taken as the consequence. The Zayanderoud basin is investigated as a case study. Different performance indices such as reliability, resiliency, and vulnerability are calculated. According to results, FIS works more effectively than the traditional reservoir operation methods such as standard operation policy (SOP or linear regression.

  6. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

    International Nuclear Information System (INIS)

    Delhaye, J.M.

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  7. A coupling model for gas diffusion and seepage in SRV section of shale gas reservoirs

    Directory of Open Access Journals (Sweden)

    Shusheng Gao

    2017-03-01

    Full Text Available A prerequisite to effective shale gas development is a complicated fracture network generated by extensive and massive fracturing, which is called SRV (stimulated reservoir volume section. Accurate description of gas flow behaviors in such section is fundamental for productivity evaluation and production performance prediction of shale gas wells. The SRV section is composed of bedrocks with varying sizes and fracture networks, which exhibit different flow behaviors – gas diffusion in bedrocks and gas seepage in fractures. According to the porosity and permeability and the adsorption, diffusion and seepage features of bedrocks and fractures in a shale gas reservoir, the material balance equations were built for bedrocks and fractures respectively and the continuity equations of gas diffusion and seepage in the SRV section were derived. For easy calculation, the post-frac bedrock cube was simplified to be a sphere in line with the principle of volume consistency. Under the assumption of quasi-steady flow behavior at the cross section of the sphere, the gas channeling equation was derived based on the Fick's laws of diffusion and the density function of gas in bedrocks and fractures. The continuity equation was coupled with the channeling equation to effectively characterize the complicated gas flow behavior in the SRV section. The study results show that the gas diffusivity in bedrocks and the volume of bedrocks formed by volume fracturing (or the scale of fracturing jointly determines the productivity and stable production period of a shale gas well. As per the actual calculation for the well field A in the Changning–Weiyuan Block in the Sichuan Basin, the matrix has low gas diffusivity – about 10−5 cm2/s and a large volume with an equivalent sphere radius of 6.2 m, hindering the gas channeling from bedrocks to fractures and thereby reducing the productivity of the shale gas well. It is concluded that larger scale of volume fracturing

  8. Reconstruction of dynamical equations for traffic flow

    OpenAIRE

    Kriso, S.; Friedrich, R.; Peinke, J.; Wagner, P.

    2001-01-01

    Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the fund...

  9. Exactly averaged equations for flow and transport in random media

    International Nuclear Information System (INIS)

    Shvidler, Mark; Karasaki, Kenzi

    2001-01-01

    It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)

  10. Equations for the kinetic modeling of supersonically flowing electrically excited lasers

    International Nuclear Information System (INIS)

    Lind, R.C.

    1973-01-01

    The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

  11. Pore size determination using normalized J-function for different hydraulic flow units

    Directory of Open Access Journals (Sweden)

    Ali Abedini

    2015-06-01

    Full Text Available Pore size determination of hydrocarbon reservoirs is one of the main challenging areas in reservoir studies. Precise estimation of this parameter leads to enhance the reservoir simulation, process evaluation, and further forecasting of reservoir behavior. Hence, it is of great importance to estimate the pore size of reservoir rocks with an appropriate accuracy. In the present study, a modified J-function was developed and applied to determine the pore radius in one of the hydrocarbon reservoir rocks located in the Middle East. The capillary pressure data vs. water saturation (Pc–Sw as well as routine reservoir core analysis include porosity (φ and permeability (k were used to develop the J-function. First, the normalized porosity (φz, the rock quality index (RQI, and the flow zone indicator (FZI concepts were used to categorize all data into discrete hydraulic flow units (HFU containing unique pore geometry and bedding characteristics. Thereafter, the modified J-function was used to normalize all capillary pressure curves corresponding to each of predetermined HFU. The results showed that the reservoir rock was classified into five separate rock types with the definite HFU and reservoir pore geometry. Eventually, the pore radius for each of these HFUs was determined using a developed equation obtained by normalized J-function corresponding to each HFU. The proposed equation is a function of reservoir rock characteristics including φz, FZI, lithology index (J*, and pore size distribution index (ɛ. This methodology used, the reservoir under study was classified into five discrete HFU with unique equations for permeability, normalized J-function and pore size. The proposed technique is able to apply on any reservoir to determine the pore size of the reservoir rock, specially the one with high range of heterogeneity in the reservoir rock properties.

  12. Computational issues of solving the 1D steady gradually varied flow equation

    Directory of Open Access Journals (Sweden)

    Artichowicz Wojciech

    2014-09-01

    Full Text Available In this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution. This fact implies that the nonlinear algebraic equation approximating the ordinary differential energy equation, which additionally coincides with the wellknown standard step method usually applied for computing of the flow profile, can have variable number of roots. Consequently, more than one alternative solution corresponding to the same initial condition can be provided. Using this property it is possible to compute the water flow profile passing through the critical stage.

  13. Multigrid Methods for Fully Implicit Oil Reservoir Simulation

    Science.gov (United States)

    Molenaar, J.

    1996-01-01

    In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for

  14. Coupling of a reservoir model and of a poro-mechanical model. Application to the study of the compaction of petroleum reservoirs and of the associated subsidence; Couplage d'un modele de gisement et d'un modele mecanique. Application a l'etude de la compaction des reservoirs petroliers et de la subsidence associee

    Energy Technology Data Exchange (ETDEWEB)

    Bevillon, D.

    2000-11-30

    The aim of this study is to provide a better description of the rock contribution to fluid flows in petroleum reservoirs. The production of oil/gas in soft highly compacting reservoirs induces important reduction of the pore volume, which increases oil productivity. This compaction leads to undesirable effects such as surface subsidence or damage of well equipment. Analysis of compaction and subsidence can be performed using either engineering reservoir models or coupled poro-mechanical models. Poro-mechanical model offers a rigorous mechanical framework, but does not permit a complete description of the fluids. The reservoir model gives a good description of the fluid phases, but the description of the mechanic phenomenon is then simplified. To satisfy the set of equations (mechanical equilibrium and diffusivity equations), two simulators can be used together sequentially. Each of the two simulators solves its own system independently, and information passed both directions between simulators. This technique is usually referred to the partially coupled scheme. In this study, reservoir and hydro-mechanical simulations show that reservoir theory is not a rigorous framework to represent the evolution of the high porous rocks strains. Then, we introduce a partially coupled scheme that is shown to be consistent and unconditionally stable, which permits to describe correctly poro-mechanical theory in reservoir models. (author)

  15. Bones and oil reservoirs : bioengineers use oilpatch technology to study fluid flow in bones

    Energy Technology Data Exchange (ETDEWEB)

    Marsters, S.

    2003-06-01

    The fact that porosity and the presence of channels are qualities that are common to oil reservoirs and bones, led to the use of reservoir modelling technology in investigating bone disorders and to the discovery of dramatic changes in the structure and blood supply of osteoarthritic bones that lie under degenerating cartilage. CMG (Computer Modelling Group) Ltd., developers of reservoir simulation software claim that their software packages can help with the modelling of cellular responses to strains and deformations that occur as fluid flows through bone after a traumatic event such as a tear in the anterior cruciate ligament, a common sports-related injury. Researchers at the University of Calgary expect that by looking at the changes in blood and fluid flow within the bone, they can attain a better understanding of the chain of events that leads to osteoarthritis. Better understanding of the progression of the disease could eventually lead to more precise administration of drugs to deal with osteoarthritic pain, and even to the prevention of painful arthritic joints.

  16. On the One-Dimensional Steady and Unsteady Porous Flow Equation

    DEFF Research Database (Denmark)

    Andersen, O. H.; Burcharth, H. F.

    1995-01-01

    Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative...... derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow...... resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available....

  17. Successful flow testing of a gas reservoir in 3,500 feet of water

    International Nuclear Information System (INIS)

    Shaughnessy, J.M.; Carpenter, R.S.; Coleman, R.A.; Jackson, C.W.

    1992-01-01

    The test of Viosca Knoll Block 957 Well No. 1 Sidetrack No. 2 was Amoco Production Co.'s deepest test from a floating rig. Viosca Knoll 957 is 115 miles southeast of New Orleans in 3,500 ft of water. The test, at a record water depth for the Gulf of Mexico, also set a world water-depth record for testing a gas reservoir. Safety to crew and the environmental were top priorities during the planning. A team consisting of drilling, completion, reservoir, and facilities engineers and a foreman were assigned to plan and implement the test. Early planning involved field, service company, and engineering groups. Every effort was made to identify potential problems and to design the system to handle them. This paper reports that the goals of the test were to determine reservoir properties and reservoir limits. Several significant challenges were involved in the well test. The reservoir was gas with a potentially significant condensate yield. The ability to dispose of the large volumes of produced fluids safely without polluting was critical to maintaining uninterrupted flow. Potential shut-in surface pressure was 6,500 psi. Seafloor temperature in 3,500 ft of water was 39 degrees F

  18. A generalised groundwater flow equation using the concept of non ...

    African Journals Online (AJOL)

    The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of ...

  19. Geologic storage of carbon dioxide and enhanced oil recovery. I. Uncertainty quantification employing a streamline based proxy for reservoir flow simulation

    International Nuclear Information System (INIS)

    Kovscek, A.R.; Wang, Y.

    2005-01-01

    Carbon dioxide (CO 2 ) is already injected into a limited class of reservoirs for oil recovery purposes; however, the engineering design question for simultaneous oil recovery and storage of anthropogenic CO 2 is significantly different from that of oil recovery alone. Currently, the volumes of CO 2 injected solely for oil recovery are minimized due to the purchase cost of CO 2 . If and when CO 2 emissions to the atmosphere are managed, it will be necessary to maximize simultaneously both economic oil recovery and the volumes of CO 2 emplaced in oil reservoirs. This process is coined 'cooptimization'. This paper proposes a work flow for cooptimization of oil recovery and geologic CO 2 storage. An important component of the work flow is the assessment of uncertainty in predictions of performance. Typical methods for quantifying uncertainty employ exhaustive flow simulation of multiple stochastic realizations of the geologic architecture of a reservoir. Such approaches are computationally intensive and thereby time consuming. An analytic streamline based proxy for full reservoir simulation is proposed and tested. Streamline trajectories represent the three-dimensional velocity field during multiphase flow in porous media and so are useful for quantifying the similarity and differences among various reservoir models. The proxy allows rational selection of a representative subset of equi-probable reservoir models that encompass uncertainty with respect to true reservoir geology. The streamline approach is demonstrated to be thorough and rapid

  20. Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs

    KAUST Repository

    Simon, Moritz

    2014-11-14

    © 2014, Springer Science+Business Media New York. With the target of optimizing CO2 sequestration in underground reservoirs, we investigate constrained optimal control problems with partially miscible two-phase flow in porous media. Our objective is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE system, formulate the optimal control problem and derive the continuous adjoint equations. For the discretization we apply a variant of the so-called BOX method, a locally conservative control-volume FE method that we further stabilize by a periodic averaging feature to reduce oscillations. The timestep-wise Lagrange function of the control problem is implemented as a variational form in Sundance, a toolbox for rapid development of parallel FE simulations, which is part of the HPC software Trilinos. We discuss the BOX method and our implementation in Sundance. The MPI parallelized Sundance state and adjoint solvers are linked to the interior point optimization package IPOPT, using limited-memory BFGS updates for approximating second derivatives. Finally, we present and discuss different types of optimal control results.

  1. Flow equation, conformal symmetry, and anti-de Sitter geometry

    Science.gov (United States)

    Aoki, Sinya; Yokoyama, Shuichi

    2018-03-01

    We argue that the anti-de Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d-dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.

  2. Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

    1996-12-31

    Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

  3. Basic equations of interfacial area transport in gas-liquid two-phase flow

    International Nuclear Information System (INIS)

    Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.

    2011-01-01

    The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)

  4. Statistically derived conservation equations for fluid particle flows

    International Nuclear Information System (INIS)

    Reyes, J.N. Jr.

    1989-01-01

    The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior

  5. Transport of reservoir fines

    DEFF Research Database (Denmark)

    Yuan, Hao; Shapiro, Alexander; Stenby, Erling Halfdan

    Modeling transport of reservoir fines is of great importance for evaluating the damage of production wells and infectivity decline. The conventional methodology accounts for neither the formation heterogeneity around the wells nor the reservoir fines’ heterogeneity. We have developed an integral...... dispersion equation in modeling the transport and the deposition of reservoir fines. It successfully predicts the unsymmetrical concentration profiles and the hyperexponential deposition in experiments....

  6. An Efficient Upscaling Process Based on a Unified Fine-scale Multi-Physics Model for Flow Simulation in Naturally Fracture Carbonate Karst Reservoirs

    KAUST Repository

    Bi, Linfeng

    2009-01-01

    The main challenges in modeling fluid flow through naturally-fractured carbonate karst reservoirs are how to address various flow physics in complex geological architectures due to the presence of vugs and caves which are connected via fracture networks at multiple scales. In this paper, we present a unified multi-physics model that adapts to the complex flow regime through naturally-fractured carbonate karst reservoirs. This approach generalizes Stokes-Brinkman model (Popov et al. 2007). The fracture networks provide the essential connection between the caves in carbonate karst reservoirs. It is thus very important to resolve the flow in fracture network and the interaction between fractures and caves to better understand the complex flow behavior. The idea is to use Stokes-Brinkman model to represent flow through rock matrix, void caves as well as intermediate flows in very high permeability regions and to use an idea similar to discrete fracture network model to represent flow in fracture network. Consequently, various numerical solution strategies can be efficiently applied to greatly improve the computational efficiency in flow simulations. We have applied this unified multi-physics model as a fine-scale flow solver in scale-up computations. Both local and global scale-up are considered. It is found that global scale-up has much more accurate than local scale-up. Global scale-up requires the solution of global flow problems on fine grid, which generally is computationally expensive. The proposed model has the ability to deal with large number of fractures and caves, which facilitate the application of Stokes-Brinkman model in global scale-up computation. The proposed model flexibly adapts to the different flow physics in naturally-fractured carbonate karst reservoirs in a simple and effective way. It certainly extends modeling and predicting capability in efficient development of this important type of reservoir.

  7. Multicomponent fluid flow analysis using a new set of conservation equations

    International Nuclear Information System (INIS)

    Kamali, Reza; Emdad, Homayoon; Alishahi, Mohammad M

    2008-01-01

    In this work hydrodynamics of multicomponent ideal gas mixtures have been studied. Starting from the kinetic equations, the Eulerian approach is used to derive a new set of conservation equations for the multicomponent system where each component may have different velocity and kinetic temperature. The equations are based on the Grad's method of moment derived from the kinetic model in a relaxation time approximation (RTA). Based on this model which contains separate equation sets for each component of the system, a computer code has been developed for numerical computation of compressible flows of binary gas mixture in generalized curvilinear boundary conforming coordinates. Since these equations are similar to the Navier-Stokes equations for the single fluid systems, the same numerical methods are applied to these new equations. The Roe's numerical scheme is used to discretize the convective terms of governing fluid flow equations. The prepared algorithm and the computer code are capable of computing and presenting flow fields of each component of the system separately as well as the average flow field of the multicomponent gas system as a whole. Comparison of the present code results with those of a more common algorithm based on the mixture theory in a supersonic converging-diverging nozzle provides the validation of the present formulation. Afterwards, a more involved nozzle cooling problem with a binary ideal gas (helium-xenon) is chosen to compare the present results with those of the ordinary mixture theory. The present model provides the details of the flow fields of each component separately which is not available otherwise. It is also shown that the separate fluids treatment, such as the present study, is crucial when considering time scales on the order of (or shorter than) the intercollisions relaxation times.

  8. Stochastic Differential Equations and Kondratiev Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Vaage, G.

    1995-05-01

    The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

  9. Analytical solution to the diffusion, sorption and decay chain equation in a saturated porous medium between two reservoirs

    International Nuclear Information System (INIS)

    Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario

    2015-01-01

    The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain

  10. Rapid reservoir erosion, hyperconcentrated flow, and downstream deposition triggered by breaching of 38 m tall Condit Dam, White Salmon River, Washington

    Science.gov (United States)

    Wilcox, Andrew C.; O'Connor, James E.; Major, Jon J.

    2014-01-01

    Condit Dam on the White Salmon River, Washington, a 38 m high dam impounding a large volume (1.8 million m3) of fine-grained sediment (60% sand, 35% silt and clay, and 5% gravel), was rapidly breached in October 2011. This unique dam decommissioning produced dramatic upstream and downstream geomorphic responses in the hours and weeks following breaching. Blasting a 5 m wide hole into the base of the dam resulted in rapid reservoir drawdown, abruptly releasing ~1.6 million m3 of reservoir water, exposing reservoir sediment to erosion, and triggering mass failures of the thickly accumulated reservoir sediment. Within 90 min of breaching, the reservoir's water and ~10% of its sediment had evacuated. At a gauging station 2.3 km downstream, flow increased briefly by 400 m3 s−1during passage of the initial pulse of released reservoir water, followed by a highly concentrated flow phase—up to 32% sediment by volume—as landslide-generated slurries from the reservoir moved downstream. This hyperconcentrated flow, analogous to those following volcanic eruptions or large landslides, draped the downstream river with predominantly fine sand. During the ensuing weeks, suspended-sediment concentration declined and sand and gravel bed load derived from continued reservoir erosion aggraded the channel by >1 m at the gauging station, after which the river incised back to near its initial elevation at this site. Within 15 weeks after breaching, over 1 million m3 of suspended load is estimated to have passed the gauging station, consistent with estimates that >60% of the reservoir's sediment had eroded. This dam removal highlights the influence of interactions among reservoir erosion processes, sediment composition, and style of decommissioning on rate of reservoir erosion and consequent downstream behavior of released sediment.

  11. Derivation of Inviscid Quasi-geostrophic Equation from Rotational Compressible Magnetohydrodynamic Flows

    Science.gov (United States)

    Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang

    2018-04-01

    In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.

  12. Considering heterogeneities by transmissibilities averaging on adapted meshes in reservoir simulation; Prise en compte des heterogeneites par prise de moyenne des transmissivites sur maillages adaptes en simulation de reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Urgelli, D

    1998-10-16

    Reservoir heterogeneity can be described using geostatistical models. But these models generate the heterogeneity on millions of fine grid blocks, which leads to prohibitive computational costs for reservoir simulations. In order to reduce the number of grid blocks, averaging techniques are needed to up-scale the fine scale permeabilities to the larger scales appropriate for flow simulation and engineering calculations. Grid block permeability up-scaling for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description. But, the equivalent permeability on coarse grid blocks cannot be used directly on the numerical scheme. Usually, the harmonic average of the coarse grid block permeability is used for the transmissibility calculation, but it might cause a loss of accuracy. The purpose of this thesis is to present a new procedure for computing the equivalent transmissibility in the discretized flow equations on Cartesian grids and Corner Point Geometry grids. An application of this technique to a finite volume type numerical scheme is detailed. The principle of this technique is to calculate a permeability term on a shifted block placed between the two adjacent blocks where the transmissibility must be determined. At the field scale, the flow region can be divided into two types : a linear flow pattern with a low pressure gradient far from the wells and a radial flow pattern with a high pressure gradient in the vicinity of the wells. The radial flow region is usually more important for the prediction of production forecast, because it is directly related to the well. This was demonstrated theoretically and numerically for 2-D problem. The transmissibility up-scaling in radial flow pattern consists to determine the transmissibilities in the vicinity of wells and the numerical Productivity Index simultaneously. This new method called `shifted

  13. Experiments and Simulations of Fluid Flow in Heterogeneous Reservoir Models - Emphasis on Impacts from Crossbeds and Fractures

    Energy Technology Data Exchange (ETDEWEB)

    Boerresen, Knut Arne

    1996-12-31

    Hydrocarbon recovery from subsurface reservoirs has become increasingly dependent on advanced recovery techniques that require improved understanding of the physics of fluid flow within and across geological units including small-scale heterogeneities and fractures. In this thesis, impacts from heterogeneities on local fluid flow are studied experimentally by means of imaging techniques to visualize fluid flow in two dimensions during flooding of larger reservoir models. Part 1 reflects the multi-disciplinary collaboration, by briefly introducing the relevant geology, the literature on experiments on fluid flow in bedded structures, and outlining the applied numerical simulator and imaging techniques applied to visualize fluid flow. The second part contains a synopsis of displacement experiments in naturally laminated sandstones and in crossbed laboratory models, and of the impact from incipient shear fractures on oil recovery. The detailed results obtained from the experiments and simulations are described in six papers, all included. 215 refs., 108 figs., 16 tabs.

  14. Experiments and Simulations of Fluid Flow in Heterogeneous Reservoir Models - Emphasis on Impacts from Crossbeds and Fractures

    Energy Technology Data Exchange (ETDEWEB)

    Boerresen, Knut Arne

    1997-12-31

    Hydrocarbon recovery from subsurface reservoirs has become increasingly dependent on advanced recovery techniques that require improved understanding of the physics of fluid flow within and across geological units including small-scale heterogeneities and fractures. In this thesis, impacts from heterogeneities on local fluid flow are studied experimentally by means of imaging techniques to visualize fluid flow in two dimensions during flooding of larger reservoir models. Part 1 reflects the multi-disciplinary collaboration, by briefly introducing the relevant geology, the literature on experiments on fluid flow in bedded structures, and outlining the applied numerical simulator and imaging techniques applied to visualize fluid flow. The second part contains a synopsis of displacement experiments in naturally laminated sandstones and in crossbed laboratory models, and of the impact from incipient shear fractures on oil recovery. The detailed results obtained from the experiments and simulations are described in six papers, all included. 215 refs., 108 figs., 16 tabs.

  15. A Simple Approach to Dynamic Material Balance in Gas-Condensate Reservoirs

    Directory of Open Access Journals (Sweden)

    Heidari Sureshjani M.

    2013-02-01

    Full Text Available In traditional material balance calculations, shut-in well pressure data are used to determine average reservoir pressure while recent techniques do not require the well to be shut-in and use instead flowing well pressure-rate data. These methods, which are known as “dynamic” material balance, are developed for single-phase flow (oil or gas in reservoirs. However, utilization of such methods for gas-condensate reservoirs may create significant errors in prediction of average reservoir pressure due to violation of the single-phase assumption in such reservoirs. In a previous work, a method for production data analysis in gas-condensate reservoirs was developed. The method required standard gas production rate, producing gas-oil ratio, flowing well pressure, CVD data and relative permeability curves. This paper presents a new technique which does not need relative permeability curves and flowing well pressure. In this method, the producing oil-gas ratio is interpolated in the vaporized oil in gas phase (Rv versus pressure (p data in the CVD table and the corresponding pressure is located. The parameter pressure/two-phase deviation factor (p/ztp is then evaluated at the determined pressure points and is plotted versus produced moles (np which forms a straight line. The nature of this plot is such that its extrapolation to point where p/ztp = 0 will give initial moles in place. Putting initial pressure/initial two-phase deviation factor (pi/ztp,i (known parameter and estimated initial moles (ni into the material balance equation, average reservoir pressure can be determined. A main assumption behind the method is that the region where both gas and condensate phases are mobile is of negligible size compared to the reservoir. The approach is quite simple and calculations are much easier than the previous work. It provides a practical engineering tool for industry studies as it requires data which are generally available in normal production

  16. Improved characterization of reservoir behavior by integration of reservoir performances data and rock type distributions

    Energy Technology Data Exchange (ETDEWEB)

    Davies, D.K.; Vessell, R.K. [David K. Davies & Associates, Kingwood, TX (United States); Doublet, L.E. [Texas A& M Univ., College Station, TX (United States)] [and others

    1997-08-01

    An integrated geological/petrophysical and reservoir engineering study was performed for a large, mature waterflood project (>250 wells, {approximately}80% water cut) at the North Robertson (Clear Fork) Unit, Gaines County, Texas. The primary goal of the study was to develop an integrated reservoir description for {open_quotes}targeted{close_quotes} (economic) 10-acre (4-hectare) infill drilling and future recovery operations in a low permeability, carbonate (dolomite) reservoir. Integration of the results from geological/petrophysical studies and reservoir performance analyses provide a rapid and effective method for developing a comprehensive reservoir description. This reservoir description can be used for reservoir flow simulation, performance prediction, infill targeting, waterflood management, and for optimizing well developments (patterns, completions, and stimulations). The following analyses were performed as part of this study: (1) Geological/petrophysical analyses: (core and well log data) - {open_quotes}Rock typing{close_quotes} based on qualitative and quantitative visualization of pore-scale features. Reservoir layering based on {open_quotes}rock typing {close_quotes} and hydraulic flow units. Development of a {open_quotes}core-log{close_quotes} model to estimate permeability using porosity and other properties derived from well logs. The core-log model is based on {open_quotes}rock types.{close_quotes} (2) Engineering analyses: (production and injection history, well tests) Material balance decline type curve analyses to estimate total reservoir volume, formation flow characteristics (flow capacity, skin factor, and fracture half-length), and indications of well/boundary interference. Estimated ultimate recovery analyses to yield movable oil (or injectable water) volumes, as well as indications of well and boundary interference.

  17. Ill-posedness of Dynamic Equations of Compressible Granular Flow

    Science.gov (United States)

    Shearer, Michael; Gray, Nico

    2017-11-01

    We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.

  18. A new method in predicting productivity of multi-stage fractured horizontal well in tight gas reservoirs

    Directory of Open Access Journals (Sweden)

    Yunsheng Wei

    2016-10-01

    Full Text Available The generally accomplished technique for horizontal wells in tight gas reservoirs is by multi-stage hydraulic fracturing, not to mention, the flow characteristics of a horizontal well with multiple transverse fractures are very intricate. Conventional methods, well as an evaluation unit, are difficult to accurately predict production capacity of each fracture and productivity differences between wells with a different number of fractures. Thus, a single fracture sets the minimum evaluation unit, matrix, fractures, and lateral wellbore model that are then combined integrally to approximate horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. This paper presents a new semi-analytical methodology for predicting the production capacity of a horizontal well with multiple transverse hydraulic fractures in tight gas reservoirs. Firstly, a mathematical flow model used as a medium, which is disturbed by finite conductivity vertical fractures and rectangular shaped boundaries, is established and explained by the Fourier integral transform. Then the idea of a single stage fracture analysis is incorporated to establish linear flow model within a single fracture with a variable rate. The Fredholm integral numerical solution is applicable for the fracture conductivity function. Finally, the pipe flow model along the lateral wellbore is adapted to couple multi-stages fracture mathematical models, and the equation group of predicting productivity of a multi-stage fractured horizontal well. The whole flow process from the matrix to bottom-hole and production interference between adjacent fractures is also established. Meanwhile, the corresponding iterative algorithm of the equations is given. In this case analysis, the productions of each well and fracture are calculated under the different bottom-hole flowing pressure, and this method also contributes to obtaining the distribution of pressure drop and production for every

  19. Determination of multiple solutions of load flow equations

    Indian Academy of Sciences (India)

    This paper is concerned with the problem of finding all the real solutions (all components of the solution vector must be real values) of load flow equations. Solutions in which some of the components are complex values are of no interest as they have no physical significance as a load flow solution. This problem issignificant ...

  20. An adaptive nonlinear solution scheme for reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Lett, G.S. [Scientific Software - Intercomp, Inc., Denver, CO (United States)

    1996-12-31

    Numerical reservoir simulation involves solving large, nonlinear systems of PDE with strongly discontinuous coefficients. Because of the large demands on computer memory and CPU, most users must perform simulations on very coarse grids. The average properties of the fluids and rocks must be estimated on these grids. These coarse grid {open_quotes}effective{close_quotes} properties are costly to determine, and risky to use, since their optimal values depend on the fluid flow being simulated. Thus, they must be found by trial-and-error techniques, and the more coarse the grid, the poorer the results. This paper describes a numerical reservoir simulator which accepts fine scale properties and automatically generates multiple levels of coarse grid rock and fluid properties. The fine grid properties and the coarse grid simulation results are used to estimate discretization errors with multilevel error expansions. These expansions are local, and identify areas requiring local grid refinement. These refinements are added adoptively by the simulator, and the resulting composite grid equations are solved by a nonlinear Fast Adaptive Composite (FAC) Grid method, with a damped Newton algorithm being used on each local grid. The nonsymmetric linear system of equations resulting from Newton`s method are in turn solved by a preconditioned Conjugate Gradients-like algorithm. The scheme is demonstrated by performing fine and coarse grid simulations of several multiphase reservoirs from around the world.

  1. Non-darcy flow behavior mean high-flux injection wells in porous and fractured formations

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yu-Shu

    2003-04-25

    This paper presents a study of non-Darcy fluid flow through porous and fractured rock, which may occur near wells during high-flux injection of waste fluids into underground formations. Both numerical and analytical models are used in this study. General non-Darcy flow is described using the Forchheimer equation, implemented in a three-dimensional, multiphase flow reservoir simulator. The non-Darcy flow through a fractured reservoir is handled using a general dual continuum approach, covering commonly used conceptual models, such as double porosity, dual permeability, explicit fracture, etc. Under single-phase flow conditions, an approximate analytical solution, as an extension of the Warren-Root solution, is discussed. The objectives of this study are (1) to obtain insights into the effect of non-Darcy flow on transient pressure behavior through porous and fractured reservoirs and (2) to provide type curves for well test analyses of non-Darcy flow wells. The type curves generated include various types of drawdown, injection, and buildup tests with non-Darcy flow occurring in porous and fractured reservoirs. In addition, non-Darcy flow into partially penetrating wells is also considered. The transient-pressure type curves for flow in fractured reservoirs are based on the double-porosity model. Type curves provided in this work for non-Darcy flow in porous and fractured reservoirs will find their applications in well test interpretation using a type-curve matching technique.

  2. A Comparative Study between a Pseudo-Forward Equation (PFE and Intelligence Methods for the Characterization of the North Sea Reservoir

    Directory of Open Access Journals (Sweden)

    Saeed Mojeddifar

    2014-12-01

    Full Text Available This paper presents a comparative study between three versions of adaptive neuro-fuzzy inference system (ANFIS algorithms and a pseudo-forward equation (PFE to characterize the North Sea reservoir (F3 block based on seismic data. According to the statistical studies, four attributes (energy, envelope, spectral decomposition and similarity are known to be useful as fundamental attributes in porosity estimation. Different ANFIS models were constructed using three clustering methods of grid partitioning (GP, subtractive clustering method (SCM and fuzzy c-means clustering (FCM. An experimental equation, called PFE and based on similarity attributes, was also proposed to estimate porosity values of the reservoir. When the validation set derived from training wells was used, the R-square coefficient between two variables (actual and predicted values was obtained as 0.7935 and 0.7404 for the ANFIS algorithm and the PFE model, respectively. But when the testing set derived from testing wells was used, the same coefficients decreased to 0.252 and 0.5133 for the ANFIS algorithm and the PFE model, respectively. According to these results, and the geological characteristics observed in the F3 block, it seems that the ANFIS algorithms cannot estimate the porosity acceptably. By contrast, in the outputs of PFE, the ability to detect geological structures such as faults (gas chimney, folds (salt dome, and bright spots, alongside the porosity estimation of sandstone reservoirs, could help in determining the drilling target locations. Finally, this work proposes that the developed PFE could be a good technique for characterizing the reservoir of the F3 block.

  3. Scale-up of miscible flood processes for heterogeneous reservoirs. 1993 annual report

    Energy Technology Data Exchange (ETDEWEB)

    Orr, F.M. Jr.

    1994-05-01

    Progress is reported for a comprehensive investigation of the scaling behavior of gas injection processes in heterogeneous reservoirs. The interplay of phase behavior, viscous fingering, gravity segregation, capillary imbibition and drainage, and reservoir heterogeneity is examined in a series of simulations and experiments. Compositional and first-contact miscable simulations of viscous fingering and gravity segregation are compared to show that the two techniques can give very different results. Also, analyzed are two-dimensional and three-dimensional flows in which gravity segregation and viscous fingering interact. The simulations show that 2D and 3D flows can differ significantly. A comparison of analytical solutions for three-component two-phase flow with experimental results for oil/water/alcohol systems is reported. While the experiments and theory show reasonable agreement, some differences remain to be explained. The scaling behavior of the interaction of gravity segregation and capillary forces is investigated through simulations and through scaling arguments based on analysis of the differential equations. The simulations show that standard approaches do not agree well with results of low IFT displacements. The scaling analyses, however, reveal flow regimes where capillary, gravity, or viscous forces dominate the flow.

  4. Performance Analysis of Depleted Oil Reservoirs for Underground Gas Storage

    Directory of Open Access Journals (Sweden)

    Dr. C.I.C. Anyadiegwu

    2014-02-01

    Full Text Available The performance of underground gas storage in depleted oil reservoir was analysed with reservoir Y-19, a depleted oil reservoir in Southern region of the Niger Delta. Information on the geologic and production history of the reservoir were obtained from the available field data of the reservoir. The verification of inventory was done to establish the storage capacity of the reservoir. The plot of the well flowing pressure (Pwf against the flow rate (Q, gives the deliverability of the reservoir at various pressures. Results of the estimated properties signified that reservoir Y-19 is a good candidate due to its storage capacity and its flow rate (Q of 287.61 MMscf/d at a flowing pressure of 3900 psig

  5. A New Understanding of Particles by G-Flow Interpretation of Differential Equation

    Directory of Open Access Journals (Sweden)

    Mao L.

    2015-07-01

    Full Text Available Applying mathematics to the understanding of particles classically with an assumption that if the variables t and x 1 , x 2 , x 3 hold with a system of dynamical equations (1.4, then they are a point ( t , x 1 , x 2 , x 3 in R 4 . However, if we put off this assumption, how can we interpret the solution space of equations? And are the se resultants important for understanding the world? Recently, the author extended Ban ach and Hilbert spaces on a topological graph to introduce −→ G -flows and showed that all such flows on a topological graph −→ G also form a Banach or Hilbert space, which enables one to find t he multiverse solution of these equations on −→ G . Applying this result, this paper discusses the −→ G -flow solutions on Schrödinger equation, Klein-Gordon equation and Dirac equation, i.e., the field equations of particles, bosons or fermions, answers previous questions by ”yes“, and establishes the many world interpretation of quantum mechanics of H. Everett by purely mathematics in logic, i.e., mathematical combinatorics.

  6. High-performance modeling of CO2 sequestration by coupling reservoir simulation and molecular dynamics

    KAUST Repository

    Bao, Kai

    2013-01-01

    The present work describes a parallel computational framework for CO2 sequestration simulation by coupling reservoir simulation and molecular dynamics (MD) on massively parallel HPC systems. In this framework, a parallel reservoir simulator, Reservoir Simulation Toolbox (RST), solves the flow and transport equations that describe the subsurface flow behavior, while the molecular dynamics simulations are performed to provide the required physical parameters. Numerous technologies from different fields are employed to make this novel coupled system work efficiently. One of the major applications of the framework is the modeling of large scale CO2 sequestration for long-term storage in the subsurface geological formations, such as depleted reservoirs and deep saline aquifers, which has been proposed as one of the most attractive and practical solutions to reduce the CO2 emission problem to address the global-warming threat. To effectively solve such problems, fine grids and accurate prediction of the properties of fluid mixtures are essential for accuracy. In this work, the CO2 sequestration is presented as our first example to couple the reservoir simulation and molecular dynamics, while the framework can be extended naturally to the full multiphase multicomponent compositional flow simulation to handle more complicated physical process in the future. Accuracy and scalability analysis are performed on an IBM BlueGene/P and on an IBM BlueGene/Q, the latest IBM supercomputer. Results show good accuracy of our MD simulations compared with published data, and good scalability are observed with the massively parallel HPC systems. The performance and capacity of the proposed framework are well demonstrated with several experiments with hundreds of millions to a billion cells. To our best knowledge, the work represents the first attempt to couple the reservoir simulation and molecular simulation for large scale modeling. Due to the complexity of the subsurface systems

  7. High-Performance Modeling of Carbon Dioxide Sequestration by Coupling Reservoir Simulation and Molecular Dynamics

    KAUST Repository

    Bao, Kai

    2015-10-26

    The present work describes a parallel computational framework for carbon dioxide (CO2) sequestration simulation by coupling reservoir simulation and molecular dynamics (MD) on massively parallel high-performance-computing (HPC) systems. In this framework, a parallel reservoir simulator, reservoir-simulation toolbox (RST), solves the flow and transport equations that describe the subsurface flow behavior, whereas the MD simulations are performed to provide the required physical parameters. Technologies from several different fields are used to make this novel coupled system work efficiently. One of the major applications of the framework is the modeling of large-scale CO2 sequestration for long-term storage in subsurface geological formations, such as depleted oil and gas reservoirs and deep saline aquifers, which has been proposed as one of the few attractive and practical solutions to reduce CO2 emissions and address the global-warming threat. Fine grids and accurate prediction of the properties of fluid mixtures under geological conditions are essential for accurate simulations. In this work, CO2 sequestration is presented as a first example for coupling reservoir simulation and MD, although the framework can be extended naturally to the full multiphase multicomponent compositional flow simulation to handle more complicated physical processes in the future. Accuracy and scalability analysis are performed on an IBM BlueGene/P and on an IBM BlueGene/Q, the latest IBM supercomputer. Results show good accuracy of our MD simulations compared with published data, and good scalability is observed with the massively parallel HPC systems. The performance and capacity of the proposed framework are well-demonstrated with several experiments with hundreds of millions to one billion cells. To the best of our knowledge, the present work represents the first attempt to couple reservoir simulation and molecular simulation for large-scale modeling. Because of the complexity of

  8. Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

    Energy Technology Data Exchange (ETDEWEB)

    Leitner, David M., E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557 (United States); Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Buchenberg, Sebastian; Brettel, Paul [Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany); Stock, Gerhard, E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany)

    2015-02-21

    We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.

  9. Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

    International Nuclear Information System (INIS)

    Leitner, David M.; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard

    2015-01-01

    We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water

  10. Theoretical and pragmatic modelling of governing equations for a two-phase flow in bubbly and annular flow regimes

    International Nuclear Information System (INIS)

    Bottoni, M.; Sengpiel, W.

    1992-01-01

    Starting from the rigorous formulation of the conservation equations for mass, momentum and enthalpy, derived for a two-phase flow by volume averaging microscopic balance equations over Eulerian control cells, the article discusses the formulation of the terms describing exchanges between the phases. Two flow regimes are taken into consideration, bubbly flow, applicable for small or medium void fractions, and annular flow, for large void fractions. When lack of knowledge of volume-averaged physical quantities make the rigorously formulated terms useless for computational purposes, modelling of these terms is discussed. 3 figs., 15 refs

  11. A Note on Unsteady Temperature Equation For Gravity Flow of A ...

    African Journals Online (AJOL)

    We present an analytical study of unsteady temperature energy equation for gravity of a fluid with non – Newtonian behaviour through a porous medium. For the case of radial axisymmetric flow, the governing partial differential equation is transformed into an ordinary differential equation through similarity variables.

  12. Local Refinement of the Super Element Model of Oil Reservoir

    Directory of Open Access Journals (Sweden)

    A.B. Mazo

    2017-12-01

    Full Text Available In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailing to describe hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves is modeled (characteristic scale of such changes is km / year. The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200-500 m. The tensor coefficients of the super-element model are calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model is constructed for calculating small-scale processes (with a scale of m / day, which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem are formulated on the basis of the super-element solution. This approach allows us to reduce the computational costs in order to solve the problems of designing and monitoring the oil reservoir. To demonstrate the proposed approach, we give an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We show a good compliance between the locally refined solution of the super-element model in the area of measure exposure and the results of numerical modeling of the whole history of reservoir

  13. On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow

    Energy Technology Data Exchange (ETDEWEB)

    Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: mnjmhd@am.uva.es

    2008-06-16

    While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.

  14. Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data

    Science.gov (United States)

    Schmitt, François G.

    2007-10-01

    Several nonlinear constitutive equations have been proposed to overcome the limitations of the linear eddy-viscosity models to describe complex turbulent flows. These nonlinear equations have often been compared to experimental data through the outputs of numerical models. Here we perform a priori analysis of nonlinear eddy-viscosity models using direct numerical simulation (DNS) of simple shear flows. In this paper, the constitutive equation is directly checked using a tensor projection which involves several invariants of the flow. This provides a 3 terms development which is exact for 2D flows, and a best approximation for 3D flows. We provide the quadratic nonlinear constitutive equation for the near-wall region of simple shear flows using DNS data, and estimate their coefficients. We show that these coefficients have several common properties for the different simple shear flow databases considered. We also show that in the central region of pipe flows, where the shear rate is very small, the coefficients of the constitutive equation diverge, indicating the failure of this representation for vanishing shears.

  15. 3D Sedimentological and geophysical studies of clastic reservoir analogs: Facies architecture, reservoir properties, and flow behavior within delta front facies elements of the Cretaceous Wall Creek Member, Frontier Formation, Wyoming

    Energy Technology Data Exchange (ETDEWEB)

    Christopher D. White

    2009-12-21

    Significant volumes of oil and gas occur in reservoirs formed by ancient river deltas. This has implications for the spatial distribution of rock types and the variation of transport properties. A between mudstones and sandstones may form baffles that influence productivity and recovery efficiency. Diagenetic processes such as compaction, dissolution, and cementation can also alter flow properties. A better understanding of these properties and improved methods will allow improved reservoir development planning and increased recovery of oil and gas from deltaic reservoirs. Surface exposures of ancient deltaic rocks provide a high-resolution view of variability. Insights gleaned from these exposures can be used to model analogous reservoirs, for which data is sparser. The Frontier Formation in central Wyoming provides an opportunity for high-resolution models. The same rocks exposed in the Tisdale anticline are productive in nearby oil fields. Kilometers of exposure are accessible, and bedding-plane exposures allow use of high-resolution ground-penetrating radar. This study combined geologic interpretations, maps, vertical sections, core data, and ground-penetrating radar to construct geostatistical and flow models. Strata-conforming grids were use to reproduce the observed geometries. A new Bayesian method integrates outcrop, core, and radar amplitude and phase data. The proposed method propagates measurement uncertainty and yields an ensemble of plausible models for calcite concretions. These concretions affect flow significantly. Models which integrate more have different flow responses from simpler models, as demonstrated an exhaustive two-dimensional reference image and in three dimensions. This method is simple to implement within widely available geostatistics packages. Significant volumes of oil and gas occur in reservoirs that are inferred to have been formed by ancient river deltas. This geologic setting has implications for the spatial distribution of

  16. A Finite Difference, Semi-implicit, Equation-of-State Efficient Algorithm for the Compositional Flow Modeling in the Subsurface: Numerical Examples

    KAUST Repository

    Saavedra, Sebastian

    2012-07-01

    The mathematical model that has been recognized to have the more accurate approximation to the physical laws govern subsurface hydrocarbon flow in reservoirs is the Compositional Model. The features of this model are adequate to describe not only the performance of a multiphase system but also to represent the transport of chemical species in a porous medium. Its importance relies not only on its current relevance to simulate petroleum extraction processes, such as, Primary, Secondary, and Enhanced Oil Recovery Process (EOR) processes but also, in the recent years, carbon dioxide (CO2) sequestration. The purpose of this study is to investigate the subsurface compositional flow under isothermal conditions for several oil well cases. While simultaneously addressing computational implementation finesses to contribute to the efficiency of the algorithm. This study provides the theoretical framework and computational implementation subtleties of an IMplicit Pressure Explicit Composition (IMPEC)-Volume-balance (VB), two-phase, equation-of-state, approach to model isothermal compositional flow based on the finite difference scheme. The developed model neglects capillary effects and diffusion. From the phase equilibrium premise, the model accounts for volumetric performances of the phases, compressibility of the phases, and composition-dependent viscosities. The Equation of State (EoS) employed to approximate the hydrocarbons behaviour is the Peng Robinson Equation of State (PR-EOS). Various numerical examples were simulated. The numerical results captured the complex physics involved, i.e., compositional, gravitational, phase-splitting, viscosity and relative permeability effects. Regarding the numerical scheme, a phase-volumetric-flux estimation eases the calculation of phase velocities by naturally fitting to phase-upstream-upwinding. And contributes to a faster computation and an efficient programming development.

  17. Modeling of Multi Phase Flow in Porous Media: Operator Splitting, Front Tracking, Interfacial Area and Network Models

    Energy Technology Data Exchange (ETDEWEB)

    Nordhaug, Hans Fredrik

    2001-07-01

    In reservoir problems we consider some or all of the following phases: Oil, gas, water and solid. The solid phase is normally assumed to be immobile and non-deforming, but in general this does not need to be the case. By multi phase flow we will mean the flow of oil, gas and water. The phases are categorized according to their different physical quantities. A hydrocarbon phase, may consist of different hydrocarbon components, e.g., the oil phase can contain several oil and gas types. In this work the components are neglected and only the phases are considered. A porous medium is any solid phase, e.g. sand stone, that is permeable. The flow in a porous medium takes place through connected pores in the rock. Regions on a larger scale that contain oil or gas are called reservoirs. The typical size of a reservoir is kilometers in each direction while the pore scale size is millimeters or less. Solving the Navier-Stokes equation at the pore scale to obtain the transport on a larger scale is not numerically feasible because of the huge difference in scales. Therefore, some averaging is necessary to go from the pore scale (micro scale) to the reservoir scale (macro scale). In this process the Navier-Stokes equations are replaced by macro scale equations that are solved for macro scale variables. The papers presented herein cover several topics in multi phase flow in porous media, and they address some central problems both on the micro scale as well as on the macro scale. In addition, operator splitting techniques have been developed for convection dominated non-linear transport equations.

  18. Naturally fractured reservoirs-yet an unsolved mystery

    International Nuclear Information System (INIS)

    Zahoor, M.K.

    2013-01-01

    Some of the world's most profitable reservoirs are assumed to be naturally fractured reservoirs (NFR). Effective evaluation, prediction and planning of these reservoirs require an early recognition of the role of natural fractures and then a comprehensive study of factors which affect the flowing performance through these fractures is necessary. As NFRs are the combination of matrix and fractures mediums so their analysis varies from non-fractured reservoirs. Matrix acts as a storage medium while mostly fluid flow takes place from fracture network. Many authors adopted different approaches to understand the flow behavior in such reservoirs. In this paper a broad review about the previous work done in naturally fractured reservoirs area is outlined and a different idea is initiated for the NFR simulation studies. The role of capillary pressure in natural fractures is always been a key factor for accurate recovery estimations. Also recovery through these reservoirs is dependent upon grid block shape while doing NFR simulation. Some authors studied above mentioned factors in combination with other rock properties to understand the flow behavior in such reservoirs but less emphasis was given for checking the effects on recovery estimations by the variations of only fracture capillary pressures and grid block shapes. So there is need to analyze the behavior of NFR for the mentioned conditions. (author)

  19. Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

    Directory of Open Access Journals (Sweden)

    M. L. Kavvas

    2017-10-01

    Full Text Available Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

  20. One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows

    Science.gov (United States)

    Rigas, Georgios; Colonius, Tim; Towne, Aaron; Beyar, Michael

    2016-11-01

    For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, a regularization of the equations of motion sometimes permits a fast spatial marching procedure that results in a huge reduction in computational cost. Recently, a novel one-way spatial marching algorithm has been developed by Towne & Colonius. The new method overcomes the principle flaw observed in Parabolized Stability Equations (PSE), namely the ad hoc regularization that removes upstream propagating modes. The one-way method correctly parabolizes the flow equations based on estimating, in a computationally efficient way, the local spectrum in each cross-stream plane and an efficient spectral filter eliminates modes with upstream group velocity. Results from the application of the method to wall-bounded flows will be presented and compared with predictions from the full linearized compressible Navier-Stokes equations and PSE.

  1. Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change

    International Nuclear Information System (INIS)

    Spindler, B.

    1983-01-01

    The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods

  2. Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change

    Science.gov (United States)

    Spindler, B.

    1983-08-01

    The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods.

  3. Two-phase flow visualization under reservoir conditions for highly heterogeneous conglomerate rock: A core-scale study for geologic carbon storage.

    Science.gov (United States)

    Kim, Kue-Young; Oh, Junho; Han, Weon Shik; Park, Kwon Gyu; Shinn, Young Jae; Park, Eungyu

    2018-03-20

    Geologic storage of carbon dioxide (CO 2 ) is considered a viable strategy for significantly reducing anthropogenic CO 2 emissions into the atmosphere; however, understanding the flow mechanisms in various geological formations is essential for safe storage using this technique. This study presents, for the first time, a two-phase (CO 2 and brine) flow visualization under reservoir conditions (10 MPa, 50 °C) for a highly heterogeneous conglomerate core obtained from a real CO 2 storage site. Rock heterogeneity and the porosity variation characteristics were evaluated using X-ray computed tomography (CT). Multiphase flow tests with an in-situ imaging technology revealed three distinct CO 2 saturation distributions (from homogeneous to non-uniform) dependent on compositional complexity. Dense discontinuity networks within clasts provided well-connected pathways for CO 2 flow, potentially helping to reduce overpressure. Two flow tests, one under capillary-dominated conditions and the other in a transition regime between the capillary and viscous limits, indicated that greater injection rates (potential causes of reservoir overpressure) could be significantly reduced without substantially altering the total stored CO 2 mass. Finally, the capillary storage capacity of the reservoir was calculated. Capacity ranged between 0.5 and 4.5%, depending on the initial CO 2 saturation.

  4. Developing Semi-Analytical solutions for Saint-Venant Equations in the Uniform Flow Region

    Directory of Open Access Journals (Sweden)

    M.M. Heidari

    2016-09-01

    Full Text Available Introduction: Unsteady flow in irrigation systems is the result of operations in response to changes in water demand that affect the hydraulic performance networks. The increased hydraulic performance needed to recognize unsteady flow and quantify the factors affecting it. Unsteady flow in open channels is governed by the fully dynamic Saint Venant equation, which express the principles of conservation of mass and momentum. Unsteady flow in open channels can be classified into two types: routing and operation-type problems. In the routing problems, The Saint Venant equations are solved to get the discharge and water level in the time series. Also, they are used in the operation problem to compute the inflow at the upstream section of the channel according to the prescribed downstream flow hydrographs. The Saint Venant equation has no analytical solution and in the majority cases of such methods use numerical integration of continuity and momentum equations, and are characterized by complicated numerical procedures that are not always convenient for carrying out practical engineering calculations. Therefore, approximate methods deserve attention since they would allow the solution of dynamic problems in analytical form with enough exactness. There are effective methods for automatic controller synthesis in control theory that provide the required performance optimization. It is therefore important to get simplified models of irrigation canals for control design. It would be even more interesting to have linear models that explicitly depend on physical parameters. Such models would allow one to, handle the dynamics of the system with fewer parameters, understand the impact of physical parameters on the dynamics, and facilitate the development a systematic design method. Many analytical models have been proposed in the literature, Most of them have been obtained in the frequency domain by applying Laplace transform to linearized Saint

  5. The Effect of Model Grid Resolution on the Distributed Hydrologic Simulations for Forecasting Stream Flows and Reservoir Storage

    Science.gov (United States)

    Turnbull, S. J.

    2017-12-01

    Within the US Army Corps of Engineers (USACE), reservoirs are typically operated according to a rule curve that specifies target water levels based on the time of year. The rule curve is intended to maximize flood protection by specifying releases of water before the dominant rainfall period for a region. While some operating allowances are permissible, generally the rule curve elevations must be maintained. While this operational approach provides for the required flood control purpose, it may not result in optimal reservoir operations for multi-use impoundments. In the Russian River Valley of California a multi-agency research effort called Forecast-Informed Reservoir Operations (FIRO) is assessing the application of forecast weather and streamflow predictions to potentially enhance the operation of reservoirs in the watershed. The focus of the study has been on Lake Mendocino, a USACE project important for flood control, water supply, power generation and ecological flows. As part of this effort the Engineer Research and Development Center is assessing the ability of utilizing the physics based, distributed watershed model Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model to simulate stream flows, reservoir stages, and discharges while being driven by weather forecast products. A key question in this application is the effect of watershed model resolution on forecasted stream flows. To help resolve this question, GSSHA models of multiple grid resolutions, 30, 50, and 270m, were developed for the upper Russian River, which includes Lake Mendocino. The models were derived from common inputs: DEM, soils, land use, stream network, reservoir characteristics, and specified inflows and discharges. All the models were calibrated in both event and continuous simulation mode using measured precipitation gages and then driven with the West-WRF atmospheric model in prediction mode to assess the ability of the model to function in short term, less than one week

  6. THE STATEMENT OF CASH FLOWS USING FINANCIAL STATEMENT EQUATIONS

    OpenAIRE

    Harold Fletcher; Thomas Ulrich

    2010-01-01

    This paper addresses one of the more difficult topics in teaching MBA level financial management, the statement of cash flows. By employing financial statement equations in preparing the statement of cash flows, students: (1) are employing tools that they are more familiar and comfortable with which mitigates their anxiety and enhances their understanding, (2) are better able to understand the logic of the statement of cash flows and the relationships that exist between it and the income stat...

  7. Irregular conformal block, spectral curve and flow equations

    International Nuclear Information System (INIS)

    Choi, Sang Kwan; Rim, Chaiho; Zhang, Hong

    2016-01-01

    Irregular conformal block is motivated by the Argyres-Douglas type of N=2 super conformal gauge theory. We investigate the classical/NS limit of irregular conformal block using the spectral curve on a Riemann surface with irregular punctures, which is equivalent to the loop equation of irregular matrix model. The spectral curve is reduced to the second order (Virasoro symmetry, SU(2) for the gauge theory) and third order (W_3 symmetry, SU(3)) differential equations of a polynomial with finite degree. The conformal and W symmetry generate the flow equations in the spectral curve and determine the irregular conformal block, hence the partition function of the Argyres-Douglas theory ala AGT conjecture.

  8. Parallel Numerical Simulations of Water Reservoirs

    Science.gov (United States)

    Torres, Pedro; Mangiavacchi, Norberto

    2010-11-01

    The study of the water flow and scalar transport in water reservoirs is important for the determination of the water quality during the initial stages of the reservoir filling and during the life of the reservoir. For this scope, a parallel 2D finite element code for solving the incompressible Navier-Stokes equations coupled with scalar transport was implemented using the message-passing programming model, in order to perform simulations of hidropower water reservoirs in a computer cluster environment. The spatial discretization is based on the MINI element that satisfies the Babuska-Brezzi (BB) condition, which provides sufficient conditions for a stable mixed formulation. All the distributed data structures needed in the different stages of the code, such as preprocessing, solving and post processing, were implemented using the PETSc library. The resulting linear systems for the velocity and the pressure fields were solved using the projection method, implemented by an approximate block LU factorization. In order to increase the parallel performance in the solution of the linear systems, we employ the static condensation method for solving the intermediate velocity at vertex and centroid nodes separately. We compare performance results of the static condensation method with the approach of solving the complete system. In our tests the static condensation method shows better performance for large problems, at the cost of an increased memory usage. Performance results for other intensive parts of the code in a computer cluster are also presented.

  9. Equations for transient flow-boiling in a duct

    International Nuclear Information System (INIS)

    Mathers, W.G.; Ferch, R.L.; Hancox, W.T.; McDonald, B.H.

    1981-01-01

    In this paper we derive a separated phase model for weakly coupled flows which extends a model presented elsewhere (BANERJEE, FERCH, MATHERS and McDONALD, 1978). A hyperbolic system of seven partial differential equations results with ensemble-averaged phase velocities, enthalpies and pressures, and void fraction as dependent variables (UVUTUP model). The required constitutive equations for mass, momentum and energy transfer between phases and between the phases and the boundaries are discussed. The relationship of the UVUTUP model to other existing models is also presented

  10. Adjustment of pipe flow explicit friction factor equations for application to tube bundles

    International Nuclear Information System (INIS)

    Wiltz, Christopher L.; Bowen, Mike D.; Von Olnhausen, Wayne A.

    2005-01-01

    Full text of publication follows: The accurate determination of single phase friction losses or friction pressure drop in tube bundles is essential in the thermal-hydraulic analyses of components such as nuclear fuel assemblies, heat exchangers and steam generators. Such friction losses are normally calculated using a friction factor, f, along with the experimental observation that the friction pressure drop in a pipe is proportional to the dynamic pressure (1/2 ρV 2 ) of the flow: ΔP = 1/2 ρV 2 (fL/D). In this equation L is the pipe or tube bundle length and D is the hydraulic diameter of the pipe or tube bundle. The friction factor is normally calculated using one of a number of explicit friction factor equations. A significant amount of work has been accomplished in developing explicit friction factor equations. These explicit equations range from approximations, which were developed for ease of numerical evaluation, to those which are mathematically complex but yield very good fits to the test data. These explicit friction factor equations are based on a large experimental data base, nearly all of which comes from pipe flow geometry information, and have been historically applied to tube bundles. This paper presents an adjustment method which may be applied to various explicit friction factor equations developed for pipe flow to accurately predict the friction factor for tube bundles. The characteristic of the adjustment is based on experimental friction pressure loss data obtained by Framatome ANP through flow testing of a nuclear fuel assembly (tube bundle) at its Richland Test Facility (RTF). Through adjustment of previously developed explicit friction factor equations for pipe flow, the vast amount of historical development and experimentation in the area of single phase pipe flow friction loss may be incorporated into the evaluation of single phase friction losses within tube bundles. Comparisons of the application of one or more of the previously

  11. On the water saturation calculation in hydrocarbon sandstone reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Stalheim, Stein Ottar

    2002-07-01

    The main goal of this work was to identify the most important uncertainty sources in water saturation calculation and examine the possibility for developing new S{sub w} - equations or possibility to develop methods to remove weaknesses and uncertainties in existing S{sub w} - equations. Due to the need for industrial applicability of the equations we aimed for results with the following properties: The accuracy in S{sub w} should increase compared with existing S{sub w} - equations. The equations should be simple to use in petrophysical evaluations. The equations should be based on conventional logs and use as few as possible input parameters. The equations should be numerical stable. This thesis includes an uncertainty and sensitivity analysis of the most common S{sub w} equations. The results are addressed in chapter 3 and were intended to find the most important uncertainty sources in water saturation calculation. To increase the knowledge of the relationship between R{sub t} and S{sub w} in hydrocarbon sandstone reservoirs and to understand how the pore geometry affects the conductivity (n and m) of the rock a theoretical study was done. It was also an aim to examine the possibility for developing new S{sub w} - equations (or investigation an effective medium model) valid inhydrocarbon sandstone reservoirs. The results are presented in paper 1. A new equation for water saturation calculation in clean sandstone oil reservoirs is addressed in paper 2. A recommendation for best practice of water saturation calculation in non water wet formation is addressed in paper 3. Finally a new equation for water saturation calculation in thinly interbedded sandstone/mudstone reservoirs is presented in paper 4. The papers are titled: 1) Is the saturation exponent n a constant. 2) A New Model for Calculating Water Saturation In 3) Influence of wettability on water saturation modeling. 4) Water Saturation Calculations in Thinly Interbedded Sandstone/mudstone Reservoirs. A

  12. Computer Modeling of the Displacement Behavior of Carbon Dioxide in Undersaturated Oil Reservoirs

    Directory of Open Access Journals (Sweden)

    Ju Binshan

    2015-11-01

    Full Text Available The injection of CO2 into oil reservoirs is performed not only to improve oil recovery but also to store CO2 captured from fuel combustion. The objective of this work is to develop a numerical simulator to predict quantitatively supercritical CO2 flooding behaviors for Enhanced Oil Recovery (EOR. A non-isothermal compositional flow mathematical model is developed. The phase transition diagram is designed according to the Minimum Miscibility Pressure (MMP and CO2 maximum solubility in oil phase. The convection and diffusion of CO2 mixtures in multiphase fluids in reservoirs, mass transfer between CO2 and crude and phase partitioning are considered. The governing equations are discretized by applying a fully implicit finite difference technique. Newton-Raphson iterative technique was used to solve the nonlinear equation systems and a simulator was developed. The performances of CO2 immiscible and miscible flooding in oil reservoirs are predicted by the new simulator. The distribution of pressure and temperature, phase saturations, mole fraction of each component in each phase, formation damage caused by asphaltene precipitation and the improved oil recovery are predicted by the simulator. Experimental data validate the developed simulator by comparison with simulation results. The applications of the simulator in prediction of CO2 flooding in oil reservoirs indicate that the simulator is robust for predicting CO2 flooding performance.

  13. Estimation of Bank Erosion Due To Reservoir Operation in Cascade (Case Study: Citarum Cascade Reservoir

    Directory of Open Access Journals (Sweden)

    Sri Legowo

    2009-11-01

    Full Text Available Sedimentation is such a crucial issue to be noted once the accumulated sediment begins to fill the reservoir dead storage, this will then influence the long-term reservoir operation. The sediment accumulated requires a serious attention for it may influence the storage capacity and other reservoir management of activities. The continuous inflow of sediment to the reservoir will decrease the capacity of reservoir storage, the reservoir value in use, and the useful age of reservoir. Because of that, the rate of the sediment needs to be delayed as possible. In this research, the delay of the sediment rate is considered based on the rate of flow of landslide of the reservoir slope. The rate of flow of the sliding slope can be minimized by way of each reservoir autonomous efforts. This effort can be performed through; the regulation of fluctuating rate of reservoir surface current that does not cause suddenly drawdown and upraising as well. The research model is compiled using the searching technique of Non Linear Programming (NLP.The rate of bank erosion for the reservoir variates from 0.0009 to 0.0048 MCM/year, which is no sigrificant value to threaten the life time of reservoir.Mean while the rate of watershed sediment has a significant value, i.e: 3,02 MCM/year for Saguling that causes to fullfill the storage capacity in 40 next years (from years 2008.

  14. Application of parallel computing techniques to a large-scale reservoir simulation

    International Nuclear Information System (INIS)

    Zhang, Keni; Wu, Yu-Shu; Ding, Chris; Pruess, Karsten

    2001-01-01

    Even with the continual advances made in both computational algorithms and computer hardware used in reservoir modeling studies, large-scale simulation of fluid and heat flow in heterogeneous reservoirs remains a challenge. The problem commonly arises from intensive computational requirement for detailed modeling investigations of real-world reservoirs. This paper presents the application of a massive parallel-computing version of the TOUGH2 code developed for performing large-scale field simulations. As an application example, the parallelized TOUGH2 code is applied to develop a three-dimensional unsaturated-zone numerical model simulating flow of moisture, gas, and heat in the unsaturated zone of Yucca Mountain, Nevada, a potential repository for high-level radioactive waste. The modeling approach employs refined spatial discretization to represent the heterogeneous fractured tuffs of the system, using more than a million 3-D gridblocks. The problem of two-phase flow and heat transfer within the model domain leads to a total of 3,226,566 linear equations to be solved per Newton iteration. The simulation is conducted on a Cray T3E-900, a distributed-memory massively parallel computer. Simulation results indicate that the parallel computing technique, as implemented in the TOUGH2 code, is very efficient. The reliability and accuracy of the model results have been demonstrated by comparing them to those of small-scale (coarse-grid) models. These comparisons show that simulation results obtained with the refined grid provide more detailed predictions of the future flow conditions at the site, aiding in the assessment of proposed repository performance

  15. An effective dead oil model for two-phase flow in inhomogeneous porous media

    International Nuclear Information System (INIS)

    Bourgeat, A.

    1988-01-01

    The authors are investigating displacement process of incompressible two phase flow miscible or immiscible in heterogeneous porous media, including capillary and gravity effects. The authors' aim is to derive rigorously a Global or Effective Model which then allow, in Numerical Simulations, to disconnect the numerical mesh size from the heterogeneities size inside the reservoir itself. The reservoir is assumed to be made of uniformly (or non uniformly) periodically repeated cells. Each cell being made with different types of porous media. Then, calling ε the ratio of the cell size to the Reservoir size, we get equations depending on the parameter ε because the Porosity and Permeabilities, say Phi/sup ε/ and Κ/sup ε/ are themselves rapidly oscillating. From these ε-parametrized equations the authors derive simpler ''Effective Equations'' no more dependant on ε, called ''Homongenized Equations by the mathematical technique of Homogenization. In these new equations, which are describing Global Displacement process throughout a Globally Equivallent homogenous media where now //Phi and Κ are no more depending on the space variable or ε

  16. The Pore-scale modeling of multiphase flows in reservoir rocks using the lattice Boltzmann method

    Science.gov (United States)

    Mu, Y.; Baldwin, C. H.; Toelke, J.; Grader, A.

    2011-12-01

    Digital rock physics (DRP) is a new technology to compute the physical and fluid flow properties of reservoir rocks. In this approach, pore scale images of the porous rock are obtained and processed to create highly accurate 3D digital rock sample, and then the rock properties are evaluated by advanced numerical methods at the pore scale. Ingrain's DRP technology is a breakthrough for oil and gas companies that need large volumes of accurate results faster than the current special core analysis (SCAL) laboratories can normally deliver. In this work, we compute the multiphase fluid flow properties of 3D digital rocks using D3Q19 immiscible LBM with two relaxation times (TRT). For efficient implementation on GPU, we improved and reformulated color-gradient model proposed by Gunstensen and Rothmann. Furthermore, we only use one-lattice with the sparse data structure: only allocate memory for pore nodes on GPU. We achieved more than 100 million fluid lattice updates per second (MFLUPS) for two-phase LBM on single Fermi-GPU and high parallel efficiency on Multi-GPUs. We present and discuss our simulation results of important two-phase fluid flow properties, such as capillary pressure and relative permeabilities. We also investigate the effects of resolution and wettability on multiphase flows. Comparison of direct measurement results with the LBM-based simulations shows practical ability of DRP to predict two-phase flow properties of reservoir rock.

  17. Low-frequency logarithmic discretization of the reservoir spectrum for improving the efficiency of hierarchical equations of motion approach.

    Science.gov (United States)

    Ye, LvZhou; Zhang, Hou-Dao; Wang, Yao; Zheng, Xiao; Yan, YiJing

    2017-08-21

    An efficient low-frequency logarithmic discretization (LFLD) scheme for the decomposition of fermionic reservoir spectrum is proposed for the investigation of quantum impurity systems. The scheme combines the Padé spectrum decomposition (PSD) and a logarithmic discretization of the residual part in which the parameters are determined based on an extension of the recently developed minimum-dissipaton ansatz [J. J. Ding et al., J. Chem. Phys. 145, 204110 (2016)]. A hierarchical equations of motion (HEOM) approach is then employed to validate the proposed scheme by examining the static and dynamic system properties in both the Kondo and noninteracting regimes. The LFLD scheme requires a much smaller number of exponential functions than the conventional PSD scheme to reproduce the reservoir correlation function and thus facilitates the efficient implementation of the HEOM approach in extremely low temperature regimes.

  18. Correlation Analysis of Rainstorm Runoff and Density Current in a Canyon-Shaped Source Water Reservoir: Implications for Reservoir Optimal Operation

    Directory of Open Access Journals (Sweden)

    Yang Li

    2018-04-01

    Full Text Available Extreme weather has recently become frequent. Heavy rainfall forms storm runoff, which is usually very turbid and contains a high concentration of organic matter, therefore affecting water quality when it enters reservoirs. The large canyon-shaped Heihe Reservoir is the most important raw water source for the city of Xi’an. During the flood season, storm runoff flows into the reservoir as a density current. We determined the relationship among inflow peak discharge (Q, suspended sediment concentration, inflow water temperature, and undercurrent water density. The relationships between (Q and inflow suspended sediment concentration (CS0 could be described by the equation CS0 = 0.3899 × e0.0025Q, that between CS0 and suspended sediment concentration at the entrance of the main reservoir area S1 (CS1 was determined using CS1 = 0.0346 × e0.2335CS0, and air temperature (Ta and inflow water temperature (Tw based on the meteorological data were related as follows: Tw = 0.7718 × Ta + 1.0979. Then, we calculated the density of the undercurrent layer. Compared to the vertical water density distribution at S1 before rainfall, the undercurrent elevation was determined based on the principle of equivalent density inflow. Based on our results, we proposed schemes for optimizing water intake selection and flood discharge during the flood season.

  19. Pipe Flow and Wall Turbulence Using a Modified Navier-Stokes Equation

    International Nuclear Information System (INIS)

    Jirkovsky, L.; Muriel, A.

    2012-01-01

    We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  20. Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

    International Nuclear Information System (INIS)

    Zheng, Lin; Zheng, Song; Zhai, Qinglan

    2016-01-01

    In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

  1. Continuous surface force based lattice Boltzmann equation method for simulating thermocapillary flow

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, Lin, E-mail: lz@njust.edu.cn [School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094 (China); Zheng, Song [School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018 (China); Zhai, Qinglan [School of Economics Management and Law, Chaohu University, Chaohu 238000 (China)

    2016-02-05

    In this paper, we extend a lattice Boltzmann equation (LBE) with continuous surface force (CSF) to simulate thermocapillary flows. The model is designed on our previous CSF LBE for athermal two phase flow, in which the interfacial tension forces and the Marangoni stresses as the results of the interface interactions between different phases are described by a conception of CSF. In this model, the sharp interfaces between different phases are separated by a narrow transition layers, and the kinetics and morphology evolution of phase separation would be characterized by an order parameter via Cahn–Hilliard equation which is solved in the frame work of LBE. The scalar convection–diffusion equation for temperature field is resolved by thermal LBE. The models are validated by thermal two layered Poiseuille flow, and two superimposed planar fluids at negligibly small Reynolds and Marangoni numbers for the thermocapillary driven convection, which have analytical solutions for the velocity and temperature. Then thermocapillary migration of two/three dimensional deformable droplet are simulated. Numerical results show that the predictions of present LBE agreed with the analytical solution/other numerical results. - Highlights: • A CSF LBE to thermocapillary flows. • Thermal layered Poiseuille flows. • Thermocapillary migration.

  2. Comparative study of the two-fluid momentum equations for multi-dimensional bubbly flows: Modification of Reynolds stress

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seung Jun; Park, Ik Kyu; Yoon, Han Young [Thermal-Hydraulic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jae, Byoung [School of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)

    2017-01-15

    Two-fluid equations are widely used to obtain averaged behaviors of two-phase flows. This study addresses a problem that may arise when the two-fluid equations are used for multi-dimensional bubbly flows. If steady drag is the only accounted force for the interfacial momentum transfer, the disperse-phase velocity would be the same as the continuous-phase velocity when the flow is fully developed without gravity. However, existing momentum equations may show unphysical results in estimating the relative velocity of the disperse phase against the continuous-phase. First, we examine two types of existing momentum equations. One is the standard two-fluid momentum equation in which the disperse-phase is treated as a continuum. The other is the averaged momentum equation derived from a solid/ fluid particle motion. We show that the existing equations are not proper for multi-dimensional bubbly flows. To resolve the problem mentioned above, we modify the form of the Reynolds stress terms in the averaged momentum equation based on the solid/fluid particle motion. The proposed equation shows physically correct results for both multi-dimensional laminar and turbulent flows.

  3. Flow characteristic of Hijiori HDR reservoir from circulation test in 1991; Koon tantai Hijiori jikkenjo ni okeru senbu choryuso shiken (1991 nendo) kekka to ryudo kaiseki

    Energy Technology Data Exchange (ETDEWEB)

    Shiga, T; Hyodo, M; Shinohara, N; Takasugi, S [Geothermal Energy Research and Development Co. Ltd., Tokyo (Japan)

    1996-05-01

    This paper reports one example of flow analyses on a circulation test carried out in fiscal 1991 at the Hijiori hot dry rock experimental field (Yamagata Prefecture). A fluid circulation model was proposed to simulate an HDR circulation system for a shallow reservoir (at a depth of about 1800 m) demonstrated in the circulation test by using an electric circuit network (which expresses continuity impedance in resistance and fluid storage in capacitance). Storage capacity of the reservoir was estimated by deriving time constant of the system from data of time-based change in reservoir pressure associated with transition phenomena during the circulation test. The storage capacity was estimated separately by dividing change of storage in the reservoir by change in the reservoir pressure. To derive the storage in the reservoir, a method to calculate non-recovered flows in the circulation test was utilized. The results of evaluating the reservoir capacity in the shallow reservoir using the above two independent methods were found substantially consistent. 3 refs., 6 figs., 1 tab.

  4. Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

    Science.gov (United States)

    Wang, Chi R.

    2005-01-01

    This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation

  5. Mixed Finite Element Simulation with Stability Analysis for Gas Transport in Low-Permeability Reservoirs

    Directory of Open Access Journals (Sweden)

    Mohamed F. El-Amin

    2018-01-01

    Full Text Available Natural gas exists in considerable quantities in tight reservoirs. Tight formations are rocks with very tiny or poorly connected pors that make flow through them very difficult, i.e., the permeability is very low. The mixed finite element method (MFEM, which is locally conservative, is suitable to simulate the flow in porous media. This paper is devoted to developing a mixed finite element (MFE technique to simulate the gas transport in low permeability reservoirs. The mathematical model, which describes gas transport in low permeability formations, contains slippage effect, as well as adsorption and diffusion mechanisms. The apparent permeability is employed to represent the slippage effect in low-permeability formations. The gas adsorption on the pore surface has been described by Langmuir isotherm model, while the Peng-Robinson equation of state is used in the thermodynamic calculations. Important compatibility conditions must hold to guarantee the stability of the mixed method by adding additional constraints to the numerical discretization. The stability conditions of the MFE scheme has been provided. A theorem and three lemmas on the stability analysis of the mixed finite element method (MFEM have been established and proven. A semi-implicit scheme is developed to solve the governing equations. Numerical experiments are carried out under various values of the physical parameters.

  6. Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

    International Nuclear Information System (INIS)

    Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin

    2014-01-01

    Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body

  7. Non-Markovian decay of a three-level cascade atom in a structured reservoir

    International Nuclear Information System (INIS)

    Dalton, B.J.; Garraway, B.M.

    2003-01-01

    The dynamics of a three-level atom in a cascade (or ladder) configuration with both transitions coupled to a single structured reservoir of quantized electromagnetic field modes is treated using Laplace transform methods applied to the coupled amplitude equations. In this system two-photon excitation of the reservoir occurs, and both sequences for emitting the two photons are allowed and included in the theory. An integral equation is found to govern the complex amplitudes of interest. It is shown that the dynamics of the atomic system is completely determined in terms of reservoir structure functions, which are products of the mode density with the coupling constant squared. This dependence on reservoir structure functions rather than on the mode density or coupling constants alone, shows that it may be possible to extend pseudomode theory to treat multiphoton excitation of a structured reservoir--pseudomodes being introduced in one-one correspondence with the poles of reservoir structure functions in the complex frequency plane. A general numerical method for solving the integral equations based on discretizing frequency space, and applicable to different structured reservoirs such as high-Q cavities and photonic band-gap systems, is presented. An application to a high-Q-cavity case with identical Lorentzian reservoir structure functions is made, and the non-Markovian decay of the excited state shown. A formal solution to the integral equations in terms of right and left eigenfunctions of a non-Hermitian kernel is also given. The dynamics of the cascade atom, with the two transitions coupled to two separate structured reservoirs of quantized electromagnetic field modes, is treated similarly to the single structured reservoir situation. Again the dynamics only depends on reservoir structure functions. As only one sequence of emitting the two photons now occurs, the integral equation for the amplitudes can be solved analytically. The non-Markovian decay of the

  8. Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

    Science.gov (United States)

    Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

    2014-03-01

    In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

  9. Tensor formulation of the model equations on strong conservation form for an incompressible flow in general coordinates

    DEFF Research Database (Denmark)

    Jørgensen, Bo Hoffmann

    2003-01-01

    This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....

  10. Experimental calibration and validation of sewer/surface flow exchange equations in steady and unsteady flow conditions

    Science.gov (United States)

    Rubinato, Matteo; Martins, Ricardo; Kesserwani, Georges; Leandro, Jorge; Djordjević, Slobodan; Shucksmith, James

    2017-09-01

    The linkage between sewer pipe flow and floodplain flow is recognised to induce an important source of uncertainty within two-dimensional (2D) urban flood models. This uncertainty is often attributed to the use of empirical hydraulic formulae (the one-dimensional (1D) weir and orifice steady flow equations) to achieve data-connectivity at the linking interface, which require the determination of discharge coefficients. Because of the paucity of high resolution localised data for this type of flows, the current understanding and quantification of a suitable range for those discharge coefficients is somewhat lacking. To fulfil this gap, this work presents the results acquired from an instrumented physical model designed to study the interaction between a pipe network flow and a floodplain flow. The full range of sewer-to-surface and surface-to-sewer flow conditions at the exchange zone are experimentally analysed in both steady and unsteady flow regimes. Steady state measured discharges are first analysed considering the relationship between the energy heads from the sewer flow and the floodplain flow; these results show that existing weir and orifice formulae are valid for describing the flow exchange for the present physical model, and yield new calibrated discharge coefficients for each of the flow conditions. The measured exchange discharges are also integrated (as a source term) within a 2D numerical flood model (a finite volume solver to the 2D Shallow Water Equations (SWE)), which is shown to reproduce the observed coefficients. This calibrated numerical model is then used to simulate a series of unsteady flow tests reproduced within the experimental facility. Results show that the numerical model overestimated the values of mean surcharge flow rate. This suggests the occurrence of additional head losses in unsteady conditions which are not currently accounted for within flood models calibrated in steady flow conditions.

  11. Amplitude various angles (AVA) phenomena in thin layer reservoir: Case study of various reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Nurhandoko, Bagus Endar B., E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com [Wave Inversion and Subsurface Fluid Imaging Research Laboratory (WISFIR), Basic Science Center A 4" t" hfloor, Physics Dept., FMIPA, Institut Teknologi Bandung (Indonesia); Rock Fluid Imaging Lab., Bandung (Indonesia); Susilowati, E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com [Rock Fluid Imaging Lab., Bandung (Indonesia)

    2015-04-16

    Amplitude various offset is widely used in petroleum exploration as well as in petroleum development field. Generally, phenomenon of amplitude in various angles assumes reservoir’s layer is quite thick. It also means that the wave is assumed as a very high frequency. But, in natural condition, the seismic wave is band limited and has quite low frequency. Therefore, topic about amplitude various angles in thin layer reservoir as well as low frequency assumption is important to be considered. Thin layer reservoir means the thickness of reservoir is about or less than quarter of wavelength. In this paper, I studied about the reflection phenomena in elastic wave which considering interference from thin layer reservoir and transmission wave. I applied Zoeppritz equation for modeling reflected wave of top reservoir, reflected wave of bottom reservoir, and also transmission elastic wave of reservoir. Results show that the phenomena of AVA in thin layer reservoir are frequency dependent. Thin layer reservoir causes interference between reflected wave of top reservoir and reflected wave of bottom reservoir. These phenomena are frequently neglected, however, in real practices. Even though, the impact of inattention in interference phenomena caused by thin layer in AVA may cause inaccurate reservoir characterization. The relation between classes of AVA reservoir and reservoir’s character are different when effect of ones in thin reservoir and ones in thick reservoir are compared. In this paper, I present some AVA phenomena including its cross plot in various thin reservoir types based on some rock physics data of Indonesia.

  12. Amplitude various angles (AVA) phenomena in thin layer reservoir: Case study of various reservoirs

    International Nuclear Information System (INIS)

    thfloor, Physics Dept., FMIPA, Institut Teknologi Bandung (Indonesia); Rock Fluid Imaging Lab., Bandung (Indonesia))" data-affiliation=" (Wave Inversion and Subsurface Fluid Imaging Research Laboratory (WISFIR), Basic Science Center A 4thfloor, Physics Dept., FMIPA, Institut Teknologi Bandung (Indonesia); Rock Fluid Imaging Lab., Bandung (Indonesia))" >Nurhandoko, Bagus Endar B.; Susilowati

    2015-01-01

    Amplitude various offset is widely used in petroleum exploration as well as in petroleum development field. Generally, phenomenon of amplitude in various angles assumes reservoir’s layer is quite thick. It also means that the wave is assumed as a very high frequency. But, in natural condition, the seismic wave is band limited and has quite low frequency. Therefore, topic about amplitude various angles in thin layer reservoir as well as low frequency assumption is important to be considered. Thin layer reservoir means the thickness of reservoir is about or less than quarter of wavelength. In this paper, I studied about the reflection phenomena in elastic wave which considering interference from thin layer reservoir and transmission wave. I applied Zoeppritz equation for modeling reflected wave of top reservoir, reflected wave of bottom reservoir, and also transmission elastic wave of reservoir. Results show that the phenomena of AVA in thin layer reservoir are frequency dependent. Thin layer reservoir causes interference between reflected wave of top reservoir and reflected wave of bottom reservoir. These phenomena are frequently neglected, however, in real practices. Even though, the impact of inattention in interference phenomena caused by thin layer in AVA may cause inaccurate reservoir characterization. The relation between classes of AVA reservoir and reservoir’s character are different when effect of ones in thin reservoir and ones in thick reservoir are compared. In this paper, I present some AVA phenomena including its cross plot in various thin reservoir types based on some rock physics data of Indonesia

  13. Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow

    Science.gov (United States)

    Bae, Hyeong-Ohk

    2018-04-01

    The regularity of 2D Navier-Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver-Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.

  14. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  15. Heat-flow equation motivated by the ideal-gas shock wave.

    Science.gov (United States)

    Holian, Brad Lee; Mareschal, Michel

    2010-08-01

    We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

  16. Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows

    International Nuclear Information System (INIS)

    Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.

    2013-01-01

    The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.

  17. Ecological operation for Three Gorges Reservoir

    Directory of Open Access Journals (Sweden)

    Wen-xian Guo

    2011-06-01

    Full Text Available The traditional operation of the Three Gorges Reservoir has mainly focused on water for flood control, power generation, navigation, water supply, and recreation, and given less attention to the negative impacts of reservoir operation on the river ecosystem. In order to reduce the negative influence of reservoir operation, ecological operation of the reservoir should be studied with a focus on maintaining a healthy river ecosystem. This study considered ecological operation targets, including maintaining the river environmental flow and protecting the spawning and reproduction of the Chinese sturgeon and four major Chinese carps. Using flow data from 1900 to 2006 at the Yichang gauging station as the control station data for the Yangtze River, the minimal and optimal river environmental flows were analyzed, and eco-hydrological targets for the Chinese sturgeon and four major Chinese carps in the Yangtze River were calculated. This paper proposes a reservoir ecological operation model, which comprehensively considers flood control, power generation, navigation, and the ecological environment. Three typical periods, wet, normal, and dry years, were selected, and the particle swarm optimization algorithm was used to analyze the model. The results show that ecological operation modes have different effects on the economic benefit of the hydropower station, and the reservoir ecological operation model can simulate the flood pulse for the requirements of spawning of the Chinese sturgeon and four major Chinese carps. According to the results, by adopting a suitable re-operation scheme, the hydropower benefit of the reservoir will not decrease dramatically while the ecological demand is met. The results provide a reference for designing reasonable operation schemes for the Three Gorges Reservoir.

  18. Equations of motion for two-phase flow in a pin bundle of a nuclear reactor

    International Nuclear Information System (INIS)

    Chawla, T.C.; Ishii, M.

    1978-01-01

    By performing Eulerian area averaging over a channel area of the local continuity, momentum, and energy equations for single phase turbulent flow and assuming each phase in two-phase flows to be continuum but coupled by the appropriate 'jump' conditions at the interface, the corresponding axial macroscopic balances for two-fluid model in a pin bundle are obtained. To determine the crossflow, a momentum equation in transverse (to the gap between the pins) direction is obtained for each phase by carrying out Eulerian segment averaging of the local momentum equation, where the segment is taken parallel to the gap. By considering the mixture as a whole, a diffusion model based on drift-flux velocity is formulated. In the axial direction it is expressed in terms of three mixture conservation equations of mass, momentum, and energy with one additional continuity equation for the vapor phase. For the determination of crossflow, transverse momentum equation for a mixture is obtained. It is considered that the previous formulation of the two-phase flow based on the 'slip' flow model and the integral subchannel balances using finite control volumes is inadequate in that the model is heuristic and, a priori, assumes the order of magnitude of the terms, also the model is incomplete and incorrect when applied to two-phase mixtures in thermal non-equilibrium such as during accidental depressurization of a water cooled reactor. The governing equations presented are shown to be a very formal and sound physical basis and are indispensable for physically correct methods of analyzing two-phase flows in a pin bundle. (author)

  19. Dredged Material Management Plan and Environmental Impact Statement. McNary Reservoir and Lower Snake River Reservoirs. Appendix C: Economic Analysis

    National Research Council Canada - National Science Library

    2002-01-01

    ...; for managment of dredged material from these reservoirs; and for maintenance of flow conveyance capacity at the most upstream extent of the Lower Granite reservoir for the remaining economic life of the dam and reservoir project (to year 2074...

  20. Flow units classification for geostatisitical three-dimensional modeling of a non-marine sandstone reservoir: A case study from the Paleocene Funing Formation of the Gaoji Oilfield, east China

    Science.gov (United States)

    Zhang, Penghui; Zhang, Jinliang; Wang, Jinkai; Li, Ming; Liang, Jie; Wu, Yingli

    2018-05-01

    Flow units classification can be used in reservoir characterization. In addition, characterizing the reservoir interval into flow units is an effective way to simulate the reservoir. Paraflow units (PFUs), the second level of flow units, are used to estimate the spatial distribution of continental clastic reservoirs at the detailed reservoir description stage. In this study, we investigate a nonroutine methodology to predict the external and internal distribution of PFUs. The methodology outlined enables the classification of PFUs using sandstone core samples and log data. The relationships obtained between porosity, permeability and pore throat aperture radii (r35) values were established for core and log data obtained from 26 wells from the Funing Formation, Gaoji Oilfield, Subei Basin, China. The present study refines predicted PFUs at logged (0.125-m) intervals, whose scale is much smaller than routine methods. Meanwhile, three-dimensional models are built using sequential indicator simulation to characterize PFUs in wells. Four distinct PFUs are classified and located based on the statistical methodology of cluster analysis, and each PFU has different seepage ability. The results of this study demonstrate the obtained models are able to quantify reservoir heterogeneity. Due to different petrophysical characteristics and seepage ability, PFUs have a significant impact on the distribution of the remaining oil. Considering these allows a more accurate understanding of reservoir quality, especially within non-marine sandstone reservoirs.

  1. Analysis and application of classification methods of complex carbonate reservoirs

    Science.gov (United States)

    Li, Xiongyan; Qin, Ruibao; Ping, Haitao; Wei, Dan; Liu, Xiaomei

    2018-06-01

    There are abundant carbonate reservoirs from the Cenozoic to Mesozoic era in the Middle East. Due to variation in sedimentary environment and diagenetic process of carbonate reservoirs, several porosity types coexist in carbonate reservoirs. As a result, because of the complex lithologies and pore types as well as the impact of microfractures, the pore structure is very complicated. Therefore, it is difficult to accurately calculate the reservoir parameters. In order to accurately evaluate carbonate reservoirs, based on the pore structure evaluation of carbonate reservoirs, the classification methods of carbonate reservoirs are analyzed based on capillary pressure curves and flow units. Based on the capillary pressure curves, although the carbonate reservoirs can be classified, the relationship between porosity and permeability after classification is not ideal. On the basis of the flow units, the high-precision functional relationship between porosity and permeability after classification can be established. Therefore, the carbonate reservoirs can be quantitatively evaluated based on the classification of flow units. In the dolomite reservoirs, the average absolute error of calculated permeability decreases from 15.13 to 7.44 mD. Similarly, the average absolute error of calculated permeability of limestone reservoirs is reduced from 20.33 to 7.37 mD. Only by accurately characterizing pore structures and classifying reservoir types, reservoir parameters could be calculated accurately. Therefore, characterizing pore structures and classifying reservoir types are very important to accurate evaluation of complex carbonate reservoirs in the Middle East.

  2. Notes on Well-Posed, Ensemble Averaged Conservation Equations for Multiphase, Multi-Component, and Multi-Material Flows

    International Nuclear Information System (INIS)

    Ray A. Berry

    2005-01-01

    At the INL researchers and engineers routinely encounter multiphase, multi-component, and/or multi-material flows. Some examples include: Reactor coolant flows Molten corium flows Dynamic compaction of metal powders Spray forming and thermal plasma spraying Plasma quench reactor Subsurface flows, particularly in the vadose zone Internal flows within fuel cells Black liquor atomization and combustion Wheat-chaff classification in combine harvesters Generation IV pebble bed, high temperature gas reactor The complexity of these flows dictates that they be examined in an averaged sense. Typically one would begin with known (or at least postulated) microscopic flow relations that hold on the ''small'' scale. These include continuum level conservation of mass, balance of species mass and momentum, conservation of energy, and a statement of the second law of thermodynamics often in the form of an entropy inequality (such as the Clausius-Duhem inequality). The averaged or macroscopic conservation equations and entropy inequalities are then obtained from the microscopic equations through suitable averaging procedures. At this stage a stronger form of the second law may also be postulated for the mixture of phases or materials. To render the evolutionary material flow balance system unique, constitutive equations and phase or material interaction relations are introduced from experimental observation, or by postulation, through strict enforcement of the constraints or restrictions resulting from the averaged entropy inequalities. These averaged equations form the governing equation system for the dynamic evolution of these mixture flows. Most commonly, the averaging technique utilized is either volume or time averaging or a combination of the two. The flow restrictions required for volume and time averaging to be valid can be severe, and violations of these restrictions are often found. A more general, less restrictive (and far less commonly used) type of averaging known as

  3. Methods for estimating flow-duration curve and low-flow frequency statistics for ungaged locations on small streams in Minnesota

    Science.gov (United States)

    Ziegeweid, Jeffrey R.; Lorenz, David L.; Sanocki, Chris A.; Czuba, Christiana R.

    2015-12-24

    Knowledge of the magnitude and frequency of low flows in streams, which are flows in a stream during prolonged dry weather, is fundamental for water-supply planning and design; waste-load allocation; reservoir storage design; and maintenance of water quality and quantity for irrigation, recreation, and wildlife conservation. This report presents the results of a statewide study for which regional regression equations were developed for estimating 13 flow-duration curve statistics and 10 low-flow frequency statistics at ungaged stream locations in Minnesota. The 13 flow-duration curve statistics estimated by regression equations include the 0.0001, 0.001, 0.02, 0.05, 0.1, 0.25, 0.50, 0.75, 0.9, 0.95, 0.99, 0.999, and 0.9999 exceedance-probability quantiles. The low-flow frequency statistics include annual and seasonal (spring, summer, fall, winter) 7-day mean low flows, seasonal 30-day mean low flows, and summer 122-day mean low flows for a recurrence interval of 10 years. Estimates of the 13 flow-duration curve statistics and the 10 low-flow frequency statistics are provided for 196 U.S. Geological Survey continuous-record streamgages using streamflow data collected through September 30, 2012.

  4. Fracture Evolution Following a Hydraulic Stimulation within an EGS Reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Mella, Michael [Univ. of Utah, Salt Lake City, UT (United States). Energy and Geoscience Inst.

    2016-08-31

    The objective of this project was to develop and demonstrate an approach for tracking the evolution of circulation immediately following a hydraulic stimulation in an EGS reservoir. Series of high-resolution tracer tests using conservative and thermally reactive tracers were designed at recently created EGS reservoirs in order to track changes in fluid flow parameters such as reservoir pore volume, flow capacity, and effective reservoir temperature over time. Data obtained from the project would be available for the calibration of reservoir models that could serve to predict EGS performance following a hydraulic stimulation.

  5. On the Eikonal equation in the pedestrian flow problem

    Science.gov (United States)

    Felcman, J.; Kubera, P.

    2017-07-01

    We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.

  6. DEVELOPMENT OF RESERVOIR CHARACTERIZATION TECHNIQUES AND PRODUCTION MODELS FOR EXPLOITING NATURALLY FRACTURED RESERVOIRS

    Energy Technology Data Exchange (ETDEWEB)

    Michael L. Wiggins; Raymon L. Brown; Faruk Civan; Richard G. Hughes

    2002-12-31

    For many years, geoscientists and engineers have undertaken research to characterize naturally fractured reservoirs. Geoscientists have focused on understanding the process of fracturing and the subsequent measurement and description of fracture characteristics. Engineers have concentrated on the fluid flow behavior in the fracture-porous media system and the development of models to predict the hydrocarbon production from these complex systems. This research attempts to integrate these two complementary views to develop a quantitative reservoir characterization methodology and flow performance model for naturally fractured reservoirs. The research has focused on estimating naturally fractured reservoir properties from seismic data, predicting fracture characteristics from well logs, and developing a naturally fractured reservoir simulator. It is important to develop techniques that can be applied to estimate the important parameters in predicting the performance of naturally fractured reservoirs. This project proposes a method to relate seismic properties to the elastic compliance and permeability of the reservoir based upon a sugar cube model. In addition, methods are presented to use conventional well logs to estimate localized fracture information for reservoir characterization purposes. The ability to estimate fracture information from conventional well logs is very important in older wells where data are often limited. Finally, a desktop naturally fractured reservoir simulator has been developed for the purpose of predicting the performance of these complex reservoirs. The simulator incorporates vertical and horizontal wellbore models, methods to handle matrix to fracture fluid transfer, and fracture permeability tensors. This research project has developed methods to characterize and study the performance of naturally fractured reservoirs that integrate geoscience and engineering data. This is an important step in developing exploitation strategies for

  7. A dual-porosity model for two-phase flow in deforming porous media

    Science.gov (United States)

    Shu, Zhengying

    Only recently has one realized the importance of the coupling of fluid flow with rock matrix deformations for accurately modeling many problems in petroleum, civil, environmental, geological and mining engineering. In the oil industry, problems such as reservoir compaction, ground subsidence, borehole stability and sanding need to be simulated using a coupled approach to make more precise predictions than when each process is considered to be independent of the other. Due to complications associated with multiple physical processes and mathematical representation of a multiphase now system in deformable fractured reservoirs, very few references, if any, are available in the literature. In this dissertation, an approach, which is based on the dual-porosity concept and takes into account rock deformations, is presented to derive rigorously a set of coupled differential equations governing the behavior of fractured porous media and two-phase fluid flow. The finite difference numerical method, as an alternative method for finite element, is applied to discretize the governing equations both in time and space domains. Throughout the derived set of equations, the fluid pressures and saturations as well as the solid displacements are considered as the primary unknowns. The model is tested against the case of single-phase flow in a 1-D consolidation problem for which analytical solutions are available. An example of coupled two-phase fluid flow and rock deformations for a scenario of a one-dimensional, fractured porous medium is also discussed. The numerical model and simulator, RFIA (Rock Fluid InterAction), developed in this dissertation can be a powerful tool to solve difficult problems not only in petroleum engineering such as ground subsidence, borehole stability and sand control, but also in civil engineering such as groundwater flow through fractured bedrock and in environmental engineering such as waste deposit concerns in fractured and unconsolidated formations

  8. Quantifying Fracture Heterogeneity in Different Domains of Folded Carbonate Rocks to Improve Fractured Reservoir Analog Fluid Flow Models

    NARCIS (Netherlands)

    Bisdom, K.; Bertotti, G.; Gauthier, B.D.M.; Hardebol, N.J.

    2013-01-01

    Fluid flow in carbonate reservoirs is largely controlled by multiscale fracture networks. Significant variations of fracture network porosity and permeability are caused by the 3D heterogeneity of the fracture network characteristics, such as intensity, orientation and size. Characterizing fracture

  9. Rarefied gas flows through a curved channel: Application of a diffusion-type equation

    Science.gov (United States)

    Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

    2010-11-01

    Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

  10. Test of a new heat-flow equation for dense-fluid shock waves.

    Science.gov (United States)

    Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

    2010-09-21

    Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

  11. On the Representation of Aquifer Compressibility in General Subsurface Flow Codes: How an Alternate Definition of Aquifer Compressibility Matches Results from the Groundwater Flow Equation

    Science.gov (United States)

    Birdsell, D.; Karra, S.; Rajaram, H.

    2017-12-01

    The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.

  12. Compressible fluid flow through rocks of variable permeability

    International Nuclear Information System (INIS)

    Lin, W.

    1977-01-01

    The effectiveness of course-grained igneous rocks as shelters for burying radioactive waste can be assessed by determining the rock permeabilities at their in situ pressures and stresses. Analytical and numerical methods were used to solve differential equations of one-dimensional fluid flow through rocks with permeabilities from 10 4 to 1 nD. In these calculations, upstream and downstream reservoir volumes of 5, 50, and 500 cm 3 were used. The optimal size combinations of the two reservoirs were determined for measurements of permeability, stress, strain, acoustic velocity, and electrical conductivity on low-porosity, coarse-grained igneous rocks

  13. Scaling properties reveal regulation of river flows in the Amazon through a forest reservoir

    Science.gov (United States)

    Salazar, Juan Fernando; Villegas, Juan Camilo; María Rendón, Angela; Rodríguez, Estiven; Hoyos, Isabel; Mercado-Bettín, Daniel; Poveda, Germán

    2018-03-01

    Many natural and social phenomena depend on river flow regimes that are being altered by global change. Understanding the mechanisms behind such alterations is crucial for predicting river flow regimes in a changing environment. Here we introduce a novel physical interpretation of the scaling properties of river flows and show that it leads to a parsimonious characterization of the flow regime of any river basin. This allows river basins to be classified as regulated or unregulated, and to identify a critical threshold between these states. We applied this framework to the Amazon river basin and found both states among its main tributaries. Then we introduce the forest reservoir hypothesis to describe the natural capacity of river basins to regulate river flows through land-atmosphere interactions (mainly precipitation recycling) that depend strongly on the presence of forests. A critical implication is that forest loss can force the Amazonian river basins from regulated to unregulated states. Our results provide theoretical and applied foundations for predicting hydrological impacts of global change, including the detection of early-warning signals for critical transitions in river basins.

  14. Restoring Natural Streamflow Variability by Modifying Multi-purpose Reservoir Operation

    Science.gov (United States)

    Shiau, J.

    2010-12-01

    Multi-purpose reservoirs typically provide benefits of water supply, hydroelectric power, and flood mitigation. Hydroelectric power generations generally do not consume water. However, temporal distribution of downstream flows is highly changed due to hydro-peaking effects. Associated with offstream diversion of water supplies for municipal, industrial, and agricultural requirements, natural streamflow characteristics of magnitude, duration, frequency, timing, and rate of change is significantly altered by multi-purpose reservoir operation. Natural flow regime has long been recognized a master factor for ecosystem health and biodiversity. Restoration of altered flow regime caused by multi-purpose reservoir operation is the main objective of this study. This study presents an optimization framework that modifying reservoir operation to seeking balance between human and environmental needs. The methodology presented in this study is applied to the Feitsui Reservoir, located in northern Taiwan, with main purpose of providing stable water-supply and auxiliary purpose of electricity generation and flood-peak attenuation. Reservoir releases are dominated by two decision variables, i.e., duration of water releases for each day and percentage of daily required releases within the duration. The current releasing policy of the Feitsui Reservoir releases water for water-supply and hydropower purposes during 8:00 am to 16:00 pm each day and no environmental flows releases. Although greater power generation is obtained by 100% releases distributed within 8-hour period, severe temporal alteration of streamflow is observed downstream of the reservoir. Modifying reservoir operation by relaxing these two variables and reserve certain ratio of streamflow as environmental flow to maintain downstream natural variability. The optimal reservoir releasing policy is searched by the multi-criterion decision making technique for considering reservoir performance in terms of shortage ratio

  15. Numerical analysis of temperature and flow effects in a dry, two-dimensional, porous-media reservoir used for compressed air energy storage

    Energy Technology Data Exchange (ETDEWEB)

    Wiles, L.E.

    1979-10-01

    The purpose of the work is to define the hydrodynamic and thermodynamic response of a CAES dry porous media reservoir subjected to simulated air mass cycling. The knowledge gained will provide, or will assist in providing, design guidelines for the efficient and stable operation of the air storage reservoir. The analysis and results obtained by two-dimensional modeling of dry reservoirs are presented. While the fluid/thermal response of the underground system is dependent on many parameters, the two-dimensional model was applied only to those parameters that entered the analysis by virtue of inclusion of the vertical dimension. In particular, the parameters or responses that were quantified or characterized include wellbore heat transfer, heat losses to the vertical boundaries of the porous zone, gravitationally induced flows, producing length of the wellbore, and the effects of nonuniform permeability. The analysis of the wellbore heat transfer included consideration of insulation, preheating (bubble development with heated air), and air mass flow rate.

  16. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  17. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  18. Sediment management for reservoir

    International Nuclear Information System (INIS)

    Rahman, A.

    2005-01-01

    All natural lakes and reservoirs whether on rivers, tributaries or off channel storages are doomed to be sited up. Pakistan has two major reservoirs of Tarbela and Managla and shallow lake created by Chashma Barrage. Tarbela and Mangla Lakes are losing their capacities ever since first impounding, Tarbela since 1974 and Mangla since 1967. Tarbela Reservoir receives average annual flow of about 62 MAF and sediment deposits of 0.11 MAF whereas Mangla gets about 23 MAF of average annual flows and is losing its storage at the rate of average 34,000 MAF annually. The loss of storage is a great concern and studies for Tarbela were carried out by TAMS and Wallingford to sustain its capacity whereas no study has been done for Mangla as yet except as part of study for Raised Mangla, which is only desk work. Delta of Tarbala reservoir has advanced to about 6.59 miles (Pivot Point) from power intakes. In case of liquefaction of delta by tremor as low as 0.12g peak ground acceleration the power tunnels I, 2 and 3 will be blocked. Minimum Pool of reservoir is being raised so as to check the advance of delta. Mangla delta will follow the trend of Tarbela. Tarbela has vast amount of data as reservoir is surveyed every year, whereas Mangla Reservoir survey was done at five-year interval, which has now been proposed .to be reduced to three-year interval. In addition suspended sediment sampling of inflow streams is being done by Surface Water Hydrology Project of WAPDA as also some bed load sampling. The problem of Chasma Reservoir has also been highlighted, as it is being indiscriminately being filled up and drawdown several times a year without regard to its reaction to this treatment. The Sediment Management of these reservoirs is essential and the paper discusses pros and cons of various alternatives. (author)

  19. Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

    International Nuclear Information System (INIS)

    Anco, Stephen C

    2006-01-01

    Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps

  20. Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations

    Energy Technology Data Exchange (ETDEWEB)

    Anco, Stephen C [Department of Mathematics, Brock University, St Catharines, ON (Canada)

    2006-03-03

    Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps.

  1. Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.

  2. MULTIDISCIPLINARY IMAGING OF ROCK PROPERTIES IN CARBONATE RESERVOIRS FOR FLOW-UNIT TARGETING

    Energy Technology Data Exchange (ETDEWEB)

    Stephen C. Ruppel

    2005-02-01

    Despite declining production rates, existing reservoirs in the US contain large quantities of remaining oil and gas that constitute a huge target for improved diagnosis and imaging of reservoir properties. The resource target is especially large in carbonate reservoirs, where conventional data and methodologies are normally insufficient to resolve critical scales of reservoir heterogeneity. The objectives of the research described in this report were to develop and test such methodologies for improved imaging, measurement, modeling, and prediction of reservoir properties in carbonate hydrocarbon reservoirs. The focus of the study is the Permian-age Fullerton Clear Fork reservoir of the Permian Basin of West Texas. This reservoir is an especially appropriate choice considering (a) the Permian Basin is the largest oil-bearing basin in the US, and (b) as a play, Clear Fork reservoirs have exhibited the lowest recovery efficiencies of all carbonate reservoirs in the Permian Basin.

  3. Exact solutions of the Navier-Stokes equations generalized for flow in porous media

    Science.gov (United States)

    Daly, Edoardo; Basser, Hossein; Rudman, Murray

    2018-05-01

    Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

  4. Mass and energy-capital conservation equations to study the price evolution of non-renewable energy resources

    International Nuclear Information System (INIS)

    Gori, F.

    2006-01-01

    Mass conservation equation of non-renewable resources is employed to study the resources remaining in the reservoir according to the extraction policy. The energy conservation equation is transformed into an energy-capital conservation equation. The Hotelling rule is shown to be a special case of the general energy-capital conservation equation when the mass flow rate of extracted resources is equal to unity. Mass and energy-capital conservation equations are then coupled and solved together. It is investigated the price evolution of extracted resources. The conclusion of the Hotelling rule for non-extracted resources, i.e. an exponential increase of the price of non-renewable resources at the rate of current interest, is then generalized. A new parameter, called 'Price Increase Factor', PIF, is introduced as the difference between the current interest rate of capital and the mass flow rate of extraction of non-renewable resources. The price of extracted resources can increase exponentially only if PIF is greater than zero or if the mass flow rate of extraction is lower than the current interest rate of capital. The price is constant if PIF is zero or if the mass flow rate of extraction is equal to the current interest rate. The price is decreasing with time if PIF is smaller than zero or if the mass flow rate of extraction is higher than the current interest rate. (author)

  5. The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

    DEFF Research Database (Denmark)

    Jørgensen, Bo Hoffmann

    2003-01-01

    The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth...... by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...

  6. Reviving Abandoned Reservoirs with High-Pressure Air Injection: Application in a Fractured and Karsted Dolomite Reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Robert Loucks; Stephen C. Ruppel; Dembla Dhiraj; Julia Gale; Jon Holder; Jeff Kane; Jon Olson; John A. Jackson; Katherine G. Jackson

    2006-09-30

    Despite declining production rates, existing reservoirs in the United States contain vast volumes of remaining oil that is not being effectively recovered. This oil resource constitutes a huge target for the development and application of modern, cost-effective technologies for producing oil. Chief among the barriers to the recovery of this oil are the high costs of designing and implementing conventional advanced recovery technologies in these mature, in many cases pressure-depleted, reservoirs. An additional, increasingly significant barrier is the lack of vital technical expertise necessary for the application of these technologies. This lack of expertise is especially notable among the small operators and independents that operate many of these mature, yet oil-rich, reservoirs. We addressed these barriers to more effective oil recovery by developing, testing, applying, and documenting an innovative technology that can be used by even the smallest operator to significantly increase the flow of oil from mature U.S. reservoirs. The Bureau of Economic Geology and Goldrus Producing Company assembled a multidisciplinary team of geoscientists and engineers to evaluate the applicability of high-pressure air injection (HPAI) in revitalizing a nearly abandoned carbonate reservoir in the Permian Basin of West Texas. The Permian Basin, the largest oil-bearing basin in North America, contains more than 70 billion barrels of remaining oil in place and is an ideal venue to validate this technology. We have demonstrated the potential of HPAI for oil-recovery improvement in preliminary laboratory tests and a reservoir pilot project. To more completely test the technology, this project emphasized detailed characterization of reservoir properties, which were integrated to access the effectiveness and economics of HPAI. The characterization phase of the project utilized geoscientists and petroleum engineers from the Bureau of Economic Geology and the Department of Petroleum

  7. Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

    International Nuclear Information System (INIS)

    Kataoka, Isao; Tomiyama, Akio

    2004-01-01

    The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

  8. Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

    OpenAIRE

    M. L. Kavvas; T. Tu; A. Ercan; J. Polsinelli

    2017-01-01

    Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally...

  9. Scaling properties reveal regulation of river flows in the Amazon through a forest reservoir

    Directory of Open Access Journals (Sweden)

    J. F. Salazar

    2018-03-01

    Full Text Available Many natural and social phenomena depend on river flow regimes that are being altered by global change. Understanding the mechanisms behind such alterations is crucial for predicting river flow regimes in a changing environment. Here we introduce a novel physical interpretation of the scaling properties of river flows and show that it leads to a parsimonious characterization of the flow regime of any river basin. This allows river basins to be classified as regulated or unregulated, and to identify a critical threshold between these states. We applied this framework to the Amazon river basin and found both states among its main tributaries. Then we introduce the forest reservoir hypothesis to describe the natural capacity of river basins to regulate river flows through land–atmosphere interactions (mainly precipitation recycling that depend strongly on the presence of forests. A critical implication is that forest loss can force the Amazonian river basins from regulated to unregulated states. Our results provide theoretical and applied foundations for predicting hydrological impacts of global change, including the detection of early-warning signals for critical transitions in river basins.

  10. Approximate analytical solution to the Boussinesq equation with a sloping water-land boundary

    Science.gov (United States)

    Tang, Yuehao; Jiang, Qinghui; Zhou, Chuangbing

    2016-04-01

    An approximate solution is presented to the 1-D Boussinesq equation (BEQ) characterizing transient groundwater flow in an unconfined aquifer subject to a constant water variation at the sloping water-land boundary. The flow equation is decomposed to a linearized BEQ and a head correction equation. The linearized BEQ is solved using a Laplace transform. By means of the frozen-coefficient technique and Gauss function method, the approximate solution for the head correction equation can be obtained, which is further simplified to a closed-form expression under the condition of local energy equilibrium. The solutions of the linearized and head correction equations are discussed from physical concepts. Especially for the head correction equation, the well posedness of the approximate solution obtained by the frozen-coefficient method is verified to demonstrate its boundedness, which can be further embodied as the upper and lower error bounds to the exact solution of the head correction by statistical analysis. The advantage of this approximate solution is in its simplicity while preserving the inherent nonlinearity of the physical phenomenon. Comparisons between the analytical and numerical solutions of the BEQ validate that the approximation method can achieve desirable precisions, even in the cases with strong nonlinearity. The proposed approximate solution is applied to various hydrological problems, in which the algebraic expressions that quantify the water flow processes are derived from its basic solutions. The results are useful for the quantification of stream-aquifer exchange flow rates, aquifer response due to the sudden reservoir release, bank storage and depletion, and front position and propagation speed.

  11. Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

    Science.gov (United States)

    Adem, Abdullahi Rashid; Moawad, Salah M.

    2018-05-01

    In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

  12. Fixation of waste materials in grouts: Part 3, Equation for critical flow rate

    International Nuclear Information System (INIS)

    Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.

    1986-12-01

    Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs

  13. Effects of water-supply reservoirs on streamflow in Massachusetts

    Science.gov (United States)

    Levin, Sara B.

    2016-10-06

    State and local water-resource managers need modeling tools to help them manage and protect water-supply resources for both human consumption and ecological needs. The U.S. Geological Survey, in cooperation with the Massachusetts Department of Environmental Protection, has developed a decision-support tool to estimate the effects of reservoirs on natural streamflow. The Massachusetts Reservoir Simulation Tool is a model that simulates the daily water balance of a reservoir. The reservoir simulation tool provides estimates of daily outflows from reservoirs and compares the frequency, duration, and magnitude of the volume of outflows from reservoirs with estimates of the unaltered streamflow that would occur if no dam were present. This tool will help environmental managers understand the complex interactions and tradeoffs between water withdrawals, reservoir operational practices, and reservoir outflows needed for aquatic habitats.A sensitivity analysis of the daily water balance equation was performed to identify physical and operational features of reservoirs that could have the greatest effect on reservoir outflows. For the purpose of this report, uncontrolled releases of water (spills or spillage) over the reservoir spillway were considered to be a proxy for reservoir outflows directly below the dam. The ratio of average withdrawals to the average inflows had the largest effect on spillage patterns, with the highest withdrawals leading to the lowest spillage. The size of the surface area relative to the drainage area of the reservoir also had an effect on spillage; reservoirs with large surface areas have high evaporation rates during the summer, which can contribute to frequent and long periods without spillage, even in the absence of water withdrawals. Other reservoir characteristics, such as variability of inflows, groundwater interactions, and seasonal demand patterns, had low to moderate effects on the frequency, duration, and magnitude of spillage. The

  14. SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLEFLUID’S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS

    Directory of Open Access Journals (Sweden)

    Nadjafikhah M.

    2017-07-01

    Full Text Available Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.

  15. Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates

    Energy Technology Data Exchange (ETDEWEB)

    Holden, Helge; Karlsen, Kenneth H.; Lie, Knut-Andreas

    1999-10-01

    We present and analyze a numerical method for the solution of a class of scalar, multi-dimensional, nonlinear degenerate convection-diffusion equations. The method is based on operator splitting to separate the convective and the diffusive terms in the governing equation. The nonlinear, convective part is solved using front tracking and dimensional splitting, while the nonlinear diffusion equation is solved by a suitable difference scheme. We verify L{sup 1} compactness of the corresponding set of approximate solutions and derive precise entropy estimates. In particular, these results allow us to pass to the limit in our approximations and recover an entropy solution of the problem in question. The theory presented covers a large class of equations. Important subclasses are hyperbolic conservation laws, porous medium type equations, two-phase reservoir flow equations, and strongly degenerate equations coming from the recent theory of sedimentation-consolidation processes. A thorough numerical investigation of the method analyzed in this paper (and similar methods) is presented in a companion paper. (author)

  16. User's Guide of TOUGH2-EGS. A Coupled Geomechanical and Reactive Geochemical Simulator for Fluid and Heat Flow in Enhanced Geothermal Systems Version 1.0

    Energy Technology Data Exchange (ETDEWEB)

    Fakcharoenphol, Perapon [Colorado School of Mines, Golden, CO (United States); Xiong, Yi [Colorado School of Mines, Golden, CO (United States); Hu, Litang [Colorado School of Mines, Golden, CO (United States); Winterfeld, Philip H. [Colorado School of Mines, Golden, CO (United States); Xu, Tianfu [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Wu, Yu-Shu [Colorado School of Mines, Golden, CO (United States)

    2013-05-01

    TOUGH2-EGS is a numerical simulation program coupling geomechanics and chemical reactions for fluid and heat flows in porous media and fractured reservoirs of enhanced geothermal systems. The simulator includes the fully-coupled geomechanical (THM) module, the fully-coupled geochemical (THC) module, and the sequentially coupled reactive geochemistry (THMC) module. The fully-coupled flow-geomechanics model is developed from the linear elastic theory for the thermo-poro-elastic system and is formulated with the mean normal stress as well as pore pressure and temperature. The chemical reaction is sequentially coupled after solution of flow equations, which provides the flow velocity and phase saturation for the solute transport calculation at each time step. In addition, reservoir rock properties, such as porosity and permeability, are subjected to change due to rock deformation and chemical reactions. The relationships between rock properties and geomechanical and chemical effects from poro-elasticity theories and empirical correlations are incorporated into the simulator. This report provides the user with detailed information on both mathematical models and instructions for using TOUGH2-EGS for THM, THC or THMC simulations. The mathematical models include the fluid and heat flow equations, geomechanical equation, reactive geochemistry equations, and discretization methods. Although TOUGH2-EGS has the capability for simulating fluid and heat flows coupled with both geomechanical and chemical effects, it is up to the users to select the specific coupling process, such as THM, THC, or THMC in a simulation. There are several example problems illustrating the applications of this program. These example problems are described in details and their input data are presented. The results demonstrate that this program can be used for field-scale geothermal reservoir simulation with fluid and heat flow, geomechanical effect, and chemical reaction in porous and fractured media.

  17. Reservoir release patterns for hydropower operations at the Aspinall Unit on the Gunnison River, Colorado

    International Nuclear Information System (INIS)

    Yin, S.C.L.; Sedlacek, J.

    1995-05-01

    This report presents the development of reservoir release patterns for the Aspinall Unit, which includes Blue Mesa, Morrow Point, and Crystal Reservoirs on the Gunnison River in Colorado. Release patterns were assessed for two hydropower operational scenarios--seasonally adjusted steady flows and seasonally adjusted high fluctuating flows--and three representative hydrologic years--moderate (1987), dry (1989), and wet (1983). The release patterns for the operational scenarios were developed with the aid of monthly, daily, and hourly reservoir operational models, which simulate the linked operation of the three Aspinall Unit reservoirs. Also presented are reservoir fluctuations and downstream water surface elevations corresponding to the reservoir release patterns. Both of the hydropower operational scenarios evaluated are based on the ecological research flows proposed by the US Fish and Wildlife Service for the Aspinall Unit. The first operational scenario allows only seasonally adjusted steady flows (no hourly fluctuations at any dam within one day), whereas the second scenario permits high fluctuating flows from Blue Mesa and Morrow Point Reservoirs during certain times of the year. Crystal Reservoir would release a steady flow within each day under both operational scenarios

  18. Reservoir Characterization, Production Characteristics, and Research Needs for Fluvial/Alluvial Reservoirs in the United States

    Energy Technology Data Exchange (ETDEWEB)

    Cole, E.L.; Fowler, M.L.; Jackson, S.R.; Madden, M.P.; Raw-Schatzinger, V.; Salamy, S.P.; Sarathi, P.; Young, M.A.

    1999-04-28

    The Department of Energy's (DOE's) Oil Recovery Field Demonstration Program was initiated in 1992 to maximize the economically and environmentally sound recovery of oil from known domestic reservoirs and to preserve access to this resource. Cost-shared field demonstration projects are being initiated in geology defined reservoir classes which have been prioritized by their potential for incremental recovery and their risk of abandonment. This document defines the characteristics of the fifth geological reservoir class in the series, fluvial/alluvial reservoirs. The reservoirs of Class 5 include deposits of alluvial fans, braided streams, and meandering streams. Deposit morphologies vary as a complex function of climate and tectonics and are characterized by a high degree of heterogeneity to fluid flow as a result of extreme variations in water energy as the deposits formed.

  19. Kinetic equations for clean superconductors: Application to the flux flow hall effect

    International Nuclear Information System (INIS)

    Kopnin, N.B.

    1994-01-01

    The kinetic equations for clean superconductors (l>>ζ) are derived. expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℎE F /Δ 2 . The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of 3 He

  20. Fluid flow in porous media using image-based modelling to parametrize Richards' equation.

    Science.gov (United States)

    Cooper, L J; Daly, K R; Hallett, P D; Naveed, M; Koebernick, N; Bengough, A G; George, T S; Roose, T

    2017-11-01

    The parameters in Richards' equation are usually calculated from experimentally measured values of the soil-water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn-Hilliard-Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil-water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.

  1. Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

    Science.gov (United States)

    Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

    2017-10-01

    There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

  2. Modeling mode interactions in boundary layer flows via the Parabolized Floquet Equations

    OpenAIRE

    Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanović, Mihailo R.

    2017-01-01

    In this paper, we develop a linear model to study interactions between different modes in slowly-growing boundary layer flows. Our method consists of two steps. First, we augment the Blasius boundary layer profile with a disturbance field resulting from the linear Parabolized Stability Equations (PSE) to obtain the modified base flow; and, second, we combine Floquet analysis with the linear PSE to capture the spatial evolution of flow fluctuations. This procedure yields the Parabolized Floque...

  3. Integration of dynamical data in a geostatistical model of reservoir; Integration des donnees dynamiques dans un modele geostatistique de reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Costa Reis, L.

    2001-01-01

    We have developed in this thesis a methodology of integrated characterization of heterogeneous reservoirs, from geologic modeling to history matching. This methodology is applied to the reservoir PBR, situated in Campos Basin, offshore Brazil, which has been producing since June 1979. This work is an extension of two other thesis concerning geologic and geostatistical modeling of the reservoir PBR from well data and seismic information. We extended the geostatistical litho-type model to the whole reservoir by using a particular approach of the non-stationary truncated Gaussian simulation method. This approach facilitated the application of the gradual deformation method to history matching. The main stages of the methodology for dynamic data integration in a geostatistical reservoir model are presented. We constructed a reservoir model and the initial difficulties in the history matching led us to modify some choices in the geological, geostatistical and flow models. These difficulties show the importance of dynamic data integration in reservoir modeling. The petrophysical property assignment within the litho-types was done by using well test data. We used an inversion procedure to evaluate the petrophysical parameters of the litho-types. The up-scaling is a necessary stage to reduce the flow simulation time. We compared several up-scaling methods and we show that the passage from the fine geostatistical model to the coarse flow model should be done very carefully. The choice of the fitting parameter depends on the objective of the study. In the case of the reservoir PBR, where water is injected in order to improve the oil recovery, the water rate of the producing wells is directly related to the reservoir heterogeneity. Thus, the water rate was chosen as the fitting parameter. We obtained significant improvements in the history matching of the reservoir PBR. First, by using a method we have proposed, called patchwork. This method allows us to built a coherent

  4. BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows

    Science.gov (United States)

    Shaing, K. C.

    2010-07-01

    A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.

  5. Incorporating an approach to aid river and reservoir fisheries in an altered landscape

    Science.gov (United States)

    Brewer, Shannon K.; Shoup, Daniel E.; Dattillo, John

    2018-01-01

    Reservoir construction for human-use services alters connected riverine flow patterns and influences fish production. We sampled two pelagic fishes from two rivers and two reservoirs and related seasonal and annual hydrology patterns to the recruitment and growth of each species. River and reservoir populations of Freshwater Drum Aplodinotus grunniens reached similar ages (32 and 31, respectively). Likewise, longevity of Gizzard Shad Dorosoma cepedianum between the two systems was also similar (7 and 8 years, respectively). However, both species grew larger in the rivers compared to reservoir residents. Recruitment of Freshwater Drum in reservoirs was negatively related to water retention time (r2=0.59) suggesting moving water through the reservoir was beneficial. Riverine recruitment of Freshwater Drum populations was negatively related to the annual number of flow reversals and positively related to prespawn discharge (r2 = 0.33). Unlike Freshwater Drum, there was no relationship between flow metrics and Gizzard Shad recruitment in reservoirs. However, recruitment of riverine Gizzard Shad was positively related to high flow pulses during the prespawn and spawning seasons (r2 = 0.48). The growth of both species in reservoirs was positively related to the number of days each year that water levels were above the conservation pool. Growth of Freshwater Drum was also negatively related to minimum reservoir summer water levels (r2 = 0.84). Growth of both Freshwater Drum and Gizzard Shad occupying lotic systems was positively related to May (r2 = 0.86) and July discharge (r2 = 0.84), respectively. In general, growth and recruitment of the reservoir populations was more related to annual water patterns, whereas riverine fishes responded more to seasonal flow patterns. Results of this study provide important information on the relationship between hydrology and pelagic fish production in both rivers and reservoirs. This information is useful if agencies are interested in

  6. Pole dynamics for the Flierl-Petvishvili equation and zonal flow

    International Nuclear Information System (INIS)

    Spineanu, F.; Vlad, M.; Itoh, K.; Sanuki, H.; Itoh, S.-I.

    2003-09-01

    We use a systematic method which allows us to identify a class of exact solutions of the Flierl-Petvishvili equation. The solutions are periodic and have one dimensional geometry. We examine the physical properties and find that these structures can have a significant effect on the zonal flow generation. (author)

  7. IMPROVING CO2 EFFICIENCY FOR RECOVERING OIL IN HETEROGENEOUS RESERVOIRS

    Energy Technology Data Exchange (ETDEWEB)

    Reid B. Grigg; Robert K. Svec; Zhengwen Zeng; Baojun Bai; Yi Liu

    2004-09-27

    much longer than one hour, with Berea sandstone requiring the longest time. In Chapter 4, comparisons of static adsorption of CLS, CD, and CLS/CD mixtures onto five pure minerals showed that the presence of CLS decreased the adsorption of CD onto the five minerals by 20 to 70%. Dynamic CLS/CD mixture adsorption tests onto Berea sandstone and Indian limestone cores showed that competitive adsorption between CD and CLS generally takes several days to reach equilibrium. Foam stability and interfacial tension tests on both injected and effluent samples were performed which showed that both foam stability and IFT decreased due to adsorption. Also it appears that there is a chromatographic effect on the surfactants in flow through porous media. Progress was realized in developing general equations for stress sensitivity on non-Darcy parameters (permeability and non-Darcy coefficient), and the multiphase flow induced by a high flow rate was confirmed as a mechanism for injectivity loss in CO{sub 2} flooding. In Chapter 5, a general equation is defined based on 60 general equations of permeability stress sensitivity and non-Darcy coefficient stress sensitivity and definitions of nominal permeability, nominal non-Darcy coefficient, permeability stress sensitivity, and non-Darcy coefficient stress sensitivity. The equations of stress sensitivity are independent of pressure, temperature, and rock properties and existing empirical correlations of the nominal permeability and nominal non-Darcy coefficient can be used when laboratory data are not available. This provides a tool to quantify the change of permeability and non-Darcy coefficient due to change of effective stress resulted from reservoir injection and/or production.

  8. Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations

    International Nuclear Information System (INIS)

    Rowlands, G; Infeld, E; Skorupski, A A

    2013-01-01

    We find a class of exact solutions to the Lighthill–Whitham–Richards–Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg–de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end. (paper)

  9. Isentropic Gas Flow for the Compressible Euler Equation in a Nozzle

    Science.gov (United States)

    Tsuge, Naoki

    2013-08-01

    We study the motion of isentropic gas in a nozzle. Nozzles are used to increase the thrust of engines or to accelerate a flow from subsonic to supersonic. Nozzles are essential parts for jet engines, rocket engines and supersonicwind tunnels. In the present paper, we consider unsteady flow, which is governed by the compressible Euler equation, and prove the existence of global solutions for the Cauchy problem. For this problem, the existence theorem has already been obtained for initial data away from the sonic state, (Liu in Commun Math Phys 68:141-172, 1979). Here, we are interested in the transonic flow, which is essential for engineering and physics. Although the transonic flow has recently been studied (Tsuge in J Math Kyoto Univ 46:457-524, 2006; Lu in Nonlinear Anal Real World Appl 12:2802-2810, 2011), these papers assume monotonicity of the cross section area. Here, we consider the transonic flow in a nozzle with a general cross section area. When we prove global existence, the most difficult point is obtaining a bounded estimate for approximate solutions. To overcome this, we employ a new invariant region that depends on the space variable. Moreover, we introduce a modified Godunov scheme. The corresponding approximate solutions consist of piecewise steady-state solutions of an auxiliary equation, which yield a desired bounded estimate. In order to prove their convergence, we use the compensated compactness framework.

  10. Equation-Free Analysis of Macroscopic Behavior in Traffic and Pedestrian Flow

    DEFF Research Database (Denmark)

    Marschler, Christian; Sieber, Jan; Hjorth, Poul G.

    2014-01-01

    Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are explicitly given on the macroscopic level. This will fac......Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are explicitly given on the macroscopic level....... This will facilitate a study of how the model behavior depends on parameter values including an understanding of transitions between different types of qualitative behavior. These methods are introduced and explained for traffic jam formation and emergence of oscillatory pedestrian counter flow in a corridor...

  11. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

    2016-06-01

    Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

  12. Concentration dynamics in lakes and reservoirs, studies using radioactive tracers

    International Nuclear Information System (INIS)

    Gilath, C.

    1979-01-01

    The concentration dynamics in lakes and reservoirs through which water flows can be investigated by injecting a pulse of radioactive tracer and measuring the response at the outlet or any other point of interest inside the lake. The methodology developed for this Kind of investigation is presented. It was found that concentration dynamics in shallow reservoirs can be described by a model consisting of a time delay in series with one or two time constants. Procedures for the determination of the volumes of these regions are presented for reservoirs considered as either constant or variable parameter systems. The flow pattern in the reservoirs was investigated by measuring the response of the concentration through the lake and was analyzed in relation to the prevailing wind conditions. Wind induced currents have a dominant influence on the flow pattern. (Author) [pt

  13. On a modified form of navier-stokes equations for three-dimensional flows.

    Science.gov (United States)

    Venetis, J

    2015-01-01

    A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

  14. CCC, Heat Flow and Mass Flow in Liquid Saturated Porous Media

    International Nuclear Information System (INIS)

    Mangold, D.C.; Lippmann, M.J.; Bodvarsson, G.S.

    1982-01-01

    1 - Description of problem or function: The numerical model CCC (conduction-convection-consolidation) solves the heat and mass flow equations for a fully, liquid-saturated, anisotropic porous medium and computes one-dimensional (vertical) consolidation of the simulated systems. The model has been applied to problems in the fields of geothermal reservoir engineering, aquifer thermal energy storage, well testing, radioactive waste isolation, and in situ coal combustion. The code has been validated against analytic solutions for fluid and heat flow, and against a field experiment for underground storage of hot water. 2 - Method of solution: The model employs the Integrated Finite Difference Method (IFDM) in discretizing the saturated porous medium and formulating the governing equations. The sets of equations are sol- ved by an iterative solution technique. The vertical deformation of the medium is calculated using the one-dimensional consolidation theory of Terzaghi. 3 - Restrictions on the complexity of the problem: Maximum of 12 materials. It is assumed that: (a) Darcy's law adequately describes fluid movement through fractured and porous media. (b) The rock and fluid are in thermal equilibrium at any given time. (c) Energy changes due to the fluid compressibility, acceleration and viscous dissipation are neglected. (d) One-dimensional consolidation theory adequately describes the vertical deformation of the medium

  15. Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

    Science.gov (United States)

    Ladiges, Daniel R.; Sader, John E.

    2018-05-01

    Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.

  16. Development of two-group interfacial area transport equation for confined flow-1. Modeling of bubble interactions

    International Nuclear Information System (INIS)

    Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

    2003-01-01

    This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)

  17. Chemical-potential flow equations for graphene with Coulomb interactions

    Science.gov (United States)

    Fräßdorf, Christian; Mosig, Johannes E. M.

    2018-06-01

    We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results are consistent with a charge carrier-independent Fermi velocity v (k ) for small densities n ≲k2/π , supporting the comparison of the zero-density fRG calculation of Bauer et al. [Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409], with the experiment of Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].

  18. Characteristics and stability analyses of transient one-dimensional two-phase flow equations and their finite difference approximations

    International Nuclear Information System (INIS)

    Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W.; Hughes, E.D.

    1975-01-01

    Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

  19. Behaviour of gas production from type 3 hydrate reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Pooladi-Darvish, M. [Calgary Univ., AB (Canada). Dept. of Chemical and Petroleum Engineering]|[Fekete Associates Inc., Calgary, AB (Canada); Zatsepina, O. [Calgary Univ., AB (Canada). Dept. of Chemical and Petroleum Engineering; Hong, H. [Fekete Associates Inc., Calgary, AB (Canada)

    2008-07-01

    The possible role of gas hydrates as a potential energy resource was discussed with particular reference to methods for estimating the rate of gas production from hydrate reservoirs under different operating conditions. This paper presented several numerical simulations studies of gas production from type 3 hydrate reservoirs in 1-D and 2-D geometries. Type 3 reservoirs include gas production from hydrate-reservoirs that lie totally within the hydrate stability zone and are sandwiched by impermeable layers on top and bottom. The purpose of this study was to better understand hydrate decomposition by depressurization. The study questioned whether 1-D modeling of type 3 hydrate reservoirs is a reasonable approximation. It also determined whether gas rate increases or decreases with time. The important reservoir characteristics for determining the rate of gas production were identified. Last, the study determined how competition between fluid and heat flow affects hydrate decomposition. This paper also described the relation and interaction between the heat and fluid flow mechanisms in depressurization of type 3 hydrate reservoirs. All results of 1-D and 2-D numerical simulation and analyses were generated using the STARS simulator. It was shown that the rate of gas production depends on the initial pressure/temperature conditions and permeability of the hydrate bearing formation. A high peak rate may be achieved under favourable conditions, but this peak rate is obtained after an initial period where the rate of gas production increases with time. The heat transfer in the direction perpendicular to the direction of fluid flow is significant, requiring 2D modeling. The hydraulic diffusivity is low because of the low permeability of hydrate-bearing formations. This could result in competition between heat and fluid flow, thereby influencing the behaviour of decomposition. 6 refs., 3 tabs., 12 figs.

  20. Numerical modelling of two phase flow with hysteresis in heterogeneous porous media

    Energy Technology Data Exchange (ETDEWEB)

    Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)

    2008-07-01

    Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)

  1. Governing equations for a seriated continuum: an unequal velocity model for two-phase flow

    International Nuclear Information System (INIS)

    Solbrig, C.W.; Hughes, E.D.

    1975-05-01

    The description of the flow of two-phase fluids is important in many engineering devices. Unexpected transient conditions which occur in these devices cannot, in general, be treated with single-component momentum equations. Instead, the use of momentum equations for each phase is necessary in order to describe the varied transient situations which can occur. These transient conditions can include phases moving in the opposite directions, such as steam moving upward and liquid moving downward, as well as phases moving in the same direction. The derivation of continuity and momentum equations for each phase and an overall energy equation for the mixture are presented. Terms describing interphase forces are described. A seriated (series of) continuum is distinguished from an interpenetrating medium by the representation of interphase friction with velocity differences in the former and velocity gradients in the latter. The seriated continuum also considers imbedded stationary solid surfaces such as occur in nuclear reactor cores. These stationary surfaces are taken into account with source terms. Sufficient constitutive equations are presented to form a complete set of equations. Methods are presented to show that all these coefficients are determinable from microscopic models and well known experimental results. Comparison of the present deviation with previous work is also given. The equations derived here may also be employed in certain multiphase, multicomponent flow applications. (U.S.)

  2. Multi-zone coupling productivity of horizontal well fracturing with complex fracture networks in shale gas reservoirs

    Directory of Open Access Journals (Sweden)

    Weiyao Zhu

    2018-02-01

    Full Text Available In this paper, a series of specific studies were carried out to investigate the complex form of fracture networks and figure out the multi-scale flowing laws of nano/micro pores–complex fracture networks–wellbore during the development of shale reservoirs by means of horizontal well fracturing. First, hydraulic fractures were induced by means of Brazilian splitting tests. Second, the forms of the hydraulic fractures inside the rock samples were observed by means of X-ray CT scanning to measure the opening of hydraulic fractures. Third, based on the multi-scale unified flowing model, morphological description of fractures and gas flowing mechanism in the matrix–complex fracture network–wellbore, the productivity equation of single-stage horizontal well fracturing which includes diffusion, slipping and desorption was established. And fourthly, a productivity prediction model of horizontal well multi-stage fracturing in the shale reservoir was established considering the interference between the multi-stage fracturing zones and the pressure drop in the horizontal wellbore. The following results were obtained. First, hydraulic fractures are in the form of a complex network. Second, the measured opening of hydraulic fractures is in the range of 4.25–453 μm, averaging 112 μm. Third, shale gas flowing in different shapes of fracture networks follows different nonlinear flowing laws. Forth, as the fracture density in the strongly stimulated zones rises and the distribution range of the hydraulic fractures in strongly/weakly stimulated zones enlarges, gas production increases gradually. As the interference occurs in the flowing zones of fracture networks between fractured sections, the increasing amplitude of gas production rates decreases. Fifth, when the length of a simulated horizontal well is 1500 m and the half length of a fracture network in the strongly stimulated zone is 100 m, the productivity effect of stage 10 fracturing is the

  3. Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

    Science.gov (United States)

    Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

    2015-04-01

    This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive

  4. Coupled Thermo-Hydro-Mechanical-Chemical Modeling of Water Leak-Off Process during Hydraulic Fracturing in Shale Gas Reservoirs

    Directory of Open Access Journals (Sweden)

    Fei Wang

    2017-11-01

    Full Text Available The water leak-off during hydraulic fracturing in shale gas reservoirs is a complicated transport behavior involving thermal (T, hydrodynamic (H, mechanical (M and chemical (C processes. Although many leak-off models have been published, none of the models fully coupled the transient fluid flow modeling with heat transfer, chemical-potential equilibrium and natural-fracture dilation phenomena. In this paper, a coupled thermo-hydro-mechanical-chemical (THMC model based on non-equilibrium thermodynamics, hydrodynamics, thermo-poroelastic rock mechanics, and non-isothermal chemical-potential equations is presented to simulate the water leak-off process in shale gas reservoirs. The THMC model takes into account a triple-porosity medium, which includes hydraulic fractures, natural fractures and shale matrix. The leak-off simulation with the THMC model involves all the important processes in this triple-porosity medium, including: (1 water transport driven by hydraulic, capillary, chemical and thermal osmotic convections; (2 gas transport induced by both hydraulic pressure driven convection and adsorption; (3 heat transport driven by thermal convection and conduction; and (4 natural-fracture dilation considered as a thermo-poroelastic rock deformation. The fluid and heat transport, coupled with rock deformation, are described by a set of partial differential equations resulting from the conservation of mass, momentum, and energy. The semi-implicit finite-difference algorithm is proposed to solve these equations. The evolution of pressure, temperature, saturation and salinity profiles of hydraulic fractures, natural fractures and matrix is calculated, revealing the multi-field coupled water leak-off process in shale gas reservoirs. The influences of hydraulic pressure, natural-fracture dilation, chemical osmosis and thermal osmosis on water leak-off are investigated. Results from this study are expected to provide a better understanding of the

  5. Fracture Characterization in Enhanced Geothermal Systems by Wellbore and Reservoir Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Horne, Roland N.; Li, Kewen; Alaskar, Mohammed; Ames, Morgan; Co, Carla; Juliusson, Egill; Magnusdottir, Lilja

    2012-06-30

    This report highlights the work that was done to characterize fractured geothermal reservoirs using production data. That includes methods that were developed to infer characteristic functions from production data and models that were designed to optimize reinjection scheduling into geothermal reservoirs, based on these characteristic functions. The characterization method provides a robust way of interpreting tracer and flow rate data from fractured reservoirs. The flow-rate data are used to infer the interwell connectivity, which describes how injected fluids are divided between producers in the reservoir. The tracer data are used to find the tracer kernel for each injector-producer connection. The tracer kernel describes the volume and dispersive properties of the interwell flow path. A combination of parametric and nonparametric regression methods were developed to estimate the tracer kernels for situations where data is collected at variable flow-rate or variable injected concentration conditions. The characteristic functions can be used to calibrate thermal transport models, which can in turn be used to predict the productivity of geothermal systems. This predictive model can be used to optimize injection scheduling in a geothermal reservoir, as is illustrated in this report.

  6. Improved coupling of the conduction and flow equations in TRAC

    International Nuclear Information System (INIS)

    Addessio, F.L.

    1981-01-01

    Recent nuclear-reactor-systems modeling efforts have been directed toward the development of computer codes capable of simulating transients in short computational times. For this reason, a stability enhancing two-stem method (SETS) has been applied to the two-phase flow equations in the Transient Reactor Analysis Code (TRAC) allowing the Courant limit to be violated. Unfortunately, the coupling between the wall conduction equation and the fluid-dynamics equations is performed semi-implicitly, that is, the wall-heat transfer term, is evaluated using old-time heat-transfer coefficients and wall temperatures and new-time coolant temperatures. This coupling may lead to numerical instabilities at large time steps because of large variations in the heat-transfer coefficient in certain regimes of the boiling curve. Consequently, simply using new-time wall temperatures is not sufficient. A technique that also incorporates new-time heat-transfer coefficients must be used

  7. Simulation of Reservoir Sediment Flushing of the Three Gorges Reservoir Using an Artificial Neural Network

    Directory of Open Access Journals (Sweden)

    Xueying Li

    2016-05-01

    Full Text Available Reservoir sedimentation and its effect on the environment are the most serious world-wide problems in water resources development and utilization today. As one of the largest water conservancy projects, the Three Gorges Reservoir (TGR has been controversial since its demonstration period, and sedimentation is the major concern. Due to the complex physical mechanisms of water and sediment transport, this study adopts the Error Back Propagation Training Artificial Neural Network (BP-ANN to analyze the relationship between the sediment flushing efficiency of the TGR and its influencing factors. The factors are determined by the analysis on 1D unsteady flow and sediment mathematical model, mainly including reservoir inflow, incoming sediment concentration, reservoir water level, and reservoir release. Considering the distinguishing features of reservoir sediment delivery in different seasons, the monthly average data from 2003, when the TGR was put into operation, to 2011 are used to train, validate, and test the BP-ANN model. The results indicate that, although the sample space is quite limited, the whole sediment delivery process can be schematized by the established BP-ANN model, which can be used to help sediment flushing and thus decrease the reservoir sedimentation.

  8. Geomechanical production optimization in faulted and fractured reservoirs

    NARCIS (Netherlands)

    Heege, J.H. ter; Pizzocolo, F.; Osinga, S.; Veer, E.F. van der

    2016-01-01

    Faults and fractures in hydrocarbon reservoirs are key to some major production issues including (1) varying productivity of different well sections due to intersection of preferential flow paths with the wellbore, (2) varying hydrocarbon column heights in different reservoir compartments due to

  9. High resolution solutions of the Euler equations for vortex flows

    International Nuclear Information System (INIS)

    Murman, E.M.; Powell, K.G.; Rizzi, A.; Tel Aviv Univ., Israel)

    1985-01-01

    Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research. 16 references

  10. Pore-scale mechanisms of gas flow in tight sand reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Silin, D.; Kneafsey, T.J.; Ajo-Franklin, J.B.; Nico, P.

    2010-11-30

    Tight gas sands are unconventional hydrocarbon energy resource storing large volume of natural gas. Microscopy and 3D imaging of reservoir samples at different scales and resolutions provide insights into the coaredo not significantly smaller in size than conventional sandstones, the extremely dense grain packing makes the pore space tortuous, and the porosity is small. In some cases the inter-granular void space is presented by micron-scale slits, whose geometry requires imaging at submicron resolutions. Maximal Inscribed Spheres computations simulate different scenarios of capillary-equilibrium two-phase fluid displacement. For tight sands, the simulations predict an unusually low wetting fluid saturation threshold, at which the non-wetting phase becomes disconnected. Flow simulations in combination with Maximal Inscribed Spheres computations evaluate relative permeability curves. The computations show that at the threshold saturation, when the nonwetting fluid becomes disconnected, the flow of both fluids is practically blocked. The nonwetting phase is immobile due to the disconnectedness, while the permeability to the wetting phase remains essentially equal to zero due to the pore space geometry. This observation explains the Permeability Jail, which was defined earlier by others. The gas is trapped by capillarity, and the brine is immobile due to the dynamic effects. At the same time, in drainage, simulations predict that the mobility of at least one of the fluids is greater than zero at all saturations. A pore-scale model of gas condensate dropout predicts the rate to be proportional to the scalar product of the fluid velocity and pressure gradient. The narrowest constriction in the flow path is subject to the highest rate of condensation. The pore-scale model naturally upscales to the Panfilov's Darcy-scale model, which implies that the condensate dropout rate is proportional to the pressure gradient squared. Pressure gradient is the greatest near the

  11. Global mass conservation method for dual-continuum gas reservoir simulation

    KAUST Repository

    Wang, Yi; Sun, Shuyu; Gong, Liang; Yu, Bo

    2018-01-01

    In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference method. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

  12. Global mass conservation method for dual-continuum gas reservoir simulation

    KAUST Repository

    Wang, Yi

    2018-03-17

    In this paper, we find that the numerical simulation of gas flow in dual-continuum porous media may generate unphysical or non-robust results using regular finite difference method. The reason is the unphysical mass loss caused by the gas compressibility and the non-diagonal dominance of the discretized equations caused by the non-linear well term. The well term contains the product of density and pressure. For oil flow, density is independent of pressure so that the well term is linear. For gas flow, density is related to pressure by the gas law so that the well term is non-linear. To avoid these two problems, numerical methods are proposed using the mass balance relation and the local linearization of the non-linear source term to ensure the global mass conservation and the diagonal dominance of discretized equations in the computation. The proposed numerical methods are successfully applied to dual-continuum gas reservoir simulation. Mass conservation is satisfied while the computation becomes robust. Numerical results show that the location of the production well relative to the large-permeability region is very sensitive to the production efficiency. It decreases apparently when the production well is moved from the large-permeability region to the small-permeability region, even though the well is very close to the interface of the two regions. The production well is suggested to be placed inside the large-permeability region regardless of the specific position.

  13. Energy dissipation by submarine obstacles during landslide impact on reservoir - potentially avoiding catastrophic dam collapse

    Science.gov (United States)

    Kafle, Jeevan; Kattel, Parameshwari; Mergili, Martin; Fischer, Jan-Thomas; Tuladhar, Bhadra Man; Pudasaini, Shiva P.

    2017-04-01

    Dense geophysical mass flows such as landslides, debris flows and debris avalanches may generate super tsunami waves as they impact water bodies such as the sea, hydraulic reservoirs or mountain lakes. Here, we apply a comprehensive and general two-phase, physical-mathematical mass flow model (Pudasaini, 2012) that consists of non-linear and hyperbolic-parabolic partial differential equations for mass and momentum balances, and present novel, high-resolution simulation results for two-phase flows, as a mixture of solid grains and viscous fluid, impacting fluid reservoirs with obstacles. The simulations demonstrate that due to the presence of different obstacles in the water body, the intense flow-obstacle-interaction dramatically reduces the flow momentum resulting in the rapid energy dissipation around the obstacles. With the increase of obstacle height overtopping decreases but, the deflection and capturing (holding) of solid mass increases. In addition, the submarine solid mass is captured by the multiple obstacles and the moving mass decreases both in amount and speed as each obstacle causes the flow to deflect into two streams and also captures a portion of it. This results in distinct tsunami and submarine flow dynamics with multiple surface water and submarine debris waves. This novel approach can be implemented in open source GIS modelling framework r.avaflow, and be applied in hazard mitigation, prevention and relevant engineering or environmental tasks. This might be in particular for process chains, such as debris impacts in lakes and subsequent overtopping. So, as the complex flow-obstacle-interactions strongly and simultaneously dissipate huge energy at impact such installations potentially avoid great threat against the integrity of the dam. References: Pudasaini, S. P. (2012): A general two-phase debris flow model. J. Geophys. Res. 117, F03010, doi: 10.1029/ 2011JF002186.

  14. Stochastic partial differential equations a modeling, white noise functional approach

    CERN Document Server

    Holden, Helge; Ubøe, Jan; Zhang, Tusheng

    1996-01-01

    This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre­ sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in r...

  15. Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

    Science.gov (United States)

    Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

  16. The Ardross reservoir gridblock analogue: Sedimentology, statistical representivity, and flow upscaling

    Energy Technology Data Exchange (ETDEWEB)

    Ringrose, P.; Pickup, G.; Jensen, J. [Heriot-Watt Univ., Edinburgh (United Kingdom)] [and others

    1997-08-01

    We have used a reservoir gridblock-sized outcrop (10m by 100m) of fluvio-deltaic sandstones to evaluate the importance of internal heterogeneity for a hypothetical waterflood displacement process. Using a dataset based on probe permeameter measurements taken from two vertical transacts representing {open_quotes}wells{close_quotes} (5cm sampling) and one {open_quotes}core{close_quotes} sample (exhaustive 1mm-spaced sampling), we evaluate the permeability variability at different lengthscales, the correlation characteristics (structure of the variogram, function), and larger-scale trends. We then relate these statistical measures to the sedimentology. We show how the sediment architecture influences the effective tensor permeability at the lamina and bed scale, and then calculate the effective relative permeability functions for a waterflood. We compare the degree of oil recovery from the formation: (a) using averaged borehole data and no geological structure, and (b) modelling the sediment architecture of the interwell volume using mixed stochastic/deterministic methods. We find that the sediment architecture has an important effect on flow performance, mainly due to bedscale capillary trapping and a consequent reduction in the effective oil mobility. The predicted oil recovery differs by 18% when these small-scale effects are included in the model. Traditional reservoir engineering methods, using averages permeability values, only prove acceptable in high-permeability and low-heterogeneity zones. The main outstanding challenge, represented by this illustration of sub-gridblock scale heterogeneity, is how to capture the relevant geological structure along with the inherent geo-statistical variability. An approach to this problem is proposed.

  17. Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

    Science.gov (United States)

    Di Nucci, Carmine

    2018-05-01

    This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

  18. Physical Aspects in Upscaling of Fractured Reservoirs and Improved Oil Recovery Prediction

    NARCIS (Netherlands)

    Salimi, H.

    2010-01-01

    This thesis is concerned with upscaled models for waterflooded naturally fractured reservoirs (NFRs). Naturally fractured petroleum reservoirs provide over 20% of the world’s oil reserves and production. From the fluid-flow point of view, a fractured reservoir is defined as a reservoir in which a

  19. Loop Heat Pipe Temperature Oscillation Induced by Gravity Assist and Reservoir Heating

    Science.gov (United States)

    Ku, Jentung; Garrison, Matt; Patel, Deepak; Robinson, Frank; Ottenstein, Laura

    2015-01-01

    The Laser Thermal Control System (LCTS) for the Advanced Topographic Laser Altimeter System (ATLAS) to be installed on NASA's Ice, Cloud, and Land Elevation Satellite (ICESat-2) consists of a constant conductance heat pipe and a loop heat pipe (LHP) with an associated radiator. During the recent thermal vacuum testing of the LTCS where the LHP condenser/radiator was placed in a vertical position above the evaporator and reservoir, it was found that the LHP reservoir control heater power requirement was much higher than the analytical model had predicted. Even with the control heater turned on continuously at its full power, the reservoir could not be maintained at its desired set point temperature. An investigation of the LHP behaviors found that the root cause of the problem was fluid flow and reservoir temperature oscillations, which led to persistent alternate forward and reversed flow along the liquid line and an imbalance between the vapor mass flow rate in the vapor line and liquid mass flow rate in the liquid line. The flow and temperature oscillations were caused by an interaction between gravity and reservoir heating, and were exacerbated by the large thermal mass of the instrument simulator which modulated the net heat load to the evaporator, and the vertical radiator/condenser which induced a variable gravitational pressure head. Furthermore, causes and effects of the contributing factors to flow and temperature oscillations intermingled.

  20. Mathematical well-posedness of a two-fluid equations for bubbly two-phase flows

    International Nuclear Information System (INIS)

    Okawa, Tomio; Kataoka, Isao

    2000-01-01

    It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)

  1. SIMULATION OF SEDIMENT TRANSPORT IN THE JEZIORO KOWALSKIE RESERVOIR LOCATED IN THE GLOWNA RIVER

    Directory of Open Access Journals (Sweden)

    Joanna Jaskuła

    2015-07-01

    Full Text Available The purpose of the presented research is the analysis of bed elevation changes caused by sediment accumulation in the Jezioro Kowalskie reservoir. The Jezioro Kowalskie reservoir is a two stage reservoir constructed in such a way that the upper preliminary zone is separated from the main part of the reservoir. The split of the reservoir parts is done with a small pre-dam, located in Jerzykowo town. The analysis of such a construction impact on changes of bed elevations in the reservoir in different flow conditions is presented. The HEC-RAS 5.0 Beta model is used for simulations. The sediment transport intensity is calculated from England-Hansen and Meyer-Peter and Muller formulae. The results showed the processes of sediment accumulation and slight erosion occuring in the preliminary zone of the reservoir. The choice of the flow intensity does not have a huge importance. Similar results are obtained for low as well as high flows. The results confirm, that two stage construction with separated preliminary zone is effective method preventing from the sedimentation of the reservoir.

  2. Reservoir Characterization using geostatistical and numerical modeling in GIS with noble gas geochemistry

    Science.gov (United States)

    Vasquez, D. A.; Swift, J. N.; Tan, S.; Darrah, T. H.

    2013-12-01

    The integration of precise geochemical analyses with quantitative engineering modeling into an interactive GIS system allows for a sophisticated and efficient method of reservoir engineering and characterization. Geographic Information Systems (GIS) is utilized as an advanced technique for oil field reservoir analysis by combining field engineering and geological/geochemical spatial datasets with the available systematic modeling and mapping methods to integrate the information into a spatially correlated first-hand approach in defining surface and subsurface characteristics. Three key methods of analysis include: 1) Geostatistical modeling to create a static and volumetric 3-dimensional representation of the geological body, 2) Numerical modeling to develop a dynamic and interactive 2-dimensional model of fluid flow across the reservoir and 3) Noble gas geochemistry to further define the physical conditions, components and history of the geologic system. Results thus far include using engineering algorithms for interpolating electrical well log properties across the field (spontaneous potential, resistivity) yielding a highly accurate and high-resolution 3D model of rock properties. Results so far also include using numerical finite difference methods (crank-nicholson) to solve for equations describing the distribution of pressure across field yielding a 2D simulation model of fluid flow across reservoir. Ongoing noble gas geochemistry results will also include determination of the source, thermal maturity and the extent/style of fluid migration (connectivity, continuity and directionality). Future work will include developing an inverse engineering algorithm to model for permeability, porosity and water saturation.This combination of new and efficient technological and analytical capabilities is geared to provide a better understanding of the field geology and hydrocarbon dynamics system with applications to determine the presence of hydrocarbon pay zones (or

  3. Modification of Flow Stress Curves and Constitutive Equations During Hot Compression Deformation of 5083 Aluminum Alloy

    Directory of Open Access Journals (Sweden)

    FU Ping

    2017-08-01

    Full Text Available The flow stress behavior of 5083 aluminum alloy was investigated under hot compression deformation at 523-723K,strain rates of 0.01-10s-1 and true strains of 0-0.7 with Gleeble-3800 thermal simulator. Based on the heat transfer effect on alloy deformation heat effect, the flow stress curves were corrected. The results show that influence of heat conduction can not be neglected and becomes more obvious with the increase of true strain. The corrected flow stress has little influence on the peak stress, but the steady flow stress softening trends to be diminished to some degree. The flow stress can be predicted by the Zener-Hollomon parameters in the constitutive equation. The corrected measured value exhibits a good agreement with the flow stress predicted by the constitutive equation, and the average relative error is only 5.21%.

  4. Field differential equations for a potential flow from a Hamilton type variational principle

    International Nuclear Information System (INIS)

    Fierros Palacios, A.

    1992-01-01

    The same theoretical frame that was used to solve the problem of the field equations for a viscous fluid is utilized in this work. The purpose is to obtain the differential field equations for a potential flow from the Lagrangian formalism as in classical field theory. An action functional is introduced as a space-time integral over a region of three-dimensional Euclidean space, of a Lagrangian density as a function of certain field variables. A Hamilton type extremum action principle is postulated with adequate boundary conditions, and a set of differential field equations is derived. A particular Lagrangian density of the T-V type leads to the wave equation for the velocity potential. (Author)

  5. Centralized versus distributed reservoirs: an investigation of their implications on environmental flows and sustainable water resources management

    Directory of Open Access Journals (Sweden)

    N. Eriyagama

    2018-06-01

    Full Text Available Storage of surface water is widely regarded as a form of insurance against rainfall variability. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The issues of optimal size, placement and the number of reservoirs in a river basin – which maximizes sustainable benefits from storage – remain subjects for debate. This study examines the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. The study produced multiple surface storage development pathways for the basin under different scenarios of environmental flow (EF releases and reservoir network configurations. The EF scenarios ranged from zero to very healthy releases. It is shown that if the middle ground between the two extreme EF scenarios is considered, the theoretical maximum safe yield from surface storage is about 65–70 % of the mean annual runoff (MAR of the basin. It is also identified that although distribution of reservoirs in the river network reduces the cumulative yield from the basin, this cumulative yield is maximized if the ratio among the storage capacities placed in each sub drainage basin is equivalent to the ratio among their MAR. The study suggests a framework to identify drainage regions having higher surface storage potential, to plan for the right distribution of storage capacity within a river basin, as well as to plan for EF allocations.

  6. Centralized versus distributed reservoirs: an investigation of their implications on environmental flows and sustainable water resources management

    Science.gov (United States)

    Eriyagama, Nishadi; Smakhtin, Vladimir; Udamulla, Lakshika

    2018-06-01

    Storage of surface water is widely regarded as a form of insurance against rainfall variability. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The issues of optimal size, placement and the number of reservoirs in a river basin - which maximizes sustainable benefits from storage - remain subjects for debate. This study examines the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. The study produced multiple surface storage development pathways for the basin under different scenarios of environmental flow (EF) releases and reservoir network configurations. The EF scenarios ranged from zero to very healthy releases. It is shown that if the middle ground between the two extreme EF scenarios is considered, the theoretical maximum safe yield from surface storage is about 65-70 % of the mean annual runoff (MAR) of the basin. It is also identified that although distribution of reservoirs in the river network reduces the cumulative yield from the basin, this cumulative yield is maximized if the ratio among the storage capacities placed in each sub drainage basin is equivalent to the ratio among their MAR. The study suggests a framework to identify drainage regions having higher surface storage potential, to plan for the right distribution of storage capacity within a river basin, as well as to plan for EF allocations.

  7. Flow behavior of N2 huff and puff process for enhanced oil recovery in tight oil reservoirs.

    Science.gov (United States)

    Lu, Teng; Li, Zhaomin; Li, Jian; Hou, Dawei; Zhang, Dingyong

    2017-11-16

    In the present work, the potential of N 2 huff and puff process to enhance the recovery of tight oil reservoir was evaluated. N 2 huff and puff experiments were performed in micromodels and cores to investigate the flow behaviors of different cycles. The results showed that, in the first cycle, N 2 was dispersed in the oil, forming the foamy oil flow. In the second cycle, the dispersed gas bubbles gradually coalesced into the continuous gas phase. In the third cycle, N 2 was produced in the form of continuous gas phase. The results from the coreflood tests showed that, the primary recovery was only 5.32%, while the recoveries for the three N 2 huff and puff cycles were 15.1%, 8.53% and 3.22%, respectively.The recovery and the pressure gradient in the first cycle were high. With the increase of huff and puff cycles, and the oil recovery and the pressure gradient rapidly decreased. The oil recovery of N 2 huff and puff has been found to increase as the N 2 injection pressure and the soaking time increased. These results showed that, the properly designed and controlled N 2 huff and puff process can lead to enhanced recovery of tight oil reservoirs.

  8. Balance of liquid-phase turbulence kinetic energy equation for bubble-train flow

    International Nuclear Information System (INIS)

    Ilic, Milica; Woerner, Martin; Cacuci, Dan Gabriel

    2004-01-01

    In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-ε and the two-phase k-l model is evaluated. (author)

  9. Generation of hybrid meshes for the simulation of petroleum reservoirs; Generation de maillages hybrides pour la simulation de reservoirs petroliers

    Energy Technology Data Exchange (ETDEWEB)

    Balaven-Clermidy, S.

    2001-12-01

    Oil reservoir simulations study multiphase flows in porous media. These flows are described and evaluated through numerical schemes on a discretization of the reservoir domain. In this thesis, we were interested in this spatial discretization and a new kind of hybrid mesh has been proposed where the radial nature of flows in the vicinity of wells is directly taken into account in the geometry. Our modular approach described wells and their drainage area through radial circular meshes. These well meshes are inserted in a structured reservoir mesh (a Corner Point Geometry mesh) made up with hexahedral cells. Finally, in order to generate a global conforming mesh, proper connections are realized between the different kinds of meshes through unstructured transition ones. To compute these transition meshes that we want acceptable in terms of finite volume methods, an automatic method based on power diagrams has been developed. Our approach can deal with a homogeneous anisotropic medium and allows the user to insert vertical or horizontal wells as well as secondary faults in the reservoir mesh. Our work has been implemented, tested and validated in 2D and 2D1/2. It can also be extended in 3D when the geometrical constraints are simplicial ones: points, segments and triangles. (author)

  10. Multiphase flow and transport in porous media

    Science.gov (United States)

    Parker, J. C.

    1989-08-01

    Multiphase flow and transport of compositionally complex fluids in geologic media is of importance in a number of applied problems which have major social and economic effects. In petroleum reservoir engineering, efficient recovery of energy reserves is the principal goal. Unfortunately, some of these hydrocarbons and other organic chemicals often find their way unwanted into the soils and groundwater supplies. Removal in the latter case is predicated on ensuring the public health and safety. In this paper, principles of modeling fluid flow in systems containing up to three fluid phases (namely, water, air, and organic liquid) are described. Solution of the governing equations for multiphase flow requires knowledge of functional relationships between fluid pressures, saturations, and permeabilities which may be formulated on the basis of conceptual models of fluid-porous media interactions. Mechanisms of transport in multicomponent multiphase systems in which species may partition between phases are also described, and the governing equations are presented for the case in which local phase equilibrium may be assumed. A number of hypothetical numerical problems are presented to illustrate the physical behavior of systems in which multiphase flow and transport arise.

  11. Three-Phase Flow and Capillarity in Porous Media

    Energy Technology Data Exchange (ETDEWEB)

    Helset, H.M.

    1996-06-01

    Multiphase flow occurs in most production operations on the reservoir rock of an oil field. Three-phase flow occurs in many oil recovery processes, such as gas or water alternating gas injection into water flooded reservoirs, thermal oil recovery and surfactant flooding. In this doctoral thesis, three-phase flow in porous media is modeled using the method of characteristics and simple wave theory. The general mathematical methods are used to model different flow processes: secondary migration of hydrocarbons, gravity segregated three-phase flow, and displacement experiments for relative permeabilities. The main conclusions from applying the methods to the migration process through a water-saturated carrier bed to a partially permeable seal are: (1) the three-phase solutions are generally dominated by the very low gas viscosity and gas density, (2) countercurrent flow and interference between the gas and oil mobilities can lead to trapping in situations where the permeability contrast between the seal and the carrier bed is insufficient to trap oil alone, (3) zones in which pressures exceed those from hydrostatic gradients (overpressured zones) exist even when the permeability contrast between the seal and the carrier bed is modest. The discussion of gravity segregated flow identifies stable displacement fronts, which usually occur only for a single value of the gas-water injection ratio. The new method developed for interpreting displacement experiments, with capillary pressure included, is based on the travelling wave solution of the flow equations. 185 refs., 69 figs., 5 tabs.

  12. Determination of dilution factors for discharge of aluminum-containing wastes by public water-supply treatment facilities into lakes and reservoirs in Massachusetts

    Science.gov (United States)

    Colman, John A.; Massey, Andrew J.; Brandt, Sara L.

    2011-09-16

    Dilution of aluminum discharged to reservoirs in filter-backwash effluents at water-treatment facilities in Massachusetts was investigated by a field study and computer simulation. Determination of dilution is needed so that permits for discharge ensure compliance with water-quality standards for aquatic life. The U.S. Environmental Protection Agency chronic standard for aluminum, 87 micrograms per liter (μg/L), rather than the acute standard, 750 μg/L, was used in this investigation because the time scales of chronic exposure (days) more nearly match rates of change in reservoir concentrations than do the time scales of acute exposure (hours).Whereas dilution factors are routinely computed for effluents discharged to streams solely on the basis of flow of the effluent and flow of the receiving stream, dilution determination for effluents discharged to reservoirs is more complex because (1), compared to streams, additional water is available for dilution in reservoirs during low flows as a result of reservoir flushing and storage during higher flows, and (2) aluminum removal in reservoirs occurs by aluminum sedimentation during the residence time of water in the reservoir. Possible resuspension of settled aluminum was not considered in this investigation. An additional concern for setting discharge standards is the substantial concentration of aluminum that can be naturally present in ambient surface waters, usually in association with dissolved organic carbon (DOC), which can bind aluminum and keep it in solution.A method for dilution determination was developed using a mass-balance equation for aluminum and considering sources of aluminum from groundwater, surface water, and filter-backwash effluents and losses caused by sedimentation, water withdrawal, and spill discharge from the reservoir. The method was applied to 13 reservoirs. Data on aluminum and DOC concentrations in reservoirs and influent water were collected during the fall of 2009. Complete

  13. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir

    OpenAIRE

    Shams Bilal; Yao Jun; Zhang Kai; Zhang Lei

    2017-01-01

    Gas condensate reservoirs usually exhibit complex flow behaviors because of propagation response of pressure drop from the wellbore into the reservoir. When reservoir pressure drops below the dew point in two phase flow of gas and condensate, the accumulation of large condensate amount occurs in the gas condensate reservoirs. Usually, the saturation of condensate accumulation in volumetric gas condensate reservoirs is lower than the critical condensate saturation that causes trapping of large...

  14. MAPPING OF RESERVOIR PROPERTIES AND FACIES THROUGH INTEGRATION OF STATIC AND DYNAMIC DATA

    Energy Technology Data Exchange (ETDEWEB)

    Albert C. Reynolds; Dean S. Oliver; Fengjun Zhang; Yannong Dong; Jan Arild Skjervheim; Ning Liu

    2003-01-01

    Knowledge of the distribution of permeability and porosity in a reservoir is necessary for the prediction of future oil production, estimation of the location of bypassed oil, and optimization of reservoir management. But while the volume of data that can potentially provide information on reservoir architecture and fluid distributions has increased enormously in the past decade, it is not yet possible to make use of all the available data in an integrated fashion. While it is relatively easy to generate plausible reservoir models that honor static data such as core, log, and seismic data, it is far more difficult to generate plausible reservoir models that honor dynamic data such as transient pressures, saturations, and flow rates. As a result, the uncertainty in reservoir properties is higher than it could be and reservoir management can not be optimized. The goal of this project is to develop computationally efficient automatic history matching techniques for generating geologically plausible reservoir models which honor both static and dynamic data. Solution of this problem is necessary for the quantification of uncertainty in future reservoir performance predictions and for the optimization of reservoir management. Facies (defined here as regions of relatively uniform petrophysical properties) are common features of all reservoirs. Because the flow properties of the various facies can vary greatly, knowledge of the location of facies boundaries is of utmost importance for the prediction of reservoir performance and for the optimization of reservoir management. When the boundaries between facies are fairly well known, but flow properties are poorly known, the average properties for all facies can be determined using traditional techniques. Traditional history matching honors dynamic data by adjusting petrophysical properties in large areas, but in the process of adjusting the reservoir model ignores the static data and often results in implausible reservoir

  15. Characterization of transient groundwater flow through a high arch dam foundation during reservoir impounding

    Directory of Open Access Journals (Sweden)

    Yifeng Chen

    2016-08-01

    Full Text Available Even though a large number of large-scale arch dams with height larger than 200 m have been built in the world, the transient groundwater flow behaviors and the seepage control effects in the dam foundations under difficult geological conditions are rarely reported. This paper presents a case study on the transient groundwater flow behaviors in the rock foundation of Jinping I double-curvature arch dam, the world's highest dam of this type to date that has been completed. Taking into account the geological settings at the site, an inverse modeling technique utilizing the time series measurements of both hydraulic head and discharge was adopted to back-calculate the permeability of the foundation rocks, which effectively improves the uniqueness and reliability of the inverse modeling results. The transient seepage flow in the dam foundation during the reservoir impounding was then modeled with a parabolic variational inequality (PVI method. The distribution of pore water pressure, the amount of leakage, and the performance of the seepage control system in the dam foundation during the entire impounding process were finally illustrated with the numerical results.

  16. SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method

    International Nuclear Information System (INIS)

    Amsden, A.A.; Ruppel, H.M.

    1991-01-01

    1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which

  17. PREDICTION OF RESERVOIR FLOW RATE OF DEZ DAM BY THE PROBABILITY MATRIX METHOD

    Directory of Open Access Journals (Sweden)

    Mohammad Hashem Kanani

    2012-12-01

    Full Text Available The data collected from the operation of existing storage reservoirs, could offer valuable information for the better allocation and management of fresh water rates for future use to mitigation droughts effect. In this paper the long-term Dez reservoir (IRAN water rate prediction is presented using probability matrix method. Data is analyzed to find the probability matrix of water rates in Dez reservoir based on the previous history of annual water entrance during the past and present years(40 years. The algorithm developed covers both, the overflow and non-overflow conditions in the reservoir. Result of this study shows that in non-overflow conditions the most exigency case is equal to 75%. This means that, if the reservoir is empty (the stored water is less than 100 MCM this year, it would be also empty by 75% next year. The stored water in the reservoir would be less than 300 MCM by 85% next year if the reservoir is empty this year. This percentage decreases to 70% next year if the water of reservoir is less than 300 MCM this year. The percentage also decreases to 5% next year if the reservoir is full this year. In overflow conditions the most exigency case is equal to 75% again. The reservoir volume would be less than 150 MCM by 90% next year, if it is empty this year. This percentage decreases to 70% if its water volume is less than 300 MCM and 55% if the water volume is less than 500 MCM this year. Result shows that too, if the probability matrix of water rates to a reservoir is multiplied by itself repeatedly; it converges to a constant probability matrix, which could be used to predict the long-term water rate of the reservoir. In other words, the probability matrix of series of water rates is changed to a steady probability matrix in the course of time, which could reflect the hydrological behavior of the watershed and could be easily used for the long-term prediction of water storage in the down stream reservoirs.

  18. Integrated Approach to Drilling Project in Unconventional Reservoir Using Reservoir Simulation

    Science.gov (United States)

    Stopa, Jerzy; Wiśniowski, Rafał; Wojnarowski, Paweł; Janiga, Damian; Skrzypaszek, Krzysztof

    2018-03-01

    Accumulation and flow mechanisms in unconventional reservoir are different compared to conventional. This requires a special approach of field management with drilling and stimulation treatments as major factor for further production. Integrated approach of unconventional reservoir production optimization assumes coupling drilling project with full scale reservoir simulation for determine best well placement, well length, fracturing treatment design and mid-length distance between wells. Full scale reservoir simulation model emulate a part of polish shale - gas field. The aim of this paper is to establish influence of technical factor for gas production from shale gas field. Due to low reservoir permeability, stimulation treatment should be direct towards maximizing the hydraulic contact. On the basis of production scenarios, 15 stages hydraulic fracturing allows boost gas production over 1.5 times compared to 8 stages. Due to the possible interference of the wells, it is necessary to determine the distance between the horizontal parts of the wells trajectories. In order to determine the distance between the wells allowing to maximize recovery factor of resources in the stimulated zone, a numerical algorithm based on a dynamic model was developed and implemented. Numerical testing and comparative study show that the most favourable arrangement assumes a minimum allowable distance between the wells. This is related to the volume ratio of the drainage zone to the total volume of the stimulated zone.

  19. The flow behavior and constitutive equation in isothermal compression of FGH4096-GH4133B dual alloy

    International Nuclear Information System (INIS)

    Liu, Yanhui; Yao, Zekun; Ning, Yongquan; Nan, Yang; Guo, Hongzhen; Qin, Chun; Shi, Zhifeng

    2014-01-01

    Highlights: • Hot compression behaviors of the FGH4096-GH4133B dual alloy were investigated. • Constitutive equation also represented deformation behavior of a dual alloy. • The effects of deformation activation energy on the microstructures were discussed. • Constitutive equation represented an accurate and precise estimate of flow stress. - Abstract: The electron beam welding of superalloy FGH4096 and GH4133B was conducted, and the cylindrical compression specimens were machined from the central part of the electron beam weldments. Isothermal compression tests were carried out on electron beam weldments FGH4096-GH4133B alloy at the temperatures of 1020–11140 °C (the nominal γ′-transus temperature is about 1080 °C) and the strain rates of 0.001–1.0 s −1 with the height reduction of 50%. True stress–true strain curves are sensitive to the deformation temperature and strain rate, and the flow stress decreases with the increasing deformation temperature and the decreasing strain rate. The true stress–true strain curves can indicate the intrinsic relationship between the flow stress and the thermal-dynamic behavior. The apparent activation energy of deformation at the strain of 0.6 was calculated to be 550 kJ/mol, and the apparent activation energy has a great effect on the microstructure. The constitutive equation that describes the flow stress as a function of strain rate and deformation temperature was proposed for modeling the hot deformation process of FGH4096-GH4133B electron beam weldments. The constitutive equation at the strain of 0.6 was established using the hyperbolic law. The relationship between the strain and the values of parameters was studied, and the cubic functions were built. The constitutive equation during the whole process can be obtained based on the parameters under different strains. Comparing the experimental flow stress and the calculated flow stress, the constitutive equation obtained in this paper can be very good

  20. Development of two-group interfacial area transport equation for confined flow-2. Model evaluation

    International Nuclear Information System (INIS)

    Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

    2003-01-01

    The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flow. The two-group IATE is evaluated in steady state, one-dimensional form. Also, since the experiments were performed under adiabatic, air-water two-phase flow conditions, the phase change effect is omitted in the evaluation. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes. (author)

  1. Mathematical and field analysis of longitudinal reservoir infill

    Science.gov (United States)

    Ke, W. T.; Capart, H.

    2016-12-01

    In reservoirs, severe problems are caused by infilled sediment deposits. In long term, the sediment accumulation reduces the capacity of reservoir storage and flood control benefits. In the short term, the sediment deposits influence the intakes of water-supply and hydroelectricity generation. For the management of reservoir, it is important to understand the deposition process and then to predict the sedimentation in reservoir. To investigate the behaviors of sediment deposits, we propose a one-dimensional simplified theory derived by the Exner equation to predict the longitudinal sedimentation distribution in idealized reservoirs. The theory models the reservoir infill geomorphic actions for three scenarios: delta progradation, near-dam bottom deposition, and final infill. These yield three kinds of self-similar analytical solutions for the reservoir bed profiles, under different boundary conditions. Three analytical solutions are composed by error function, complementary error function, and imaginary error function, respectively. The theory is also computed by finite volume method to test the analytical solutions. The theoretical and numerical predictions are in good agreement with one-dimensional small-scale laboratory experiment. As the theory is simple to apply with analytical solutions and numerical computation, we propose some applications to simulate the long-profile evolution of field reservoirs and focus on the infill sediment deposit volume resulting the uplift of near-dam bottom elevation. These field reservoirs introduced here are Wushe Reservoir, Tsengwen Reservoir, Mudan Reservoir in Taiwan, Lago Dos Bocas in Puerto Rico, and Sakuma Dam in Japan.

  2. Numerical Approach of a Water Flow in an Unsaturated Porous Medium by Coupling Between the Navier–Stokes and Darcy–Forchheimer Equations

    Directory of Open Access Journals (Sweden)

    Hami K.

    2017-12-01

    Full Text Available In the present research, simulations have been conducted to determine numerically the dynamic behaviour of the flow of underground water fed by a river. The basic equations governing the problem studied are those of Navier–Stokes equations of conservation of momentum (flows between pores, coupled by the Darcy–Forchheimer equations (flows within these pores. To understand the phenomena involved, we first study the impact of flow rate on the pressure and the filtration velocity in the underground medium, the second part is devoted to the calculation of the elevation effect of the river water on the flow behaviour in the saturated and unsaturated zone of the aquifer.

  3. Non-isothermal compositional gas flow during carbon dioxide storage and enhanced gas recovery

    DEFF Research Database (Denmark)

    Singh, Ashok; Böettcher, N.; Wang, W.

    2011-01-01

    In this work we present the conceptual modeling and the numerical scheme for carbon dioxide storage into nearly depleted gas reservoirs for enhanced gas recovery reasons. For this we develop non-isothermal compositional gas flow model. We used a combined monolithic / staggered coupling scheme...... to solve mass balance equation for the gaseous mixture with heat and fractional mass transport equations. Temperature change resulting from fluid expansion and viscous heat dissipation is included in heat transport in addition to advection and conduction. We have used a modified version of the Peng...

  4. A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

    International Nuclear Information System (INIS)

    Bakosi, J.; Franzese, P.; Boybeyi, Z.

    2008-01-01

    In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. In the vicinity of walls the flow is resolved by an elliptic relaxation technique down to the viscous sublayer, explicitly modeling the high anisotropy and inhomogeneity of the low-Reynolds-number wall region without damping or wall-functions. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (i.e., the mean pressure and the elliptic relaxation tensor) and to track particles. All three aspects regarding the grid make use of the finite element method employing the simplest linear shapefunctions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean (IECM) model is adopted. An adaptive algorithm to compute the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory

  5. Liquid oil production from shale gas condensate reservoirs

    Science.gov (United States)

    Sheng, James J.

    2018-04-03

    A process of producing liquid oil from shale gas condensate reservoirs and, more particularly, to increase liquid oil production by huff-n-puff in shale gas condensate reservoirs. The process includes performing a huff-n-puff gas injection mode and flowing the bottom-hole pressure lower than the dew point pressure.

  6. A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations

    International Nuclear Information System (INIS)

    Liu, Hongwei; Xu, Kun

    2007-01-01

    This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method

  7. Perturbative renormalization of composite operators via flow equations. Pt. 2

    International Nuclear Information System (INIS)

    Keller, G.; Kopper, C.

    1993-01-01

    We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ 4 4 . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.)

  8. Flood Risk Mapping Using Flow Energy Equation and Geographic Information System

    Directory of Open Access Journals (Sweden)

    pourya Javan

    2013-09-01

    Full Text Available Flooding and its damages are not only found uplift water level in a region. In other words, the depth and speed parameters together have determining the level of flood risk at each point. This subject is visible in flooded plain with low height and high speed of 2 meters per second, which damages are extensive. According to the criteria of having both velocity and flow depth in the governing equation to the flows energy, this equation seems appropriate to analysis in this study. Various methods have been proposed for increase accuracy in flood zoning with different return periods and risks associated with it in land border of river. For example, some of these methods are considered factors such as analysis of past flooding in the area affected by floods, hydrological factors and consideration of hydraulic elements affecting in flood zoning (such as flow velocity. This paper investigates the effect of flood zoning by the energy flow in the areas affected by floods. Also risk due to flood based on energy flow in each section of the river is compared by the proposed graphs of hazard interval and other done flood zoning in this field. In this study, the FORDO river has been selected as the case study. This river is part of the rivers located in the city of QOM KAHAK. The characteristics of river in upstream and downstream are mountain, young and stable and adult, respectively. Also this river in different seasons is exposed the flood damage. The proposed method in this study can be improving recognition accuracy of flood risk in areas affected by flood. Also, this method facilitate the identify parts of the river bed, that is affected by severe flooding, for decision making to improve rivers organizing.

  9. Extension of the Gladstone-Dale equation for flame flow field diagnosis by optical computerized tomography

    International Nuclear Information System (INIS)

    Chen Yunyun; Li Zhenhua; Song Yang; He Anzhi

    2009-01-01

    An extended model of the original Gladstone-Dale (G-D) equation is proposed for optical computerized tomography (OCT) diagnosis of flame flow fields. For the purpose of verifying the newly established model, propane combustion is used as a practical example for experiment, and moire deflection tomography is introduced with the probe wavelength 808 nm. The results indicate that the temperature based on the extended model is more accurate than that based on the original G-D equation. In a word, the extended model can be suitable for all kinds of flame flow fields whatever the components, temperature, and ionization are.

  10. Trefftz method in solving Fourier-Kirchhoff equation for two-phase flow boiling in a vertical rectangular minichannel

    Directory of Open Access Journals (Sweden)

    Hożejowska Sylwia

    2017-01-01

    Full Text Available This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.

  11. Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

    Energy Technology Data Exchange (ETDEWEB)

    Gregoire, O

    2008-07-01

    In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

  12. analysis of pressure variation of fluid in an infinite acting reservoir

    African Journals Online (AJOL)

    user

    2017-01-01

    Jan 1, 2017 ... radial diffusivity equation for a reservoir acting as if it was infinite in size and ... differential equation there is an infinite number of a possible solution ..... [3] Van Everdingen, A. F. and Hurst, W. The Application of the. Laplace ...

  13. An Embedded 3D Fracture Modeling Approach for Simulating Fracture-Dominated Fluid Flow and Heat Transfer in Geothermal Reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Johnston, Henry [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Colorado School of Mines; Winterfeld, Philip [Colorado School of Mines; Wu, Yu-Shu [Colorado School of Mines

    2018-02-14

    An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.

  14. Hydrologic characterization of Bushy Park Reservoir, South Carolina, 2013–15

    Science.gov (United States)

    Conrads, Paul; Petkewich, Matthew D.; Falls, W. Fred; Lanier, Timothy H.

    2017-06-14

    The Bushy Park Reservoir is a relatively shallow impoundment in a semi-tropical climate and is the principal water supply for the 400,000 people of the city of Charleston, South Carolina, and the surrounding areas including the Bushy Park Industrial Complex. Although there is an adequate supply of freshwater in the reservoir, taste-and-odor water-quality issues are a concern. The U.S. Geological Survey conducted an investigation in cooperation with the Charleston Water System to study the hydrology and hydrodynamics of the Bushy Park Reservoir to identify factors affecting water-quality conditions. Specifically, five areas for monitoring and (or) analysis were addressed: (1) hydrologic monitoring of the reservoir to establish a water budget, (2) flow monitoring in the tunnels to compute flow from Bushy Park Reservoir and at critical distribution junctions, (3) water-quality sampling, profiling, and continuous monitoring to identify the causes of taste-and-odor occurrence, (4) technical evaluation of appropriate hydrodynamic and water-quality simulation models for the reservoir, and (5) preliminary evaluation of alternative reservoir operations scenarios.This report describes the hydrodynamic and hydrologic data collected from 2013 to 2015 to support the application and calibration of a three-dimensional hydrodynamic model and the water-quality monitoring and analysis to gain insight into the principal causes of the Bushy Park Reservoir taste-and-odor episodes. The existing U.S. Geological Survey real-time network on the West Branch of the Cooper River was augmented with a tidal flow gage on Durham Canal Back River, and Foster Creek. The Charleston Water System intake structure was instrumented to collect water-level, water temperature (top and bottom probes), specific conductance (top and bottom probes), wind speed and direction, and photosynthetically active radiation data. In addition to the gages attached to fixed structures, four bottom-mounted velocity

  15. Active flow control insight gained from a modified integral boundary layer equation

    Science.gov (United States)

    Seifert, Avraham

    2016-11-01

    Active Flow Control (AFC) can alter the development of boundary layers with applications (e.g., reducing drag by separation delay or separating the boundary layers and enhancing vortex shedding to increase drag). Historically, significant effects of steady AFC methods were observed. Unsteady actuation is significantly more efficient than steady. Full-scale AFC tests were conducted with varying levels of success. While clearly relevant to industry, AFC implementation relies on expert knowledge with proven intuition and or costly and lengthy computational efforts. This situation hinders the use of AFC while simple, quick and reliable design method is absent. An updated form of the unsteady integral boundary layer (UIBL) equations, that include AFC terms (unsteady wall transpiration and body forces) can be used to assist in AFC analysis and design. With these equations and given a family of suitable velocity profiles, the momentum thickness can be calculated and matched with an outer, potential flow solution in 2D and 3D manner to create an AFC design tool, parallel to proven tools for airfoil design. Limiting cases of the UIBL equation can be used to analyze candidate AFC concepts in terms of their capability to modify the boundary layers development and system performance.

  16. Modeling CO2 Storage in Fractured Reservoirs: Fracture-Matrix Interactions of Free-Phase and Dissolved CO2

    Science.gov (United States)

    Oldenburg, C. M.; Zhou, Q.; Birkholzer, J. T.

    2017-12-01

    The injection of supercritical CO2 (scCO2) in fractured reservoirs has been conducted at several storage sites. However, no site-specific dual-continuum modeling for fractured reservoirs has been reported and modeling studies have generally underestimated the fracture-matrix interactions. We developed a conceptual model for enhanced CO2 storage to take into account global scCO2 migration in the fracture continuum, local storage of scCO2 and dissolved CO2 (dsCO2) in the matrix continuum, and driving forces for scCO2 invasion and dsCO2 diffusion from fractures. High-resolution discrete fracture-matrix models were developed for a column of idealized matrix blocks bounded by vertical and horizontal fractures and for a km-scale fractured reservoir. The column-scale simulation results show that equilibrium storage efficiency strongly depends on matrix entry capillary pressure and matrix-matrix connectivity while the time scale to reach equilibrium is sensitive to fracture spacing and matrix flow properties. The reservoir-scale modeling results shows that the preferential migration of scCO2 through fractures is coupled with bulk storage in the rock matrix that in turn retards the fracture scCO2 plume. We also developed unified-form diffusive flux equations to account for dsCO2 storage in brine-filled matrix blocks and found solubility trapping is significant in fractured reservoirs with low-permeability matrix.

  17. Liquid–liquid equilibria for reservoir fluids+monoethylene glycol and reservoir fluids+monoethylene glycol+water: Experimental measurements and modeling using the CPA EoS

    DEFF Research Database (Denmark)

    Frost, Michael; Kontogeorgis, Georgios; Stenby, Erling Halfdan

    2013-01-01

    for critical temperature, pressure and acentric factor.This work presents new phase equilibrium data for binary MEG/reservoir fluid and ternary MEG/water/reservoir fluid systems, where two reservoir fluids from Statoil operated fields are used. The solubility data are reported over a range of temperatures......The complex phase equilibrium between reservoir fluids and associating compounds like water and glycols has become more and more important as the increasing global energy demand pushes the oil industry to use advanced methods to increase oil recovery, such as increasing the use of various chemicals...... to ensure a constant and safe production. The CPA equation of state has been successfully applied in the past to well defined systems and gas condensates, containing associating compounds. It has also been extended to reservoir fluids in presence of water and polar chemicals using modified correlations...

  18. A new representation of rotational flow fields satisfying Euler's equation of an ideal compressible fluid

    International Nuclear Information System (INIS)

    Kambe, Tsutomu

    2013-01-01

    A new representation of the solution to Euler's equation of motion is presented by using a system of expressions for compressible rotational flows of an ideal fluid. This is regarded as a generalization of Bernoulli's theorem to compressible rotational flows. The present expressions are derived from the variational principle. The action functional for the principle consists of the main terms of the total kinetic, potential and internal energies, together with three additional terms yielding the equations of continuity, entropy and a third term that provides the rotational component of velocity field. The last term has the form of scalar product satisfying gauge symmetry with respect to both translation and rotation. This is a generalization of the Clebsch transformation from a physical point of view. It is verified that the system of new expressions, in fact, satisfies Euler's equation of motion. (paper)

  19. Tidal phenomena in reservoirs; Fenomeno de mare em reservatorios

    Energy Technology Data Exchange (ETDEWEB)

    Pinilla Cortes, John Freddy

    1997-06-01

    This work models the oceanic tidal effect on reservoirs by coupling geomechanic principles with equations for fluid in a deformable porous media. The coupling revealed the importance of establishing properly the system compressibility under the various possible configurations of the loading system. The basic models for infinite reservoir, constant outer-pressure reservoir and closed reservoir were considered. It was verified that it was possible to apply the superposition of effects on the solution for the basic models by carrying a simple transformation on the solution variable. The problem was treated by in the context of test analysis, concerning dimensionless form of variables and the inclusion of well effects. The solution for the infinite reservoir including tidal effects. The solution for the infinite reservoir including tidal effects was obtained in the Laplace space and was inverted numerically by using Crump's routine. The results were incorporated to conventional type curves, and were validated by comparison with real and simulated pressure test data. Finally, alternate practices were suggested to integrate the well test analysis in reservoirs affected by the tidal effect. (author)

  20. A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching

    KAUST Repository

    Katterbauer, Klemens

    2014-12-10

    The oil and gas industry has been revolutionized within the last decade, with horizontal drilling and hydraulic fracturing enabling the extraction of huge amounts of shale gas in areas previously considered impossible and the recovering of hydrocarbons in harsh environments like the arctic or in previously unimaginable depths like the off-shore exploration in the South China sea and Gulf of Mexico. With the development of 4D seismic, engineers and scientists have been enabled to map the evolution of fluid fronts within the reservoir and determine the displacement caused by the injected fluids. This in turn has led to enhanced production strategies, cost reduction and increased profits. Conventional approaches to incorporate seismic data into the history matching process have been to invert these data for constraints that are subsequently employed in the history matching process. This approach makes the incorporation computationally expensive and requires a lot of manual processing for obtaining the correct interpretation due to the potential artifacts that are generated by the generally ill-conditioned inversion problems. I have presented here a novel approach via including the time-lapse cross-well seismic survey data directly into the history matching process. The generated time-lapse seismic data are obtained from the full wave 3D viscoelastic acoustic wave equation. Furthermore an extensive analysis has been performed showing the robustness of the method and enhanced forecastability of the critical reservoir parameters, reducing uncertainties and exhibiting the benefits of a full wave 3D seismic approach. Finally, the improved performance has been statistically confirmed. The improvements illustrate the significant improvements in forecasting that are obtained via readily available seismic data without the need for inversion. This further optimizes oil production in addition to increasing return-on-investment on oil & gas field development projects, especially

  1. Penerapan Dinamika Fluida dalam Perhitungan Kecepatan Aliran dan Perolehan Minyak di Reservoir

    Directory of Open Access Journals (Sweden)

    Dwi Listriana Kusumastuti

    2014-12-01

    Full Text Available Water, oil and gas inside the earth are stored in the pores of the reservoir rock. In the world of petroleum industry, calculation of volume of the oil that can be recovered from the reservoir is something important to do. This calculation involves the calculation of the velocity of fluid flow by utilizing the principles and formulas provided by the Fluid Dynamics. The formula is usually applied to the fluid flow passing through a well defined control volume, for example: cylinder, curved pipe, straight pipes with different diameters at the input and output, and so forth. However, because of reservoir rock, as the fluid flow medium, has a wide variety of possible forms of the control volumes, hence, calculation of the velocity of the fluid flow is becoming difficult as it would involve calculations of fluid flow velocity for each control volume. This difficulties is mainly caused by the fact that these control volumes, that existed in the rock, cannot be well defined. This paper will describe a method for calculating this fluid flow velocity of the control volume, which consists of a combination of laboratory measurements and the use of some theories in the Fluid Dynamics. This method has been proofed can be used for calculating fluid flow velocity as well as oil recovery in reservoir rocks, with fairly good accuration.

  2. Adjoint based optimal control of partially miscible two-phase flow in porous media with applications to CO2 sequestration in underground reservoirs

    KAUST Repository

    Simon, Moritz; Ulbrich, Michael

    2014-01-01

    is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE

  3. ECMOR 4. 4th European conference on the mathematics of oil recovery. Topic D: Simulation of fluid flow. Proceedings

    Energy Technology Data Exchange (ETDEWEB)

    1994-01-01

    The report with collected proceedings from a conference, deals with mathematics of oil recovery with the focus on simulation of fluid flow. Topics of proceedings are as follow: Validity of macroscopic viscous fingering models for 2D and 3D-flows; pressure equation for fluid flow in a stochastic medium; predicting multicomponent, multiphase flow in heterogeneous systems using streamtubes; analytic techniques in pressure transient testing; global triangular structure in four-component conservation laws; exact solution of the problem on hydrodynamic interaction between noncommunicating layers under conditions of their joint development; fluid rate in flowing granular medium with moving boundary; complex variable boundary element method for tracking streamlines across fractures; transport equations for miscible displacements in heterogeneous porous media - a streamtube approach; mathematical modelling of condensate film flow by gravity drainage; effect of capillary forces on immiscible two-phase flow in strongly heterogeneous porous media; multidomain direct method and local time steps in reservoir simulation; adaptive methods for chemical flooding; flux continuous for the full tensor equation; discretization on non-orthogonal, curvilinear grids for multi-phase flow; blending finite elements and finite volumes for the solution of miscible incompressible flow. 16 papers are prepared. 240 refs., 122 figs., 6 tabs.

  4. Equation of material balance for systems of double porosity with layer of initial gas

    International Nuclear Information System (INIS)

    Niz, Eider; Hidrobo, Eduardo A; Penuela, Gherson; Ordonez, Anibal; Calderon, Zuly H

    2004-01-01

    The physical complexity associated to naturally fractured reservoirs calls for the use of more robust formulations of the Material-Balance Equation (MBE) for determining the initial hydrocarbon in place and predicting reservoir performance. In this paper, we present an improved version of the dual-porosity MBE for naturally fractured reservoirs, published by Penuela et al. (2001), including the existence of an initial gas phase in the reservoir. Considering that a fractured reservoir may be modeled either using different properties for each porous medium or with average values for the total system, two solution techniques based on each of these assumptions are proposed. Convenient arrangements of the equation allow us to estimate not only the original oil and gas volumes but also the relative storage capacity of the porous media (fractures and matrix) and the compressibility for the fractured and total systems. The new equation can be applied to a broader range of reservoirs due to its more general character. The consistency of the expression proposed has been tested with a set of synthetic models exhibiting different storage capacity in the fractures

  5. Relative influence of deposition and diagenesis on carbonate reservoir layering

    Energy Technology Data Exchange (ETDEWEB)

    Poli, Emmanuelle [Total E and P, Courbevoie (France); Javaux, Catherine [Total E and P, Pointe Noire (Congo)

    2008-07-01

    The architecture heterogeneities and petrophysical properties of carbonate reservoirs result from a combination of platform morphology, related depositional environments, relative sea level changes and diagenetic events. The reservoir layering built for static and dynamic modelling purposes should reflect the key heterogeneities (depositional or diagenetic) which govern the fluid flow patterns. The layering needs to be adapted to the goal of the modelling, ranging from full field computations of hydrocarbon volumes, to sector-based fine-scale simulations to test the recovery improvement. This paper illustrates various reservoir layering types, including schemes dominated by depositional architecture, and those more driven by the diagenetic overprint. The examples include carbonate platform reservoirs from different stratigraphic settings (Tertiary, Cretaceous, Jurassic and Permian) and different regions (Europe, Africa and Middle East areas). This review shows how significant stratigraphic surfaces (such as sequence boundaries or maximum flooding) with their associated facies shifts, can be often considered as key markers to constrain the reservoir layering. Conversely, how diagenesis (dolomitization and karst development), resulting in units with particular poroperm characteristics, may significantly overprint the primary reservoir architecture by generating flow units which cross-cut depositional sequences. To demonstrate how diagenetic processes can create reservoir bodies with geometries that cross-cut the depositional fabric, different types of dolomitization and karst development are illustrated. (author)

  6. Analysis of turbulent separated flows for the NREL airfoil using anisotropic two-equation models at higher angles of attack

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Shijie [Tsinghua University, Beijing (China). School of Architecture; Yuan Xin; Ye Dajun [Tsinghua University, Beijing (China). Dept. of Thermal Engineering

    2001-07-01

    Numerical simulations of the turbulent flow fields at stall conditions are presented for the NREL (National Renewable Energy Laboratory) S809 airfoil. The flow is modelled as compressible, viscous, steady/unsteady and turbulent. Four two-equation turbulence models (isotropic {kappa}-{epsilon} and q-{omega} models, anisotropic {kappa}-{epsilon} and -{omega} models), are applied to close the Reynolds-averaged Navier-Stokes equations, respectively. The governing equations are integrated in time by a new LU-type implicit scheme. To accurately model the convection terms in the mean-flow and turbulence model equations, a modified fourth-order high resolution MUSCL TVD scheme is incorporated. The large-scale separated flow fields and their losses at the stall and post-stall conditions are analyzed for the NREL S809 airfoil at various angles of attack ({alpha}) from 0 to 70 degrees. The numerical results show excellent to fairly good agreement with the experimental data. The feasibility of the present numerical method and the influence of the four turbulence models are also investigated. (author)

  7. Subchannel analysis program for boiling water reactor fuel bundles based on five conservation equations of two-phase flow

    International Nuclear Information System (INIS)

    Bessho, Y.; Uchikawa, S.

    1985-01-01

    A subchannel analysis program, MENUETT, is developed for evaluation of thermal-hydraulic characteristics in boiling water reactor fuel bundles. This program is based on five conservation equations of two-phase flow with the drift-flux correlation. The cross flows are calculated separately for liquid and vapor phases from the lateral momentum conservation equation. The effects of turbulent mixing and void drift are accounted for in the program. The conservation equations are implicitly differentiated with the convective terms by the donor-cell method, and are solved iteratively in the axial and lateral directions. Data of the 3 X 3 rod bundle experiments are used for program verification. The lateral distributions of equilibrium quality and mass flow rate at the bundle exit calculated by the program compare satisfactorily with the experimental results

  8. Reservoir Performance Under Future Climate For Basins With Different Hydrologic Sensitivities

    Science.gov (United States)

    Mateus, M. C.; Tullos, D. D.

    2013-12-01

    In addition to long-standing uncertainties related to variable inflows and market price of power, reservoir operators face a number of new uncertainties related to hydrologic nonstationarity, changing environmental regulations, and rapidly growing water and energy demands. This study investigates the impact, sensitivity, and uncertainty of changing hydrology on hydrosystem performance across different hydrogeologic settings. We evaluate the performance of reservoirs in the Santiam River basin, including a case study in the North Santiam Basin, with high permeability and extensive groundwater storage, and the South Santiam Basin, with low permeability, little groundwater storage and rapid runoff response. The modeling objective is to address the following study questions: (1) for the two hydrologic regimes, how does the flood management, water supply, and environmental performance of current reservoir operations change under future 2.5, 50 and 97.5 percentile streamflow projections; and (2) how much change in inflow is required to initiate a failure to meet downstream minimum or maximum flows in the future. We couple global climate model results with a rainfall-runoff model and a formal Bayesian uncertainty analysis to simulate future inflow hydrographs as inputs to a reservoir operations model. To evaluate reservoir performance under a changing climate, we calculate reservoir refill reliability, changes in flood frequency, and reservoir time and volumetric reliability of meeting minimum spring and summer flow target. Reservoir performance under future hydrology appears to vary with hydrogeology. We find higher sensitivity to floods for the North Santiam Basin and higher sensitivity to minimum flow targets for the South Santiam Basin. Higher uncertainty is related with basins with a more complex hydrologeology. Results from model simulations contribute to understanding of the reliability and vulnerability of reservoirs to a changing climate.

  9. Integrating geologic and engineering data into 3-D reservoir models: an example from norman wells field, NWT, Canada

    International Nuclear Information System (INIS)

    Yose, L.A.

    2004-01-01

    A case study of the Norman Wells field will be presented to highlight the work-flow and data integration steps associated with characterization and modeling of a complex hydrocarbon reservoir. Norman Wells is a Devonian-age carbonate bank ('reef') located in the Northwest Territories of Canada, 60 kilometers south of the Arctic Circle. The reservoir reaches a maximum thickness of 130 meters in the reef interior and thins toward the basin due to depositional pinch outs. Norman Wells is an oil reservoir and is currently under a 5-spot water injection scheme for enhanced oil recovery (EOR). EOR strategies require a detailed understanding of how reservoir flow units, flow barriers and flow baffles are distributed to optimize hydrocarbon sweep and recovery and to minimize water handling. Reservoir models are routinely used by industry to characterize the 3-D distribution of reservoir architecture (stratigraphic layers, depositional facies, faults) and rock properties (porosity. permeability). Reservoir models are validated by matching historical performance data (e.g., reservoir pressures, well production or injection rates). Geologic models are adjusted until they produce a history match, and model adjustments are focused on inputs that have the greatest geologic uncertainty. Flow simulation models are then used to optimize field development strategies and to forecast field performance under different development scenarios. (author)

  10. Economics of Developing Hot Stratigraphic Reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Greg Mines; Hillary Hanson; Rick Allis; Joseph Moore

    2014-09-01

    Stratigraphic geothermal reservoirs at 3 – 4 km depth in high heat-flow basins are capable of sustaining 100 MW-scale power plants at about 10 c/kWh. This paper examines the impacts on the levelized cost of electricity (LCOE) of reservoir depth and temperature, reservoir productivity, and drillhole/casing options. For a reservoir at 3 km depth with a moderate productivity index by hydrothermal reservoir standards (about 50 L/s/MPa, 5.6 gpm/psi), an LCOE of 10c/kWh requires the reservoir to be at about 200°C. This is the upper temperature limit for pumps. The calculations assume standard hydrothermal drilling costs, with the production interval completed with a 7 inch liner in an 8.5 inch hole. If a reservoir at 4 km depth has excellent permeability characteristics with a productivity index of 100 L/s/MPa (11.3 gpm/psi), then the LCOE is about 11 c/kWh assuming the temperature decline rate with development is not excessive (< 1%/y, with first thermal breakthrough delayed by about 10 years). Completing wells with modest horizontal legs (e.g. several hundred meters) may be important for improving well productivity because of the naturally high, sub-horizontal permeability in this type of reservoir. Reducing the injector/producer well ratio may also be cost-effective if the injectors are drilled as larger holes.

  11. Transverse momentum spectra and elliptic flow: Hydrodynamics with QCD-based equations of state

    CERN Document Server

    Bluhm, M; Heinz, U

    2008-01-01

    We present a family of equations of state within a quasiparticle model adjusted to lattice QCD and study the impact on azimuthal flow anisotropies and transverse momentum spectra within hydrodynamic simulations for heavy-ion collisions at energies relevant for LHC.

  12. A relaxation-projection method for compressible flows. Part I: The numerical equation of state for the Euler equations

    International Nuclear Information System (INIS)

    Saurel, Richard; Franquet, Erwin; Daniel, Eric; Le Metayer, Olivier

    2007-01-01

    A new projection method is developed for the Euler equations to determine the thermodynamic state in computational cells. It consists in the resolution of a mechanical relaxation problem between the various sub-volumes present in a computational cell. These sub-volumes correspond to the ones traveled by the various waves that produce states with different pressures, velocities, densities and temperatures. Contrarily to Godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium. The pressure computation with this relaxation process replaces the use of the conventional equation of state (EOS). A simplified relaxation method is also derived and provides a specific EOS (named the Numerical EOS). The use of the Numerical EOS gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas EOS. It is then extended to the computation of interface problems separating fluids with different EOS (liquid-gas interface for example) with the Euler equations. The resulting method is very robust, accurate, oscillation free and conservative. For the sake of simplicity and efficiency the method is developed in a Lagrange-projection context and is validated over exact solutions. In a companion paper [F. Petitpas, E. Franquet, R. Saurel, A relaxation-projection method for compressible flows. Part II: computation of interfaces and multiphase mixtures with stiff mechanical relaxation. J. Comput. Phys. (submitted for publication)], the method is extended to the numerical approximation of a non-conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures

  13. Multilevel techniques for Reservoir Simulation

    DEFF Research Database (Denmark)

    Christensen, Max la Cour

    The subject of this thesis is the development, application and study of novel multilevel methods for the acceleration and improvement of reservoir simulation techniques. The motivation for addressing this topic is a need for more accurate predictions of porous media flow and the ability to carry...... Full Approximation Scheme) • Variational (Galerkin) upscaling • Linear solvers and preconditioners First, a nonlinear multigrid scheme in the form of the Full Approximation Scheme (FAS) is implemented and studied for a 3D three-phase compressible rock/fluids immiscible reservoir simulator...... is extended to include a hybrid strategy, where FAS is combined with Newton’s method to construct a multilevel nonlinear preconditioner. This method demonstrates high efficiency and robustness. Second, an improved IMPES formulated reservoir simulator is implemented using a novel variational upscaling approach...

  14. On the Representation of the Porosity-Pressure Relationship in General Subsurface Flow Codes

    Science.gov (United States)

    Birdsell, Daniel T.; Karra, Satish; Rajaram, Harihar

    2018-02-01

    The governing equations for subsurface flow codes in a deformable porous media are derived from the balance of fluid mass and Darcy's equation. One class of these codes, which we call general subsurface flow codes (GSFs), allow for more general constitutive relations for material properties such as porosity, permeability and density. Examples of GSFs include PFLOTRAN, FEHM, TOUGH2, STOMP, and some reservoir simulators such as BOAST. Depending on the constitutive relations used in GSFs, an inconsistency arises between the standard groundwater flow equation and the governing equation of GSFs, and we clarify that the reason for this inconsistency is because the Darcy's equation used in the GSFs should account for the velocity of fluid with respect to solid. Due to lack of awareness of this inconsistency, users of the GSFs tend to use a porosity-pressure relationship that comes from the standard groundwater flow equation and assumes that the relative velocity is already accounted for. For the Theis problem, we show that using this traditional relationship in the GSFs leads to significantly large errors. We propose an alternate porosity-pressure relationship that is consistent with the derivation of the governing equations in the GSFs where the solid velocity is not tracked, and show that, with this relationship, the results are more accurate for the Theis problem. The purpose of this note is to make the users and developers of these GSFs aware of this inconsistency and to advocate that the alternate porosity model derived here should be incorporated in GSFs.

  15. A Pore Scale Flow Simulation of Reconstructed Model Based on the Micro Seepage Experiment

    Directory of Open Access Journals (Sweden)

    Jianjun Liu

    2017-01-01

    Full Text Available Researches on microscopic seepage mechanism and fine description of reservoir pore structure play an important role in effective development of low and ultralow permeability reservoir. The typical micro pore structure model was established by two ways of the conventional model reconstruction method and the built-in graphics function method of Comsol® in this paper. A pore scale flow simulation was conducted on the reconstructed model established by two different ways using creeping flow interface and Brinkman equation interface, respectively. The results showed that the simulation of the two models agreed well in the distribution of velocity, pressure, Reynolds number, and so on. And it verified the feasibility of the direct reconstruction method from graphic file to geometric model, which provided a new way for diversifying the numerical study of micro seepage mechanism.

  16. Analysis of liquid metal MHD flow in multiple adjacent ducts using an iterative method to solve the core flow equations

    International Nuclear Information System (INIS)

    McCarthy, K.A.; Abdou, M.A.

    1991-01-01

    A computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics. The method which has been developed is an 'iterative' method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error. The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. (orig./AH)

  17. AI techniques for optimizing multi-objective reservoir operation upon human and riverine ecosystem demands

    Science.gov (United States)

    Tsai, Wen-Ping; Chang, Fi-John; Chang, Li-Chiu; Herricks, Edwin E.

    2015-11-01

    Flow regime is the key driver of the riverine ecology. This study proposes a novel hybrid methodology based on artificial intelligence (AI) techniques for quantifying riverine ecosystems requirements and delivering suitable flow regimes that sustain river and floodplain ecology through optimizing reservoir operation. This approach addresses issues to better fit riverine ecosystem requirements with existing human demands. We first explored and characterized the relationship between flow regimes and fish communities through a hybrid artificial neural network (ANN). Then the non-dominated sorting genetic algorithm II (NSGA-II) was established for river flow management over the Shihmen Reservoir in northern Taiwan. The ecosystem requirement took the form of maximizing fish diversity, which could be estimated by the hybrid ANN. The human requirement was to provide a higher satisfaction degree of water supply. The results demonstrated that the proposed methodology could offer a number of diversified alternative strategies for reservoir operation and improve reservoir operational strategies producing downstream flows that could meet both human and ecosystem needs. Applications that make this methodology attractive to water resources managers benefit from the wide spread of Pareto-front (optimal) solutions allowing decision makers to easily determine the best compromise through the trade-off between reservoir operational strategies for human and ecosystem needs.

  18. The role of rainfall variability in reservoir storage management at ...

    African Journals Online (AJOL)

    Reservoir operation and management is usually patterned after the background of long standing water resources management experience. Reservoir management for optimum power production at any hydropower station requires constant assessment of the quantity of available water. The hydrographic responses of flow ...

  19. Modeling of Reservoir Inflow for Hydropower Dams Using Artificial ...

    African Journals Online (AJOL)

    The stream flow at the three hydropower reservoirs in Nigeria were modeled using hydro-meteorological parameters and Artificial Neural Network (ANN). The model revealed positive relationship between the observed and the modeled reservoir inflow with values of correlation coefficient of 0.57, 0.84 and 0.92 for Kainji, ...

  20. Coupling a fluid flow simulation with a geomechanical model of a fractured reservoir

    OpenAIRE

    Segura Segarra, José María; Paz, C.M.; de Bayser, M.; Zhang, J.; Bryant, P.W.; Gonzalez, Nubia Aurora; Rodrigues, E.; Vargas, P.E.; Carol, Ignacio; Lakshmikantha, Ramasesha Mookanahallipatna; Das, K. C.; Sandha, S.S.; Cerqueira, R.; Mello,, U.

    2013-01-01

    Improving the reliability of integrated reservoir development planning and addressing subsidence, fault reactivation and other environmental impacts, requires increasingly sophisticated geomechanical models, especially in the case of fractured reservoirs where fracture deformation is strongly coupled with its permeability change. Reservoir simulation has historically treated any geomechanical effects by means of a rock compressibility term/table, which can be improved by simulating the actual...

  1. Transient pressure and productivity analysis in carbonate geothermal reservoirs with changing external boundary flux

    Directory of Open Access Journals (Sweden)

    Wang Dongying

    2017-01-01

    Full Text Available In this paper, a triple-medium flow model for carbonate geothermal reservoirs with an exponential external boundary flux is established. The pressure solution under constant production conditions in Laplace space is solved. The geothermal wellbore pressure change considering wellbore storage and skin factor is obtained by Stehfest numerical inversion. The well test interpretation charts and Fetkovich production decline chart for carbonate geothermal reservoirs are proposed for the first time. The proposed Fetkovich production decline curves are applied to analyze the production decline behavior. The results indicate that in carbonate geothermal reservoirs with exponential external boundary flux, the pressure derivative curve contains a triple dip, which represents the interporosity flow between the vugs or matrix and fracture system and the invading flow of the external boundary flux. The interporosity flow of carbonate geothermal reservoirs and changing external boundary flux can both slow down the extent of production decline and the same variation tendency is observed in the Fetkovich production decline curve.

  2. Comparative Analyses between the Zero-Inertia and Fully Dynamic Models of the Shallow Water Equations for Unsteady Overland Flow Propagation

    Directory of Open Access Journals (Sweden)

    Costanza Aricò

    2018-01-01

    Full Text Available The shallow water equations are a mathematical tool widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. The interest of many researchers has been focused on the study of simplified forms of the original set of equations. One of the most commonly applied simplifications consists of neglecting the inertial terms. The effects of such a choice on the outputs of the simulations of flooding events are controversial and are an important topic of debate. In the present paper, two numerical models recently proposed for the solution of the complete and zero-inertia forms of the shallow water equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory scenarios of unsteady flow routing, starting from very simple geometries and gradually moving towards complex topographies. Unlike the studies of the range of validity of the zero-inertia model, based on a small perturbation of the linearized flow model, in unsteady flow propagation over irregular topographies, it is more difficult to specify criteria for the applicability of the simplified set of equations. In analyzing the role of the terms in the momentum equations, we try to understand the effect of neglecting the inertial terms in the zero-inertia formulation. We also analyze the computational costs.

  3. Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

    Science.gov (United States)

    van Wonderen, A. J.; Suttorp, L. G.

    2018-04-01

    Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

  4. Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

    Science.gov (United States)

    Walters, Robert W.; Dwoyer, Douglas L.

    1987-01-01

    A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

  5. Critical review of conservation equations for two-phase flow in the U.S. NRC TRACE code

    International Nuclear Information System (INIS)

    Wulff, Wolfgang

    2011-01-01

    Research highlights: → Field equations as implemented in TRACE are incorrect. → Boundary conditions needed for cooling of nuclear fuel elements are wrong. → The two-fluid model in TRACE is not closed. → Three-dimensional flow modeling in TRACE has no basis. - Abstract: The field equations for two-phase flow in the computer code TRAC/RELAP Advanced Computational Engine or TRACE are examined to determine their validity, their capabilities and limitations in resolving nuclear reactor safety issues. TRACE was developed for the NRC to predict thermohydraulic phenomena in nuclear power plants during operational transients and postulated accidents. TRACE is based on the rigorously derived and well-established two-fluid field equations for 1-D and 3-D two-phase flow. It is shown that: (1)The two-fluid field equations for mass conservation as implemented in TRACE are wrong because local mass balances in TRACE are in conflict with mass conservation for the whole reactor system, as shown in Section . (2)Wrong equations of motion are used in TRACE in place of momentum balances, compromising at branch points the prediction of momentum transfer between, and the coupling of, loops in hydraulic networks by impedance (form loss and wall shear) and by inertia and thereby the simulation of reactor component interactions. (3)Most seriously, TRACE calculation of heat transfer from fuel elements is incorrect for single and two-phase flows, because Eq. of the TRACE Manual is wrong (see Section ). (4)Boundary conditions for momentum and energy balances in TRACE are restricted to flow regimes with single-phase wall contact because TRACE lacks constitutive relations for solid-fluid exchange of momentum and heat in prevailing flow regimes. Without a quantified assessment of consequences from (3) to (4), predictions of phasic fluid velocities, fuel temperatures and important safety parameters, e.g., peak clad temperature, are questionable. Moreover, TRACE cannot predict 3-D single- or

  6. Characterization of dynamic change of Fan-delta reservoir properties in water-drive development

    Energy Technology Data Exchange (ETDEWEB)

    Wu Shenghe; Xiong Qihua; Liu Yuhong [Univ. of Petroleum Changping, Beijing (China)

    1997-08-01

    Fan-delta reservoir in Huzhuangji oil field of east China, is a typical highly heterogeneous reservoir. The oil field has been developed by water-drive for 10 years, but the oil recovery is less than 12%, and water cut is over 90%, resulting from high heterogeneity and serious dynamic change of reservoir properties. This paper aims at the study of dynamic change of reservoir properties in water-drive development. Through quantitative imaging analysis and mercury injection analysis of cores from inspection wells, the dynamic change of reservoir pore structure in water-drive development was studied. The results show that the {open_quotes}large pore channels{close_quotes} develop in distributary channel sandstone and become larger in water-drive development, resulting in more serious pore heterogeneity. Through reservoir sensitivity experiments, the rock-fluid reaction in water-drive development is studied. The results show the permeability of some distal bar sandstone and deserted channel sandstone becomes lower due to swelling of I/S clay minerals in pore throats. OD the other hand, the permeability of distributary channel and mouth bar sandstone become larger because the authigenic Koalinites in pore throats are flushed away with the increase of flow rate of injection water. Well-logging analysis of flooded reservoirs are used to study the dynamic change of reservoir properties in various flow units. The distribution of remaining oil is closely related to the types and distribution of flow units.

  7. A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

    Science.gov (United States)

    Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

    2010-02-01

    Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

  8. Cesium reservoir and interconnective components

    International Nuclear Information System (INIS)

    1994-03-01

    The program objective is to demonstrate the technology readiness of a TFE (thermionic fuel element) suitable for use as the basic element in a thermionic reactor with electric power output in the 0.5 to 5.0 MW range. A thermionic converter must be supplied with cesium vapor for two reasons. Cesium atoms adsorbed on the surface of the emitter cause a reduction of the emitter work function to permit high current densities without excessive heating of the emitter. The second purpose of the cesium vapor is to provide space-charge neutralization in the emitter-collector gap so that the high current densities may flow across the gap unattenuated. The function of the cesium reservoir is to provide a source of cesium atoms, and to provide a reserve in the event that cesium is lost from the plasma by any mechanism. This can be done with a liquid cesium metal reservoir in which case it is heated to the desired temperature with auxiliary heaters. In a TFE, however, it is desirable to have the reservoir passively heated by the nuclear fuel. In this case, the reservoir must operate at a temperature intermediate between the emitter and the collector, ruling out the use of liquid reservoirs. Integral reservoirs contained within the TFE will produce cesium vapor pressures in the desired range at typical electrode temperatures. The reservoir material that appears to be the best able to meet requirements is graphite. Cesium intercalates easily into graphite, and the cesium pressure is insensitive to loading for a given intercalation stage. The goals of the cesium reservoir test program were to verify the performance of Cs-graphite reservoirs in the temperature-pressure range of interest to TFE operation, and to test the operation of these reservoirs after exposure to a fast neutron fluence corresponding to seven year mission lifetime. In addition, other materials were evaluated for possible use in the integral reservoir

  9. Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

    International Nuclear Information System (INIS)

    Anderson, C.R.; Reider, M.B.

    1994-01-01

    The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

  10. Large CYBER-205-model of the Euler equations for vortex-stretched turbulent flow around Delta wings

    International Nuclear Information System (INIS)

    Rizzi, A.; Purcell, C.J.

    1985-01-01

    The large-scale numerical simulation of fluid flow is described as a discipline within the field of software engineering. As an example of such work, a vortex flow field is analyzed for its essential physical flow features, an appropriate mathematical description is presented (the Euler equations with an artificial viscosity model), a numerical algorithm to solve mathematical equations is described, and the programming methodology which allows us to attain a very high degree of vectorization on the CYBER 205 is discussed. Four simulated flowfields with vorticity shed from wing edges are computed with up to as many as one million grid points and verify the realism of the simulation model. The computed solutions show all of the qualitative features that are expected in these flows. The twisted cranked-and-cropped delta case is one where the leading-edge vortex is highly stretched and unstable, displaying ultimately inviscid large-scale turbulent-like phenomena

  11. A combined CFD-experimental method for developing an erosion equation for both gas-sand and liquid-sand flows

    Science.gov (United States)

    Mansouri, Amir

    The surface degradation of equipment due to consecutive impacts of abrasive particles carried by fluid flow is called solid particle erosion. Solid particle erosion occurs in many industries including oil and gas. In order to prevent abrupt failures and costly repairs, it is essential to predict the erosion rate and identify the locations of the equipment that are mostly at risk. Computational Fluid Dynamics (CFD) is a powerful tool for predicting the erosion rate. Erosion prediction using CFD analysis includes three steps: (1) obtaining flow solution, (2) particle tracking and calculating the particle impact speed and angle, and (3) relating the particle impact information to mass loss of material through an erosion equation. Erosion equations are commonly generated using dry impingement jet tests (sand-air), since the particle impact speed and angle are assumed not to deviate from conditions in the jet. However, in slurry flows, a wide range of particle impact speeds and angles are produced in a single slurry jet test with liquid and sand particles. In this study, a novel and combined CFD/experimental method for developing an erosion equation in slurry flows is presented. In this method, a CFD analysis is used to characterize the particle impact speed, angle, and impact rate at specific locations on the test sample. Then, the particle impact data are related to the measured erosion depth to achieve an erosion equation from submerged testing. Traditionally, it was assumed that the erosion equation developed based on gas testing can be used for both gas-sand and liquid-sand flows. The erosion equations developed in this work were implemented in a CFD code, and CFD predictions were validated for various test conditions. It was shown that the erosion equation developed based on slurry tests can significantly improve the local thickness loss prediction in slurry flows. Finally, a generalized erosion equation is proposed which can be used to predict the erosion rate in

  12. Scaling Relations for Viscous and Gravitational Flow Instabilities in Multiphase Multicomponent Compressible Flow

    Science.gov (United States)

    Moortgat, J.; Amooie, M. A.; Soltanian, M. R.

    2016-12-01

    Problems in hydrogeology and hydrocarbon reservoirs generally involve the transport of solutes in a single solvent phase (e.g., contaminants or dissolved injection gas), or the flow of multiple phases that may or may not exchange mass (e.g., brine, NAPL, oil, gas). Often, flow is viscously and gravitationally unstable due to mobility and density contrasts within a phase or between phases. Such instabilities have been studied in detail for single-phase incompressible fluids and for two-phase immiscible flow, but to a lesser extent for multiphase multicomponent compressible flow. The latter is the subject of this presentation. Robust phase stability analyses and phase split calculations, based on equations of state, determine the mass exchange between phases and the resulting phase behavior, i.e., phase densities, viscosities, and volumes. Higher-order finite element methods and fine grids are used to capture the small-scale onset of flow instabilities. A full matrix of composition dependent coefficients is considered for each Fickian diffusive phase flux. Formation heterogeneity can have a profound impact and is represented by realistic geostatistical models. Qualitatively, fingering in multiphase compositional flow is different from single-phase problems because 1) phase mobilities depend on rock wettability through relative permeabilities, and 2) the initial density and viscosity ratios between phases may change due to species transfer. To quantify mixing rates in different flow regimes and for varying degrees of miscibility and medium heterogeneities, we define the spatial variance, scalar dissipation rate, dilution index, skewness, and kurtosis of the molar density of introduced species. Molar densities, unlike compositions, include compressibility effects. The temporal evolution of these measures shows that, while transport at the small-scale (cm) is described by the classical advection-diffusion-dispersion relations, scaling at the macro-scale (> 10 m) shows

  13. Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

    KAUST Repository

    Vignal, Philippe

    2015-06-01

    In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

  14. A mass conservative numerical solution of vertical water flow and mass transport equations in unsaturated porous media

    International Nuclear Information System (INIS)

    Lim, S.C.; Lee, K.J.

    1993-01-01

    The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)

  15. Mutual Solubility of MEG, Water and Reservoir Fluid: Experimental Measurements and Modeling using the CPA Equation of State

    DEFF Research Database (Denmark)

    Riaz, Muhammad; Kontogeorgis, Georgios; Stenby, Erling Halfdan

    2011-01-01

    This work presents new experimental phase equilibrium data of binary MEG-reservoir fluid and ternary MEG-water-reservoir fluid systems at temperatures 275-326 K and at atmospheric pressure. The reservoir fluid consists of a natural gas condensate from a Statoil operated gas field in the North Sea...... compounds. It has also been extended to reservoir fluids in presence of water and polar chemicals using a Pedersen like characterization method with modified correlations for critical temperature, pressure and acentric factor. In this work CPA is applied to the prediction of mutual solubility of reservoir...

  16. The solutions of Navier-Stokes equations in squeezing flow between parallel plates

    Czech Academy of Sciences Publication Activity Database

    Petrov, A. G.; Kharlamova, Irina

    2014-01-01

    Roč. 48, November–December (2014), s. 40-48 ISSN 0997-7546 Grant - others:Russian Foundation for Basic Research(RU) 14-01- 00818; Russian Foundation for Basic Research(RU) 14-01-00892 Institutional support: RVO:67985874 Keywords : closed form solution * Navier-Stokes equations * squeezing flow between plates * counterflow Subject RIV: BK - Fluid Dynamics Impact factor: 1.656, year: 2014

  17. Application of the CPA equation of state to reservoir fluids in presence of water and polar chemicals

    DEFF Research Database (Denmark)

    Yan, Wei; Kontogeorgis, Georgios; Stenby, Erling Halfdan

    2009-01-01

    to reservoir fluids in presence of water and polar chemical Such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model......The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore...

  18. Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

    Directory of Open Access Journals (Sweden)

    Li-ren Yu

    2012-03-01

    Full Text Available This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k˜−ε˜,k˜−w˜, and k˜−ω˜ , were used to close the non-simplified quasi-three dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k˜−ω˜ model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.

  19. FY 1998 report on the development of technology for reservoir mass and heat flow characterization. Theme 5-2. Monitoring and modeling of reservoir mass and heat flows (Integrated reservoir modeling and simulation techniques/Modeling support technique); 1998 nendo chinetsu tansa gijutsu nado kensho chosa choryuso hendo tansaho kaihatsu hokokusho (yoyaku). 5-2. Choryuso hendo yosoku gijutsu (modeling shien gijutsu)

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1999-03-01

    This R and D are aimed at establishing technology to support the reservoir modeling work required for predicting the reservoir variation from the geological/geochemical side. The contents of the development are (1) establishment of the practical measuring system for core fracture system, and (2) establishment of new modeling support technology. In (1), as the core fraction system measuring system, the measurement of fluid inclusion homogenization temperature and melting point and laser Raman spectroscopy were applied to the Wasabizawa area to obtain the results. In (2), the R and D were conducted of a rapid age measuring method for altered rock/unaltered rock and an analytical method for fluid flow using trace chemical components of hydrothermal minerals. In the former, 3-D thermoluminescent intensity of the age-known quartz was measured. The TL age of weak altered rock of Kijiyama dacite in the Wasabizawa area was 320Ka, almost the same result as 320Ka already reported. In the latter, trace components of quartz were measured at each well, and changes in the depth direction were made clear. It was made clear that the variation of Na/K ratio is large around the lost circulation stratum. The geothermal fluid flow was made clear by the analysis of similarity of the intensity ratio. (NEDO)

  20. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  1. Applicability of Voce equation for tensile flow and work hardening behaviour of P92 ferritic steel

    International Nuclear Information System (INIS)

    Sainath, G.; Choudhary, B.K.; Christopher, J.; Isaac Samuel, E.; Mathew, M.D.

    2015-01-01

    Detailed analysis of true stress (σ)-true plastic strain (ε) data indicated that tensile flow behaviour of P92 ferritic steel can be adequately described by Voce equation at strain rates ranging from 3.16 × 10 −5 to 1.26 × 10 −3  s −1 over a temperature range 300–923 K. The steel exhibited two-stage work hardening in the variations of instantaneous work hardening rate (θ = dσ/dε) with stress. At all the strain rates, the variations in σ-ε, θ-σ and work hardening parameters associated with Voce equation with temperature exhibited three distinct temperature regimes. At intermediate temperatures, the variations in σ-ε, θ-σ and work hardening parameters with temperature and strain rate exhibited anomalous behaviour due to the occurrence of dynamic strain ageing in the steel. The shift in θ-σ towards low stresses, and rapid decrease in flow stress and work hardening parameters with increasing temperature and decreasing strain rate suggested dominance of dynamic recovery at high temperatures. - Highlights: • Tensile flow and work hardening behaviour of P92 steel has been examined. • Applicability of Voce equation to P92 steel is demonstrated. • Three temperature regimes in flow and work hardening has been observed. • Good match between predicted and the experimental tensile properties has been shown

  2. Evaluation of natural recharge of Chingshui geothermal reservoir using tritium as a tracer

    International Nuclear Information System (INIS)

    Cheng, W.; Kuo, T.; Su, C.; Chen, C.; Fan, K.; Liang, H.; Han, Y.

    2010-01-01

    Naturally existing tritium in groundwater was applied as a tracer to evaluate the natural recharge of the Chingshui geothermal reservoir. The residence time (or, age) of Chingshui geothermal water was first determined with tritium data at 15.2 and 11.3 year using the plug flow and dispersive model, respectively. The annual natural recharge was then estimated by combining the use of the residence time and the fluid-in-place of the Chingshui geothermal reservoir. The natural recharge for Chingshui geothermal reservoir was estimated at 5.0 x 10 5 and 6.7 x 10 5 m 3 year -1 using the plug flow and dispersive model, respectively. Chingshui geothermal water is largely from a fractured zone in the Jentse Member of the Miocene Lushan Formation. The dispersive model more adequately represents the fracture flow system than the simple plug flow model.

  3. Carbon dioxide sequestration induced mineral precipitation healing of fractured reservoir seals

    Science.gov (United States)

    Welch, N.; Crawshaw, J.

    2017-12-01

    Initial experiments and the thermodynaic basis for carbon dioxide sequestration induced mineral precipitation healing of fractures through reservoir seals will be presented. The basis of this work is the potential exists for the dissolution of reservoir host rock formation carbonate minerals in the acidified injection front of CO2 during sequestration or EOR. This enriched brine and the bulk CO2 phase will then flow through the reservoir until contact with the reservoir seal. At this point any fractures present in the reservoir seal will be the preferential flow path for the bulk CO2 phase as well as the acidified brine front. These fractures would currently be filled with non-acidified brine saturated in seal formation brine. When the acidifeid brine from the host formation and the cap rock brine mix there is the potential for minerals to fall out of solution, and for these precipitated minerals to decrease or entirely cut off the fluid flow through the fractures present in a reservoir seal. Initial equilibrium simulations performed using the PHREEQC1 database drived from the PHREEQE2 database are used to show the favorable conditions under which this mineral precipitation can occurs. Bench scale fluid mixing experiments were then performed to determine the kinetics of the mineral precipitation process, and determine the progress of future experiemnts involving fluid flow within fractured anhydrite reservoir seal samples. 1Parkhurst, D.L., and Appelo, C.A.J., 2013, Description of input and examples for PHREEQC version 3—A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations: U.S. Geological Survey Techniques and Methods, book 6, chap. A43, 497 p., available only at https://pubs.usgs.gov/tm/06/a43/. 2Parkhurst, David L., Donald C. Thorstenson, and L. Niel Plummer. PHREEQE: a computer program for geochemical calculations. No. 80-96. US Geological Survey, Water Resources Division,, 1980.

  4. A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows.

    Science.gov (United States)

    Daivis, Peter J; Todd, B D

    2006-05-21

    We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.

  5. Lower Palaeozoic reservoirs of North Africa

    Energy Technology Data Exchange (ETDEWEB)

    Crossley, R.; McDougall, N. [Robertson Research International Ltd., Llandudno, Conwy (United Kingdom)

    1998-12-31

    This paper provides an overview of features considered significant in the exploration and development of Lower Palaeozoic reservoirs of North Africa. Information is derived from a review of literature on the Lower Palaeozoic successions of North Africa, combined with outcrop observations from the Anti Atlas mountains of Morocco. The focus of the exploration-oriented part of the review is on identification of potential traps other than two-way structural dip closure. Stratigraphic elements described include depositional models of reservoir facies, tectonic unconformities and possible eustatic unconformities. Cases of established or potential trapping by post-depositional faulting by diagenesis and by hydrodynamic flow are examined. Development-related topics highlighted include the impact on reservoir matrix quality of burial diagenesis and of palaeo-weathering at the Hercynian unconformity. Other issues discussed which additionally affect producibility from the reservoir matrix include tectonic fracturing, palaeotopography and unloading fracturing at the Hercynian unconformity, and induced fracturing within the present stress regimes. (author)

  6. Simulation of uncompressible fluid flow through a porous media

    International Nuclear Information System (INIS)

    Ramirez, A.; Gonzalez, J.L.; Carrillo, F.; Lopez, S.

    2009-01-01

    Recently, a great interest has been focused for investigations about transport phenomena in disordered systems. One of the most treated topics is fluid flow through anisotropic materials due to the importance in many industrial processes like fluid flow in filters, membranes, walls, oil reservoirs, etc. In this work is described the formulation of a 2D mathematical model to simulate the fluid flow behavior through a porous media (PM) based on the solution of the continuity equation as a function of the Darcy's law for a percolation system; which was reproduced using computational techniques reproduced using a random distribution of the porous media properties (porosity, permeability and saturation). The model displays the filling of a partially saturated porous media with a new injected fluid showing the non-defined advance front and dispersion of fluids phenomena.

  7. Instantaneous equations for multiphase flow in porous media without length-scale restrictions using a non-local averaging volume

    International Nuclear Information System (INIS)

    Espinosa-Paredes, Gilberto

    2010-01-01

    The aim of this paper is to propose a framework to obtain a new formulation for multiphase flow conservation equations without length-scale restrictions, based on the non-local form of the averaged volume conservation equations. The simplification of the local averaging volume of the conservation equations to obtain practical equations is subject to the following length-scale restrictions: d << l << L, where d is the characteristic length of the dispersed phases, l is the characteristic length of the averaging volume, and L is the characteristic length of the physical system. If the foregoing inequality does not hold, or if the scale of the problem of interest is of the order of l, the averaging technique and therefore, the macroscopic theories of multiphase flow should be modified in order to include appropriate considerations and terms in the corresponding equations. In these cases the local form of the averaged volume conservation equations are not appropriate to describe the multiphase system. As an example of the conservation equations without length-scale restrictions, the natural circulation boiling water reactor was consider to study the non-local effects on the thermal-hydraulic core performance during steady-state and transient behaviors, and the results were compared with the classic local averaging volume conservation equations.

  8. Is the kinetic equation for turbulent gas-particle flows ill posed?

    Science.gov (United States)

    Reeks, M; Swailes, D C; Bragg, A D

    2018-02-01

    This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

  9. Simulating cold production by a coupled reservoir-geomechanics model with sand erosion

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Y.; Xue, S. [Petro-Geotech Inc., Calgary, AB (Canada)

    2002-06-01

    This paper presents a newly developed fully coupled reservoir-geomechanics model with sand erosion. Sand production occurs during aggressive production induced by the impact of viscous fluid flow and the in situ stress concentration near a wellbore, as well as by perforation tips in poorly consolidated formations. This compromises oil production, increases well completion costs, and reduces the life cycles of equipment down hole and on the surface. The proposed model can be used for sand production studies in conventional oil/gas reservoirs such as the North Sea as well as in heavy oil reservoirs such as in northwestern Canada. Instead of generating a high permeability network in reservoirs, the enhanced oil production is determined by the increase in the effective wellbore radius. This paper presents the general model. A detailed study on the capillary pressure and the impact of multiphase flow on sanding and erosion will be conducted at a later date. It appears that 2 phase flow can be important to elastoplasticity if no significant sand erosion has occurred. It was determined that high porosity is induced by erosion and capillary pressure. Two phase flow can be important when the built-up drag force carries sand-fluid slurry into the well. It is concluded that viscosity and flow velocity can help estimate the slurry transport, sand rate and enhanced oil production. 22 refs., 3 tabs., 11 figs.

  10. Physical Model-Based Investigation of Reservoir Sedimentation Processes

    Directory of Open Access Journals (Sweden)

    Cheng-Chia Huang

    2018-03-01

    Full Text Available Sedimentation is a serious problem in the operations of reservoirs. In Taiwan, the situation became worse after the Chi-Chi Earthquake recorded on 21 September 1999. The sediment trap efficiency in several regional reservoirs has been sharply increased, adversely affecting the operations on water supplies. According to the field record, the average annual sediment deposition observed in several regional reservoirs in Taiwan has been increased. For instance, the typhoon event recorded in 2008 at the Wushe Reservoir, Taiwan, produced a 3 m sediment deposit upstream of the dam. The remaining storage capacity in the Wushe Reservoir was reduced to 35.9% or a volume of 53.79 million m3 for flood water detention in 2010. It is urgent that research should be conducted to understand the sediment movement in the Wushe Reservoir. In this study, a scale physical model was built to reproduce the flood flow through the reservoir, investigate the long-term depositional pattern, and evaluate sediment trap efficiency. This allows us to estimate the residual life of the reservoir by proposing a modification of Brune’s method. It can be presented to predict the lifespan of Taiwan reservoirs due to higher applicability in both the physical model and the observed data.

  11. Numerical simulations of air–water cap-bubbly flows using two-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Wang, Xia; Sun, Xiaodong

    2014-01-01

    Highlights: • Two-group interfacial area transport equation was implemented into a three-field two-fluid model in Fluent. • Numerical model was developed for cap-bubbly flows in a narrow rectangular flow channel. • Numerical simulations were performed for cap-bubbly flows with uniform void inlets and with central peaked void inlets. • Code simulations showed a significant improve over the conventional two-fluid model. - Abstract: Knowledge of cap-bubbly flows is of great interest due to its role in understanding of the flow regime transition from bubbly to slug or churn-turbulent flows. One of the key characteristics of such flows is the existence of bubbles in different sizes and shapes associated with their distinctive dynamic natures. This important feature is, however, generally not well captured by many available two-phase flow modeling approaches. In this study, a modified two-fluid model, namely a three-field, two-fluid model, is proposed. In this model, bubbles are categorized into two groups, i.e., spherical/distorted bubbles as Group-1 while cap/churn-turbulent bubbles as Group-2. A two-group interfacial area transport equation (IATE) is implemented to describe dynamic changes of interfacial structure in each bubble group, resulting from intra- and inter-group interactions and phase changes due to evaporation and condensation. Attention is also paid to appropriate constitutive relations of the interfacial transfers due to mechanical and thermal non-equilibrium between the different fields. The proposed three-field, two-fluid model is used to predict the phase distributions of adiabatic air–water flows in a confined rectangular duct. Good agreement between the simulation results from the proposed model and relevant experimental data indicates that the proposed model is promising as an improved computational tool for two-phase cap-bubbly flow simulations in rectangular flow ducts

  12. Multi Data Reservoir History Matching using the Ensemble Kalman Filter

    KAUST Repository

    Katterbauer, Klemens

    2015-05-01

    Reservoir history matching is becoming increasingly important with the growing demand for higher quality formation characterization and forecasting and the increased complexity and expenses for modern hydrocarbon exploration projects. History matching has long been dominated by adjusting reservoir parameters based solely on well data whose spatial sparse sampling has been a challenge for characterizing the flow properties in areas away from the wells. Geophysical data are widely collected nowadays for reservoir monitoring purposes, but has not yet been fully integrated into history matching and forecasting fluid flow. In this thesis, I present a pioneering approach towards incorporating different time-lapse geophysical data together for enhancing reservoir history matching and uncertainty quantification. The thesis provides several approaches to efficiently integrate multiple geophysical data, analyze the sensitivity of the history matches to observation noise, and examine the framework’s performance in several settings, such as the Norne field in Norway. The results demonstrate the significant improvements in reservoir forecasting and characterization and the synergy effects encountered between the different geophysical data. In particular, the joint use of electromagnetic and seismic data improves the accuracy of forecasting fluid properties, and the usage of electromagnetic data has led to considerably better estimates of hydrocarbon fluid components. For volatile oil and gas reservoirs the joint integration of gravimetric and InSAR data has shown to be beneficial in detecting the influx of water and thereby improving the recovery rate. Summarizing, this thesis makes an important contribution towards integrated reservoir management and multiphysics integration for reservoir history matching.

  13. Spectral and evolutionary analysis of advection-diffusion equations and the shear flow paradigm

    International Nuclear Information System (INIS)

    Thyagaraja, A.; Loureiro, N.; Knight, P.J.

    2002-01-01

    Advection-diffusion equations occur in a wide variety of fields in many contexts of active and passive transport in fluids and plasmas. The effects of sheared advective flows in the presence of irreversible processes such as diffusion and viscosity are of considerable current interest in tokamak and astrophysical contexts, where they are thought to play a key role in both transport and the dynamical structures characteristic of electromagnetic plasma turbulence. In this paper we investigate the spectral and evolutionary properties of relatively simple, linear, advection-diffusion equations. We apply analytical approaches based on standard Green's function methods to obtain insight into the nature of the spectra when the advective and diffusive effects occur separately and in combination. In particular, the physically interesting limit of small (but finite) diffusion is studied in detail. The analytical work is extended and supplemented by numerical techniques involving a direct solution of the eigenvalue problem as well as evolutionary studies of the initial value problem using a parallel code, CADENCE. The three approaches are complementary and entirely consistent with each other when appropriate comparison is made. They reveal different aspects of the properties of the advection-diffusion equation, such as the ability of sheared flows to generate a direct cascade to high wave numbers transverse to the advection and the consequent enhancement of even small amounts of diffusivity. The invariance properties of the spectra in the low diffusivity limit and the ability of highly sheared, jet-like flows to 'confine' transport to low shear regions are demonstrated. The implications of these properties in a wider context are discussed and set in perspective. (author)

  14. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir

    Directory of Open Access Journals (Sweden)

    Shams Bilal

    2017-08-01

    Full Text Available Gas condensate reservoirs usually exhibit complex flow behaviors because of propagation response of pressure drop from the wellbore into the reservoir. When reservoir pressure drops below the dew point in two phase flow of gas and condensate, the accumulation of large condensate amount occurs in the gas condensate reservoirs. Usually, the saturation of condensate accumulation in volumetric gas condensate reservoirs is lower than the critical condensate saturation that causes trapping of large amount of condensate in reservoir pores. Trapped condensate often is lost due to condensate accumulation-condensate blockage courtesy of high molecular weight, heavy condensate residue. Recovering lost condensate most economically and optimally has always been a challenging goal. Thus, gas cycling is applied to alleviate such a drastic loss in resources.

  15. A reduced set of gyrofluid equations for plasma flow in a diverging magnetic field

    International Nuclear Information System (INIS)

    Robertson, Scott

    2016-01-01

    Plasmas are often generated in a small diameter source with a strong magnetic field and subsequently flow into a region with greater diameter and smaller field. The magnetic mirror force that accelerates plasma in a diverging magnetic field appears in the gyrofluid equations developed for applications to toroidal devices, but this force is often absent from fluid equations. A set of gyrofluid equations with reduced complexity is developed in which drifts are assumed negligible and the mirror force is retained. The Chew–Goldberger–Low equations of state are used for a simple closure. These reduced gyrofluid equations are applied to plasma equilibrium in a magnetic mirror, to acceleration of plasma in a magnetic nozzle, and to space charge neutralization of an ion beam by electrons in a diverging magnetic field. The results from gyrofluid theory are compared with results from drift kinetic theory to find the accuracy of the gyrofluid approximation in these applications.

  16. High Temperature, high pressure equation of state density correlations and viscosity correlations

    Energy Technology Data Exchange (ETDEWEB)

    Tapriyal, D.; Enick, R.; McHugh, M.; Gamwo, I.; Morreale, B.

    2012-07-31

    Global increase in oil demand and depleting reserves has derived a need to find new oil resources. To find these untapped reservoirs, oil companies are exploring various remote and harsh locations such as deep waters in Gulf of Mexico, remote arctic regions, unexplored deep deserts, etc. Further, the depth of new oil/gas wells being drilled has increased considerably to tap these new resources. With the increase in the well depth, the bottomhole temperature and pressure are also increasing to extreme values (i.e. up to 500 F and 35,000 psi). The density and viscosity of natural gas and crude oil at reservoir conditions are critical fundamental properties required for accurate assessment of the amount of recoverable petroleum within a reservoir and the modeling of the flow of these fluids within the porous media. These properties are also used to design appropriate drilling and production equipment such as blow out preventers, risers, etc. With the present state of art, there is no accurate database for these fluid properties at extreme conditions. As we have begun to expand this experimental database it has become apparent that there are neither equations of state for density or transport models for viscosity that can be used to predict these fundamental properties of multi-component hydrocarbon mixtures over a wide range of temperature and pressure. Presently, oil companies are using correlations based on lower temperature and pressure databases that exhibit an unsatisfactory predictive capability at extreme conditions (e.g. as great as {+-} 50%). From the perspective of these oil companies that are committed to safely producing these resources, accurately predicting flow rates, and assuring the integrity of the flow, the absence of an extensive experimental database at extreme conditions and models capable of predicting these properties over an extremely wide range of temperature and pressure (including extreme conditions) makes their task even more daunting.

  17. Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation.

    Science.gov (United States)

    Fach, S; Sitzenfrei, R; Rauch, W

    2009-01-01

    It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

  18. The linearized pressure Poisson equation for global instability analysis of incompressible flows

    Science.gov (United States)

    Theofilis, Vassilis

    2017-12-01

    The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

  19. Estimated cumulative sediment trapping in future hydropower reservoirs in Africa

    Science.gov (United States)

    Lucía, Ana; Berlekamp, Jürgen; Zarfl, Christiane

    2017-04-01

    Despite a rapid economic development in Sub-Saharan Africa, almost 70% of the human population in this area remain disconnected from electricity access (International Energy Agency 2011). Mitigating climate change and a search for renewable, "climate neutral" electricity resources are additional reasons why Africa will be one key centre for future hydropower dam building, with only 8% of the technically feasible hydropower potential actually exploited. About 300 major hydropower dams with a total capacity of 140 GW are currently under construction (11.4%) or planned (88.6%) (Zarfl et al. 2015). Despite the benefits of hydropower dams, fragmentation of the rivers changes the natural flow, temperature and sediment regime. This has consequences for a high number of people that directly depend on the primary sector linked to rivers and floodplains. But sediment trapping in the reservoir also affects dam operation and decreases its life span. Thus, the objective of this work is to quantify the dimension of sediment trapping by future hydropower dams in African river basins. Soil erosion is described with the universal soil loss equation (Wischmeier & Smith 1978) and combined with the connectivity index (Cavalli et al. 2013) to estimate the amount of eroded soil that reaches the fluvial network and finally ends up in the existing (Lehner et al. 2011) and future reservoirs (Zarfl et al. 2015) per year. Different scenarios assuming parameter values from the literature are developed to include model uncertainty. Estimations for existing dams will be compared with literature data to evaluate the applied estimation method and scenario assumptions. Based on estimations for the reservoir volume of the future dams we calculated the potential time-laps of the future reservoirs due to soil erosion and depending on their planned location. This approach could support sustainable decision making for the location of future hydropower dams. References Cavalli, M., Trevisani, S., Comiti

  20. Application of Reservoir Flow Simulation Integrated with Geomechanics in Unconventional Tight Play

    Science.gov (United States)

    Lin, Menglu; Chen, Shengnan; Mbia, Ernest; Chen, Zhangxing

    2018-01-01

    Multistage hydraulic fracturing techniques, combined with horizontal drilling, have enabled commercial production from the vast reserves of unconventional tight formations. During hydraulic fracturing, fracturing fluid and proppants are pumped into the reservoir matrix to create the hydraulic fractures. Understanding the propagation mechanism of hydraulic fractures is essential to estimate their properties, such as half-length. In addition, natural fractures are often present in tight formations, which might be activated during the fracturing process and contribute to the post-stimulation well production rates. In this study, reservoir simulation is integrated with rock geomechanics to predict the well post-stimulation productivities. Firstly, a reservoir geological model is built based on the field data collected from the Montney formation in the Western Canadian Sedimentary Basin. The hydraulic fracturing process is then simulated through an integrated approach of fracturing fluid injection, rock geomechanics, and tensile failure criteria. In such a process, the reservoir pore pressure increases with a continuous injection of the fracturing fluid and proppants, decreasing the effective stress exerted on the rock matrix accordingly as the overburden pressure remains constant. Once the effective stress drops to a threshold value, tensile failure of the reservoir rock occurs, creating hydraulic fractures in the formation. The early production history of the stimulated well is history-matched to validate the predicted fracture geometries (e.g., half-length) generated from the fracturing simulation process. The effects of the natural fracture properties and well bottom-hole pressures on well productivity are also studied. It has been found that nearly 40% of hydraulic fractures propagate in the beginning stage (the pad step) of the fracturing schedule. In addition, well post-stimulation productivity will increase significantly if the natural fractures are propped or

  1. Limno-reservoirs as a new landscape, environmental and touristic resource: Pareja Limno-reservoir as a case of study (Guadalajara, Spain)

    Science.gov (United States)

    Díaz-Carrión, I.; Sastre-Merlín, A.; Martínez-Pérez, S.; Molina-Navarro, E.; Bienes-Allas, R.

    2012-04-01

    A limno-reservoir is a hydrologic infrastructure with the main goal of generating a body of water with a constant level in the riverine zone of a reservoir, building a dam that makes de limno-reservoir independent from the main body of water. This dam can be built in the main river supplying the reservoir or any tributary as well flowing into it. Despite its novel conception and design, around a dozen are already operative in some Spanish reservoirs. This infrastructure allows the new water body to be independent of the main reservoir management, so the water level stability is its main distinctive characteristic. It leads to the development of environmental, sports and cultural initiatives; which may be included in a touristic exploitation in a wide sense. An opinion poll was designed in 2009 to be carried out the Pareja Limno-reservoir (Entrepeñas reservoir area, Tajo River Basin, central Spain). The results showed that for both, Pareja inhabitants and occasional visitors, the limno-reservoir has become an important touristic resource, mainly demanded during summer season. The performance of leisure activities (especially swimming) are being the main brand of this novel hydraulic and environmental infrastructure, playing a role as corrective and/or compensatory action which is needed to apply in order to mitigate the environmental impacts of the large hydraulic constructions.

  2. Productivity Analysis of Volume Fractured Vertical Well Model in Tight Oil Reservoirs

    Directory of Open Access Journals (Sweden)

    Jiahang Wang

    2017-01-01

    Full Text Available This paper presents a semianalytical model to simulate the productivity of a volume fractured vertical well in tight oil reservoirs. In the proposed model, the reservoir is a composite system which contains two regions. The inner region is described as formation with finite conductivity hydraulic fracture network and the flow in fracture is assumed to be linear, while the outer region is simulated by the classical Warren-Root model where radial flow is applied. The transient rate is calculated, and flow patterns and characteristic flowing periods caused by volume fractured vertical well are analyzed. Combining the calculated results with actual production data at the decline stage shows a good fitting performance. Finally, the effects of some sensitive parameters on the type curves are also analyzed extensively. The results demonstrate that the effect of fracture length is more obvious than that of fracture conductivity on improving production in tight oil reservoirs. When the length and conductivity of main fracture are constant, the contribution of stimulated reservoir volume (SRV to the cumulative oil production is not obvious. When the SRV is constant, the length of fracture should also be increased so as to improve the fracture penetration and well production.

  3. On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size

    Directory of Open Access Journals (Sweden)

    Chong Liu

    2011-09-01

    Full Text Available In this work, we investigate the validity of the Navier-Stokes (NS equations for nanoscale liquid flows through molecular dynamics simulations. We focus on the role of channel size by considering the fluid-wall interaction. Liquid flows between two planar parallel walls driven by an external force with channel size ranging from 2 to 80 nm are studied. The volumetric flux is computed and the dependence of the volumetric flux on the channel size is explained both qualitatively and quantitatively. It is found that the flow is sensitive to the fluid-wall binding energy and the classical fluid mechanics falls apart in small nanochannels. However, the wall effects become insignificant and the NS equations are valid when the channel size is larger than about 150 molecular diameters (∼ 50 nm.

  4. The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution

    NARCIS (Netherlands)

    Veldman, A.E.P.

    1973-01-01

    A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag

  5. Impact of Petrophysical Properties on Hydraulic Fracturing and Development in Tight Volcanic Gas Reservoirs

    Directory of Open Access Journals (Sweden)

    Yinghao Shen

    2017-01-01

    Full Text Available The volcanic reservoir is an important kind of unconventional reservoir. The aqueous phase trapping (APT appears because of fracturing fluids filtration. However, APT can be autoremoved for some wells after certain shut-in time. But there is significant distinction for different reservoirs. Experiments were performed to study the petrophysical properties of a volcanic reservoir and the spontaneous imbibition is monitored by nuclear magnetic resonance (NMR and pulse-decay permeability. Results showed that natural cracks appear in the samples as well as high irreducible water saturation. There is a quick decrease of rock permeability once the rock contacts water. The pores filled during spontaneous imbibition are mainly the nanopores from NMR spectra. Full understanding of the mineralogical effect and sample heterogeneity benefits the selection of segments to fracturing. The fast flow-back scheme is applicable in this reservoir to minimize the damage. Because lots of water imbibed into the nanopores, the main flow channels become larger, which are beneficial to the permeability recovery after flow-back of hydraulic fracturing. This is helpful in understanding the APT autoremoval after certain shut-in time. Also, Keeping the appropriate production differential pressure is very important in achieving the long term efficient development of volcanic gas reservoirs.

  6. Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux

    International Nuclear Information System (INIS)

    Kawamura, Hiroshi

    1978-01-01

    Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)

  7. Production performance laws of vertical wells by volume fracturing in CBM reservoirs

    Directory of Open Access Journals (Sweden)

    Liehui Zhang

    2017-05-01

    Full Text Available Volume fracturing technology has been widely applied in the development of coalbed methane (CBM reservoirs. As for the stimulated reservoir volume (SRV created by volume fracturing, the seepage laws of fluids are described more accurately and rationally in the rectangular composite model than in the traditional radial composite model. However, the rectangular composite model considering SRV cannot be solved using the analytical or semi-analytical function method, and its solution from the linear flow model has larger errors. In view of this, SRV areas of CBM reservoirs were described by means of dual-medium model in this paper. The complex CBM migration mechanisms were investigated comprehensively, including adsorption, desorption, diffusion and seepage. A well testing model for rectangular composite fracturing wells in CBM reservoirs based on unsteady-state diffusion was built and solved using the boundary element method combined with Laplace transformation, Stehfest numerical inversion and computer programming technology. Thus, production performance laws of CBM reservoirs were clarified. The flow regimes of typical well testing curves were divided and the effects on change laws of production performance from the boundary size of gas reservoirs, permeability of volume fractured areas, adsorption gas content, reservoir permeability and SRV size were analyzed. Eventually, CBM reservoirs after the volume fracturing stimulation were described more accurately and rationally. This study provides a theoretical basis for a better understanding of the CBM migration laws and an approach to evaluating and developing CBM reservoirs efficiently and rationally.

  8. A framework to identify Pareto-efficient subdaily environmental flow constraints on hydropower reservoirs using a grid-wide power dispatch model

    Science.gov (United States)

    Olivares, Marcelo A.; Haas, Jannik; Palma-Behnke, Rodrigo; Benavides, Carlos

    2015-05-01

    Hydrologic alteration due to hydropeaking reservoir operations is a main concern worldwide. Subdaily environmental flow constraints (ECs) on operations can be promising alternatives for mitigating negative impacts. However, those constraints reduce the flexibility of hydropower plants, potentially with higher costs for the power system. To study the economic and environmental efficiency of ECs, this work proposes a novel framework comprising four steps: (i) assessment of the current subdaily hydrologic alteration; (ii) formulation and implementation of a short-term, grid-wide hydrothermal coordination model; (iii) design of ECs in the form of maximum ramping rates (MRRs) and minimum flows (MIFs) for selected hydropower reservoirs; and (iv) identification of Pareto-efficient solutions in terms of grid-wide costs and the Richard-Baker flashiness index for subdaily hydrologic alteration (SDHA). The framework was applied to Chile's main power grid, assessing 25 EC cases, involving five MIFs and five MRRs. Each case was run for a dry, normal, and wet water year type. Three Pareto-efficient ECs are found, with remarkably small cost increase below 2% and a SDHA improvement between 28% and 90%. While the case involving the highest MIF worsens the flashiness of another basin, the other two have no negative effect on other basins and can be recommended for implementation.

  9. Unstructured grids and an element based conservative approach for a black-oil reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Nogueira, Regis Lopes; Fernandes, Bruno Ramon Batista [Federal University of Ceara, Fortaleza, CE (Brazil). Dept. of Chemical Engineering; Araujo, Andre Luiz de Souza [Federal Institution of Education, Science and Technology of Ceara - IFCE, Fortaleza (Brazil). Industry Department], e-mail: andre@ifce.edu.br; Marcondes, Francisco [Federal University of Ceara, Fortaleza, CE (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br

    2010-07-01

    Unstructured meshes presented one upgrade in modeling the main important features of the reservoir such as discrete fractures, faults, and irregular boundaries. From several methodologies available, the Element based Finite Volume Method (EbFVM), in conjunction with unstructured meshes, is one methodology that deserves large attention. In this approach, the reservoir, for 2D domains, is discretized using a mixed two-dimensional mesh using quadrilateral and triangle elements. After the initial step of discretization, each element is divided into sub-elements and the mass balance for each component is developed for each sub-element. The equations for each control-volume using a cell vertex construction are formulated through the contribution of different neighboured elements. This paper presents an investigation of an element-based approach using the black-oil model based on pressure and global mass fractions. In this approach, even when all gas phase is dissolved in oil phase the global mass fraction of gas will be different from zero. Therefore, no additional numerical procedure is necessary in order to treat the gas phase appear/disappearance. In this paper the above mentioned approach is applied to multiphase flows involving oil, gas, and water. The mass balance equations in terms of global mass fraction of oil, gas and water are discretized through the EbFVM and linearized by the Newton's method. The results are presented in terms of volumetric rates of oil, gas, and water and phase saturations. (author)

  10. Production Optimization of Oil Reservoirs

    DEFF Research Database (Denmark)

    Völcker, Carsten

    with emphasis on optimal control of water ooding with the use of smartwell technology. We have implemented immiscible ow of water and oil in isothermal reservoirs with isotropic heterogenous permeability elds. We use the method of lines for solution of the partial differential equation (PDE) system that governs...... the uid ow. We discretize the the two-phase ow model spatially using the nite volume method (FVM), and we use the two point ux approximation (TPFA) and the single-point upstream (SPU) scheme for computing the uxes. We propose a new formulation of the differential equation system that arise...... as a consequence of the spatial discretization of the two-phase ow model. Upon discretization in time, the proposed equation system ensures the mass conserving property of the two-phase ow model. For the solution of the spatially discretized two-phase ow model, we develop mass conserving explicit singly diagonally...

  11. Hybrid meshes and domain decomposition for the modeling of oil reservoirs; Maillages hybrides et decomposition de domaine pour la modelisation des reservoirs petroliers

    Energy Technology Data Exchange (ETDEWEB)

    Gaiffe, St

    2000-03-23

    In this thesis, we are interested in the modeling of fluid flow through porous media with 2-D and 3-D unstructured meshes, and in the use of domain decomposition methods. The behavior of flow through porous media is strongly influenced by heterogeneities: either large-scale lithological discontinuities or quite localized phenomena such as fluid flow in the neighbourhood of wells. In these two typical cases, an accurate consideration of the singularities requires the use of adapted meshes. After having shown the limits of classic meshes we present the future prospects offered by hybrid and flexible meshes. Next, we consider the generalization possibilities of the numerical schemes traditionally used in reservoir simulation and we draw two available approaches: mixed finite elements and U-finite volumes. The investigated phenomena being also characterized by different time-scales, special treatments in terms of time discretization on various parts of the domain are required. We think that the combination of domain decomposition methods with operator splitting techniques may provide a promising approach to obtain high flexibility for a local tune-steps management. Consequently, we develop a new numerical scheme for linear parabolic equations which allows to get a higher flexibility in the local space and time steps management. To conclude, a priori estimates and error estimates on the two variables of interest, namely the pressure and the velocity are proposed. (author)

  12. Gradients in Catostomid assemblages along a reservoir cascade

    Science.gov (United States)

    Miranda, Leandro E.; Keretz, Kevin R.; Gilliland, Chelsea R.

    2017-01-01

    Serial impoundment of major rivers leads to alterations of natural flow dynamics and disrupts longitudinal connectivity. Catostomid fishes (suckers, family Catostomidae) are typically found in riverine or backwater habitats yet are able to persist in impounded river systems. To the detriment of conservation, there is limited information about distribution of catostomid fishes in impounded rivers. We examined the longitudinal distribution of catostomid fishes over 23 reservoirs of the Tennessee River reservoir cascade, encompassing approximately 1600 km. Our goal was to develop a basin-scale perspective to guide conservation efforts. Catostomid species composition and assemblage structure changed longitudinally along the reservoir cascade. Catostomid species biodiversity was greatest in reservoirs lower in the cascade. Assemblage composition shifted from dominance by spotted sucker Minytrema melanops and buffalos Ictiobus spp. in the lower reservoirs to carpsuckers Carpiodes spp. midway through the cascade and redhorses Moxostoma spp. in the upper reservoirs. Most species did not extend the length of the cascade, and some species were rare, found in low numbers and in few reservoirs. The observed gradients in catostomid assemblages suggest the need for basin-scale conservation measures focusing on three broad areas: (1) conservation and management of the up-lake riverine reaches of the lower reservoirs, (2) maintenance of the access to quality habitat in tributaries to the upper reservoirs and (3) reintroductions into currently unoccupied habitat within species' historic distributions

  13. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  14. Multi-Scale Coupling Between Monte Carlo Molecular Simulation and Darcy-Scale Flow in Porous Media

    KAUST Repository

    Saad, Ahmed Mohamed

    2016-06-01

    In this work, an efficient coupling between Monte Carlo (MC) molecular simulation and Darcy-scale flow in porous media is presented. The cell centered finite difference method with non-uniform rectangular mesh were used to discretize the simulation domain and solve the governing equations. To speed up the MC simulations, we implemented a recently developed scheme that quickly generates MC Markov chains out of pre-computed ones, based on the reweighting and reconstruction algorithm. This method astonishingly reduces the required computational times by MC simulations from hours to seconds. To demonstrate the strength of the proposed coupling in terms of computational time efficiency and numerical accuracy in fluid properties, various numerical experiments covering different compressible single-phase flow scenarios were conducted. The novelty in the introduced scheme is in allowing an efficient coupling of the molecular scale and the Darcy\\'s one in reservoir simulators. This leads to an accurate description of thermodynamic behavior of the simulated reservoir fluids; consequently enhancing the confidence in the flow predictions in porous media.

  15. The time-lapse AVO difference inversion for changes in reservoir parameters

    Science.gov (United States)

    Longxiao, Zhi; Hanming, Gu; Yan, Li

    2016-12-01

    The result of conventional time-lapse seismic processing is the difference between the amplitude and the post-stack seismic data. Although stack processing can improve the signal-to-noise ratio (SNR) of seismic data, it also causes a considerable loss of important information about the amplitude changes and only gives the qualitative interpretation. To predict the changes in reservoir fluid more precisely and accurately, we also need the quantitative information of the reservoir. To achieve this aim, we develop the method of time-lapse AVO (amplitude versus offset) difference inversion. For the inversion of reservoir changes in elastic parameters, we apply the Gardner equation as the constraint and convert the three-parameter inversion of elastic parameter changes into a two-parameter inversion to make the inversion more stable. For the inversion of variations in the reservoir parameters, we infer the relation between the difference of the reflection coefficient and variations in the reservoir parameters, and then invert reservoir parameter changes directly. The results of the theoretical modeling computation and practical application show that our method can estimate the relative variations in reservoir density, P-wave and S-wave velocity, calculate reservoir changes in water saturation and effective pressure accurately, and then provide reference for the rational exploitation of the reservoir.

  16. Analysis of selected reservoirs functioning in the Wielkopolska region

    Directory of Open Access Journals (Sweden)

    Mariusz Sojka

    2017-12-01

    Full Text Available The paper presents the problems related to the functioning of reservoirs in the Wielkopolska province and suggests their possible solutions. The reservoirs chosen as examples include typical dam constructions with a single water body (Jeziorsko, Rydzyna, two water body objects with separated preliminary part (Stare Miasto, Kowalskie, Radzyny and lateral constructions (Pakosław, Jutrosin. The reservoirs were built in period from 1970 to 2014. They differ in construction, functions and water management rules. Analysis of the main problems related to the reservoir functioning is aimed at finding ways of improving the construction of new reservoirs that would satisfy increasingly stringent environmental and legal restrictions and the methods of water management in the reservoirs. On the basis of a questionnaire filled in by the reservoir operators, the main problem is water quality. Especially the huge inflow of biogenic compounds causes blooms of algae and overgrowth with riparian vegetation. Some difficulties are also related to management of the reservoirs of multi-purpose operation. It is difficult to take into account the requirements of environmental flow maintenance, flood protection, water supply for agriculture and water use for tourism and recreation and hydropower generation, etc.

  17. Simulation of uncompressible fluid flow through a porous media

    Energy Technology Data Exchange (ETDEWEB)

    Ramirez, A. [Instituto Politecnico Nacional (SEPI-ESIQIE-IPN), Unidad Profesional Zacatenco, Laboratorio de Analisis Met. (Edif. ' Z' y Edif. ' 6' P.B.), Mexico City (Mexico)], E-mail: adaramil@yahoo.com.mx; Gonzalez, J.L. [Instituto Politecnico Nacional (SEPI-ESIQIE-IPN), Unidad Profesional Zacatenco, Laboratorio de Analisis Met. (Edif. ' Z' y Edif. ' 6' P.B.), Mexico City (Mexico); Carrillo, F. [Instituto Politecnico Nacional (SEPI-CICATA-IPN), Unidad Altamira Tamaulipas, Mexico (Mexico); Lopez, S. [Instituto Mexicano del Petroleo (I.M.P.-D.F.), Mexico (Mexico)

    2009-02-28

    Recently, a great interest has been focused for investigations about transport phenomena in disordered systems. One of the most treated topics is fluid flow through anisotropic materials due to the importance in many industrial processes like fluid flow in filters, membranes, walls, oil reservoirs, etc. In this work is described the formulation of a 2D mathematical model to simulate the fluid flow behavior through a porous media (PM) based on the solution of the continuity equation as a function of the Darcy's law for a percolation system; which was reproduced using computational techniques reproduced using a random distribution of the porous media properties (porosity, permeability and saturation). The model displays the filling of a partially saturated porous media with a new injected fluid showing the non-defined advance front and dispersion of fluids phenomena.

  18. Neoclassical MHD equations for tokamaks

    International Nuclear Information System (INIS)

    Callen, J.D.; Shaing, K.C.

    1986-03-01

    The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

  19. Preliminary formation analysis for compressed air energy storage in depleted natural gas reservoirs :

    Energy Technology Data Exchange (ETDEWEB)

    Gardner, William Payton

    2013-06-01

    The purpose of this study is to develop an engineering and operational understanding of CAES performance for a depleted natural gas reservoir by evaluation of relative permeability effects of air, water and natural gas in depleted natural gas reservoirs as a reservoir is initially depleted, an air bubble is created, and as air is initially cycled. The composition of produced gases will be evaluated as the three phase flow of methane, nitrogen and brine are modeled. The effects of a methane gas phase on the relative permeability of air in a formation are investigated and the composition of the produced fluid, which consists primarily of the amount of natural gas in the produced air are determined. Simulations of compressed air energy storage (CAES) in depleted natural gas reservoirs were carried out to assess the effect of formation permeability on the design of a simple CAES system. The injection of N2 (as a proxy to air), and the extraction of the resulting gas mixture in a depleted natural gas reservoir were modeled using the TOUGH2 reservoir simulator with the EOS7c equation of state. The optimal borehole spacing was determined as a function of the formation scale intrinsic permeability. Natural gas reservoir results are similar to those for an aquifer. Borehole spacing is dependent upon the intrinsic permeability of the formation. Higher permeability allows increased injection and extraction rates which is equivalent to more power per borehole for a given screen length. The number of boreholes per 100 MW for a given intrinsic permeability in a depleted natural gas reservoir is essentially identical to that determined for a simple aquifer of identical properties. During bubble formation methane is displaced and a sharp N2methane boundary is formed with an almost pure N2 gas phase in the bubble near the borehole. During cycling mixing of methane and air occurs along the boundary as the air bubble boundary moves. The extracted gas mixture changes as a

  20. Study of magnetized accretion flow with variable Γ equation of state

    Science.gov (United States)

    Singh, Kuldeep; Chattopadhyay, Indranil

    2018-05-01

    We present here the solutions of magnetized accretion flow on to a compact object with hard surface such as neutron stars. The magnetic field of the central star is assumed dipolar and the magnetic axis is assumed to be aligned with the rotation axis of the star. We have used an equation of state for the accreting fluid in which the adiabatic index is dependent on temperature and composition of the flow. We have also included cooling processes like bremsstrahlung and cyclotron processes in the accretion flow. We found all possible accretion solutions. All accretion solutions terminate with a shock very near to the star surface and the height of this primary shock does not vary much with either the spin period or the Bernoulli parameter of the flow, although the strength of the shock may vary with the period. For moderately rotating central star, there is possible formation of multiple sonic points in the flow and therefore, a second shock far away from the star surface may also form. However, the second shock is much weaker than the primary one near the surface. We found that if rotation period is below a certain value (P*), then multiple critical points or multiple shocks are not possible and P* depends upon the composition of the flow. We also found that cooling effect dominates after the shock and that the cyclotron and the bremsstrahlung cooling processes should be considered to obtain a consistent accretion solution.

  1. Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

    Science.gov (United States)

    Lu, Xiaoyi; Pantano, Carlos

    2017-11-01

    In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

  2. A pulse tube cryocooler with a cold reservoir

    Science.gov (United States)

    Zhang, X. B.; Zhang, K. H.; Qiu, L. M.; Gan, Z. H.; Shen, X.; Xiang, S. J.

    2013-02-01

    Phase difference between pressure wave and mass flow is decisive to the cooling capacity of regenerative cryocoolers. Unlike the direct phase shifting using a piston or displacer in conventional Stirling or GM cryocoolers, the pulse tube cyocooler (PTC) indirectly adjusts the cold phase due to the absence of moving parts at the cold end. The present paper proposed and validated theoretically and experimentally a novel configuration of PTC, termed cold reservoir PTC, in which a reservoir together with an adjustable orifice is connected to the cold end of the pulse tube. The impedance from the additional orifice to the cold end helps to increase the mass flow in phase with the pressure wave at the cold end. Theoretical analyses with the linear model for the orifice and double-inlet PTCs indicate that the cooling performance can be improved by introducing the cold reservoir. The preliminary experiments with a home-made single-stage GM PTC further validated the results on the premise of minor opening of the cold-end orifice.

  3. A Comprehensive Statistically-Based Method to Interpret Real-Time Flowing Measurements

    Energy Technology Data Exchange (ETDEWEB)

    Keita Yoshioka; Pinan Dawkrajai; Analis A. Romero; Ding Zhu; A. D. Hill; Larry W. Lake

    2007-01-15

    With the recent development of temperature measurement systems, continuous temperature profiles can be obtained with high precision. Small temperature changes can be detected by modern temperature measuring instruments such as fiber optic distributed temperature sensor (DTS) in intelligent completions and will potentially aid the diagnosis of downhole flow conditions. In vertical wells, since elevational geothermal changes make the wellbore temperature sensitive to the amount and the type of fluids produced, temperature logs can be used successfully to diagnose the downhole flow conditions. However, geothermal temperature changes along the wellbore being small for horizontal wells, interpretations of a temperature log become difficult. The primary temperature differences for each phase (oil, water, and gas) are caused by frictional effects. Therefore, in developing a thermal model for horizontal wellbore, subtle temperature changes must be accounted for. In this project, we have rigorously derived governing equations for a producing horizontal wellbore and developed a prediction model of the temperature and pressure by coupling the wellbore and reservoir equations. Also, we applied Ramey's model (1962) to the build section and used an energy balance to infer the temperature profile at the junction. The multilateral wellbore temperature model was applied to a wide range of cases at varying fluid thermal properties, absolute values of temperature and pressure, geothermal gradients, flow rates from each lateral, and the trajectories of each build section. With the prediction models developed, we present inversion studies of synthetic and field examples. These results are essential to identify water or gas entry, to guide flow control devices in intelligent completions, and to decide if reservoir stimulation is needed in particular horizontal sections. This study will complete and validate these inversion studies.

  4. Reservoir engineering and hydrogeology

    International Nuclear Information System (INIS)

    Anon.

    1983-01-01

    Summaries are included which show advances in the following areas: fractured porous media, flow in single fractures or networks of fractures, hydrothermal flow, hydromechanical effects, hydrochemical processes, unsaturated-saturated systems, and multiphase multicomponent flows. The main thrust of these efforts is to understand the movement of mass and energy through rocks. This has involved treating fracture rock masses in which the flow phenomena within both the fractures and the matrix must be investigated. Studies also address the complex coupling between aspects of thermal, hydraulic, and mechanical processes associated with a nuclear waste repository in a fractured rock medium. In all these projects, both numerical modeling and simulation, as well as field studies, were employed. In the theoretical area, a basic understanding of multiphase flow, nonisothermal unsaturated behavior, and new numerical methods have been developed. The field work has involved reservoir testing, data analysis, and case histories at a number of geothermal projects

  5. Kelvin Equation for a Non-Ideal Multicomponent Mixture

    DEFF Research Database (Denmark)

    Shapiro, Alexander; Stenby, Erling Halfdan

    1997-01-01

    The Kelvin equation is generalized by application to a case of a multicomponent non-ideal mixture. Such a generalization is necessary in order to describe the two-phase equilibrium in a capillary medium with respect to both normal and retrograde condensation. The equation obtained is applied...... to the equilibrium state of a hydrocarbon mixture ina gas-condensate reservoir....

  6. CO{sub 2} interfacial properties: application to multiphase flow at reservoir conditions; Proprietes interfaciales du CO{sub 2}: application aux ecoulements en milieu poreux en pression et temperature

    Energy Technology Data Exchange (ETDEWEB)

    Chalbaud, C

    2007-07-15

    In this work we deal with the interfacial properties of CO{sub 2} at reservoir conditions with a special interest on deep saline aquifers. Each chapter of this dissertation represents a different physical scale studied with different experimental devices and simulation tools. The results obtained in the first part of this study represent a complete data set of brine-CO{sub 2} interfacial tension at reservoir conditions. A semi-analytical equation is proposed in order to facilitate the work of reservoir engineers. The second deals with the interfacial properties at the pore scale using glass micro-models at different wettability conditions. This part shows the wetting behavior of CO{sub 2} on hydrophobic or oil-wet solid surfaces. A pore network model was used for the interpretation and exploitation of these results. The third part corresponds to two different experimental approaches at the core scale at different wettability conditions associated to a modelling at flue Darcy scale. This part is a significant contribution to the validation of COORES compositional reservoir simulator developed by IFP. It has also allow us to estimate multiphase properties, Pc and kr, for brine-CO{sub 2} systems at reservoir conditions. This study presents the necessary scales to model CO{sub 2} storage in deep saline aquifers. (author)

  7. Relations between the kinetic equation and the Langevin models in two-phase flow modelling

    International Nuclear Information System (INIS)

    Minier, J.P.; Pozorski, J.

    1997-05-01

    The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)

  8. Approaches to identifying reservoir heterogeneity and reserve growth opportunities from subsurface data: The Oficina Formation, Budare field, Venezuela

    Energy Technology Data Exchange (ETDEWEB)

    Hamilton, D.S.; Raeuchle, S.K.; Holtz, M.H. [Bureau of Economic Geology, Austin, TX (United States)] [and others

    1997-08-01

    We applied an integrated geologic, geophysical, and engineering approach devised to identify heterogeneities in the subsurface that might lead to reserve growth opportunities in our analysis of the Oficina Formation at Budare field, Venezuela. The approach involves 4 key steps: (1) Determine geologic reservoir architecture; (2) Investigate trends in reservoir fluid flow; (3) Integrate fluid flow trends with reservoir architecture; and (4) Estimate original oil-in-place, residual oil saturation, and remaining mobile oil, to identify opportunities for reserve growth. There are three main oil-producing reservoirs in the Oficina Formation that were deposited in a bed-load fluvial system, an incised valley-fill, and a barrier-strandplain system. Reservoir continuity is complex because, in addition to lateral facies variability, the major Oficina depositional systems were internally subdivided by high-frequency stratigraphic surfaces. These surfaces define times of intermittent lacustrine and marine flooding events that punctuated the fluvial and marginal marine sedimentation, respectively. Syn and post depositional faulting further disrupted reservoir continuity. Trends in fluid flow established from initial fluid levels, response to recompletion workovers, and pressure depletion data demonstrated barriers to lateral and vertical fluid flow caused by a combination of reservoir facies pinchout, flooding shale markers, and the faults. Considerable reserve growth potential exists at Budare field because the reservoir units are highly compartment by the depositional heterogeneity and structural complexity. Numerous reserve growth opportunities were identified in attics updip of existing production, in untapped or incompletely drained compartments, and in field extensions.

  9. Characterization of floodflows along the Arkansas River without regulation by Pueblo Reservoir, Portland to John Martin Reservoir, Southeastern Colorado

    Science.gov (United States)

    Little, John R.; Bauer, Daniel P.

    1981-01-01

    The need for a method for estimating flow characteristics of flood hydrographs between Portland, Colo., and John Martin Reservoir has been promoted with the construction of the Pueble Reservoir. To meet this need a procedure was developed for predicting floodflow peaks, traveltimes, and volumes at any point along the Arkansas River between Portland and John Martin Reservoir without considering the existing Pueble Reservoir detention effects. A streamflow-routing model was calibrated initially and then typical flood simulations were made for the 164.8-mile study reach. Simulations were completed for varying magnitudes of floods and antecedent streamflow conditions. Multiple regression techniques were then used with simulation results as input to provide predictive relationships for food peak, volume, and traveltime. Management practices that may be used to benefit water users in the area include providing methods for the distribution and allotment of the flood waters upstream of Portland to different downstream water users according to Colorado water law and also under the Arkansas River Compact. (USGS)

  10. APPLICATION OF INTEGRATED RESERVOIR MANAGEMENT AND RESERVOIR CHARACTERIZATION

    Energy Technology Data Exchange (ETDEWEB)

    Jack Bergeron; Tom Blasingame; Louis Doublet; Mohan Kelkar; George Freeman; Jeff Callard; David Moore; David Davies; Richard Vessell; Brian Pregger; Bill Dixon; Bryce Bezant

    2000-03-01

    Reservoir performance and characterization are vital parameters during the development phase of a project. Infill drilling of wells on a uniform spacing, without regard to characterization does not optimize development because it fails to account for the complex nature of reservoir heterogeneities present in many low permeability reservoirs, especially carbonate reservoirs. These reservoirs are typically characterized by: (1) large, discontinuous pay intervals; (2) vertical and lateral changes in reservoir properties; (3) low reservoir energy; (4) high residual oil saturation; and (5) low recovery efficiency. The operational problems they encounter in these types of reservoirs include: (1) poor or inadequate completions and stimulations; (2) early water breakthrough; (3) poor reservoir sweep efficiency in contacting oil throughout the reservoir as well as in the nearby well regions; (4) channeling of injected fluids due to preferential fracturing caused by excessive injection rates; and (5) limited data availability and poor data quality. Infill drilling operations only need target areas of the reservoir which will be economically successful. If the most productive areas of a reservoir can be accurately identified by combining the results of geological, petrophysical, reservoir performance, and pressure transient analyses, then this ''integrated'' approach can be used to optimize reservoir performance during secondary and tertiary recovery operations without resorting to ''blanket'' infill drilling methods. New and emerging technologies such as geostatistical modeling, rock typing, and rigorous decline type curve analysis can be used to quantify reservoir quality and the degree of interwell communication. These results can then be used to develop a 3-D simulation model for prediction of infill locations. The application of reservoir surveillance techniques to identify additional reservoir ''pay'' zones

  11. Small Reservoir Impact on Simulated Watershed-Scale Nutrient Yield

    Directory of Open Access Journals (Sweden)

    Shane J. Prochnow

    2007-01-01

    Full Text Available The soil and water assessment tool (SWAT is used to assess the influence of small upland reservoirs (PL566 on watershed nutrient yield. SWAT simulates the impact of collectively increasing and decreasing PL566 magnitudes (size parameters on the watershed. Totally removing PL566 reservoirs results in a 100% increase in total phosphorus and an 82% increase in total nitrogen, while a total maximum daily load (TMDL calling for a 50% reduction in total phosphorus can be achieved with a 500% increase in the magnitude of PL566s in the watershed. PL566 reservoirs capture agriculture pollution in surface flow, providing long-term storage of these constituents when they settle to the reservoir beds. A potential strategy to reduce future downstream nutrient loading is to enhance or construct new PL566 reservoirs in the upper basin to better capture agricultural runoff.

  12. An evaluation of seepage gains and losses in Indian Creek Reservoir, Ada County, Idaho, April 2010–November 2011

    Science.gov (United States)

    Williams, Marshall L.; Etheridge, Alexandra B.

    2013-01-01

    The U.S. Geological Survey, in cooperation with the Idaho Department of Water Resources, conducted an investigation on Indian Creek Reservoir, a small impoundment in east Ada County, Idaho, to quantify groundwater seepage into and out of the reservoir. Data from the study will assist the Idaho Water Resources Department’s Comprehensive Aquifer Management Planning effort to estimate available water resources in Ada County. Three independent methods were utilized to estimate groundwater seepage: (1) the water-budget method; (2) the seepage-meter method; and (3) the segmented Darcy method. Reservoir seepage was quantified during the periods of April through August 2010 and February through November 2011. With the water-budget method, all measureable sources of inflow to and outflow from the reservoir were quantified, with the exception of groundwater; the water-budget equation was solved for groundwater inflow to or outflow from the reservoir. The seepage-meter method relies on the placement of seepage meters into the bottom sediments of the reservoir for the direct measurement of water flux across the sediment-water interface. The segmented-Darcy method utilizes a combination of water-level measurements in the reservoir and in adjacent near-shore wells to calculate water-table gradients between the wells and the reservoir within defined segments of the reservoir shoreline. The Darcy equation was used to calculate groundwater inflow to and outflow from the reservoir. Water-budget results provided continuous, daily estimates of seepage over the full period of data collection, while the seepage-meter and segmented Darcy methods provided instantaneous estimates of seepage. As a result of these and other difference in methodologies, comparisons of seepage estimates provided by the three methods are considered semi-quantitative. The results of the water-budget derived estimates of seepage indicate seepage to be seasonally variable in terms of the direction and magnitude

  13. Numerical simulations of highly buoyant flows in the Castel Giorgio - Torre Alfina deep geothermal reservoir

    Science.gov (United States)

    Volpi, Giorgio; Crosta, Giovanni B.; Colucci, Francesca; Fischer, Thomas; Magri, Fabien

    2017-04-01

    Geothermal heat is a viable source of energy and its environmental impact in terms of CO2 emissions is significantly lower than conventional fossil fuels. However, nowadays its utilization is inconsistent with the enormous amount of energy available underneath the surface of the earth. This is mainly due to the uncertainties associated with it, as for example the lack of appropriate computational tools, necessary to perform effective analyses. The aim of the present study is to build an accurate 3D numerical model, to simulate the exploitation process of the deep geothermal reservoir of Castel Giorgio - Torre Alfina (central Italy), and to compare results and performances of parallel simulations performed with TOUGH2 (Pruess et al. 1999), FEFLOW (Diersch 2014) and the open source software OpenGeoSys (Kolditz et al. 2012). Detailed geological, structural and hydrogeological data, available for the selected area since early 70s, show that Castel Giorgio - Torre Alfina is a potential geothermal reservoir with high thermal characteristics (120 ° C - 150 ° C) and fluids such as pressurized water and gas, mainly CO2, hosted in a carbonate formation. Our two steps simulations firstly recreate the undisturbed natural state of the considered system and then perform the predictive analysis of the industrial exploitation process. The three adopted software showed a strong numerical simulations accuracy, which has been verified by comparing the simulated and measured temperature and pressure values of the geothermal wells in the area. The results of our simulations have demonstrated the sustainability of the investigated geothermal field for the development of a 5 MW pilot plant with total fluids reinjection in the same original formation. From the thermal point of view, a very efficient buoyant circulation inside the geothermal system has been observed, thus allowing the reservoir to support the hypothesis of a 50 years production time with a flow rate of 1050 t

  14. Using laboratory flow experiments and reactive chemical transport modeling for designing waterflooding of the Agua Fria Reservoir, Poza Rica-Altamira Field, Mexico

    Energy Technology Data Exchange (ETDEWEB)

    Birkle, P.; Pruess, K.; Xu, T.; Figueroa, R.A. Hernandez; Lopez, M. Diaz; Lopez, E. Contreras

    2008-10-01

    Waterflooding for enhanced oil recovery requires that injected waters must be chemically compatible with connate reservoir waters, in order to avoid mineral dissolution-and-precipitation cycles that could seriously degrade formation permeability and injectivity. Formation plugging is a concern especially in reservoirs with a large content of carbonates, such as calcite and dolomite, as such minerals typically react rapidly with an aqueous phase, and have strongly temperature-dependent solubility. Clay swelling can also pose problems. During a preliminary waterflooding pilot project, the Poza Rica-Altamira oil field, bordering the Gulf coast in the eastern part of Mexico, experienced injectivity loss after five months of reinjection of formation waters into well AF-847 in 1999. Acidizing with HCl restored injectivity. We report on laboratory experiments and reactive chemistry modeling studies that were undertaken in preparation for long-term waterflooding at Agua Frma. Using analogous core plugs obtained from the same reservoir interval, laboratory coreflood experiments were conducted to examine sensitivity of mineral dissolution and precipitation effects to water composition. Native reservoir water, chemically altered waters, and distilled water were used, and temporal changes in core permeability, mineral abundances and aqueous concentrations of solutes were monitored. The experiments were simulated with the multi-phase, nonisothermal reactive transport code TOUGHREACT, and reasonable to good agreement was obtained for changes in solute concentrations. Clay swelling caused an additional impact on permeability behavior during coreflood experiments, whereas the modeled permeability depends exclusively on chemical processes. TOUGHREACT was then used for reservoir-scale simulation of injecting ambient-temperature water (30 C, 86 F) into a reservoir with initial temperature of 80 C (176 F). Untreated native reservoir water was found to cause serious porosity and

  15. Hydrodynamic modeling of petroleum reservoirs using simulator MUFITS

    Science.gov (United States)

    Afanasyev, Andrey

    2015-04-01

    MUFITS is new noncommercial software for numerical modeling of subsurface processes in various applications (www.mufits.imec.msu.ru). To this point, the simulator was used for modeling nonisothermal flows in geothermal reservoirs and for modeling underground carbon dioxide storage. In this work, we present recent extension of the code to petroleum reservoirs. The simulator can be applied in conventional black oil modeling, but it also utilizes a more complicated models for volatile oil and gas condensate reservoirs as well as for oil rim fields. We give a brief overview of the code by providing the description of internal representation of reservoir models, which are constructed of grid blocks, interfaces, stock tanks as well as of pipe segments and pipe junctions for modeling wells and surface networks. For conventional black oil approach, we present the simulation results for SPE comparative tests. We propose an accelerated compositional modeling method for sub- and supercritical flows subjected to various phase equilibria, particularly to three-phase equilibria of vapour-liquid-liquid type. The method is based on the calculation of the thermodynamic potential of reservoir fluid as a function of pressure, total enthalpy and total composition and storing its values as a spline table, which is used in hydrodynamic simulation for accelerated PVT properties prediction. We provide the description of both the spline calculation procedure and the flashing algorithm. We evaluate the thermodynamic potential for a mixture of two pseudo-components modeling the heavy and light hydrocarbon fractions. We develop a technique for converting black oil PVT tables to the potential, which can be used for in-situ hydrocarbons multiphase equilibria prediction under sub- and supercritical conditions, particularly, in gas condensate and volatile oil reservoirs. We simulate recovery from a reservoir subject to near-critical initial conditions for hydrocarbon mixture. We acknowledge

  16. Sediment problems in reservoirs. Control of sediment deposits

    Energy Technology Data Exchange (ETDEWEB)

    Jacobsen, Tom

    1997-12-31

    When a reservoir is formed on a river, sediment will deposit in the reservoir. Such processes are unfortunate, for instance, for the implementation of hydroelectric energy. This thesis studies the problem of reservoir sedimentation and discusses methods of removing the sediments. Various aspects of reservoir sedimentation are discussed. Anthropogenic impacts seem to greatly affect the erosion processes. Temporal distribution is uneven, mainly because of the very large flood events. A world map showing the Reservoir Capacity: Annual Sediment Inflow ratio for reservoirs with volume equal to 10% of annual inflow has been prepared. The map shows that sedimentation is severe in the western parts of North and South America, eastern, southern and northern Africa, parts of Australia and most of Asia. The development of medium-sized reservoirs is difficult, as they are too large for conventional flushing technique and too small to store the sediment that accumulates during their economic lifetime. A computer model, SSIIM, was used with good results in a case study of two flood drawdown trials in Lake Roxburg, New Zealand. Two techniques have been developed that permits controlled suction of sediment and water into a pipe: the Slotted Pipe Sediment Sluicer (SPSS) and the Saxophone Sediment Sluicer (SSS). The techniques exploit the inflow pattern in through a slot in a pipe. An equation describing this inflow pattern was derived and verified experimentally. The SPSS is fixed near the reservoir bed, and sediment that deposits on top of it is removed in the sluicing process. The SSS sluices sediment from the surface of the sediment deposits. Some technical and economic conditions affecting the economics of sediment removal from reservoirs have been identified and studied. 79 refs., 112 figs., 14 tabs.

  17. Speeding up compositional reservoir simulation through an efficient implementation of phase equilibrium calculation

    DEFF Research Database (Denmark)

    Belkadi, Abdelkrim; Yan, Wei; Moggia, Elsa

    2013-01-01

    Compositional reservoir simulations are widely used to simulate reservoir processes with strong compositional effects, such as gas injection. The equations of state (EoS) based phase equilibrium calculation is a time consuming part in this type of simulations. The phase equilibrium problem can....... Application of the shadow region method to skip stability analysis can further cut the phase equilibrium calculation time. Copyright 2013, Society of Petroleum Engineers....

  18. Reflection Phenomena in Underground Pumped Storage Reservoirs

    Directory of Open Access Journals (Sweden)

    Elena Pummer

    2018-04-01

    Full Text Available Energy storage through hydropower leads to free surface water waves in the connected reservoirs. The reason for this is the movement of water between reservoirs at different elevations, which is necessary for electrical energy storage. Currently, the expansion of renewable energies requires the development of fast and flexible energy storage systems, of which classical pumped storage plants are the only technically proven and cost-effective technology and are the most used. Instead of classical pumped storage plants, where reservoirs are located on the surface, underground pumped storage plants with subsurface reservoirs could be an alternative. They are independent of topography and have a low surface area requirement. This can be a great advantage for energy storage expansion in case of environmental issues, residents’ concerns and an unusable terrain surface. However, the reservoirs of underground pumped storage plants differ in design from classical ones for stability and space reasons. The hydraulic design is essential to ensure their satisfactory hydraulic performance. The paper presents a hybrid model study, which is defined here as a combination of physical and numerical modelling to use the advantages and to compensate for the disadvantages of the respective methods. It shows the analysis of waves in ventilated underground reservoir systems with a great length to height ratio, considering new operational aspects from energy supply systems with a great percentage of renewable energies. The multifaceted and narrow design of the reservoirs leads to complex free surface flows; for example, undular and breaking bores arise. The results show excessive wave heights through wave reflections, caused by the impermeable reservoir boundaries. Hence, their knowledge is essential for a successful operational and constructive design of the reservoirs.

  19. Electrolyte CPA equation of state for very high temperature and pressure reservoir and basin applications

    Science.gov (United States)

    Courtial, Xavier; Ferrando, Nicolas; de Hemptinne, Jean-Charles; Mougin, Pascal

    2014-10-01

    In this work, an electrolyte version of the Cubic Plus Association (eCPA) equation of state has been adapted to systems containing CH4, CO2, H2O and NaCl (up to 5 molal) at pressures up to 200 MPa and temperatures up to 773 K for salt-free systems and 573 K for salt-containing systems. Its purpose is to represent the phase behavior (including salting-out effect and critical point) and the phase densities in a range of temperature and pressure encountered in deep reservoirs and basins. The goal of the parameterization proposed is not to reach a very high accuracy for phase equilibrium and volumetric properties, but rather to develop a semi-predictive approach to model the phase and volumetric behavior of this system while allowing an easy extension to other compounds. Without salt, predictions for pure component vapor pressures and liquid molar volumes present an average absolute deviation (AAD) lower than 3% compared to experimental reference values. The pure component molar volumes out of saturation show an AAD lower than 4%. The highest deviations in densities are observed as expected in the vicinity of the critical coordinates of pure water and this effect increases when gases or salts are added to the system. For each binary system, CH4 + CO2, CH4 + H2O and CO2 + H2O, binary interaction parameters have been fitted to correctly represent the shape of the fluid phase envelopes (including all critical points) in the entire temperature and pressure range considered (219 K to 633 K and up to 250 MPa). The methane concentration in both phases of the CH4 + CO2 binary system is represented with an AAD lower than 9%. The methane solubility in water is represented within 16% and 8% for the methane content of the vapor. The CO2 solubility in water is within 26%, while the CO2 in the vapor phase shows an average deviation of 12%. All molar volumes are represented with an AAD lower than 3%. The few VLE experimental data for the CH4 + CO2 + H2O ternary system are fairly well

  20. Integration of two-phase solid fluid equations in a catchment model for flashfloods, debris flows and shallow slope failures

    KAUST Repository

    Bout, B.; Lombardo, Luigi; van Westen, C.J.; Jetten, V.G.

    2018-01-01

    An integrated, modeling method for shallow landslides, debris flows and catchment hydrology is developed and presented in this paper. Existing two-phase debris flow equations and an adaptation on the infinite slope method are coupled with a full

  1. Impact of higher-order flows in the moment equations on Pfirsch-Schlüter friction coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Honda, M., E-mail: honda.mitsuru@jaea.go.jp [Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 (Japan)

    2014-09-15

    The impact of the higher-order flows in the moment approach on an estimate of the friction coefficients is numerically examined. The higher-order flows are described by the lower-order hydrodynamic flows using the collisional plasma assumption. Their effects have not been consistently taken into account thus far in the widely used neoclassical transport codes based on the moment equations in terms of the Pfirsch-Schlüter flux. Due to numerically solving the friction-flow matrix without using the small-mass ratio expansion, it is clearly revealed that incorporating the higher-order flow effects is of importance especially for plasmas including multiple hydrogenic ions and other lighter species with similar masses.

  2. Using PIV to determine relative pressures in a stenotic phantom under steady flow based on the pressure-poisson equation.

    Science.gov (United States)

    Khodarahmi, Iman; Shakeri, Mostafa; Sharp, M; Amini, Amir A

    2010-01-01

    Pressure gradient across a Gaussian-shaped 87% area stenosis phantom was estimated by solving the pressure Poisson equation (PPE) for a steady flow mimicking the blood flow through the human iliac artery. The velocity field needed to solve the pressure equation was obtained using particle image velocimetry (PIV). A steady flow rate of 46.9 ml/s was used, which corresponds to a Reynolds number of 188 and 595 at the inlet and stenosis throat, respectively (in the range of mean Reynolds number encountered in-vivo). In addition, computational fluid dynamics (CFD) simulation of the same flow was performed. Pressure drops across the stenosis predicted by PPE/PIV and CFD were compared with those measured by a pressure catheter transducer. RMS errors relative to the measurements were 17% and 10% for PPE/PIV and CFD, respectively.

  3. Dynamics of Quantum Entanglement in Reservoir with Memory Effects

    International Nuclear Information System (INIS)

    Hao Xiang; Sha Jinqiao; Sun Jian; Zhu Shiqun

    2012-01-01

    The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects. The completely positive reduced dynamical map can be constructed in the Kraus representation. Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased with the change of the memory kernel. It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants. (general)

  4. EOS simulation and GRNN modeling of the constant volume depletion behavior of gas condensate reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Elsharkawy, A.M.; Foda, S.G. [Kuwait University, Safat (Kuwait). Petroleum Engineering Dept.

    1998-03-01

    Currently, two approaches are being used to predict the changes in retrograde gas condensate composition and estimate the pressure depletion behavior of gas condensate reservoirs. The first approach uses the equation of states whereas the second uses empirical correlations. Equations of states (EOS) are poor predictive tools for complex hydrocarbon systems. The EOS needs adjustment against phase behavior data of reservoir fluid of known composition. The empirical correlation does not involve numerous numerical computations but their accuracy is limited. This study presents two general regression neural network (GRNN) models. The first model, GRNNM1, is developed to predict dew point pressure and gas compressibility at dew point using initial composition of numerous samples while the second model, GRNNM2, is developed to predict the changes in well stream effluent composition at any stages of pressure depletion. GRNNM2 can also be used to determine the initial reservoir fluid composition using dew point pressure, gas compressibility at dew point, and reservoir temperature. These models are based on analysis of 142 sample of laboratory studies of constant volume depletion (CVD) for gas condensate systems forming a total of 1082 depletion stages. The database represents a wide range of gas condensate systems obtained worldwide. The performance of the GRNN models has been compared to simulation results of the equation of state. The study shows that the proposed general regression neural network models are accurate, valid, and reliable. These models can be used to forecast CVD data needed for many reservoir engineering calculations in case laboratory data is unavailable. The GRNN models save computer time involved in EOS calculations. The study also show that once these models are properly trained they can be used to cut expenses of frequent sampling and laborious experimental CVD tests required for gas condensate reservoirs. 55 refs., 13 figs., 6 tabs.

  5. Integration of rock typing methods for carbonate reservoir characterization

    International Nuclear Information System (INIS)

    Aliakbardoust, E; Rahimpour-Bonab, H

    2013-01-01

    Reservoir rock typing is the most important part of all reservoir modelling. For integrated reservoir rock typing, static and dynamic properties need to be combined, but sometimes these two are incompatible. The failure is due to the misunderstanding of the crucial parameters that control the dynamic behaviour of the reservoir rock and thus selecting inappropriate methods for defining static rock types. In this study, rock types were defined by combining the SCAL data with the rock properties, particularly rock fabric and pore types. First, air-displacing-water capillary pressure curues were classified because they are representative of fluid saturation and behaviour under capillary forces. Next the most important rock properties which control the fluid flow and saturation behaviour (rock fabric and pore types) were combined with defined classes. Corresponding petrophysical properties were also attributed to reservoir rock types and eventually, defined rock types were compared with relative permeability curves. This study focused on representing the importance of the pore system, specifically pore types in fluid saturation and entrapment in the reservoir rock. The most common tests in static rock typing, such as electrofacies analysis and porosity–permeability correlation, were carried out and the results indicate that these are not appropriate approaches for reservoir rock typing in carbonate reservoirs with a complicated pore system. (paper)

  6. Comparison of pressure transient response in intensely and sparsely fractured reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Johns, R.T.

    1989-04-01

    A comprehensive analytical model is presented to study the pressure transient behavior of a naturally fractured reservoir with a continuous matrix block size distribution. Geologically realistic probability density functions of matrix block size are used to represent reservoirs of varying fracture intensity and uniformity. Transient interporosity flow is assumed and interporosity skin is incorporated. Drawdown and interference pressure transient tests are investigated. The results show distinctions in the pressure response from intensely and sparsely fractured reservoirs in the absence of interporosity skin. Also, uniformly and nonuniformly fractured reservoirs exhibit distinct responses, irrespective of the degree of fracture intensity. The pressure response in a nonuniformly fractured reservoir with large block size variability, approaches a nonfractured (homogeneous) reservoir response. Type curves are developed to estimate matrix block size variability and the degree of fracture intensity from drawdown and interference well tests.

  7. Integrating gravimetric and interferometric synthetic aperture radar data for enhancing reservoir history matching of carbonate gas and volatile oil reservoirs

    KAUST Repository

    Katterbauer, Klemens

    2016-08-25

    Reservoir history matching is assuming a critical role in understanding reservoir characteristics, tracking water fronts, and forecasting production. While production data have been incorporated for matching reservoir production levels and estimating critical reservoir parameters, the sparse spatial nature of this dataset limits the efficiency of the history matching process. Recently, gravimetry techniques have significantly advanced to the point of providing measurement accuracy in the microgal range and consequently can be used for the tracking of gas displacement caused by water influx. While gravity measurements provide information on subsurface density changes, i.e., the composition of the reservoir, these data do only yield marginal information about temporal displacements of oil and inflowing water. We propose to complement gravimetric data with interferometric synthetic aperture radar surface deformation data to exploit the strong pressure deformation relationship for enhancing fluid flow direction forecasts. We have developed an ensemble Kalman-filter-based history matching framework for gas, gas condensate, and volatile oil reservoirs, which synergizes time-lapse gravity and interferometric synthetic aperture radar data for improved reservoir management and reservoir forecasts. Based on a dual state-parameter estimation algorithm separating the estimation of static reservoir parameters from the dynamic reservoir parameters, our numerical experiments demonstrate that history matching gravity measurements allow monitoring the density changes caused by oil-gas phase transition and water influx to determine the saturation levels, whereas the interferometric synthetic aperture radar measurements help to improve the forecasts of hydrocarbon production and water displacement directions. The reservoir estimates resulting from the dual filtering scheme are on average 20%-40% better than those from the joint estimation scheme, but require about a 30% increase in

  8. A lattice based solution of the collisional Boltzmann equation with applications to microchannel flows

    International Nuclear Information System (INIS)

    Green, B I; Vedula, Prakash

    2013-01-01

    An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)

  9. An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

    Science.gov (United States)

    Subramanian, Ramanathan Vishnampet Ganapathi

    Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvement. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs. Such methods have enabled sensitivity analysis and active control of turbulence at engineering flow conditions by providing gradient information at computational cost comparable to that of simulating the flow. They accelerate convergence of numerical design optimization algorithms, though this is predicated on the availability of an accurate gradient of the discretized flow equations. This is challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. We analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space--time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge--Kutta-like scheme

  10. NH4+ adsorption and adsorption kinetics by sediments in a drinking water reservoir

    Directory of Open Access Journals (Sweden)

    Suna Hongyan

    2016-12-01

    Full Text Available The sorption isotherm and sorption kinetics of NH4+ by the Fen River reservoir sediment were investigated for a better understanding of the NH4+ sorption characteristics and parameters. The results showed that Q (adsorption content increased with the increase of Ceq (equilibrium concentration, sorption isotherms could be described by Freundlich equation (R2 from 0.97 to 0.99. Cation exchange capacity (CEC had a significant correlation with the parameters K and n (R2 was 0.85 and 0.95, respectively. The ENC0 (Ceq as Q was zero of S1, S2, S3 and S4 was 1.25, 0.57, 1.15 and 1.14 mg L-1, respectively, and they were less than the NH4+ concentrations in reservoir water. The sediments released NH4+ to the Fen River reservoir water and acted as a pollution source, in the form of complex and heterogeneous adsorbents. The NH4+ adsorption kinetic process was composed of ‘fast’ and ‘slow’ reaction patterns and could be fitted using both Elovich equation and Pseudo second-equation. More than one-step may be involved in the NH4+ sorption processes, and interior diffusion was not dominant ion action.

  11. Advanced Techniques for Reservoir Simulation and Modeling of Non-Conventional Wells

    Energy Technology Data Exchange (ETDEWEB)

    Durlofsky, Louis J.

    2000-08-28

    This project targets the development of (1) advanced reservoir simulation techniques for modeling non-conventional wells; (2) improved techniques for computing well productivity (for use in reservoir engineering calculations) and well index (for use in simulation models), including the effects of wellbore flow; and (3) accurate approaches to account for heterogeneity in the near-well region.

  12. SGS Modeling of the Internal Energy Equation in LES of Supersonic Channel Flow

    Science.gov (United States)

    Raghunath, Sriram; Brereton, Giles

    2011-11-01

    DNS of fully-developed turbulent supersonic channel flows (Reτ = 190) at up to Mach 3 indicate that the turbulent heat fluxes depend only weakly on Mach number, while the viscous dissipation and pressure dilatation do so strongly. Moreover, pressure dilatation makes a significant contribution to the internal energy budget at Mach 3 and higher. The balance between these terms is critical to determining the temperature (and so molecular viscosity) from the internal energy equation and so, in LES of these flows, it is essential to use accurate SGS models for the viscous dissipation and the pressure dilatation. In this talk, we present LES results for supersonic channel flow, using SGS models for these terms that are based on the resolved-scale dilatation, an inverse timescale, and SGS momentum fluxes, which intrinsically represent this Mach number effect.

  13. Numerical solution of compressible flow equations inside an ejector

    International Nuclear Information System (INIS)

    Omid khah, M. R.; Navid Famili, M. H.; Jalili Keshtiban, E.

    2002-01-01

    Ejector is important equipment in the chemical industry. It is mainly used for vaccuming and mixing of flows. In the present work a computer modeling of the flow inside an ejector is used to give a better understanding of the principle of the operation of an ejector. Since the fluid inside an ejector passes through subsonic, sonic and supersonic regimens, the pressure field is used as the controlling variable and the density is found through the constitutive equations. The control volume method with a co-location grid, attached to the boundary is used to discretize the domain. The overall solution is obtained by the SIMPLEC method and to dissociate the pressure and the velocity grid Rhie-Chow interpolation method is employed. A central difference approximation method is used to approximate the density on the elements borders and the upwind approximation is used to correct the density correction factors. Both upwind, quick and minimum gradient methods were used to approximate the momentum variables on the control volumes. The resultant matrices are solved with the tri-diagonal method. The accuracy of the model is checked by simulating a flow regiment in a converging-diverging nozzle, and comparing the results with the available experimental data. The results show that for an inviscid the first order approximation produce as an accurate results as the higher order approximations while it has a better stability. However, for the viscous fluid the second order approximation produces a better understanding of the physics of the problem. The solution also showes that the flow field inside an ejector is a complex one and the shock wave has a great influence on the pressure field especially close to the walls. The upper convective quick method did not converge well in the shock calculations while the slowest descent method had a very stable behavior in the analysis of the shock behavior

  14. Experiments with Interaction between the National Water Model and the Reservoir System Simulation Model: A Case Study of Russian River Basin

    Science.gov (United States)

    Kim, J.; Johnson, L.; Cifelli, R.; Chandra, C. V.; Gochis, D.; McCreight, J. L.; Yates, D. N.; Read, L.; Flowers, T.; Cosgrove, B.

    2017-12-01

    NOAA National Water Center (NWC) in partnership with the National Centers for Environmental Prediction (NCEP), the National Center for Atmospheric Research (NCAR) and other academic partners have produced operational hydrologic predictions for the nation using a new National Water Model (NWM) that is based on the community WRF-Hydro modeling system since the summer of 2016 (Gochis et al., 2015). The NWM produces a variety of hydrologic analysis and prediction products, including gridded fields of soil moisture, snowpack, shallow groundwater levels, inundated area depths, evapotranspiration as well as estimates of river flow and velocity for approximately 2.7 million river reaches. Also included in the NWM are representations for more than 1,200 reservoirs which are linked into the national channel network defined by the USGS NHDPlusv2.0 hydrography dataset. Despite the unprecedented spatial and temporal coverage of the NWM, many known deficiencies exist, including the representation of lakes and reservoirs. This study addresses the implementation of a reservoir assimilation scheme through coupling of a reservoir simulation model to represent the influence of managed flows. We examine the use of the reservoir operations to dynamically update lake/reservoir storage volume states, characterize flow characteristics of river reaches flowing into and out of lakes and reservoirs, and incorporate enhanced reservoir operating rules for the reservoir model options within the NWM. Model experiments focus on a pilot reservoir domain-Lake Mendocino, CA, and its contributing watershed, the East Fork Russian River. This reservoir is modeled using United States Army Corps of Engineers (USACE) HEC-ResSim developed for application to examine forecast informed reservoir operations (FIRO) in the Russian River basin.

  15. Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

    Science.gov (United States)

    Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

    2014-07-01

    Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay differential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We tackle some problems associated to the lack of task-universality for individually operating reservoirs and propose a solution based on the use of parallel arrays of time-delay reservoirs. Copyright © 2014 Elsevier Ltd. All rights reserved.

  16. Viscosity measurement in the capillary tube viscometer under unsteady flow

    International Nuclear Information System (INIS)

    Park, Heung Jun; Yoo, Sang Sin; Suh, Sang Ho

    2000-01-01

    The objective of the present study is to develop a new device that the viscous characteristics of fluids are determined by applying the unsteady flow concept to the traditional capillary tube viscometer. The capillary tube viscometer consists of a small cylindrical reservoir, capillary tube, a load cell system that measures the mass flow rate, interfaces, and computer. Due to the small size of the reservoir the height of liquid in the reservoir decreases as soon as the liquid in the reservoir drains out through the capillary and the mass flow rate in the capillary decreases as the hydrostatic pressure in the reservoir decreases resulting in a decrease of the shear rate in the capillary tube. The instantaneous shear rate and driving force in the capillary tube are determined by measuring the mass flow rate through the capillary, and the fluid viscosity is determined from the measured flow rate and the driving force

  17. Nets solution of flow for gases, using the Balance Pattern of Nodes and the method of linealization of equations

    International Nuclear Information System (INIS)

    Narvaez, Paulo Cesar

    1999-01-01

    The dimension of nets of distribution of gases is a complex problem, so much for the diversity of the phenomena that they are presented, like for the variation of the properties of the fluids, especially, the density for effect of the changes in the pressure along the net. This work presents a model for its simulation starting from the deduction of the general equation of flow in stable and isothermal state, its inclusion in the pattern of balance of nodes and the solution of this for the method of linealization of equations. Additionally, a summary of the empiric equations more used is made for the calculation of the fall of pressure for gases flowing in pipes and an example that it illustrates the application of the pattern and the developed method

  18. Compositional simulations of producing oil-gas ratio behaviour in low permeable gas condensate reservoir

    OpenAIRE

    Gundersen, Pål Lee

    2013-01-01

    Master's thesis in Petroleum engineering Gas condensate flow behaviour below the dew point in low permeable formations can make accurate fluid sampling a difficult challenge. The objective of this study was to investigate the producing oil-gas ratio behaviour in the infinite-acting period for a low permeable gas condensate reservoir. Compositional isothermal flow simulations were performed using a single-layer, radial and two-dimensional, gas condensate reservoir model with low permeabili...

  19. Flood hydrology and dam-breach hydraulic analyses of four reservoirs in the Black Hills, South Dakota

    Science.gov (United States)

    Hoogestraat, Galen K.

    2011-01-01

    Extensive information about the construction of dams or potential downstream hazards in the event of a dam breach is not available for many small reservoirs within the Black Hills National Forest. In 2009, the U.S. Forest Service identified the need for reconnaissance-level dam-breach assessments for four of these reservoirs within the Black Hills National Forest (Iron Creek, Horsethief, Lakota, and Mitchell Lakes) with the potential to flood downstream structures. Flood hydrology and dam-breach hydraulic analyses for the four selected reservoirs were conducted by the U.S. Geological Survey in cooperation with the U.S. Forest service to estimate the areal extent of downstream inundation. Three high-flow breach scenarios were considered for cases when the dam is in place (overtopped) and when a dam break (failure) occurs: the 100-year recurrence 24-hour precipitation, 500-year recurrence peak flow, and the probable maximum precipitation. Inundation maps were developed that show the estimated extent of downstream floodwaters from simulated scenarios. Simulation results were used to determine the hazard classification of a dam break (high, significant, or low), based primarily on the potential for loss of life or property damage resulting from downstream inundation because of the flood surge.The inflow design floods resulting from the two simulated storm events (100-year 24-hour and probable maximum precipitation) were determined using the U.S. Army Corps of Engineers Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS). The inflow design flood for the 500-year recurrence peak flow was determined by using regional regression equations developed for streamflow-gaging stations with similar watershed characteristics. The step-backwater hydraulic analysis model, Hydrologic Engineering Center's River Analysis System (HEC-RAS), was used to determine water-surface profiles of in-place and dam-break scenarios for the three inflow design floods that were

  20. PRELIMINARY RESULTS OF QUALITY STUDY OF WATER FROM SMALL MICHALICE RESERVOIR ON WIDAWA RIVER

    Directory of Open Access Journals (Sweden)

    Mirosław Wiatkowski

    2014-10-01

    Full Text Available The paper presents an analysis of water quality of the small Michalice reservoir. A preliminary assessment of the reservoir water quality and its usability was made. The quality of water in the reservoir is particularly important as the main functions of the reservoir are agricultural irrigation, recreation and flood protection . The following physico-chemical parameters of the Widawa River were analyzed: NO3 -, NO2 -, NH4 +, PO4 3-, COD, water temperature, pH and electrolytic conductivity. Main descriptive statistical data were presented for the analyzed water quality indicators. The research results indicate that the reservoir contributed to the reduced concentrations of the following water quality indicators: nitrates, nitrites, phosphates, electrolytic conductivity and COD (in the outflowing water – St.3 in comparison to the water flowing into the reservoir – St.1. In the water flowing out of the Psurów reservoir higher values of the remaining indicators were observed if compared with the inflowing water. It was stated, as well, that analised waters are not vulnerable to nitrogen compounds pollution coming from the agricultural sources and are eutrophic. For purpose obtaining of the précised information about condition of Michalice reservoir water purity as well as river Widawa it becomes to continue the hydrological monitoring and water quality studies.

  1. Cross-fault pressure depletion, Zechstein carbonate reservoir, Weser-Ems area, Northern German Gas Basin

    Energy Technology Data Exchange (ETDEWEB)

    Corona, F.V.; Brauckmann, F.; Beckmann, H.; Gobi, A.; Grassmann, S.; Neble, J.; Roettgen, K. [ExxonMobil Production Deutschland GmbH (EMPG), Hannover (Germany)

    2013-08-01

    A cross-fault pressure depletion study in Upper Permian Zechstein Ca2 carbonate reservoir was undertaken in the Weser-Ems area of the Northern German Gas Basin. The primary objectives are to develop a practical workflow to define cross-fault pressures scenarios for Zechstein Ca2 reservoir drillwells, to determine the key factors of cross-fault pressure behavior in this platform carbonate reservoir, and to translate the observed cross-fault pressure depletion to fault transmissibility for reservoir simulation models. Analysis of Zechstein Ca2 cross-fault pressures indicates that most Zechstein-cutting faults appear to act as fluid-flow baffles with some local occurrences of fault seal. Moreover, there appears to be distinct cross-fault baffling or pressure depletion trends that may be related to the extent of the separating fault or fault system, degree of reservoir flow-path tortuosity, and quality of reservoir juxtaposition. Based on the above observations, a three-part workflow was developed consisting of (1) careful interpretation and mapping of faults and fault networks, (2) analysis of reservoir juxtaposition and reservoir juxtaposition quality, and (3) application of the observed cross-fault pressure depletion trends. This approach is field-analog based, is practical, and is being used currently to provide reliable and supportable pressure prediction scenarios for subsequent Zechstein fault-bounded drill-well opportunities.

  2. Numerical simulation of energy equation with viscous dissipation for compressible flow over cones

    International Nuclear Information System (INIS)

    Asif, M.; Chughtai, I.R.

    1998-01-01

    A finite volume discretization technique has been used to solve the energy equation with viscous dissipation. The effects of viscous heat dissipation for Mach numbers 1.5 and 2.0, at an angle of attack of 0 degree, over sharp and blunt cones have been studied. Algebraic equations have been solved using line-by-line Tda method. Supersonic flow over cones has been analyzed and discussed with and without considering the viscous dissipation effects. It has been found that the effects of viscous dissipation increase with the increase in Mach number. Viscous dissipation affects the temperature distribution of the body. However, the temperature difference in these cases was insignificant. This may be due to the fact that these analysis have been done at 0 km altitude. (author)

  3. Unconventional Tight Reservoirs Characterization with Nuclear Magnetic Resonance

    Science.gov (United States)

    Santiago, C. J. S.; Solatpour, R.; Kantzas, A.

    2017-12-01

    The increase in tight reservoir exploitation projects causes producing many papers each year on new, modern, and modified methods and techniques on estimating characteristics of these reservoirs. The most ambiguous of all basic reservoir property estimations deals with permeability. One of the logging methods that is advertised to predict permeability but is always met by skepticism is Nuclear Magnetic Resonance (NMR). The ability of NMR to differentiate between bound and movable fluids and providing porosity increased the capability of NMR as a permeability prediction technique. This leads to a multitude of publications and the motivation of a review paper on this subject by Babadagli et al. (2002). The first part of this presentation is dedicated to an extensive review of the existing correlation models for NMR based estimates of tight reservoir permeability to update this topic. On the second part, the collected literature information is used to analyze new experimental data. The data are collected from tight reservoirs from Canada, the Middle East, and China. A case study is created to apply NMR measurement in the prediction of reservoir characterization parameters such as porosity, permeability, cut-offs, irreducible saturations etc. Moreover, permeability correlations are utilized to predict permeability. NMR experiments were conducted on water saturated cores. NMR T2 relaxation times were measured. NMR porosity, the geometric mean relaxation time (T2gm), Irreducible Bulk Volume (BVI), and Movable Bulk Volume (BVM) were calculated. The correlation coefficients were computed based on multiple regression analysis. Results are cross plots of NMR permeability versus the independently measured Klinkenberg corrected permeability. More complicated equations are discussed. Error analysis of models is presented and compared. This presentation is beneficial in understanding existing tight reservoir permeability models. The results can be used as a guide for choosing

  4. The management of subsurface uncertainty using probabilistic modeling of life cycle production forecasts and cash flows

    International Nuclear Information System (INIS)

    Olatunbosun, O. O.

    1998-01-01

    The subject pertains to the implementation of the full range of subsurface uncertainties in life cycle probabilistic forecasting and its extension to project cash flows using the methodology of probabilities. A new tool has been developed in the probabilistic application of Crystal-Ball which can model reservoir volumetrics, life cycle production forecasts and project cash flows in a single environment. The tool is modular such that the volumetrics and cash flow modules are optional. Production forecasts are often generated by applying a decline equation to single best estimate values of input parameters such as initial potential, decline rate, abandonment rate etc -or sometimes by results of reservoir simulation. This new tool provides a means of implementing the full range of uncertainties and interdependencies of the input parameters into the production forecasts by defining the input parameters as probability density functions, PDFs and performing several iterations to generate an expectation curve forecast. Abandonment rate is implemented in each iteration via a link to an OPEX model. The expectation curve forecast is input into a cash flow model to generate a probabilistic NPV. Base case and sensitivity runs from reservoir simulation can likewise form the basis for a probabilistic production forecast from which a probabilistic cash flow can be generated. A good illustration of the application of this tool is in the modelling of the production forecast for a well that encounters its target reservoirs in OUT/ODT situation and thus has significant uncertainties. The uncertainty in presence and size (if present) of gas cap and dependency between ultimate recovery and initial potential amongst other uncertainties can be easily implemented in the production forecast with this tool. From the expectation curve forecast, a probabilistic NPV can be easily generated. Possible applications of this tool include: i. estimation of range of actual recoverable volumes based

  5. assessment of the hydropower potential of kangimi reservoir

    African Journals Online (AJOL)

    2012-11-03

    Nov 3, 2012 ... other renewable energy sources such as wind, small or mini hydropower ... plied to Kaduna treatment plant during the periods of low flow in River .... following functional reservoir relationships that are very site specific: i.

  6. Reservoir management

    International Nuclear Information System (INIS)

    Satter, A.; Varnon, J.E.; Hoang, M.T.

    1992-01-01

    A reservoir's life begins with exploration leading to discovery followed by delineation of the reservoir, development of the field, production by primary, secondary and tertiary means, and finally to abandonment. Sound reservoir management is the key to maximizing economic operation of the reservoir throughout its entire life. Technological advances and rapidly increasing computer power are providing tools to better manage reservoirs and are increasing the gap between good and neural reservoir management. The modern reservoir management process involves goal setting, planning, implementing, monitoring, evaluating, and revising plans. Setting a reservoir management strategy requires knowledge of the reservoir, availability of technology, and knowledge of the business, political, and environmental climate. Formulating a comprehensive management plan involves depletion and development strategies, data acquisition and analyses, geological and numerical model studies, production and reserves forecasts, facilities requirements, economic optimization, and management approval. This paper provides management, engineers, geologists, geophysicists, and field operations staff with a better understanding of the practical approach to reservoir management using a multidisciplinary, integrated team approach

  7. Reservoir management

    International Nuclear Information System (INIS)

    Satter, A.; Varnon, J.E.; Hoang, M.T.

    1992-01-01

    A reservoir's life begins with exploration leading to discovery followed by delineation of the reservoir, development of the field, production by primary, secondary and tertiary means, and finally to abandonment. Sound reservoir management is the key to maximizing economic operation of the reservoir throughout its entire life. Technological advances and rapidly increasing computer power are providing tools to better manage reservoirs and are increasing the gap between good and neutral reservoir management. The modern reservoir management process involves goal setting, planning, implementing, monitoring, evaluating, and revising plans. Setting a reservoir management strategy requires knowledge of the reservoir, availability of technology, and knowledge of the business, political, and environmental climate. Formulating a comprehensive management plan involves depletion and development strategies, data acquisition and analyses, geological and numerical model studies, production and reserves forecasts, facilities requirements, economic optimization, and management approval. This paper provides management, engineers geologists, geophysicists, and field operations staff with a better understanding of the practical approach to reservoir management using a multidisciplinary, integrated team approach

  8. A Study of Sedimentation at the River Estuary on the Change of Reservoir Storage

    Directory of Open Access Journals (Sweden)

    Iskahar

    2018-01-01

    Full Text Available Estuary of the river that leads to the reservoir has characteristics include: relatively flat, there is a change in the increase of wet cross-sectional area and backwater. The backwater will cause the flow velocity to be reduced, so that the grains of sediment with a certain diameter carried by the flow will settle in the estuary of the river. The purpose of this research is to know the distribution and sedimentation pattern at the river estuary that leads to the reservoir with the change of water level in the reservoir storage, so the solution can be found to remove / reduce sediment before entering the reservoir. The method used is the experimental, by making the physical model of the river estuary leading to the reservoir. This study expects a solution to reduce sedimentation, so that sedimentation can be removed / minimized before entering the reservoir. This research tries to apply bypass channel to reduce the sedimentation at the river estuary. Bypass channels can be applied to overcome sedimentation at the river estuary, but in order for the sediment to be removed optimally, it is necessary to modify the mouth of bypass channel and channel angle.

  9. A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

    International Nuclear Information System (INIS)

    Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

    2015-01-01

    This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

  10. Monitoring of magnetic EOR fluids in reservoir under production by using the electromagnetic method

    Science.gov (United States)

    KIM, S.; Min, D. J.; Moon, S.; Kim, W. K.; Shin, Y.

    2014-12-01

    To increase the amount of oil and gas extracted during production, some techniques like EOR (Enhanced Oil Recovery) are applied by injecting some materials such as water and CO2. Recently, there are some researches for injecting magnetic nanoparticles with fluids during EOR. The size of particle is nano-scale, which can prevent particles from adhering to the pores of reservoir. The main purpose of injecting magnetic nanoparticles is to monitor movement or distribution of EOR fluids. To monitor the injected magnetic EOR fluids in the reservoir, CSEM (controlled source electromagnetic method) can be the most optimized geophysical method among various geophysical monitoring methods. Depending on the reservoir circumstances, we can control the electric or magnetic sources to monitor reservoir during oil or gas production. In this study, we perform numerical simulation of CSEM for 3D horizontal-layered models assuming a reservoir under production. We suppose that there are two wells: one is for the controlled source; the other is for the receiver. By changing the distribution, movement and magnetization of EOR fluids, we compare the electric or magnetic fields recorded at the receiver. Maxwell's equations are the governing equation of CSEM and are approximated by using the edge-based finite-element method. Direct solver is applied to solve the linear equations. Because injected magnetic nanoparticle changes the conductivity of EOR fluid, there is high contrast of conductivity of reservoir. This high contrast of conductivity induces secondary electric or magnetic fields that are recorded at the receiver well. We compare these recorded secondary fields generated by various movement or distribution of magnetic EOR fluid. Acknowledgements This work was supported by the "Development of Technology for CO2 Marine Geological Storage" grant funded by the Ministry of Oceans and Fisheries of Korea, by the "Civil Military Technology Cooperation Center", and by the International

  11. Development of interfacial area transport equation

    International Nuclear Information System (INIS)

    Kim, Seung Jin; Ishii, Mamoru; Kelly, Joseph

    2005-01-01

    The interfacial area transport equation dynamically models the changes in interfacial structures along the flow field by mechanistically modeling the creation and destruction of dispersed phase. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport mechanism for various sizes of bubbles, the transport equation is formulated for two characteristic groups of bubbles. The group 1 equation describes the transport of small-dispersed bubbles, whereas the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. To evaluate the feasibility and reliability of interfacial area transport equation available at present, it is benchmarked by an extensive database established in various two-phase flow configurations spanning from bubbly to churn-turbulent flow regimes. The geometrical effect in interfacial area transport is examined by the data acquired in vertical air-water two-phase flow through round pipes of various sizes and a confined flow duct, and by those acquired in vertical co-current downward air-water two-phase flow through round pipes of two different sizes

  12. Ground-water quality, levels, and flow direction near Fort Cobb Reservoir, Caddo County, Oklahoma, 1998-2000

    Science.gov (United States)

    Becker, Carol J.

    2001-01-01

    Fort Cobb Reservoir in northwest Caddo County Oklahoma is managed by the Bureau of Reclamation for water supply, recreation, flood control, and wildlife. Excessive amounts of nitrogen in the watershed have the potential to cause long-term eutrophication of the reservoir and increase already elevated concentrations of nitrogen in the Rush Springs aquifer. The U.S. Geological Survey in cooperation with the Bureau of Reclamation studied ground water in the area surrounding a swine feeding operation located less than 2 miles upgradient from Fort Cobb Reservoir in Caddo County, Oklahoma. Objectives of the study were to (1) determine if the operation was contributing nitrogen to the ground water and (2) measure changes in ground-water levels and determine the local ground-water flow direction in the area surrounding the swine feeding operation. Nitrate concentrations (28.1 and 31.5 milligrams per liter) were largest in two ground-water samples from a well upgradient of the wastewater lagoon. Nitrate concentrations ranged from 4.30 to 8.20 milligrams per liter in samples from downgradient wells. Traces of ammonia and nitrite were detected in a downgradient well, but not in upgradient wells. d15N values indicate atmospheric nitrogen, synthetic fertilizer, or plants were the predominate sources of nitrate in ground water from the downgradient wells. The d15N values in these samples are depleted in nitrogen-15, indicating that animal waste was not a significant contributor of nitrate. Manganese concentrations (1,150 and 965 micrograms per liter) in samples from a downgradient well were substantially larger than concentrations in samples from other wells, exceeding the secondary drinking-water standard of 50 micrograms per liter. Larger concentrations of bicarbonate, magnesium, fluoride, and iron and a higher pH were also measured in water from a downgradient well. Ground-water levels in an observation well were higher from April to mid-July and lower during the late summer

  13. Lattice Boltzmann Simulations of Fluid Flow in Continental Carbonate Reservoir Rocks and in Upscaled Rock Models Generated with Multiple-Point Geostatistics

    Directory of Open Access Journals (Sweden)

    J. Soete

    2017-01-01

    Full Text Available Microcomputed tomography (μCT and Lattice Boltzmann Method (LBM simulations were applied to continental carbonates to quantify fluid flow. Fluid flow characteristics in these complex carbonates with multiscale pore networks are unique and the applied method allows studying their heterogeneity and anisotropy. 3D pore network models were introduced to single-phase flow simulations in Palabos, a software tool for particle-based modelling of classic computational fluid dynamics. In addition, permeability simulations were also performed on rock models generated with multiple-point geostatistics (MPS. This allowed assessing the applicability of MPS in upscaling high-resolution porosity patterns into large rock models that exceed the volume limitations of the μCT. Porosity and tortuosity control fluid flow in these porous media. Micro- and mesopores influence flow properties at larger scales in continental carbonates. Upscaling with MPS is therefore necessary to overcome volume-resolution problems of CT scanning equipment. The presented LBM-MPS workflow is applicable to other lithologies, comprising different pore types, shapes, and pore networks altogether. The lack of straightforward porosity-permeability relationships in complex carbonates highlights the necessity for a 3D approach. 3D fluid flow studies provide the best understanding of flow through porous media, which is of crucial importance in reservoir modelling.

  14. Perturbative renormalization of composite operators via flow equations. Pt. 2. Short distance expansion

    Energy Technology Data Exchange (ETDEWEB)

    Keller, G. (Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)

    1993-04-01

    We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive [Phi][sub 4][sup 4]. The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.).

  15. A Comparative Study of the Neural Network, Fuzzy Logic, and Nero-fuzzy Systems in Seismic Reservoir Characterization: An Example from Arab (Surmeh Reservoir as an Iranian Gas Field, Persian Gulf Basin

    Directory of Open Access Journals (Sweden)

    Reza Mohebian

    2017-10-01

    Full Text Available Intelligent reservoir characterization using seismic attributes and hydraulic flow units has a vital role in the description of oil and gas traps. The predicted model allows an accurate understanding of the reservoir quality, especially at the un-cored well location. This study was conducted in two major steps. In the first step, the survey compared different intelligent techniques to discover an optimum relationship between well logs and seismic data. For this purpose, three intelligent systems, including probabilistic neural network (PNN,fuzzy logic (FL, and adaptive neuro-fuzzy inference systems (ANFISwere usedto predict flow zone index (FZI. Well derived FZI logs from three wells were employed to estimate intelligent models in the Arab (Surmeh reservoir. The validation of the produced models was examined by another well. Optimal seismic attributes for the estimation of FZI include acoustic impedance, integrated absolute amplitude, and average frequency. The results revealed that the ANFIS method performed better than the other systems and showed a remarkable reduction in the measured errors. In the second part of the study, the FZI 3D model was created by using the ANFIS system.The integrated approach introduced in the current survey illustrated that the extracted flow units from intelligent models compromise well with well-logs. Based on the results obtained, the intelligent systems are powerful techniques to predict flow units from seismic data (seismic attributes for distant well location. Finally, it was shown that ANFIS method was efficient in highlighting high and low-quality flow units in the Arab (Surmeh reservoir, the Iranian offshore gas field.

  16. Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation with reference to aeronautical operating systems

    Science.gov (United States)

    Frost, W.; Harper, W. L.

    1975-01-01

    Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.

  17. Scale-up of miscible flood processes for heterogeneous reservoirs. Second annual report

    Energy Technology Data Exchange (ETDEWEB)

    Orr, F.M. Jr.

    1995-03-01

    Progress is reported for a comprehensive investigation of the scaling behavior of gas injection processes in heterogeneous reservoirs. The interplay of phase behavior, viscous fingering, gravity segregation, capillary imbibition and drainage, and reservoir heterogeneity is examined in a series of simulations and experiments. Use of streamtube to model multiphase flow is demonstrated to be a fast and accurate approach for displacements that are dominated by reservoir heterogeneity. The streamtube technique is particularly powerful for multiphase compositional displacements because it represents the effects of phase behavior with a one-dimensional flow and represents the effects of heterogeneity through the locations of streamtubes. A new approach for fast calculations of critical tie-lines directly from criticality conditions is reported. A global triangular structure solution for four-component flow systems, whose tie-lies meet at the edge of a quaternary phase diagram or lie in planes is presented. Also demonstrated is the extension of this solution to multicomponent systems under the same assumptions. The interplay of gravity, capillary and viscous forces on final residual oil saturation is examined experimentally and theoretically. The analysis of vertical equilibrium conditions for three-phase gravity drainage shows that almost all oil can be recovered from the top part of a reservoir. The prediction of spreading and stability of thin film is performed to investigate three-phase gravity drainage mechanisms. Finally, experimental results from gravity drainage of crude oil in the presence of CO{sub 2} suggest that gravity drainage could be an efficient oil recovery process for vertically fractured reservoirs.

  18. Petroacoustic Modelling of Heterolithic Sandstone Reservoirs: A Novel Approach to Gassmann Modelling Incorporating Sedimentological Constraints and NMR Porosity data

    Science.gov (United States)

    Matthews, S.; Lovell, M.; Davies, S. J.; Pritchard, T.; Sirju, C.; Abdelkarim, A.

    2012-12-01

    Heterolithic or 'shaly' sandstone reservoirs constitute a significant proportion of hydrocarbon resources. Petroacoustic models (a combination of petrophysics and rock physics) enhance the ability to extract reservoir properties from seismic data, providing a connection between seismic and fine-scale rock properties. By incorporating sedimentological observations these models can be better constrained and improved. Petroacoustic modelling is complicated by the unpredictable effects of clay minerals and clay-sized particles on geophysical properties. Such effects are responsible for erroneous results when models developed for "clean" reservoirs - such as Gassmann's equation (Gassmann, 1951) - are applied to heterolithic sandstone reservoirs. Gassmann's equation is arguably the most popular petroacoustic modelling technique in the hydrocarbon industry and is used to model elastic effects of changing reservoir fluid saturations. Successful implementation of Gassmann's equation requires well-constrained drained rock frame properties, which in heterolithic sandstones are heavily influenced by reservoir sedimentology, particularly clay distribution. The prevalent approach to categorising clay distribution is based on the Thomas - Stieber model (Thomas & Stieber, 1975), this approach is inconsistent with current understanding of 'shaly sand' sedimentology and omits properties such as sorting and grain size. The novel approach presented here demonstrates that characterising reservoir sedimentology constitutes an important modelling phase. As well as incorporating sedimentological constraints, this novel approach also aims to improve drained frame moduli estimates through more careful consideration of Gassmann's model assumptions and limitations. A key assumption of Gassmann's equation is a pore space in total communication with movable fluids. This assumption is often violated by conventional applications in heterolithic sandstone reservoirs where effective porosity, which

  19. Sampling from stochastic reservoir models constrained by production data

    Energy Technology Data Exchange (ETDEWEB)

    Hegstad, Bjoern Kaare

    1997-12-31

    When a petroleum reservoir is evaluated, it is important to forecast future production of oil and gas and to assess forecast uncertainty. This is done by defining a stochastic model for the reservoir characteristics, generating realizations from this model and applying a fluid flow simulator to the realizations. The reservoir characteristics define the geometry of the reservoir, initial saturation, petrophysical properties etc. This thesis discusses how to generate realizations constrained by production data, that is to say, the realizations should reproduce the observed production history of the petroleum reservoir within the uncertainty of these data. The topics discussed are: (1) Theoretical framework, (2) History matching, forecasting and forecasting uncertainty, (3) A three-dimensional test case, (4) Modelling transmissibility multipliers by Markov random fields, (5) Up scaling, (6) The link between model parameters, well observations and production history in a simple test case, (7) Sampling the posterior using optimization in a hierarchical model, (8) A comparison of Rejection Sampling and Metropolis-Hastings algorithm, (9) Stochastic simulation and conditioning by annealing in reservoir description, and (10) Uncertainty assessment in history matching and forecasting. 139 refs., 85 figs., 1 tab.

  20. Bernoulli's Equation

    Indian Academy of Sciences (India)

    regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.

  1. Characterizing hydraulic fractures in shale gas reservoirs using transient pressure tests

    Directory of Open Access Journals (Sweden)

    Cong Wang

    2015-06-01

    This work presents an unconventional gas reservoir simulator and its application to quantify hydraulic fractures in shale gas reservoirs using transient pressure data. The numerical model incorporates most known physical processes for gas production from unconventional reservoirs, including two-phase flow of liquid and gas, Klinkenberg effect, non-Darcy flow, and nonlinear adsorption. In addition, the model is able to handle various types and scales of fractures or heterogeneity using continuum, discrete or hybrid modeling approaches under different well production conditions of varying rate or pressure. Our modeling studies indicate that the most sensitive parameter of hydraulic fractures to early transient gas flow through extremely low permeability rock is actually the fracture-matrix contacting area, generated by fracturing stimulation. Based on this observation, it is possible to use transient pressure testing data to estimate the area of fractures generated from fracturing operations. We will conduct a series of modeling studies and present a methodology using typical transient pressure responses, simulated by the numerical model, to estimate fracture areas created or to quantity hydraulic fractures with traditional well testing technology. The type curves of pressure transients from this study can be used to quantify hydraulic fractures in field application.

  2. Effect of hypolimnetic oxygenation on oxygen depletion rates in two water-supply reservoirs.

    Science.gov (United States)

    Gantzer, Paul A; Bryant, Lee D; Little, John C

    2009-04-01

    Oxygenation systems, such as bubble-plume diffusers, are used to improve water quality by replenishing dissolved oxygen (DO) in the hypolimnia of water-supply reservoirs. The diffusers induce circulation and mixing, which helps distribute DO throughout the hypolimnion. Mixing, however, has also been observed to increase hypolimnetic oxygen demand (HOD) during system operation, thus accelerating oxygen depletion. Two water-supply reservoirs (Spring Hollow Reservoir (SHR) and Carvins Cove Reservoir (CCR)) that employ linear bubble-plume diffusers were studied to quantify diffuser effects on HOD. A recently validated plume model was used to predict oxygen addition rates. The results were used together with observed oxygen accumulation rates to evaluate HOD over a wide range of applied gas flow rates. Plume-induced mixing correlated well with applied gas flow rate and was observed to increase HOD. Linear relationships between applied gas flow rate and HOD were found for both SHR and CCR. HOD was also observed to be independent of bulk hypolimnion oxygen concentration, indicating that HOD is controlled by induced mixing. Despite transient increases in HOD, oxygenation caused an overall decrease in background HOD, as well as a decrease in induced HOD during diffuser operation, over several years. This suggests that the residual or background oxygen demand decreases from one year to the next. Despite diffuser-induced increases in HOD, hypolimnetic oxygenation remains a viable method for replenishing DO in thermally-stratified water-supply reservoirs such as SHR and CCR.

  3. Reservoir Models for Gas Hydrate Numerical Simulation

    Science.gov (United States)

    Boswell, R.

    2016-12-01

    /linear way. Significant progress has also occurred in recent years with regard to the geologic characterization of reservoir boundaries. Vertical boundaries with overlying clay-rich "seals" are now widely-appreciated to have non-zero permeability, and lateral boundaries are sources of potential lateral fluid flow.

  4. Simulation of a SAGD well blowout using a reservoir-wellbore coupled simulator

    Energy Technology Data Exchange (ETDEWEB)

    Walter, J.; Vanegas, P.; Cunha, L.B. [Alberta Univ., Edmonton, AB (Canada); Worth, D.J. [C-FER Technologies, Edmonton, AB (Canada); Crepin, S. [Petrocedeno, Caracas (Venezuela)

    2008-10-15

    Single barrier completion systems are typically used in SAGD projects due to the lack of equipment suitable for high temperature SAGD downhole environments. This study used a wellbore and reservoir coupled thermal simulator tool to investigate the blowout behaviour of a steam assisted gravity drainage (SAGD) well pair when the safety barrier has failed. Fluid flow pressure drop through the wellbore and heat losses between the wellbore and the reservoir were modelled using a discretized wellbore option and a semi-analytical model. The fully coupled mechanistic model accounted for the simultaneous transient pressure and temperature variations along the wellbore and the reservoir. The simulations were used to predict flowing potential and fluid compositions of both wells in a SAGD well pair under various flowing conditions. Blowout scenarios were created for 3 different points in the well pair's life. Three flow paths during the blowout were evaluated for both the production and injection wells. Results of the study were used to conduct a comparative risk assessment between a double barrier and a single barrier completion. The modelling study confirmed that both the injection and production wells had the potential for blowouts lasting significant periods of time, with liquid rates over 50 times the normal production liquid rates. The model successfully predicted the blowout flow potential of the SAGD well pairs. 8 refs., 3 tabs., 18 figs.

  5. Producing Light Oil from a Frozen Reservoir: Reservoir and Fluid Characterization of Umiat Field, National Petroleum Reserve, Alaska

    Energy Technology Data Exchange (ETDEWEB)

    Hanks, Catherine

    2012-12-31

    Umiat oil field is a light oil in a shallow, frozen reservoir in the Brooks Range foothills of northern Alaska with estimated oil-in-place of over 1 billion barrels. Umiat field was discovered in the 1940’s but was never considered viable because it is shallow, in the permafrost, and far from any transportation infrastructure. The advent of modern drilling and production techniques has made Umiat and similar fields in northern Alaska attractive exploration and production targets. Since 2008 UAF has been working with Renaissance Alaska Inc. and, more recently, Linc Energy, to develop a more robust reservoir model that can be combined with rock and fluid property data to simulate potential production techniques. This work will be used to by Linc Energy as they prepare to drill up to 5 horizontal wells during the 2012-2013 drilling season. This new work identified three potential reservoir horizons within the Cretaceous Nanushuk Formation: the Upper and Lower Grandstand sands, and the overlying Ninuluk sand, with the Lower Grandstand considered the primary target. Seals are provided by thick interlayered shales. Reserve estimates for the Lower Grandstand alone range from 739 million barrels to 2437 million barrels, with an average of 1527 million bbls. Reservoir simulations predict that cold gas injection from a wagon-wheel pattern of multilateral injectors and producers located on 5 drill sites on the crest of the structure will yield 12-15% recovery, with actual recovery depending upon the injection pressure used, the actual Kv/Kh encountered, and other geologic factors. Key to understanding the flow behavior of the Umiat reservoir is determining the permeability structure of the sands. Sandstones of the Cretaceous Nanushuk Formation consist of mixed shoreface and deltaic sandstones and mudstones. A core-based study of the sedimentary facies of these sands combined with outcrop observations identified six distinct facies associations with distinctive permeability

  6. Constitutive equations for extensional flow of wormlike micelles : stability analysis of the Bautista-Manero model

    NARCIS (Netherlands)

    Boek, E.S.; Padding, J.T.; Anderson, V.J.; Tardy, P.M.J.; Crawshaw, J.P.; Pearson, J.R.A.

    2005-01-01

    We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real

  7. User's guide of TOUGH2-EGS-MP: A Massively Parallel Simulator with Coupled Geomechanics for Fluid and Heat Flow in Enhanced Geothermal Systems VERSION 1.0

    Energy Technology Data Exchange (ETDEWEB)

    Xiong, Yi [Colorado School of Mines, Golden, CO (United States); Fakcharoenphol, Perapon [Colorado School of Mines, Golden, CO (United States); Wang, Shihao [Colorado School of Mines, Golden, CO (United States); Winterfeld, Philip H. [Colorado School of Mines, Golden, CO (United States); Zhang, Keni [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Wu, Yu-Shu [Colorado School of Mines, Golden, CO (United States)

    2013-12-01

    TOUGH2-EGS-MP is a parallel numerical simulation program coupling geomechanics with fluid and heat flow in fractured and porous media, and is applicable for simulation of enhanced geothermal systems (EGS). TOUGH2-EGS-MP is based on the TOUGH2-MP code, the massively parallel version of TOUGH2. In TOUGH2-EGS-MP, the fully-coupled flow-geomechanics model is developed from linear elastic theory for thermo-poro-elastic systems and is formulated in terms of mean normal stress as well as pore pressure and temperature. Reservoir rock properties such as porosity and permeability depend on rock deformation, and the relationships between these two, obtained from poro-elasticity theories and empirical correlations, are incorporated into the simulation. This report provides the user with detailed information on the TOUGH2-EGS-MP mathematical model and instructions for using it for Thermal-Hydrological-Mechanical (THM) simulations. The mathematical model includes the fluid and heat flow equations, geomechanical equation, and discretization of those equations. In addition, the parallel aspects of the code, such as domain partitioning and communication between processors, are also included. Although TOUGH2-EGS-MP has the capability for simulating fluid and heat flows coupled with geomechanical effects, it is up to the user to select the specific coupling process, such as THM or only TH, in a simulation. There are several example problems illustrating applications of this program. These example problems are described in detail and their input data are presented. Their results demonstrate that this program can be used for field-scale geothermal reservoir simulation in porous and fractured media with fluid and heat flow coupled with geomechanical effects.

  8. Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

    DEFF Research Database (Denmark)

    Separdar, Leila; Bailey, Nicholas; Schrøder, Thomas

    2013-01-01

    fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows......Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal...... of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of strain rates were simulated to test for the predicted invariance, covering both the linear...

  9. Effects of water inlet configuration in a service reservoir applying CFD modelling

    Directory of Open Access Journals (Sweden)

    Carolina Montoya Pachongo

    2016-01-01

    Full Text Available This study investigated the state of a service reservoir of a drinking water distribution network. Numerical simulation was applied to establish its flow pattern, mixing conditions, and free residual chlorine decay. The influence of the change in the water inlet configuration on these characteristics was evaluated. Four scenarios were established with different water level and flow rate as the differences between the first three scenarios. The fourth scenario was evaluated to assess the influence of the inlet configuration, momentum flow and water level on hydrodynamic conditions within the service reservoir. The distribution of four nozzles of 152.4mm diameter was identified as a viable measure to preserve the water quality in this type of hydraulic structures.

  10. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  11. Flow patterns in vertical two-phase flow

    International Nuclear Information System (INIS)

    McQuillan, K.W.; Whalley, P.B.

    1985-01-01

    This paper is concerned with the flow patterns which occur in upwards gas-liquid two-phase flow in vertical tubes. The basic flow patterns are described and the use of flow patter maps is discussed. The transition between plug flow and churn flow is modelled under the assumption that flooding of the falling liquid film limits the stability of plug flow. The resulting equation is combined with other flow pattern transition equations to produce theoretical flow pattern maps, which are then tested against experimental flow pattern data. Encouraging agreement is obtained

  12. The influence of lumping on the behavior of reservoir with light oil and CO2

    Energy Technology Data Exchange (ETDEWEB)

    Scanavini, Helena Finardi Alvares [Universidade Estadual de Campinas (UNISIM/UNICAMP), SP (Brazil). Dept. de Engenharia de Petroleo. Pesquisa em Simulacao e Gerenciamento de Reservatorios; Schiozer, Denis Jose [Universidade Estadual de Campinas (DEP/FEM/UNICAMP), SP (Brazil). Fac. de Engenharia Mecanica. Dept. de Engenharia de Petroleo

    2012-07-01

    Compositional simulation demands a large number of equations and functions to be solved, once fluid properties depend on reservoir pressure and temperature and also on fluid composition. As a consequence, the number of components used influences considerably in the simulation run time and accuracy: more components yield more equations to be solved with expected higher run time. Giant petroleum fields discovered recently in Brazil (pre-salt reservoirs) demand compositional simulation due to the fluid characteristics (light oil with the presence of CO2). However, the computational time can be a limitation because of the number of grid blocks that are necessary to represent the reservoir. So, reducing the number of components is an important step for the simulation models. Under this context, this paper presents a study on the influence of different lumping clusters, used to reduce the number of components in a volatile oil, on reservoir simulation. Phase diagram, saturation pressure and simulation results were used for comparison purposes. The best results were obtained for the cases with 14, 9 and 7 pseudo components, which represented correctly the original fluid, reducing till three times the simulation run time, for the same production volumes of oil and gas. (author)

  13. 78 FR 42030 - Reservoirs at Headwaters of the Mississippi River; Use and Administration

    Science.gov (United States)

    2013-07-15

    ... Headwaters of the Mississippi River; Use and Administration AGENCY: U.S. Army Corps of Engineers, DoD. ACTION... proposing to amend the rules regarding use and administration of the reservoirs at the headwaters of the... Headwaters reservoirs containing minimum flow values that differ from those currently codified in the Code of...

  14. Entropy-based viscous regularization for the multi-dimensional Euler equations in low-Mach and transonic flows

    Energy Technology Data Exchange (ETDEWEB)

    Marc O Delchini; Jean E. Ragusa; Ray A. Berry

    2015-07-01

    We present a new version of the entropy viscosity method, a viscous regularization technique for hyperbolic conservation laws, that is well-suited for low-Mach flows. By means of a low-Mach asymptotic study, new expressions for the entropy viscosity coefficients are derived. These definitions are valid for a wide range of Mach numbers, from subsonic flows (with very low Mach numbers) to supersonic flows, and no longer depend on an analytical expression for the entropy function. In addition, the entropy viscosity method is extended to Euler equations with variable area for nozzle flow problems. The effectiveness of the method is demonstrated using various 1-D and 2-D benchmark tests: flow in a converging–diverging nozzle; Leblanc shock tube; slow moving shock; strong shock for liquid phase; low-Mach flows around a cylinder and over a circular hump; and supersonic flow in a compression corner. Convergence studies are performed for smooth solutions and solutions with shocks present.

  15. An $h$-Adaptive Operator Splitting Method for Two-Phase Flow in 3D Heterogeneous Porous Media

    KAUST Repository

    Chueh, Chih-Che; Djilali, Ned; Bangerth, Wolfgang

    2013-01-01

    The simulation of multiphase flow in porous media is a ubiquitous problem in a wide variety of fields, such as fuel cell modeling, oil reservoir simulation, magma dynamics, and tumor modeling. However, it is computationally expensive. This paper presents an interconnected set of algorithms which we show can accelerate computations by more than two orders of magnitude compared to traditional techniques, yet retains the high accuracy necessary for practical applications. Specifically, we base our approach on a new adaptive operator splitting technique driven by an a posteriori criterion to separate the flow from the transport equations, adaptive meshing to reduce the size of the discretized problem, efficient block preconditioned solver techniques for fast solution of the discrete equations, and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. We demonstrate the accuracy and efficiency of our approach using numerical experiments in one, two, and three dimensions using a program that is made available as part of a large open source library. © 2013 Society for Industrial and Applied Mathematics.

  16. Thermodynamic evolution of the Los Azufres, Mexico, geothermal reservoir from 1982 to 2002

    Energy Technology Data Exchange (ETDEWEB)

    Arellano, Victor Manuel; Barragan, Rosa Maria [Instituto de Investigaciones Electricas, Gerencia de Geotermia, Reforma 113, Col. Palmira, 62490 Cuernavaca, Morelos (Mexico); Torres, Marco Antonio [Comision Federal de Electricidad, Residencia Los Azufres, Campamento Agua Fria, Los Azufres, Michoacan (Mexico)

    2005-10-01

    An investigation has been made of the response of the Los Azufres geothermal reservoir to 20 years of development, beginning in 1982. The simulator WELFLO was used to characterize the thermodynamic conditions of the reservoir fluids. The first response to exploitation consisted of a decrease in pressure and an increase in enthalpy. Small decreases in reservoir pressure associated with large increases in fluid enthalpy characterize the long-term response in the northern production area. In the southern production area, long-term changes include decreases in pressure and mass flow rate, increases in steam production and, in wells affected by injection, increases in both pressure and total mass flow rate. These changes reflect the effects of boiling, cooling and fluid mixing, processes resulting from large-scale fluid production. (author)

  17. Potential urban runoff impacts and contaminant distributions in shoreline and reservoir environments of Lake Havasu, southwestern United States.

    Science.gov (United States)

    Wilson, Doyle C

    2018-04-15

    Heavy metal, nutrient, and hydrocarbon levels in and adjacent to Lake Havasu, a regionally significant water supply reservoir with a highly controlled, dynamic flow regime, are assessed in relation to possible stormwater runoff impacts from an arid urban center. Shallow groundwater and sediment analyses from ephemeral drainage (wash) mouths that convey stormwater runoff from Lake Havasu City, Arizona to the reservoir, provided contaminant control points and correlation ties with the reservoir environment. Fine-grain sediments tend to contain higher heavy metal concentrations whereas nutrients are more evenly distributed, except low total organic carbon levels from young wash mouth surfaces devoid of vegetation. Heavy metal and total phosphate sediment concentrations in transects from wash mouths into the reservoir have mixed and decreasing trends, respectively. Both series may indicate chemical depositional influences from urban runoff, yet no statistically significant concentration differences occur between specific wash mouths and corresponding offshore transects. Heavy metal pollution indices of all sediments indicate no discernible to minor contamination, indicating that runoff impacts are minimal. Nevertheless, several heavy metal concentrations from mid-reservoir sediment sites increase southward through the length of the reservoir. Continual significant water flow through the reservoir may help to disperse locally derived runoff particulates, which could mix and settle down gradient with chemical loads from upriver sources and local atmospheric deposition. Incorporating the shoreline environment with the reservoir investigation provides spatial continuity in assessing contaminant sources and distribution patterns. This is particularly acute in the investigation of energetic, flow-through reservoirs in which sources may be overlooked if solely analyzing the reservoir environment. Copyright © 2017 Elsevier B.V. All rights reserved.

  18. Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

    Science.gov (United States)

    Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

    2018-04-01

    We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

  19. Modeling of reservoir operation in UNH global hydrological model

    Science.gov (United States)

    Shiklomanov, Alexander; Prusevich, Alexander; Frolking, Steve; Glidden, Stanley; Lammers, Richard; Wisser, Dominik

    2015-04-01

    Climate is changing and river flow is an integrated characteristic reflecting numerous environmental processes and their changes aggregated over large areas. Anthropogenic impacts on the river flow, however, can significantly exceed the changes associated with climate variability. Besides of irrigation, reservoirs and dams are one of major anthropogenic factor affecting streamflow. They distort hydrological regime of many rivers by trapping of freshwater runoff, modifying timing of river discharge and increasing the evaporation rate. Thus, reservoirs is an integral part of the global hydrological system and their impacts on rivers have to be taken into account for better quantification and understanding of hydrological changes. We developed a new technique, which was incorporated into WBM-TrANS model (Water Balance Model-Transport from Anthropogenic and Natural Systems) to simulate river routing through large reservoirs and natural lakes based on information available from freely accessible databases such as GRanD (the Global Reservoir and Dam database) or NID (National Inventory of Dams for US). Different formulations were applied for unregulated spillway dams and lakes, and for 4 types of regulated reservoirs, which were subdivided based on main purpose including generic (multipurpose), hydropower generation, irrigation and water supply, and flood control. We also incorporated rules for reservoir fill up and draining at the times of construction and decommission based on available data. The model were tested for many reservoirs of different size and types located in various climatic conditions using several gridded meteorological data sets as model input and observed daily and monthly discharge data from GRDC (Global Runoff Data Center), USGS Water Data (US Geological Survey), and UNH archives. The best results with Nash-Sutcliffe model efficiency coefficient in the range of 0.5-0.9 were obtained for temperate zone of Northern Hemisphere where most of large

  20. Calibration of the 7—Equation Transition Model for High Reynolds Flows at Low Mach

    Science.gov (United States)

    Colonia, S.; Leble, V.; Steijl, R.; Barakos, G.

    2016-09-01

    The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients that need tuning. In this paper, the γ—equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. An aerofoil is used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solutions for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected.

  1. Micro/Nano-pore Network Analysis of Gas Flow in Shale Matrix.

    Science.gov (United States)

    Zhang, Pengwei; Hu, Liming; Meegoda, Jay N; Gao, Shengyan

    2015-08-27

    The gas flow in shale matrix is of great research interests for optimized shale gas extraction. The gas flow in the nano-scale pore may fall in flow regimes such as viscous flow, slip flow and Knudsen diffusion. A 3-dimensional nano-scale pore network model was developed to simulate dynamic gas flow, and to describe the transient properties of flow regimes. The proposed pore network model accounts for the various size distributions and low connectivity of shale pores. The pore size, pore throat size and coordination number obey normal distribution, and the average values can be obtained from shale reservoir data. The gas flow regimes were simulated using an extracted pore network backbone. The numerical results show that apparent permeability is strongly dependent on pore pressure in the reservoir and pore throat size, which is overestimated by low-pressure laboratory tests. With the decrease of reservoir pressure, viscous flow is weakening, then slip flow and Knudsen diffusion are gradually becoming dominant flow regimes. The fingering phenomenon can be predicted by micro/nano-pore network for gas flow, which provides an effective way to capture heterogeneity of shale gas reservoir.

  2. Stress, Flow and Particle Transport in Rock Fractures

    Energy Technology Data Exchange (ETDEWEB)

    Koyama, Tomofumi

    2007-09-15

    by the coupled shear-flow tests of fracture specimens with visualization of the fluid flow. From the obtained flow velocity fields, the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Peclet number, Pe, respectively. The fluid flow in the vertical 2-D cross-sections of a rock fracture was also simulated by solving both Navier-Stokes (NS) and Reynolds equations, and the particle transport was predicted by streamline particle tracking method. The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for large scale problems. The flow simulation results show that the total flow rate and the flow velocity predicted by NS equations are quite different from that as predicted by the Reynolds equation. The results show that a roughly 5-10 % overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Peclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear. The scientific findings from these studies provided new insights to the physical behavior of fluid flow and mass transport in rock fractures which is the scientific basis for many rock mechanics problems at the fundamental

  3. A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

    Science.gov (United States)

    Sohn, J. L.; Heinrich, J. C.

    1990-01-01

    The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

  4. Cased-hole log analysis and reservoir performance monitoring

    CERN Document Server

    Bateman, Richard M

    2015-01-01

    This book addresses vital issues, such as the evaluation of shale gas reservoirs and their production. Topics include the cased-hole logging environment, reservoir fluid properties; flow regimes; temperature, noise, cement bond, and pulsed neutron logging; and casing inspection. Production logging charts and tables are included in the appendices. The work serves as a comprehensive reference for production engineers with upstream E&P companies, well logging service company employees, university students, and petroleum industry training professionals. This book also: ·       Provides methods of conveying production logging tools along horizontal well segments as well as measurements of formation electrical resistivity through casing ·       Covers new information on fluid flow characteristics in inclined pipe and provides new and improved nuclear tool measurements in cased wells ·       Includes updates on cased-hole wireline formation testing  

  5. Adaptive implicit method for thermal compositional reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Agarwal, A.; Tchelepi, H.A. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Stanford Univ., Palo Alto (United States)

    2008-10-15

    As the global demand for oil increases, thermal enhanced oil recovery techniques are becoming increasingly important. Numerical reservoir simulation of thermal methods such as steam assisted gravity drainage (SAGD) is complex and requires a solution of nonlinear mass and energy conservation equations on a fine reservoir grid. The most currently used technique for solving these equations is the fully IMplicit (FIM) method which is unconditionally stable, allowing for large timesteps in simulation. However, it is computationally expensive. On the other hand, the method known as IMplicit pressure explicit saturations, temperature and compositions (IMPEST) is computationally inexpensive, but it is only conditionally stable and restricts the timestep size. To improve the balance between the timestep size and computational cost, the thermal adaptive IMplicit (TAIM) method uses stability criteria and a switching algorithm, where some simulation variables such as pressure, saturations, temperature, compositions are treated implicitly while others are treated with explicit schemes. This presentation described ongoing research on TAIM with particular reference to thermal displacement processes such as the stability criteria that dictate the maximum allowed timestep size for simulation based on the von Neumann linear stability analysis method; the switching algorithm that adapts labeling of reservoir variables as implicit or explicit as a function of space and time; and, complex physical behaviors such as heat and fluid convection, thermal conduction and compressibility. Key numerical results obtained by enhancing Stanford's General Purpose Research Simulator (GPRS) were also presented along with a list of research challenges. 14 refs., 2 tabs., 11 figs., 1 appendix.

  6. Resonance oscillations of the Soufrière Hills Volcano (Montserrat, W.I.) magmatic system induced by forced magma flow from the reservoir into the upper plumbing dike

    Science.gov (United States)

    Chen, Chin-Wu; Huang, Hsin-Fu; Hautmann, Stefanie; Sacks, I. Selwyn; Linde, Alan T.; Taira, Taka'aki

    2018-01-01

    Short-period deformation cycles are a common phenomenon at active volcanoes and are often attributed to the instability of magma flow in the upper plumbing system caused by fluctuations in magma viscosity related to cooling, degassing, and crystallization. Here we present 20-min periodic oscillations in ground deformation based on high-precision continuous borehole strain data that were associated with the 2003 massive dome-collapse at the Soufrière Hills Volcano, Montserrat (West Indies). These high-frequency oscillations lasted 80 min and were preceded by a 4-hour episode of rapid expansion of the shallow magma reservoir. Strain amplitude ratios indicate that the deformational changes were generated by pressure variations in the shallow magma reservoir and - with reversed polarity - the adjacent plumbing dike. The unusually short period of the oscillations cannot be explained with thermally induced variations in magma properties. We investigate the underlying mechanism of the oscillations via a numerical model of forced magma flow through a reservoir-dike system accounting for time-dependent dilation/contraction of the dike due to a viscous response in the surrounding host rock. Our results suggest that the cyclic pressure variations are modulated by the dynamical interplay between rapid expansion of the magma chamber and the incapacity of the narrow dike to take up fast enough the magma volumes supplied by the reservoir. Our results allow us to place first order constraints on the viscosity of crustal host rocks and consequently its fractional melt content. Hence, we present for the first time crustal-scale in situ measurements of rheological properties of mush zones surrounding magmatic systems.

  7. On the effect of operation of the hydropower plant on the water quality of Rapel reservoir, central Chile

    Science.gov (United States)

    Rossel, V.; De La Fuente, A.

    2013-12-01

    the hydropower plant outflows are obtained using an alternative of the ISO's economic optimization tool. A number of 20 simulations are conducted depending on the hydrological regime (dry, normal or wet) and on the presence or absence of an environmental flow. First of all, it was obtained that the hydropower plant operation depends on the hydrological regime, which produces changes in the storage volume, and on the environmental flow. Particularly, wet regime promotes high fluctuation on the storage, and the definition of an environmental flow reduces the outflow peaks.The numerical results show that there is a direct influence of hydropeaking on the water quality of Rapel reservoir, particularly in the area near the dam. This result is due to both changes in the storage volume, produced by different environmental flows and hydrological regime, and hydrodynamics and vertical mixing. The simulations also show that the introduction of an environmental flow downstream has an adverse impact on the internal quality of the reservoir, which is increased in the dry scenario. The study evidences the conflicting goals among environmental flow, SIC's operation costs and internal water quality of the reservoir.

  8. Molecular Simulation towards Efficient and Representative Subsurface Reservoirs Modeling

    KAUST Repository

    Kadoura, Ahmad Salim

    2016-01-01

    This dissertation focuses on the application of Monte Carlo (MC) molecular simulation and Molecular Dynamics (MD) in modeling thermodynamics and flow of subsurface reservoir fluids. At first, MC molecular simulation is proposed as a promising method

  9. A Thermoelastic Hydraulic Fracture Design Tool for Geothermal Reservoir Development

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad Ghassemi

    2003-06-30

    Geothermal energy is recovered by circulating water through heat exchange areas within a hot rock mass. Geothermal reservoir rock masses generally consist of igneous and metamorphic rocks that have low matrix permeability. Therefore, cracks and fractures play a significant role in extraction of geothermal energy by providing the major pathways for fluid flow and heat exchange. Thus, knowledge of conditions leading to formation of fractures and fracture networks is of paramount importance. Furthermore, in the absence of natural fractures or adequate connectivity, artificial fracture are created in the reservoir using hydraulic fracturing. At times, the practice aims to create a number of parallel fractures connecting a pair of wells. Multiple fractures are preferred because of the large size necessary when using only a single fracture. Although the basic idea is rather simple, hydraulic fracturing is a complex process involving interactions of high pressure fluid injections with a stressed hot rock mass, mechanical interaction of induced fractures with existing natural fractures, and the spatial and temporal variations of in-situ stress. As a result it is necessary to develop tools that can be used to study these interactions as an integral part of a comprehensive approach to geothermal reservoir development, particularly enhanced geothermal systems. In response to this need we have set out to develop advanced thermo-mechanical models for design of artificial fractures and rock fracture research in geothermal reservoirs. These models consider the significant hydraulic and thermo-mechanical processes and their interaction with the in-situ stress state. Wellbore failure and fracture initiation is studied using a model that fully couples poro-mechanical and thermo-mechanical effects. The fracture propagation model is based on a complex variable and regular displacement discontinuity formulations. In the complex variable approach the displacement discontinuities are

  10. Modeling the Influence of Variable Tributary Inflow on Circulation and Contaminant Transport in a Water Supply Reservoir

    Science.gov (United States)

    Nguyen, L. H.; Wildman, R.

    2012-12-01

    This study characterizes quantitatively the flow and mixing regimes of a water supply reservoir, while also conducting numerical tracer experiments on different operation scenarios. We investigate the effects of weather events on water quality via storm water inflows. Our study site the Kensico Reservoir, New York, the penultimate reservoir of New York City's water supply, is never filtered and thus dependent on stringent watershed protection. This reservoir must meet federal drinking water standards under changing conditions such as increased suburban, commercial, and highway developments that are much higher than the rest of the watershed. Impacts from these sources on water quality are magnified by minor tributary flows subject to contaminants from development projects as other tributaries providing >99% of water to this reservoir are exceedingly clean due to management practices upstream. These threats, coupled with possible changes in the frequency/intensity of weather events due to climate change, increase the potential for contaminants to enter the reservoir and drinking water intakes. This situation provides us with the unique ability to study the effects of weather events on water quality via insignificant storm water inflows, without influence from the major tributaries due to their pristine water quality characteristics. The concentration of contaminants at the drinking water intake depends partially on transport from their point of entry in the reservoir. Thus, it is crucial to understand water circulation in this reservoir and to estimate residence times and water ages at different locations and under different hydrologic scenarios. We described water age, residence time, thermal structure, and flow dynamics of tributary plumes in Kensico Reservoir during a 22-year simulation period using a two-dimensional hydrodynamic and water quality model (CE-QUAL-W2). Our estimates of water age can reach a maximum of ~300 days in deep-reservoir-cells, with

  11. analysis of pressure variation of fluid in bounded circular reservoirs

    African Journals Online (AJOL)

    user

    analysis of the analysed finite element, imposing the boundary conditions and finally, getting the results that ... in reservoir engineering applications [2–7]. ... THEORY. The law of conservation of mass, Darcy's law and the equation of state has been combined to obtain the ..... fields in laser-two-layer solids weak interactions.

  12. Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

    Directory of Open Access Journals (Sweden)

    Yichao Gao

    2011-01-01

    Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

  13. Ensemble Flow Forecasts for Risk Based Reservoir Operations of Lake Mendocino in Mendocino County, California: A Framework for Objectively Leveraging Weather and Climate Forecasts in a Decision Support Environment

    Science.gov (United States)

    Delaney, C.; Hartman, R. K.; Mendoza, J.; Whitin, B.

    2017-12-01

    Forecast informed reservoir operations (FIRO) is a methodology that incorporates short to mid-range precipitation and flow forecasts to inform the flood operations of reservoirs. The Ensemble Forecast Operations (EFO) alternative is a probabilistic approach of FIRO that incorporates ensemble streamflow predictions (ESPs) made by NOAA's California-Nevada River Forecast Center (CNRFC). With the EFO approach, release decisions are made to manage forecasted risk of reaching critical operational thresholds. A water management model was developed for Lake Mendocino, a 111,000 acre-foot reservoir located near Ukiah, California, to evaluate the viability of the EFO alternative to improve water supply reliability but not increase downstream flood risk. Lake Mendocino is a dual use reservoir, which is owned and operated for flood control by the United States Army Corps of Engineers and is operated for water supply by the Sonoma County Water Agency. Due to recent changes in the operations of an upstream hydroelectric facility, this reservoir has suffered from water supply reliability issues since 2007. The EFO alternative was simulated using a 26-year (1985-2010) ESP hindcast generated by the CNRFC. The ESP hindcast was developed using Global Ensemble Forecast System version 10 precipitation reforecasts processed with the Hydrologic Ensemble Forecast System to generate daily reforecasts of 61 flow ensemble members for a 15-day forecast horizon. Model simulation results demonstrate that the EFO alternative may improve water supply reliability for Lake Mendocino yet not increase flood risk for downstream areas. The developed operations framework can directly leverage improved skill in the second week of the forecast and is extendable into the S2S time domain given the demonstration of improved skill through a reliable reforecast of adequate historical duration and consistent with operationally available numerical weather predictions.

  14. Reservoir characterization by multiattribute analysis: The Orito field case

    Directory of Open Access Journals (Sweden)

    Montes Luis

    2010-12-01

    Full Text Available

    In order to characterize the Caballos formation reservoir in the Orito field in the Putumayo basin - Colombia, a multiattribute analysis was applied to a 50 km2 seismic volume along with 16 boreholes. Some properties of the reservoir were reliably estimated and very accurate when compared with well data. The porosity, permeability and volume of shale were calculated in the seismic volume by at least second order multivariate polynomial. A good correlation between porosity and acoustic impedance was observed by means of crossplot analysis performed on properties measured and estimated in cores or borehole logs as well as on properties calculated in the seismic volume. The estimated property values were well behaved according to the rocks physics analysis. With the property maps generated and the geological environments of the reservoir a new interpretation of the Caballos formation was established. High correlation coefficients and low estimated errors point out competence to calculate these three reservoir properties in places far from the influence of the wells. The multiple equation system was established through weighted hierarchical grouping of attributes and their coefficients calculated applying the inverse generalized matrix method.

  15. Molecular Simulation towards Efficient and Representative Subsurface Reservoirs Modeling

    KAUST Repository

    Kadoura, Ahmad

    2016-09-01

    This dissertation focuses on the application of Monte Carlo (MC) molecular simulation and Molecular Dynamics (MD) in modeling thermodynamics and flow of subsurface reservoir fluids. At first, MC molecular simulation is proposed as a promising method to replace correlations and equations of state in subsurface flow simulators. In order to accelerate MC simulations, a set of early rejection schemes (conservative, hybrid, and non-conservative) in addition to extrapolation methods through reweighting and reconstruction of pre-generated MC Markov chains were developed. Furthermore, an extensive study was conducted to investigate sorption and transport processes of methane, carbon dioxide, water, and their mixtures in the inorganic part of shale using both MC and MD simulations. These simulations covered a wide range of thermodynamic conditions, pore sizes, and fluid compositions shedding light on several interesting findings. For example, the possibility to have more carbon dioxide adsorbed with more preadsorbed water concentrations at relatively large basal spaces. The dissertation is divided into four chapters. The first chapter corresponds to the introductory part where a brief background about molecular simulation and motivations are given. The second chapter is devoted to discuss the theoretical aspects and methodology of the proposed MC speeding up techniques in addition to the corresponding results leading to the successful multi-scale simulation of the compressible single-phase flow scenario. In chapter 3, the results regarding our extensive study on shale gas at laboratory conditions are reported. At the fourth and last chapter, we end the dissertation with few concluding remarks highlighting the key findings and summarizing the future directions.

  16. Modelling of fractured reservoirs. Case of multi-scale media; Modelisation des reservoirs fractures. Cas des milieux multi-echelles

    Energy Technology Data Exchange (ETDEWEB)

    Henn, N.

    2000-12-13

    Some of the most productive oil and gas reservoirs are found in formations crossed by multi-scale fractures/faults. Among them, conductive faults may closely control reservoir performance. However, their modelling encounters numerical and physical difficulties linked with (a) the necessity to keep an explicit representation of faults through small-size grid blocks, (b) the modelling of multiphase flow exchanges between the fault and the neighbouring medium. In this thesis, we propose a physically-representative and numerically efficient modelling approach in order to incorporate sub-vertical conductive faults in single and dual-porosity simulators. To validate our approach and demonstrate its efficiency, simulation results of multiphase displacements in representative field sector models are presented. (author)

  17. A Study of Sedimentation at the River Estuary on the Change of Reservoir Storage

    OpenAIRE

    Iskahar; Suripin; Isdiyana

    2018-01-01

    Estuary of the river that leads to the reservoir has characteristics include: relatively flat, there is a change in the increase of wet cross-sectional area and backwater. The backwater will cause the flow velocity to be reduced, so that the grains of sediment with a certain diameter carried by the flow will settle in the estuary of the river. The purpose of this research is to know the distribution and sedimentation pattern at the river estuary that leads to the reservoir with the change of ...

  18. STIMULI-RESPONSIVE POLYMERS WITH ENHANCED EFFICIENCY IN RESERVOIR RECOVERY PROCESSES

    Energy Technology Data Exchange (ETDEWEB)

    Charles McCormick; Roger Hester

    2004-09-30

    This sixth and final progress report for DOE Award Number DE-FC26-01BC15317 describes research during the period March 01, 2004 through August 31, 2004 performed at the University of Southern Mississippi on ''Stimuli Responsive Polymers with Enhanced Efficiency in Reservoir Recovery'' processes. Significantly, terpolymers that are responsive to changes in pH and ionic strength have been synthesized, characterized, and their solution properties have been extensively examined. Terpolymers composed of acrylamide, a carboxylated acrylamido monomer (AMBA), and a quaternary ammonium monomer (AMBATAC) with balanced compositions of the latter two, exhibit increases in aqueous solution viscosity as NaCl concentration is increased. This increase in polymer coil size can be expected upon injection of this type of polymer into oil reservoirs of moderate-to-high salinity, leading to better mobility control. The opposite effect (loss of viscosity) is observed for conventional polymer systems. Additionally polymer mobility characteristics have been conducted for a number of hydrophilic copolymers utilizing an extensional flow apparatus and size exclusion chromatography. This study reveled that oil recovery enhancement through use of polymers in a water flood is due to the polymer's resistance to deformation as it flows through the reservoir. Individual polymers when in aqueous solution form coils. The larger the polymer's coil size, the greater the polymer's resistance to extensional flow and the more effective the polymer is in enhancing oil recovery. Large coil sizes are obtained by increasing the polymer molecular weight and having macromolecular structures that favor greater swelling of the coil by the aqueous solvent conditions (temperature, pH and electrolyte concentration) existing in the reservoir.

  19. Scale Model Simulation of Enhanced Geothermal Reservoir Creation

    Science.gov (United States)

    Gutierrez, M.; Frash, L.; Hampton, J.

    2012-12-01

    Geothermal energy technology has successfully provided a means of generating stable base load electricity for many years. However, implementation has been spatially limited to limited availability of high quality traditional hydro-thermal resources possessing the combination of a shallow high heat flow anomaly and an aquifer with sufficient permeability and continuous fluid recharge. Enhanced Geothermal Systems (EGS) has been proposed as a potential solution to enable additional energy production from the non-conventional hydro-thermal resources. Hydraulic fracturing is considered the primary means of creating functional EGS reservoirs at sites where the permeability of the rock is too limited to allow cost effective heat recovery. EGS reservoir creation requires improved fracturing methodology, rheologically controllable fracturing fluids, and temperature hardened proppants. Although large fracture volumes (several cubic km) have been created in the field, circulating fluid through these full volumes and maintaining fracture volumes have proven difficult. Stimulation technology and methodology as used in the oil and gas industry for sedimentary formations are well developed; however, they have not sufficiently been demonstrated for EGS reservoir creation. Insufficient data and measurements under geothermal conditions make it difficult to directly translate experience from the oil and gas industries to EGS applications. To demonstrate the feasibility of EGS reservoir creation and subsequent geothermal energy production, and to improve the understanding of hydraulic and propping in EGS reservoirs, a heated true-triaxial load cell with a high pressure fluid injection system was developed to simulate an EGS system from stimulation to production. This apparatus is capable of loading a 30x30x30 cubic cm rock sample with independent principal stresses up to 13 MPa while simultaneously providing heating up to 180 degree C. Multiple orientated boreholes of 5 to 10 mm

  20. Reservoir theory, groundwater transit time distributions, and lumped parameter models

    International Nuclear Information System (INIS)

    Etcheverry, D.; Perrochet, P.

    1999-01-01

    The relation between groundwater residence times and transit times is given by the reservoir theory. It allows to calculate theoretical transit time distributions in a deterministic way, analytically, or on numerical models. Two analytical solutions validates the piston flow and the exponential model for simple conceptual flow systems. A numerical solution of a hypothetical regional groundwater flow shows that lumped parameter models could be applied in some cases to large-scale, heterogeneous aquifers. (author)

  1. Assessment of ecologically relevant hydrological change in China due to water use and reservoirs

    Directory of Open Access Journals (Sweden)

    J. Zhang

    2008-06-01

    Full Text Available As China's economy booms, increasing water use has significantly affected hydro-geomorphic processes and thus the ecology of surface waters. A large variety of hydrological changes arising from human activities such as reservoir construction and management, water abstraction, water diversion and agricultural land expansion have been sustained throughout China. Using the global scale hydrological and water use model WaterGAP, natural and anthropogenically altered flow conditions are calculated, taking into account flow alterations due to human water consumption and 580 large reservoirs. The impacts resulting from water consumption and reservoirs have been analyzed separately. A modified "Indicators of Hydrologic Alteration" approach is used to describe the human pressures on aquatic ecosystems due to anthropogenic alterations in river flow regimes. The changes in long-term average river discharge, average monthly mean discharge and coefficients of variation of monthly river discharges under natural and impacted conditions are compared and analyzed. The indicators show very significant alterations of natural river flow regimes in a large part of northern China and only minor alterations in most of southern China. The detected large alterations in long-term average river discharge, the seasonality of flows and the inter-annual variability in the northern half of China are very likely to have caused significant ecological impacts.

  2. Regional regression equations for the estimation of selected monthly low-flow duration and frequency statistics at ungaged sites on streams in New Jersey

    Science.gov (United States)

    Watson, Kara M.; McHugh, Amy R.

    2014-01-01

    Regional regression equations were developed for estimating monthly flow-duration and monthly low-flow frequency statistics for ungaged streams in Coastal Plain and non-coastal regions of New Jersey for baseline and current land- and water-use conditions. The equations were developed to estimate 87 different streamflow statistics, which include the monthly 99-, 90-, 85-, 75-, 50-, and 25-percentile flow-durations of the minimum 1-day daily flow; the August–September 99-, 90-, and 75-percentile minimum 1-day daily flow; and the monthly 7-day, 10-year (M7D10Y) low-flow frequency. These 87 streamflow statistics were computed for 41 continuous-record streamflow-gaging stations (streamgages) with 20 or more years of record and 167 low-flow partial-record stations in New Jersey with 10 or more streamflow measurements. The regression analyses used to develop equations to estimate selected streamflow statistics were performed by testing the relation between flow-duration statistics and low-flow frequency statistics for 32 basin characteristics (physical characteristics, land use, surficial geology, and climate) at the 41 streamgages and 167 low-flow partial-record stations. The regression analyses determined drainage area, soil permeability, average April precipitation, average June precipitation, and percent storage (water bodies and wetlands) were the significant explanatory variables for estimating the selected flow-duration and low-flow frequency statistics. Streamflow estimates were computed for two land- and water-use conditions in New Jersey—land- and water-use during the baseline period of record (defined as the years a streamgage had little to no change in development and water use) and current land- and water-use conditions (1989–2008)—for each selected station using data collected through water year 2008. The baseline period of record is representative of a period when the basin was unaffected by change in development. The current period is

  3. How fast can a black hole eat. [Equation stationary spherically symmetric solutions, Thompson scattering, mass flow

    Energy Technology Data Exchange (ETDEWEB)

    Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)

    1976-11-01

    Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.

  4. Modelling and Simulation of Structural Deformation of Isothermal Subsurface Flow and Carbon Dioxide Injection

    KAUST Repository

    El-Amin, Mohamed

    2011-05-15

    Injection of CO2 in hydrocarbon reservoir has double benefit. On the one hand, it is a profitable method due to issues related to global warming, and on the other hand it is an effective mechanism to enhance hydrocarbon recovery. Such injection associates complex processes involving, e.g., solute transport of dissolved materials, in addition to local changes in density of the phases. Also, increasing carbon dioxide injection may cause a structural deformation of the medium, so it is important to include such effect into the model. The structural deformation modelling in carbon sequestration is important to evaluate the medium stability to avoid CO2 leakage to the atmosphere. On the other hand, geologic formation of the medium is usually heterogeneous and consists of several layers of different permeability. In this work we conduct numerical simulation of two-phase flow in a heterogeneous porous medium domain with dissolved solute transport as well as structural deformation effects. The solute transport of the dissolved component is described by concentration equation. The structural deformation for geomechanics is derived from a general local differential balance equation with neglecting the local mass balance of solid phase and the inertial force term. The flux continuity condition is used at interfaces between different permeability layers of the heterogeneous medium. We analyze the vertical migration of a CO2 plume injected into a 2D layered reservoir. Analysis of distribution of flow field components such as saturation, pressures, velocities, and CO2 concentration are presented.

  5. Exact RG flow equations and quantum gravity

    Science.gov (United States)

    de Alwis, S. P.

    2018-03-01

    We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

  6. Geothermal reservoir simulation to enhance confidence in predictions for nuclear waste disposal

    International Nuclear Information System (INIS)

    Kneafsey, Timothy J.; Pruess, Karsten; O'Sullivan, Michael J.; Bodvarsson, Gudmundur S.

    2002-01-01

    Numerical simulation of geothermal reservoirs is useful and necessary in understanding and evaluating reservoir structure and behavior, designing field development, and predicting performance. Models vary in complexity depending on processes considered, heterogeneity, data availability, and study objectives. They are evaluated using computer codes written and tested to study single and multiphase flow and transport under nonisothermal conditions. Many flow and heat transfer processes modeled in geothermal reservoirs are expected to occur in anthropogenic thermal (AT) systems created by geologic disposal of heat-generating nuclear waste. We examine and compare geothermal systems and the AT system expected at Yucca Mountain, Nevada, and their modeling. Time frames and spatial scales are similar in both systems, but increased precision is necessary for modeling the AT system, because flow through specific repository locations will affect long-term ability radionuclide retention. Geothermal modeling experience has generated a methodology, used in the AT modeling for Yucca Mountain, yielding good predictive results if sufficient reliable data are available and an experienced modeler is involved. Codes used in geothermal and AT modeling have been tested extensively and successfully on a variety of analytical and laboratory problems

  7. Reducing the memory requirement in reverse mode automatic differentiation by solving TBR flow equations

    International Nuclear Information System (INIS)

    Naumann, U.

    2002-01-01

    The fast computation of gradients in reverse mode Automatic Differentiation (AD) requires the generation of adjoint versions of every statement in the original code. Due to the resulting reversal of the control flow certain intermediate values have to be made available in reverse order to compute the local partial derivatives. This can be achieved by storing these values or by recomputing them when they become required. In any case one is interested in minimizing the size of this set. Following an extensive introduction of the ''To-Be-Recorded'' (TBR) problem the authors present flow equations for propagating the TBR status of variables in the context of reverse mode AD of structured programs

  8. Assessment of water management tools for the geothermal reservoir Waiwera (New Zealand)

    Science.gov (United States)

    Kühn, Michael; Altmannsberger, Charlotte

    2016-04-01

    Water management tools are essential to ensure the conservation of natural resources. The geothermal hot water reservoir below the village of Waiwera, on the Northern Island of New Zealand is used commercially since 1863. The continuous production of 50 °C hot geothermal water, to supply hotels and spas, has a negative impact on the reservoir. Until the year 1969 from all wells drilled the warm water flow was artesian. Due to overproduction the water needs to be pumped up nowadays. Further, within the years 1975 to 1976 the warm water seeps on the beach of Waiwera ran dry. In order to protect the reservoir and the historical and tourist site in the early 1980s a Water Management Plan was deployed. The "Auckland Regional Water Board" today "Auckland Regional Council" established guidelines to enable a sustainable management [1]. The management plan demands that the water level in the official and appropriate observation well of the council is 0.5 m above sea level throughout the year in average. Almost four decades of data (since 1978 until today) are now available [2]. The minimum water level was observed beginning of the 1980s with -1.25 m and the maximum recently with 1.6 m. The higher the production rates from the field, the lower the water level in the observation well. Highest abstraction rates reached almost 1,500 m3/day and lowest were just above 500 m3/day. Several models of varying complexity where used from purely data driven statistical to fully coupled process simulation models. In all cases the available data were used for calibration and the models were then applied for predictive purposes. We used the Nash-Sutcliffe efficiency index to quantify their predictive ability. The recommendation for the full implementation of the water management plan is the regular revision of an existing multivariate regression model which is based on the Theis well equation. Further, we suggest improving the underlying geological model of the process simulations to

  9. Up scaling two-phase flow in heterogeneous porous media; Mise a l'echelle des ecoulements diphasiques dans les milieux poreux heterogenes

    Energy Technology Data Exchange (ETDEWEB)

    Artus, V.

    2003-11-01

    For two-phase flow in heterogeneous media, the emergence of different flow regimes at large-scale is driven by local interactions between the viscous coupling and the heterogeneity. In particular, when the viscosity ratio is favorable, viscous effects induce a transverse flow that stabilizes the front while flooding. However, most of recent stochastic models neglect the influence of the viscous coupling. We developed a stochastic model for the dynamics of the front, taking the viscous coupling into account. For stable cases, this model relates the statistical properties of the front to the statistical properties of the permeability field. For stable flow in stratified media, we show that the front is stationary by parts in the reservoir. These parts can be identified as large-scale hydrodynamic layers and separately coarsened in the large-scale simulation model. For flows with favorable viscosity ratios in isotropic reservoirs, we show that a stationary front occurs, in a statistical sense. For unfavorable viscosity ratios, the flow is driven by the development of viscous fingering. These different regimes lead to different large-scale saturation profiles that can be matched with a macro-dispersion equation, if the effective convective flux is modified to take into account stabilizing or destabilizing viscous effects. (author)

  10. A numerical study of EGS heat extraction process based on a thermal non-equilibrium model for heat transfer in subsurface porous heat reservoir

    Science.gov (United States)

    Chen, Jiliang; Jiang, Fangming

    2016-02-01

    With a previously developed numerical model, we perform a detailed study of the heat extraction process in enhanced or engineered geothermal system (EGS). This model takes the EGS subsurface heat reservoir as an equivalent porous medium while it considers local thermal non-equilibrium between the rock matrix and the fluid flowing in the fractured rock mass. The application of local thermal non-equilibrium model highlights the temperature-difference heat exchange process occurring in EGS reservoirs, enabling a better understanding of the involved heat extraction process. The simulation results unravel the mechanism of preferential flow or short-circuit flow forming in homogeneously fractured reservoirs of different permeability values. EGS performance, e.g. production temperature and lifetime, is found to be tightly related to the flow pattern in the reservoir. Thermal compensation from rocks surrounding the reservoir contributes little heat to the heat transmission fluid if the operation time of an EGS is shorter than 15 years. We find as well the local thermal equilibrium model generally overestimates EGS performance and for an EGS with better heat exchange conditions in the heat reservoir, the heat extraction process acts more like the local thermal equilibrium process.

  11. Geochemistry of formation waters from the Wolfcamp and “Cline” shales: Insights into brine origin, reservoir connectivity, and fluid flow in the Permian Basin, USA

    Science.gov (United States)

    Engle, Mark A.; Reyes, Francisco R.; Varonka, Matthew S.; Orem, William H.; Lin, Ma; Ianno, Adam J.; Westphal, Tiffani M.; Xu, Pei; Carroll, Kenneth C.

    2016-01-01

    Despite being one of the most important oil producing provinces in the United States, information on basinal hydrogeology and fluid flow in the Permian Basin of Texas and New Mexico is lacking. The source and geochemistry of brines from the basin were investigated (Ordovician- to Guadalupian-age reservoirs) by combining previously published data from conventional reservoirs with geochemical results for 39 new produced water samples, with a focus on those from shales. Salinity of the Ca–Cl-type brines in the basin generally increases with depth reaching a maximum in Devonian (median = 154 g/L) reservoirs, followed by decreases in salinity in the Silurian (median = 77 g/L) and Ordovician (median = 70 g/L) reservoirs. Isotopic data for B, O, H, and Sr and ion chemistry indicate three major types of water. Lower salinity fluids (100 g/L), isotopically heavy (O and H) water in Leonardian [Permian] to Pennsylvanian reservoirs (2–3.2 km depth) is evaporated, Late Permian seawater. Water from the Permian Wolfcamp and Pennsylvanian “Cline” shales, which are isotopically similar but lower in salinity and enriched in alkalis, appear to have developed their composition due to post-illitization diffusion into the shales. Samples from the “Cline” shale are further enriched with NH4, Br, I and isotopically light B, sourced from the breakdown of marine kerogen in the unit. Lower salinity waters (3 km depth), which plot near the modern local meteoric water line, are distinct from the water in overlying reservoirs. We propose that these deep meteoric waters are part of a newly identified hydrogeologic unit: the Deep Basin Meteoric Aquifer System. Chemical, isotopic, and pressure data suggest that despite over-pressuring in the Wolfcamp shale, there is little potential for vertical fluid migration to the surface environment via natural conduits.

  12. Reservoir pressure evolution model during exploration drilling

    Directory of Open Access Journals (Sweden)

    Korotaev B. A.

    2017-03-01

    Full Text Available Based on the analysis of laboratory studies and literature data the method for estimating reservoir pressure in exploratory drilling has been proposed, it allows identify zones of abnormal reservoir pressure in the presence of seismic data on reservoir location depths. This method of assessment is based on developed at the end of the XX century methods using d- and σ-exponentials taking into account the mechanical drilling speed, rotor speed, bit load and its diameter, lithological constant and degree of rocks' compaction, mud density and "regional density". It is known that in exploratory drilling pulsation of pressure at the wellhead is observed. Such pulsation is a consequence of transferring reservoir pressure through clay. In the paper the mechanism for transferring pressure to the bottomhole as well as the behaviour of the clay layer during transmission of excess pressure has been described. A laboratory installation has been built, it has been used for modelling pressure propagation to the bottomhole of the well through a layer of clay. The bulge of the clay layer is established for 215.9 mm bottomhole diameter. Functional correlation of pressure propagation through the layer of clay has been determined and a reaction of the top clay layer has been shown to have bulge with a height of 25 mm. A pressure distribution scheme (balance has been developed, which takes into account the distance from layers with abnormal pressure to the bottomhole. A balance equation for reservoir pressure evaluation has been derived including well depth, distance from bottomhole to the top of the formation with abnormal pressure and density of clay.

  13. Exploitation and Optimization of Reservoir Performance in Hunton Formation, Oklahoma, Budget Period I, Class Revisit

    Energy Technology Data Exchange (ETDEWEB)

    Kelkar, Mohan

    2002-04-02

    This report explains the unusual characteristics of West Carney Field based on detailed geological and engineering analyses. A geological history that explains the presence of mobile water and oil in the reservoir was proposed. The combination of matrix and fractures in the reservoir explains the reservoir?s flow behavior. We confirm our hypothesis by matching observed performance with a simulated model and develop procedures for correlating core data to log data so that the analysis can be extended to other, similar fields where the core coverage may be limited.

  14. On the feasibility of inducing oil mobilization in existing reservoirs via wellbore harmonic fluid action

    KAUST Repository

    Jeong, Chanseok

    2011-03-01

    Although vibration-based mobilization of oil remaining in mature reservoirs is a promising low-cost method of enhanced oil recovery (EOR), research on its applicability at the reservoir scale is still at an early stage. In this paper, we use simplified models to study the potential for oil mobilization in homogeneous and fractured reservoirs, when harmonically oscillating fluids are injected/produced within a well. To this end, we investigate first whether waves, induced by fluid pressure oscillations at the well site, and propagating radially and away from the source in a homogeneous reservoir, could lead to oil droplet mobilization in the reservoir pore-space. We discuss both the fluid pore-pressure wave and the matrix elastic wave cases, as potential agents for increasing oil mobility. We then discuss the more realistic case of a fractured reservoir, where we study the fluid pore-pressure wave motion, while taking into account the leakage effect on the fracture wall. Numerical results show that, in homogeneous reservoirs, the rock-stress wave is a better energy-delivery agent than the fluid pore-pressure wave. However, neither the rock-stress wave nor the pore-pressure wave is likely to result in any significant residual oil mobilization at the reservoir scale. On the other hand, enhanced oil production from the fractured reservoir\\'s matrix zone, induced by cross-flow vibrations, appears to be feasible. In the fractured reservoir, the fluid pore-pressure wave is only weakly attenuated through the fractures, and thus could induce fluid exchange between the rock formation and the fracture space. The vibration-induced cross-flow is likely to improve the imbibition of water into the matrix zone and the expulsion of oil from it. © 2011 Elsevier B.V.

  15. Temporal-spatial distribution of non-point source pollution in a drinking water source reservoir watershed based on SWAT

    Directory of Open Access Journals (Sweden)

    M. Wang

    2015-05-01

    Full Text Available The conservation of drinking water source reservoirs has a close relationship between regional economic development and people’s livelihood. Research on the non-point pollution characteristics in its watershed is crucial for reservoir security. Tang Pu Reservoir watershed was selected as the study area. The non-point pollution model of Tang Pu Reservoir was established based on the SWAT (Soil and Water Assessment Tool model. The model was adjusted to analyse the temporal-spatial distribution patterns of total nitrogen (TN and total phosphorus (TP. The results showed that the loss of TN and TP in the reservoir watershed were related to precipitation in flood season. And the annual changes showed an "M" shape. It was found that the contribution of loss of TN and TP accounted for 84.5% and 85.3% in high flow years, and for 70.3% and 69.7% in low flow years, respectively. The contributions in normal flow years were 62.9% and 63.3%, respectively. The TN and TP mainly arise from Wangtan town, Gulai town, and Wangyuan town, etc. In addition, it was found that the source of TN and TP showed consistency in space.

  16. The influence of reservoir heterogeneities on geothermal doublet performance

    NARCIS (Netherlands)

    Doddema, Leon

    2012-01-01

    SUMMARY The current main problem with deep geothermal energy in the Netherlands is the uncertainty in terms of attainable flow rate and life time. The goal of this research is therefore modeling a geothermal doublet in a heterogeneous reservoir, using a

  17. TROPHIC STATE OF SMALL RETENTION RESERVOIRS IN PODLASIE VOIVODESHIP

    Directory of Open Access Journals (Sweden)

    Joanna Szczykowska

    2017-09-01

    Full Text Available The study was carried out using water samples from two small retention reservoirs located in the communes: Czarna Białostocka and Turośń Kościelna in Podlaskie Voivodeship. The main tasks of both reservoirs are to improve the water balance by means of regulating the levels and water outflow. Three characteristic measurement and control points were selected on both reservoirs in accordance to the water flow in the longitudinal section. The first and third points were located near the inflow and outflow of water, while the second in the middle of the reservoirs. Samples of water for the study were collected from the surface layer of the shore zone of the reservoirs once a month from March 2015 to February 2017 (water from two hydrological years was analyzed. Water samples were subject to determination of total phosphorus, total nitrogen, and chlorophyll “a” concentrations, as well as turbidity. Contamination of the water reservoirs with biogenic compounds is a common problem and at the same time difficult to eliminate due to the scattered nature of external sources of pollution, especially in the case of agricultural catchments, as well as the inflow of untreated sewage from areas directly adjacent to the reservoirs. Based on achieved results, high values of TSI (TN, TSI (TP, TSI (Chl, and overall TSI, clearly indicate the progressive degradation of water quality in analyzed reservoirs. Appearing water blooms due to the mass development of phytoplankton adversely affect the quality of water in the reservoirs and biochemical processes occurring both in water and bottom sediments, are conditioned by progressive eutrophication.

  18. Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection-diffusion equation

    Science.gov (United States)

    Cholet, Cybèle; Charlier, Jean-Baptiste; Moussa, Roger; Steinmann, Marc; Denimal, Sophie

    2017-07-01

    The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection-diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection-diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space - between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) - as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit-matrix exchanges, inducing a complex water mixing effect in the saturated zone

  19. Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

    Directory of Open Access Journals (Sweden)

    C. Cholet

    2017-07-01

    Full Text Available The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection–diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection–diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space – between the two reaches located in the unsaturated zone (R1, and in the zone that is both unsaturated and saturated (R2 – as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions and localized infiltration in the secondary conduit network (tributaries in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit–matrix exchanges, inducing a complex water mixing effect

  20. Monitoring Reservoirs Using MERIS And LANDSAT Fused Images : A Case Study Of Polyfitos Reservoir - West Macedonia - Greece

    Science.gov (United States)

    Stefouli, M.; Charou, E.; Vasileiou, E.; Stathopoulos, N.; Perrakis, A.

    2012-04-01

    Research and monitoring is essential to assess baseline conditions in reservoirs and their watershed and provide necessary information to guide decision-makers. Erosion and degradation of mountainous areas can lead to gradual aggradation of reservoirs reducing their lifetime. Collected measurements and observations have to be communicated to the managers of the reservoirs so as to achieve a common / comprehensive management of a large watershed and reservoir system. At this point Remote Sensing could help as the remotely sensed data are repeatedly and readily available to the end users. Aliakmon is the longest river in Greece, it's length is about 297 km and the surface of the river basin is 9.210 km2.The flow of the river starts from Northwest of Greece and ends in Thermaikos Gulf. The riverbed is not natural throughout the entire route, because constructed dams restrict water and create artificial lakes, such as lake of Polyfitos, that prevent flooding. This lake is used as reservoir, for covering irrigational water needs and the water is used to produce energy from the hydroelectric plant of Public Power Corporation-PPC. The catchment basin of Polyfitos' reservoir covers an area of 847.76 km2. Soil erosion - degradation in the mountainous watershed of streams of Polyfitos reservoir is taking place. It has been estimated that an annual volume of sediments reaching the reservoir is of the order of 244 m3. Geomatic based techniques are used in processing multiple data of the study area. A data inventory was formulated after the acquisition of topographic maps, compilation of geological and hydro-geological maps, compilation of digital elevation model for the area of interest based on satellite data and available maps. It also includes the acquisition of various hydro-meteorological data when available. On the basis of available maps and satellite data, digital elevation models are used in order to delineate the basic sub-catchments of the Polyfytos basin as well as