HESS Opinions: Linking Darcy's equation to the linear reservoir
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.
Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir
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.
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.
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.
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.
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
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
Seismic imaging of reservoir flow properties: Time-lapse pressurechanges
Energy Technology Data Exchange (ETDEWEB)
Vasco, Don W.
2003-04-08
Time-lapse fluid pressure and saturation estimates are sensitive to reservoir flow properties such as permeability. In fact, given time-lapse estimates of pressure and saturation changes, one may define a linear partial differential equation for permeability variations within the reservoir. The resulting linear inverse problem can be solved quite efficiently using sparse matrix techniques. An application to a set of crosswell saturation and pressure estimates from a CO{sub 2} flood at the Lost Hills field in California demonstrates the utility of this approach. From the crosswell estimates detailed estimates of reservoir permeability are produced. The resulting permeability estimates agree with a permeability log in an adjacent well and are in accordance with water and CO{sub 2} saturation changes in the interwell region.
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.
Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs
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
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.
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...
AUTOMATED TECHNIQUE FOR FLOW MEASUREMENTS FROM MARIOTTE RESERVOIRS.
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.
Reservoir resistivity characterization incorporating flow dynamics
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.
Determination of volume and direction of flow of Kainji Reservoir ...
African Journals Online (AJOL)
geomatics techniques. ... river bed were produced to create a 3D effect of Kainji reservoir flow direction. A depth of 23.50m was obtained during the sounding field operation. Keywords: Kainji Dam, Reservoir, Bathymetry, Volume, Direction of flow ...
Application of Stochastic Partial Differential Equations to Reservoir Property Modelling
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.
Environmental flows in the context of small reservoirs in Ghana
Gao, Y.; Kirshen, P.; Vogel, R.; Walker, P.
2009-04-01
Modification of rivers by dams reduces the magnitude and frequency of floods, and impacts the entire flow regime. In many cases, these modifications have adversely affected the ecological and hydrological integrity of the watershed as well as impacting food security and livelihood choices of the local community. There is now an increasing consensus that modification to river flows needs to be balanced with maintenance of essential water-dependent ecological services. Many small multi-purpose reservoirs have been built in West Africa, where rainfall is highly variable, and droughts and flash floods are frequent. These small reservoirs are an important source of water for domestic use, livestock watering, small-scale irrigation and other beneficial uses in rural communities. The small reservoirs are hydrologically linked by their associated stream network. The reservoirs alter the hydrology of the streams and the groundwater resources within the region. When an individual reservoir is considered, alteration to the entire watershed is usually not significant. However, when considered as a system, together the small reservoirs store a significant quantity of water and influence downstream flows. The small reservoirs have rarely been considered as a system, thus little consideration has been given to their collective impact on the natural environment and livelihoods of the local population in the long term. Furthermore, the impact is difficult to quantify given the diffuse nature of the small reservoirs. Therefore, a comprehensive environmental flow assessment is needed to investigate the effect of the small reservoirs as a system on the watershed, and appropriate water policy should be formulated to implement the finding from the assessment. Our project is specifically aimed at addressing this topic. We will present a case study conducted in the Upper East Region of Ghana and will discuss the findings on the hydrological, ecological and socio-economic implications of
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.
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
Coupled equations for transient water flow, heat flow, and ...
Indian Academy of Sciences (India)
presented on coupled equations from a perspective of energy optimization. 1. Introduction. Given an appropriate time scale, all earth systems are transient. The evolution of the earth's crust ... tem, in combination with transient heat flow and three-dimensional deformation. .... hydraulic capacity by analogy with heat capacity.
New Heat Flow Models in Fractured Geothermal Reservoirs - Final Report
Energy Technology Data Exchange (ETDEWEB)
Reis, John
2001-03-31
This study developed new analytical models for predicting the temperature distribution within a geothermal reservoir following reinjection of water having a temperature different from that of the reservoir. The study consisted of two parts: developing new analytical models for the heat conduction rate into multi-dimensional, parallelepiped matrix blocks and developing new analytical models for the advance of the thermal front through the geothermal reservoir. In the first part of the study, a number of semi-empirical models for the multi-dimensional heat conduction were developed to overcome the limitations to the exact solutions. The exact solution based on a similarity solution to the heat diffusion equation is the best model for the early-time period, but fails when thermal conduction fronts from opposing sides of the matrix block merge. The exact solution based on an infinite series solution was found not to be useful because it required tens of thousands of terms to be include d for accuracy. The best overall model for the entire conduction time was a semi-empirical model based on an exponential conduction rate. In the second part of the study, the early-time period exact solution based on similarity methods and the semi-empirical exponential model were used to develop new analytical models for the location of the thermal front within the reservoir during injection. These equations were based on an energy balance on the water in the fractured network. These convective models allowed for both dual and triple porosity reservoirs, i.e., one or two independent matrix domains. A method for incorporating measured fracture spacing distributions into these convective models was developed. It was found that there were only minor differences in the predicted areal extent of the heated zone between the dual and triple porosity models. Because of its simplicity, the dual porosity model is recommended. These new models can be used for preliminary reservoir studies
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.
Wang, Zenghui; Xia, Junqiang; Li, Tao; Deng, Shanshan; Zhang, Junhua
2016-12-01
The ever growing importance of sustainable management of reservoir sedimentation has promoted the development and applications of turbidity current models. However, there are few effective and practical models in literature for turbidity currents in a reservoir where the impounded area involves both the main river and its many tributaries. An integrated numerical model coupling open-channel flow, turbidity current and flow exchanges between main river and tributaries is proposed, which can simulate the complex flow and sediment transport in a reservoir where these three physical processes coexist. The model consists of two sets of governing equations for the open-channel flow and turbidity current, which are based on the modified St. Venant equations by taking into account the effect of lateral flow exchanges. These two sets of equations are solved in the finite volume method framework and the solutions are executed in an alternating calculation mode. Different methods are respectively proposed to calculate the discharge of flow exchange caused by free surface gradient and turbidity current intrusion. For the surface-gradient driven flow exchange, a storage cell method, which re-defines the relationship between water level and representative cross-sectional area, is used to update the water level at confluence. For the turbidity current intrusion, a discharge formula is proposed based on the analysis of the energy and momentum transformation in the intruding turbid water body. This formula differs from previous ones in that the effect of tributary bed slope is considered. Two events of water-sediment regulation conducted in the Xiaolangdi Reservoir in 2004 and 2006 were simulated to test the ability of this model. The predicted reservoir drawdown process, the turbidity current evolution and the sediment venting efficiency were in close agreement with the measurements. The necessity to couple the flow exchanges was demonstrated by comparing the performance of the
Xie, Wei-Yang; Li, Xiao-Ping; Zhang, Lie-Hui; Tan, Xiao-Hua; Wang, Jun-Chao; Wang, Hai-Tao
2015-01-01
After multistage fracturing, the flowback of fracturing fluid will cause two-phase flow through hydraulic fractures in shale gas reservoirs. With the consideration of two-phase flow and desorbed gas transient diffusion in shale gas reservoirs, a two-phase transient flow model of multistage fractured horizontal well in shale gas reservoirs was created. Accurate solution to this flow model is obtained by the use of source function theory, Laplace transform, three-dimensional eigenvalue method, ...
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.
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....... They are solved numerically, based on an upstream finite difference algorithm. Self-similarity of the solution makes it possible to compute pseudofractional flow functions depending on the average saturation. The computer partial differential equation solver COMSOL is used for comparison of the complete 2D...... solutions with averaged 1D simulations. Cases of both discrete and continuous (log-normal) permeability distribution are studied. Generally, saturation profiles of the 1D model are only slightly different from the 2D simulation results. Recovery curves and fractional flow curves fit well. Calculations show...
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.
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.
Symmetries of the Euler compressible flow equations for general equation of state
International Nuclear Information System (INIS)
Boyd, Zachary M.; Ramsey, Scott D.; Baty, Roy S.
2015-01-01
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.
Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
Directory of Open Access Journals (Sweden)
Xie Haojun
2017-03-01
Full Text Available Caves in fractured-vuggy reservoir usually contain lots of filling medium, so the two-phase flow in formations is the coupling of free flow and porous flow, and that usually leads to low oil recovery. Considering geological interpretation results, the physical filled cave models with different filling mediums are designed. Through physical experiment, the displacement mechanism between un-filled areas and the filling medium was studied. Based on the experiment model, we built a mathematical model of laminar two-phase coupling flow considering wettability of the porous media. The free fluid region was modeled using the Navier-Stokes and Cahn-Hilliard equations, and the two-phase flow in porous media used Darcy's theory. Extended BJS conditions were also applied at the coupling interface. The numerical simulation matched the experiment very well, so this numerical model can be used for two-phase flow in fracture-vuggy reservoir. In the simulations, fluid flow between inlet and outlet is free flow, so the pressure difference was relatively low compared with capillary pressure. In the process of water injection, the capillary resistance on the surface of oil-wet filling medium may hinder the oil-water gravity differentiation, leading to no fluid exchange on coupling interface and remaining oil in the filling medium. But for the water-wet filling medium, capillary force on the surface will coordinate with gravity. So it will lead to water imbibition and fluid exchange on the interface, high oil recovery will finally be reached at last.
Directory of Open Access Journals (Sweden)
Wei-Yang Xie
2015-01-01
Full Text Available After multistage fracturing, the flowback of fracturing fluid will cause two-phase flow through hydraulic fractures in shale gas reservoirs. With the consideration of two-phase flow and desorbed gas transient diffusion in shale gas reservoirs, a two-phase transient flow model of multistage fractured horizontal well in shale gas reservoirs was created. Accurate solution to this flow model is obtained by the use of source function theory, Laplace transform, three-dimensional eigenvalue method, and orthogonal transformation. According to the model’s solution, the bilogarithmic type curves of the two-phase model are illustrated, and the production decline performance under the effects of hydraulic fractures and shale gas reservoir properties are discussed. The result obtained in this paper has important significance to understand pressure response characteristics and production decline law of two-phase flow in shale gas reservoirs. Moreover, it provides the theoretical basis for exploiting this reservoir efficiently.
A generalised groundwater flow equation using the concept of non ...
African Journals Online (AJOL)
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 the derivatives are compared with experimental data and the Barker generalised radial flow model for which a fractal dimension for ...
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.
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.
SWE-SPHysics Simulation of Dam Break Flows at South-Gate Gorges Reservoir
Directory of Open Access Journals (Sweden)
Shenglong Gu
2017-05-01
Full Text Available This paper applied a Smoothed Particle Hydrodynamics (SPH approach to solve Shallow Water Equations (SWEs to study practical dam-break flows. The computational program is based on the open source code SWE-SPHysics, where a Monotone Upstream-centered Scheme for Conservation Laws (MUSCL reconstruction method is used to improve the Riemann solution with Lax-Friedrichs flux. A virtual boundary particle method is applied to treat the solid boundary. The model is first tested on two benchmark collapses of water columns with the existence of downstream obstacle. Subsequently the model is applied to forecast a prototype dam-break flood, which might occur in South-Gate Gorges Reservoir area of Qinghai Province, China. It shows that the SWE-SPH modeling approach could provide a promising simulation tool for practical dam-break flows in engineering scale.
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
Exact RG flow equations and quantum gravity
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.
Derivation of stable Burnett equations for rarefied gas flows.
Singh, Narendra; Jadhav, Ravi Sudam; Agrawal, Amit
2017-07-01
A set of constitutive relations for the stress tensor and heat flux vector for the hydrodynamic description of rarefied gas flows is derived in this work. A phase density function consistent with Onsager's reciprocity principle and H theorem is utilized to capture nonequilibrium thermodynamics effects. The phase density function satisfies the linearized Boltzmann equation and the collision invariance property. Our formulation provides the correct value of the Prandtl number as it involves two different relaxation times for momentum and energy transport by diffusion. Generalized three-dimensional constitutive equations for different kinds of molecules are derived using the phase density function. The derived constitutive equations involve cross single derivatives of field variables such as temperature and velocity, with no higher-order derivative in higher-order terms. This is remarkable feature of the equations as the number of boundary conditions required is the same as needed for conventional Navier-Stokes equations. Linear stability analysis of the equations is performed, which shows that the derived equations are unconditionally stable. A comparison of the derived equations with existing Burnett-type equations is presented and salient features of our equations are outlined. The classic internal flow problem, force-driven compressible plane Poiseuille flow, is chosen to verify the stable Burnett equations and the results for equilibrium variables are presented.
Directory of Open Access Journals (Sweden)
Jin-Zhou Zhao
2015-01-01
Full Text Available This study uses similar construction method of solution (SCMS to solve mathematical models of fluid spherical flow in a fractal reservoir which can avoid the complicated mathematical deduction. The models are presented in three kinds of outer boundary conditions (infinite, constant pressure, and closed. The influence of wellbore storage effect, skin factor, and variable flow rate production is also involved in the inner boundary conditions. The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. The mathematical beauty of fractal is that the infinite complexity is formed with relatively simple equations. So the relation of reservoir parameters (wellbore storage effect, the skin factor, fractal dimension, and conductivity index, the formation pressure, and the wellbore pressure can be learnt easily. Type curves of the wellbore pressure and pressure derivative are plotted and analyzed in real domain using the Stehfest numerical invention algorithm. The SCMS and type curves can interpret intuitively transient pressure response of fractal spherical flow reservoir. The results obtained in this study have both theoretical and practical significance in evaluating fluid flow in such a fractal reservoir and embody the convenience of the SCMS.
Localization transition in one dimension using Wegner flow equations
Quito, Victor L.; Titum, Paraj; Pekker, David; Refael, Gil
2016-09-01
The flow-equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one-dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent α . We derive the flow equations and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for α 1/2 , we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point (α =1 ). This method correctly reproduces the critical level-spacing statistics and the fractal dimensionality of the eigenfunctions.
Navier-Stokes-like equations for traffic flow.
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.
Energy Technology Data Exchange (ETDEWEB)
Merletti, G.D.; Hewitt, N.; Barrios, F.; Vega, V.; Carias, J. [BP Exploration, Houston, TX (United States); Bueno, J.C.; Lopez, L. [PDVSA Petroleos de Venezuela SA, Caracas (Venezuela, Bolivarian Republic of)
2009-07-01
An accurate integrated reservoir description is necessary in extra-heavy oil prospects where pore throat geometries are the ultimate control on hydrocarbon primary recovery. The key element in producing accurate oil reservoir descriptions and improving productivity is to determine relationships between core-derived pore-throat parameters and log-derived macroscopic attributes. This paper described the use of the flow zone indicator technique (FZI) to identify hydraulic units within depositional facies. It focused on a petrophysical analysis aimed at improving the description of reservoir sandstones containing heavy or extra heavy oil in the eastern Orinoco belt in Venezuela. The Petromonagas license area contains large volumes of crude oil in-place with an API gravity of 8. Production comes primarily from the lowermost stratigraphic unit of the Oficina Formation, the Miocene Morichal Member. Facies analysis has revealed various depositional settings and core measurements depict a wide range in reservoir quality within specific depositional facies. The reservoir is divided into 4 different rock qualities and 5 associated non-reservoir rocks. The use of the FZI technique provides a better understanding of the relationship between petrophysical rock types and depositional facies. 4 refs., 4 tabs., 8 figs.
Interaction between Proppant Packing, Reservoir Depletion, and Fluid Flow in Pore Space
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
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 ...
Density Weighted FDF Equations for Simulations of Turbulent Reacting Flows
Shih, Tsan-Hsing; Liu, Nan-Suey
2011-01-01
In this report, we briefly revisit the formulation of density weighted filtered density function (DW-FDF) for large eddy simulation (LES) of turbulent reacting flows, which was proposed by Jaberi et al. (Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for Large-eddy simulation of turbulent reacting flows, J. Fluid Mech., vol. 401, pp. 85-121, 1999). At first, we proceed the traditional derivation of the DW-FDF equations by using the fine grained probability density function (FG-PDF), then we explore another way of constructing the DW-FDF equations by starting directly from the compressible Navier-Stokes equations. We observe that the terms which are unclosed in the traditional DW-FDF equations are now closed in the newly constructed DW-FDF equations. This significant difference and its practical impact on the computational simulations may deserve further studies.
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)
A new method of well test analysis in naturally fractured reservoirs based on elliptical flow
Energy Technology Data Exchange (ETDEWEB)
Igbokoyi, A.O.; Tiab, D. [Oklahoma Univ., Norman, OK (United States)
2008-07-01
Well testing analysis in naturally fractured reservoirs is usually based on the radial flow model. However, this model is only applicable to purely homogeneous system and long time solution and cannot provide complete formation analysis in a reservoir that exhibits anisotropy. This paper presented a new method of estimating permeability anisotropy in naturally fractured reservoirs. Maximum and minimum permeability were obtained in one well test. The paper discussed the mathematical formulation for the study which used Warren and Root's matrix pseudo-steady state model. The paper presented the assumptions for this model which included an isotropic homogeneous or anisotropic homogeneous formation; a slightly compressible fluid with single phase flow in both the matrix and fracture; initial reservoir pressure; two-dimensional flow; and laminar flow which obeys Darcy's law. The paper also discussed the computation of wellbore pressure and interpretation methods for both early linear flow and the long time radial flow regimes. Anisotropy was also outlined as the purpose of the study was to use an elliptical flow model in quantifying the permeability anisotropy of the reservoir. The type curve model was also explained to demonstrate the validity of the method of quantifying the permeability anisotropy with a known problem. Last, the paper explained the direct method with several example. It was concluded that the elliptical flow model is the most appropriate method of analyzing pressure transient data in naturally fractured reservoirs. 22 refs., 5 tabs., 15 figs., 3 appendices.
Coupled equations for transient water flow, heat flow, and ...
Indian Academy of Sciences (India)
Hydrogeological systems are earth systems influenced by water. Their behaviors are governed by interacting processes, including flow of fluids, deformation of porous materials, chemical reactions, and transport of matter and energy. Here, coupling among three of these processes is considered: flow of water, heat, and ...
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.
Flow resistance equations for mountain rivers
Energy Technology Data Exchange (ETDEWEB)
Lopez Alonso, R.; Barragan Fernandez, J.; Colomer Cugat, M. A.
2009-07-01
Three models of flow resistance (a Keulegan-type logarithmic law and two models developed for large-scale roughness conditions: the full logarithmic law and a model based on an inflectional velocity profile) were calibrated, validated and compared using an extensive database (N = 1,533) from rivers and flumes, representative of a wide hydraulic and geomorphologic range in the field of gravel-bed and mountain channels. It is preferable to apply the model based on an inflectional velocity profile in the relative submergence (y/d90) interval between 0.5 and 15, while the full logarithmic law is preferable for values below 0.5. For high relative submergence, above 15, either the logarithmic law or the full logarithmic law can be applied. The models fitted to the coarser percentiles are preferable to those fitted to the median diameter, owing to the higher explanatory power achieved by setting a model, the smaller difference in the goodness-of-fit between the different models and the lower influence of the origin of the data (river or flume). (Author) 28 refs.
On the Eikonal equation in the pedestrian flow problem
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.
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.
Huang, Bolin; Yin, Yueping; Wang, Shichang; Tan, Jianmin; Liu, Guangning
2017-05-01
A rocky granular flow is commonly formed after the failure of rocky bank slopes. An impulse wave disaster may also be initiated if the rocky granular flow rushes into a river with a high velocity. Currently, the granular mass-water body coupling study is an important trend in the field of landslide-induced impulse waves. In this paper, a full coupling numerical model for landslide-induced impulse waves is developed based on a non-coherent granular flow equation, i.e., the Mih equation. In this model, the Mih equation for continuous non-coherent granular flow controls movements of sliding mass, the two-phase flow equation regulates the interaction between sliding mass and water, and the renormalization group (RNG) turbulence model governs the movement of the water body. The proposed model is validated and applied for the 2014 Tangjiaxi landslide of the Zhexi Reservoir located in Hunan Province, China, to analyze the characteristics of both landslide motion and its following impulse waves. On 16 July 2014, a rocky debris flow was formed after the failure of the Tangjiaxi landslide, damming the Tangjiaxi stream and causing an impulse wave disaster with three dead and nine missing bodies. Based on the full coupling numerical analysis, the granular flow impacts the water with a maximum velocity of about 22.5 m s-1. Moreover, the propagation velocity of the generated waves reaches up to 12 m s-1. The maximum calculated run-up of 21.8 m is close enough to the real value of 22.7 m. The predicted landslide final deposit and wave run-up heights are in a good agreement with the field survey data. These facts verify the ability of the proposed model for simulating the real impulse wave generated by rocky granular flow events.
Flow equation, conformal symmetry, and anti-de Sitter geometry
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.
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.
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.
Modification of fluid flow equation in saturated porous media ...
African Journals Online (AJOL)
Experimental investigations have shown that variation of porosity and hydraulic gradient are responsible for the deviations from Darcy's law, which is perfectly obeyed only when the fluid flow is laminar in porous media. Previous attempts to modify this equation considered only the effects of porosity of surface-active ...
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
DEFF Research Database (Denmark)
Yan, Wei; Kontogeorgis, Georgios; Stenby, Erling Halfdan
2009-01-01
reservoirs. Conventional equation of state (EoS) with classical mixing rules cannot satisfactorily predict or even correlate the phase equilibrium of those systems. A promising model for such systems is the Cubic-Plus-Association (CPA) EoS, which has been successfully applied to well-defined systems...
Quantifying the clay content with borehole depth and impact on reservoir flow
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.
A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching
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
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
Two-equation turbulence modeling for 3-D hypersonic flows
Bardina, J. E.; Coakley, T. J.; Marvin, J. G.
1992-01-01
An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.
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
The fractional Boussinesq equation of groundwater flow and its applications
Su, Ninghu
2017-04-01
This paper presents a set of fractional Boussinesq equations (fBEs) for groundwater flow in confined and unconfined aquifers and demonstrates the application of one of the fBEs for groundwater discharges known as recession curves. The fBEs are formulated with two-term distributed fractional orders in time and symmetrical fractional derivatives (SFD) in space applicable to both confined and unconfined aquifers. The SFD in theory consists of the forward fractional derivative (FFD) and the backward fractional derivative (BFD). The FFD represents the forward movement of water along the direction of mainstream flow while the BFD accounts for the backward motion of water in the direction opposite to the mainstream flow. The backward flow at the pore level can be referred to as the micro-scale backwater effect. The analogue of the backwater effect on a micro-scale using the BFD coincides with the wandering processes based on the continuous-time random walk (CTRW) theory which results in the fractional governing equation. With the analytical solutions of the fBE for given initial and boundary conditions of the first type for a finite depth, a set of formulae for groundwater recession has been derived using approximate solutions of the fBE. The examples of the applications of the recession curves are graphically illustrated and the effects of the orders of fractional derivatives on the geometry of the flow curves examined.
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.
Ren, Junjie; Guo, Ping
2017-11-01
The real fluid flow in porous media is consistent with the mass conservation which can be described by the nonlinear governing equation including the quadratic gradient term (QGT). However, most of the flow models have been established by ignoring the QGT and little work has been conducted to incorporate the QGT into the flow model of the multiple fractured horizontal (MFH) well with stimulated reservoir volume (SRV). This paper first establishes a semi-analytical model of an MFH well with SRV including the QGT. Introducing the transformed pressure and flow-rate function, the nonlinear model of a point source in a composite system including the QGT is linearized. Then the Laplace transform, principle of superposition, numerical discrete method, Gaussian elimination method and Stehfest numerical inversion are employed to establish and solve the seepage model of the MFH well with SRV. Type curves are plotted and the effects of relevant parameters are analyzed. It is found that the nonlinear effect caused by the QGT can increase the flow capacity of fluid flow and influence the transient pressure positively. The relevant parameters not only have an effect on the type curve but also affect the error in the pressure calculated by the conventional linear model. The proposed model, which is consistent with the mass conservation, reflects the nonlinear process of the real fluid flow, and thus it can be used to obtain more accurate transient pressure of an MFH well with SRV.
Global-scale analysis of river flow alterations due to water withdrawals and reservoirs
Directory of Open Access Journals (Sweden)
P. Döll
2009-12-01
Full Text Available Global-scale information on natural river flows and anthropogenic river flow alterations is required to identify areas where aqueous ecosystems are expected to be strongly degraded. Such information can support the identification of environmental flow guidelines and a sustainable water management that balances the water demands of humans and ecosystems. This study presents the first global assessment of the anthropogenic alteration of river flow regimes, in particular of flow variability, by water withdrawals and dams/reservoirs. Six ecologically relevant flow indicators were quantified using an improved version of the global water model WaterGAP. WaterGAP simulated, with a spatial resolution of 0.5 degree, river discharge as affected by human water withdrawals and dams around the year 2000, as well as naturalized discharge without this type of human interference. Compared to naturalized conditions, long-term average global discharge into oceans and internal sinks has decreased by 2.7% due to water withdrawals, and by 0.8% due to dams. Mainly due to irrigation, long-term average river discharge and statistical low flow Q_{90} (monthly river discharge that is exceeded in 9 out of 10 months have decreased by more than 10% on one sixth and one quarter of the global land area (excluding Antarctica and Greenland, respectively. Q_{90} has increased significantly on only 5% of the land area, downstream of reservoirs. Due to both water withdrawals and reservoirs, seasonal flow amplitude has decreased significantly on one sixth of the land area, while interannual variability has increased on one quarter of the land area mainly due to irrigation. It has decreased on only 8% of the land area, in areas downstream of reservoirs where consumptive water use is low. The impact of reservoirs is likely underestimated by our study as small reservoirs are not taken into account. Areas most affected by anthropogenic river flow
Directory of Open Access Journals (Sweden)
Wang Ruifei
2017-12-01
Full Text Available The mathematical model of coupled flow and geomechanics for a vertical fractured well in tight gas reservoirs was established. The analytical modeling of unidirectional flow and radial flow was achieved by Laplace transforms and integral transforms. The results show that uncoupled flow would lead to an overestimate in performance of a vertical fractured well, especially in the later stage. The production rate decreases with elastic modulus because porosity and permeability decrease accordingly. Drawdown pressure should be optimized to lower the impact of coupled flow and geomechanics as a result of permeability decreasing. Production rate increases with fracture half-length significantly in the initial stage and becomes stable gradually. This study could provide a theoretical basis for effective development of tight gas reservoirs.
Wang, Ruifei; Gao, Xuhua; Song, Hongqing; Shang, Xinchun
2017-12-01
The mathematical model of coupled flow and geomechanics for a vertical fractured well in tight gas reservoirs was established. The analytical modeling of unidirectional flow and radial flow was achieved by Laplace transforms and integral transforms. The results show that uncoupled flow would lead to an overestimate in performance of a vertical fractured well, especially in the later stage. The production rate decreases with elastic modulus because porosity and permeability decrease accordingly. Drawdown pressure should be optimized to lower the impact of coupled flow and geomechanics as a result of permeability decreasing. Production rate increases with fracture half-length significantly in the initial stage and becomes stable gradually. This study could provide a theoretical basis for effective development of tight gas reservoirs.
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...... fluid and polar compounds such as water and MEG. Satisfactory results are obtained for mutual solubility of MEG and gas condensate whereas some deviations are observed for the ternary system of MEG-water-gas condensate........ Prediction of mutual solubility of water, MEG and hydrocarbon fluids is important for the oil industry to ensure production and processing as well as to satisfy environmental regulations. The CPA equation of state has been successfully applied in the past to well defined systems containing associating...
determination of volume and direction of flow of kainji reservoir ...
African Journals Online (AJOL)
HOD
by equations 1 and 2 as follows [2]. ⁄. In (1), D is the depth, V is the average velocity of sound ... Niger state on the 27th of August 1991, thereafter became the headquarter of Borgu Local Government. Area of ... cubic meters covering an area of 1,270 sq. kilometres. It has a power plant with initial six generating units and.
Seismic imaging of reservoir flow properties: Time-lapse amplitude changes
Energy Technology Data Exchange (ETDEWEB)
Vasco, D.W.; Datta-Gupta, Akhil; Behrens, Ron; Condon, Pat; Rickett, Jame s
2003-03-13
Asymptotic methods provide an efficient means by which to infer reservoir flow properties, such as permeability, from time-lapse seismic data. A trajectory-based methodology, much like ray-based methods for medical and seismic imaging, is the basis for an iterative inversion of time-lapse amplitude changes. In this approach a single reservoir simulation is required for each iteration of the algorithm. A comparison between purely numerical and the trajectory-based sensitivities demonstrates their accuracy. An application to a set of synthetic amplitude changes indicates that they can recover large-scale reservoir permeability variations from time-lapse data. In an application of actual time-lapse amplitude changes from the Bay Marchand field in the Gulf of Mexico we are able to reduce the misfit by 81% in twelve iterations. The time-lapse observations indicate lower permeabilities are required in the central portion of the reservoir.
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
Gas-Water Flow Behavior in Water-Bearing Tight Gas Reservoirs
Directory of Open Access Journals (Sweden)
Renyi Cao
2017-01-01
Full Text Available Some tight sandstone gas reservoirs contain mobile water, and the mobile water generally has a significant impact on the gas flowing in tight pores. The flow behavior of gas and water in tight pores is different than in conventional formations, yet there is a lack of adequate models to predict the gas production and describe the gas-water flow behaviors in water-bearing tight gas reservoirs. Based on the experimental results, this paper presents mathematical models to describe flow behaviors of gas and water in tight gas formations; the threshold pressure gradient, stress sensitivity, and relative permeability are all considered in our models. A numerical simulator using these models has been developed to improve the flow simulation accuracy for water-bearing tight gas reservoirs. The results show that the effect of stress sensitivity becomes larger as water saturation increases, leading to a fast decline of gas production; in addition, the nonlinear flow of gas phase is aggravated with the increase of water saturation and the decrease of permeability. The gas recovery decreases when the threshold pressure gradient (TPG and stress sensitivity are taken into account. Therefore, a reasonable drawdown pressure should be set to minimize the damage of nonlinear factors to gas recovery.
Buoyancy-driven CO2/brine flow at reservoir conditions
Oh, J.; Kim, K.; Han, W.; Kim, T.; Kim, J.; Park, E.
2013-12-01
Suitable geological formations should guarantee a long-term safe and reliable storage of the injected supercritical CO2. In this study we targeted the cases of gravity-driven CO2 plume migration in a storage formation and the resulting CO2 leakage to overlying formation through a possible fractures or abandoned wells. A laboratory experiment and numerical model for two-phase core-flooding tests were designed to understand the buoyancy effect on supercritical CO2 migration under reservoir conditions. A series of core flooding tests were performed with Berea sandstone cores which have 20 % porosity and 1.7×10-13 m2 permeability. Unlike the normal core-flooding tests, the core was set up in a vertical direction and the CO2 was released at the bottom of the core to investigate the gravity effect on CO2 migration. During the test, the downstream pressure was maintained at 10 MPa, and the confining pressure was kept at 20 MPa. The temperature was set to be 40 °C to reflect the 1 km subsurface environment. The CO2-flooding (drainage) tests with brine-saturated core were performed with various CO2-release periods. The CO2 saturation was measured with a linear X-ray scanner. In addition to laboratory experiments, numerical simulations were performed to provide further insight into the CO2 migration behavior. TOUGH2 with ECO2N module was used to simulate CO2/brine core-flooding tests. Dimensionless numbers (Capillary number and Bond number) were calculated with the simulation results at various time points covering both the release and monitoring period.
Phenomenological friction equation for turbulent flow of Bingham fluids.
Anbarlooei, H R; Cruz, D O A; Ramos, F; Santos, Cecilia M M; Silva Freire, A P
2017-08-01
Most discussions in the literature on the friction coefficient of turbulent flows of fluids with complex rheology are empirical. As a rule, theoretical frameworks are not available even for some relatively simple constitutive models. In the present work, a formula is proposed for the evaluation of the friction coefficient of turbulent flows of Bingham fluids. The developments combine a fresh analysis for the description of the microscales of Kolmogorov and the phenomenological turbulence model of Gioia and Chakraborty [G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.044502]. The resulting Blasius-type friction equation is tested against some experimental data and shows good agreement over a significant range of Hedstrom and Reynolds numbers. Comments on pressure measurements in yielding fluids are made. The limits of the proposed model are also discussed.
Kavousi Ghahfarokhi, Payam
results to build an 8 component equation of the state. A fully compositional flow simulation is conducted to acquire a history match between model production and production history. The history matching process reveals that high fracture permeabilities enhance water conning around the producers and decreases the oil production. Moreover, increasing apertures in the model DFN will result in higher oil production from the field. Thus, aperture and vertical permeabilities are adjusted for the model DFN to approximate the production history. We analyzed two CO2-EOR cases with different injection patterns. One has the injectors parallel to the main fracture set and the second one has injectors perpendicular to the main fracture set. Results show that the former model has higher oil recovery with later CO2 breakthrough than the second model. The dominant fracture set (N76°W) affects the CO2-EOR sweep efficiency in the Tensleep reservoir. We show that CO2 breakthrough is inevitable in both cases. The fault transmissibility multipliers are also assumed; they are uncertain parameters that could influence CO2-EOR. The model with completely impermeable faults yields a lower CO2-EOR sweep efficiency compared to the case for which all faults are fully permeable.
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
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...
Dual permeability modeling of flow in a fractured geothermal reservoir
Energy Technology Data Exchange (ETDEWEB)
Miller, J.D.; Allman, D.W.
1986-01-01
A three dimensional fracture system synthesis and flow simulation has been developed to correlate drawdown characteristics measured in a geothermal well and to provide the basis for an analysis of tracer tests. A new dual permeability approach was developed which incorporates simulations at two levels to better represent a discrete fracture system within computer limitations. The first incorporates a discrete simulation of the largest fractures in the system plus distributed or representative element stimulation of the smaller fractures. The second determines the representative element properties by discrete simulation of the smaller fractures. The fracture system was synthesized from acoustic televiewer data on the orientation and separation of three distinct fracture sets, together with additional data from the literature. Lognormal and exponential distributions of fracture spacing and radius were studied with the exponential distribution providing more reasonable results. Hydraulic apertures were estimated as a function of distance from the model boundary to a constant head boundary. Mean values of 6.7, 101 and 46 ..mu..m were chosen as the most representative values for the three fracture sets. Recommendations are given for the additional fracture characterization needed to reduce the uncertainties in the model. 20 refs., 6 figs.
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
Anderson transition in one-dimension using Wegner's Flow equations
Bhattacharjee, Paraj; Quito, Victor; Pekker, David; Refael, Gil
2015-03-01
We study the Anderson transition in one-dimensional random single-particle Hamiltonians with long-range hoppings decaying in a power-law. Explicitly, we consider the single particle tight-binding model in the spin representation with disorder both in the fields and hoppings. It has been shown by Mirlin et. al. that this model shows an extended-to-localized transition as a function of the power-law exponent with a critical multi-fractal regime when the decay exponent is equal to one. We generalize the flow equation technique, first introduced by Wegner, to the disordered system and use it to study the model and elucidate the character of this transition. This method allows us to efficiently compute the eigenvalues and local observables. We follow, analytically and numerically, the flow of the coupling distributions for the different exponents as a function of the flow-time and look for signatures of the two distinct phases as well as a characterization of the critical point.
Modeling flow in nanoporous, membrane reservoirs and interpretation of coupled fluxes
Geren, Filiz
The average pore size in unconventional, tight-oil reservoirs is estimated to be less than 100 nm. At this pore size, Darcy flow is no longer the dominating flow mechanism and a combination of diffusive flows determines the flow characteristics. Concentration driven self-diffusion has been well known and included in the flow and transport models in porous media. However, when the sizes of the pores and pore-throats decrease down to the size of the hydrocarbon molecules, the porous medium acts like a semi-permeable membrane, and the size of the pore openings dictates the direction of transport between adjacent pores. Accordingly, characterization of flow and transport in tight unconventional plays requires understanding of their membrane properties. This Master of Science thesis first highlights the membrane properties of nanoporous, unconventional reservoirs and then discusses how filtration effects can be incorporated into the models of transport in nanoporous media within the coupled flux concept. The effect of filtration on fluid composition and its impact on black-oil fluid properties like bubble point pressure is also demonstrated. To define filtration and filtration pressure in unconventional, tight-oil reservoirs, analogy to chemical osmosis is applied two pore systems connected with a pore throat, which shows membrane properties. Because the pore throat selectivity permits the passage of fluid molecules by their sizes, given a filtration pressure difference between the two pore systems, the concentration difference between the systems is determined by flash calculations. The results are expressed in the form of filtration (membrane) efficiency, which is essential parameter to define coupled fluxes for porous media flow.
Conservation Laws for Gyrokinetic Equations for Large Perturbations and Flows
Dimits, Andris
2017-10-01
Gyrokinetic theory has proved to be very useful for the understanding of magnetized plasmas, both to simplify analytical treatments and as a basis for efficient numerical simulations. Gyrokinetic theories were previously developed in two extended orderings that are applicable to large fluctuations and flows as may arise in the tokamak edge and scrapeoff layer. In the present work, we cast the resulting equations in a field-theoretical variational form, and derive, up to second order in the respective orderings, the associated global and local energy and (linear and toroidal) momentum conservation relations that result from Noether's theorem. The consequences of these for the various possible choices of numerical discretization used in gyrokinetic simulations are considered. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and supported by the U.S. DOE, OFES.
Hao, Y.; Settgast, R. R.; Fu, P.; Tompson, A. F. B.; Morris, J.; Ryerson, F. J.
2016-12-01
It has long been recognized that multiphase flow and transport in fractured porous media is very important for various subsurface applications. Hydrocarbon fluid flow and production from hydraulically fractured shale reservoirs is an important and complicated example of multiphase flow in fractured formations. The combination of horizontal drilling and hydraulic fracturing is able to create extensive fracture networks in low permeability shale rocks, leading to increased formation permeability and enhanced hydrocarbon production. However, unconventional wells experience a much faster production decline than conventional hydrocarbon recovery. Maintaining sustainable and economically viable shale gas/oil production requires additional wells and re-fracturing. Excessive fracturing fluid loss during hydraulic fracturing operations may also drive up operation costs and raise potential environmental concerns. Understanding and modeling processes that contribute to decreasing productivity and fracturing fluid loss represent a critical component for unconventional hydrocarbon recovery analysis. Towards this effort we develop a discrete fracture model (DFM) in GEOS (LLNL multi-physics computational code) to simulate multiphase flow and transfer in hydraulically fractured reservoirs. The DFM model is able to explicitly account for both individual fractures and their surrounding rocks, therefore allowing for an accurate prediction of impacts of fracture-matrix interactions on hydrocarbon production. We apply the DFM model to simulate three-phase (water, oil, and gas) flow behaviors in fractured shale rocks as a result of different hydraulic stimulation scenarios. Numerical results show that multiphase flow behaviors at the fracture-matrix interface play a major role in controlling both hydrocarbon production and fracturing fluid recovery rates. The DFM model developed in this study will be coupled with the existing hydro-fracture model to provide a fully integrated
Solving the power flow equations: a monotone operator approach
Energy Technology Data Exchange (ETDEWEB)
Dvijotham, Krishnamurthy [California Inst. of Technology (CalTech), Pasadena, CA (United States); Low, Steven [California Inst. of Technology (CalTech), Pasadena, CA (United States); Chertkov, Michael [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-07-21
The AC power flow equations underlie all operational aspects of power systems. They are solved routinely in operational practice using the Newton-Raphson method and its variants. These methods work well given a good initial “guess” for the solution, which is always available in normal system operations. However, with the increase in levels of intermittent generation, the assumption of a good initial guess always being available is no longer valid. In this paper, we solve this problem using the theory of monotone operators. We show that it is possible to compute (using an offline optimization) a “monotonicity domain” in the space of voltage phasors. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or provably certify that no solutions exist in it. We validate the approach on several IEEE test cases and demonstrate that the offline optimization can be performed tractably and the computed “monotonicity domain” includes all practically relevant power flow solutions.
Production Optimization for Two-Phase Flow in an Oil Reservoir
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2012-01-01
time. When the natural pressure becomes insufficient, the pressure must be maintained artificially by injection of water. Conventional technologies for recovery leaves more than 50% of the oil in the reservoir. Wells with adjustable downhole flow control devices coupled with modern control technology...... offer the potential to increase the oil recovery significantly. In optimal control of smart wells, downhole sensor equipment and remotely controlled valves are used in combination with large-scale subsurface flow models and gradient based optimization methods in a Nonlinear Model Predictive Control...
Flow rate and flow equation of pharmaceutical free-flowable powder excipients.
Sklubalová, Zdenka; Zatloukal, Zdenek
2013-02-01
Basic aspect of powder handling is powder flow which depends on mechanical properties of the solid material. This experimental work presents the results of flowability testing of the free-flowable particle size fraction of 0.0250-0.0315 cm of five powder excipients. The single-point determination of the mass flow rate from a cylindrical, flat-bottomed hopper was primarily influenced by the diameter of a circular orifice. The significant effect of the orifice height was also noted. Increasing the orifice height, the flow under gravity is directed resulting in the sudden acceleration of the flow rate. The critical zone relates to the orifice diameter. The multi-point determination of flowability employed the actual parameters of the flow equation which allows the prediction of the mass flow rate. The precision of the prediction was the basic criterion in optimization of the orifice geometry. Based on the results, the orifice height of 1.6 cm can be recommended for the correction of faster powder flow. For the slower powder flow, an orifice height of 0.2 cm can be used alternatively. In conclusion, the information about the orifice height used should be referred to whenever test the powder flowability and compare the results.
The Pore-scale modeling of multiphase flows in reservoir rocks using the lattice Boltzmann method
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.
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
Talmon, A.M.
1992-01-01
Flow equations for application in river bends are derived. Coordinate transformations are achieved by tensor calculus. The momentum equations are formulated in a cylindrical coordinate system and in a cylindrical bed-following coordinate system. The depth-averaged momentum equations in a cylindrical
Prosperetti, Andrea; van Wijngaarden, L.
1976-01-01
For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly
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
STRUCTURAL HETEROGENEITIES AND PALEO FLUID FLOW IN AN ANALOG SANDSTONE RESERVOIR 2001-2004
Energy Technology Data Exchange (ETDEWEB)
Pollard, David; Aydin, Atilla
2005-02-22
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
The lower limit of the flowing pore throat radius in the extra-low permeability reservoir
Xiang, Junhui; Yin, Daiyin
2018-02-01
In this paper, a method for determining the lower limit of flowing pore throat radius of the extra low permeability reservoir in the periphery of Changyuan Oil Fields is given. The capillary pressure curve is divided into linear type and concave type. The nuclear magnetic resonance (NMR) T2 spectrum is divided into 3 types: the left peak is greater than the right peak, the left peak is equal to the right one, and the left peak is smaller than the right one. The method for determining the lower limit of flowing pore throat radius is, first, converting the nuclear magnetic resonance T2 spectrum to the capillary pressure curve calculated, then fitting the capillary pressure curves measured by the constant speed mercury injection experiment and the capillary pressure curve calculated. After finding the relevant parameters, converting the horizontal axis of the NMR T2 spectra from relaxation time to pore throat radius, and the pore throat radius corresponding to the T2 cutoff value is the lower limit of the flowing pore throat radius. The lower limit of the flowing pore throat radius of the extra low permeability Fuyang Oil Reservoir in the periphery of Changyuan Oil Fields is about 0.68μm
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
Modeling energy flow in a large Neotropical reservoir: a tool do evaluate fishing and stability
Directory of Open Access Journals (Sweden)
Ronaldo Angelini
Full Text Available Recently, there is an increasing perception that the ecosystem approach gives important insights to support fisheries stock assessment and management. This paper aims to quantify energy flows in the Itaipu Reservoir (Brazil and to simulate increase of the fishing effort of some species, using Ecopath with Ecosim software, which could allow inferences on stability. Therefore, two steady-state Itaipu models were built (1983-87 and 1988-92. Results showed that: a there are no differences between models, and results on aging trends do not vary over time indicating that fishery does not alter the ecosystem as a whole; b results of fisheries simulations are approximate to mono-specific stock assessment for the same species and periods; c many authors believe that tropical ecosystems are environments where biotic and abiotic oscillations are annual and sometimes unexpected, but the results found for the Itaipu Reservoir indicate that stability was met after 16 years.
Cash flow in the context of economic equation of continuity
Directory of Open Access Journals (Sweden)
Fernando Gómez Villarraga
2006-07-01
Full Text Available The mathematic scheme, known as economic equation of continuity, is established for the balance of economic resources. In order to apply this equation it is necessary to determine an economic volume of control. The patrimonial equation is also proposed as a speed equationfor this volurne. The integral equation of economic continuity is applied to the «cash» system along with the integral patrimonial equation and so it gets expressions that correspond to model to elaborate cashflow statement with the particularities of the direct and indirect method. This model generales a useful definition for the calculation of this basic financial statement classified by operating, investing and financing activities.
Viscous flow computations with the lattice-Boltzmann equation method
Yu, Dazhi
2002-09-01
The lattice Boltzmann equation (LBE) method is a kinetics-based approach for fluid flow computations, and it is amenable to parallel computing. Compared to the well-established Navier-Stokes (NS) approaches, critical issues remain with the LBE method, noticeably flexible spatial resolution, boundary treatments, and dispersion and relaxation time mode. Those issues are addressed in this dissertation with improved practice presented. At the formulation level, both the single-relaxation-time (SRT) and multiple-relaxation-time (MRT) models are analyzed. The SRT model involves no artificial parameters, with a constant relaxation time regulating the physical value of fluid viscosity. The MRT model allows different relaxation time scales for different variables. Computational assessment shows that the MRT model has advantages over the SRT model in maintaining stability, reducing the oscillation, and improving the convergence rate in the computation. A multi-block method is developed for both the SRT and MRT model to facilitate flexible spatial resolutions according to the flow structures. The formulae for information exchange at the interface between coarse and fine grids are derived to ensure the mass and momentum conservation while maintaining the second-order accuracy. A customized time matching between coarse and fine grids is also presented to ensure smooth exchange information. Results show that the multi-block method can greatly increase the computational efficiency of the LBE method without losing the accuracy. Two methods of force evaluation in LBE are examined: one based on stress integration on the solid boundary and the other momentum exchange between fluid and solid. The momentum exchange method is found to be simpler to implement while the integration of stress requires evaluation of the detailed surface geometry and extrapolation of stress-related variables to the same surface. The momentum exchange method performs better overall. Improved treatments for
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.
Regularity of the 3D Navier-Stokes equations with viewpoint of 2D flow
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.
A physical five-equation model for compressible two-fluid flow, and its numerical treatment
J.J. Kreeft (Jasper); B. Koren (Barry)
2009-01-01
htmlabstractA novel five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The model uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which
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.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
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.
Gong, J.; Rossen, W.R.
2016-01-01
The flow properties of naturally fractured reservoirs are dominated by flow through the fractures. In a previous study we showed that even a well-connected fracture network behaves like a much sparser network when the aperture distribution is broad enough: i.e., most fractures can be eliminated
Reference population equations using peak expiratory flow meters ...
African Journals Online (AJOL)
Many formulae for predicting lung function values for Nigerians have been produced by a lot of investigators. The same principle but different statistical methods were adopted by different authors in generating these equations, hence the variability observed among these formulae. Most equations in current use are based on ...
Scaling properties reveal regulation of river flows in the Amazon through a forest reservoir
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.
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.
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
Flow-based dissimilarity measures for reservoir models : a spatial-temporal tensor approach
Insuasty, Edwin; van den Hof, P.M.J.; Weiland, Siep; Jansen, J.D.
2017-01-01
In reservoir engineering, it is attractive to characterize the difference between reservoir models in metrics that relate to the economic performance of the reservoir as well as to the underlying geological structure. In this paper, we develop a dissimilarity measure that is based on reservoir
Long-term affects of experimental flows on riverine biota below a reservoir
Robinson, Chris; Ortlepp, Johannes
2010-05-01
Large dams have altered the flow regime of most rivers on the globe with consequent effects on riverine biota. Experimental flows (multiple floods per year) have been used on the regulated Spöl River below Livigno Reservoir for over 9 years to enhance the ecological condition of the river. The flow program has improved the brown trout fishery in the river as indicated by an increased number of redds. Floods have reset periphyton assemblages from a moss-dominated streambed to one dominated by diatoms and patches of filamentous algae. Zoobenthic assemblages have shown dramatic shifts in benthic structure in line with predictions from altered state models. Ecosystem regime shifts have been characterized with increases in parameter variances followed by periods of stable states. The system appears to be entering a second zoobenthic regime shift after year 8, perhaps in response to biotic interactions due to changes in the fishery. The response patterns clearly show that a long-term perspective must be in place when assessing biotic responses to changes in physical habitat properties resulting from flow experiments.
Yang, Yunping; Zhang, Mingjin; Zhu, Lingling; Liu, Wanli; Han, Jianqiao; Yang, Yanhua
2017-11-15
The Three Gorges Project (TGP) is the world's largest water conservation project. The post-construction low-flow water level at the same discharge below the dam has declined, but there remains disagreement over whether the flood level has increased. Measured water levels and upstream and downstream flow data from 1955 to 2016 show that, post-construction: (1) the low-flow water level at the same discharge decreased, and the lowest water level increased due to dry-season reservoir discharge; (2) the decline of the low-flow water level below the dam was less than the undercutting value of the flow channel of the river; (3) the flood level at the same discharge below the dam was slightly elevated, although peak water levels decreased; (4) flood characteristics changed from a high discharge-high flood level to a medium discharge - high flood level; and (5) an expected decline in the flood level downstream was not observed. Channel erosion and the adjustment of rivers and lakes tend to reduce flood levels, while river bed coarsening, vegetation, and human activities downstream increase the flood level. Although the flood control benefits of the Three Gorges Dam (TGD) and the upstream reservoirs are obvious, increased elevation of the downstream flood level remains a concern.
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.
DEFF Research Database (Denmark)
Lerch, Dariusz Michal; Völcker, Carsten; Capolei, Andrea
2012-01-01
Natural petroleum reservoirs are characterised by 2-phase flow of oil and water in the porous media (e.g. rocks) which they are built of. Conventional methods of extracting oil from those fields, which utilise high initial pressure obtained from natural drive, leave more than 70 % of oil in the r......Natural petroleum reservoirs are characterised by 2-phase flow of oil and water in the porous media (e.g. rocks) which they are built of. Conventional methods of extracting oil from those fields, which utilise high initial pressure obtained from natural drive, leave more than 70 % of oil...... structure leading to change of permeability with position in the reservoir, or high oil viscosity. Therefore it is desired to take into account all these phenomena by implementing a realistic simulator of the 2-phase flow reservoir, which imposes the set of constraints on the state variables of optimisation...... problem. Then, thanks to optimal control, it is possible to adjust effectively injection valves to control 2 phase immiscible flow in every grid block of the reservoir and navigate oil to the production wells so it does not remain in the porous media. The use of such a smart technology known also as smart...
Cubic Plus Association Equation of State for Flow Assurance Projects
DEFF Research Database (Denmark)
dos Santos, Leticia Cotia; Abunahman, Samir Silva; Tavares, Frederico Wanderley
2015-01-01
-built model: To validate the implementation, we show calulations for binary systems containing hydrate inhibitors and water or hydrocarbons using the Cubic Plus Association (CPA) and Soave-Redlich-Kwong (SRK) equation of states, also comparing against experimental data. For streams containing natural gas......Thermodynamic hydrate inhibitors such as methanol, ethanol, (mono) ethylene glycol (MEG), and triethylene glycol (TEG) are widely used in the oil and gas industry. On modeling these compounds, we show here how the CPA equation of state was implemented in an in-house process simulator as an in...
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.
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.
16 reference population equations using peak expiratory flow meters
African Journals Online (AJOL)
DR. AMINU
Many formulae for predicting lung function values for Nigerians have been produced by a lot of investigators. The same principle ... equations in current use are based on linear statistical models which are subject to change and they did not express the .... that present lower limits of normal or present information from which ...
A Differential Equation for Downhill Compressible Flow in Pipes and ...
African Journals Online (AJOL)
The differential equation was first numerically solved by use of the classical fourth order Runge-Kutta method in the form of a FORTRAN program. A test of the accuracy of the solution was ... The formula was tested with a problem from the book “Fluid Mechanics and Hydraulics”. The test showed the formula to be accurate.
16 reference population equations using peak expiratory flow meters
African Journals Online (AJOL)
DR. AMINU
Department of Human Physiology Faculty of Medicine, Bayero University, Kano. ABSTRACT. Many formulae for predicting lung function values for Nigerians have been produced by a lot of investigators. The same principle but different statistical methods were adopted by different authors in generating these equations, ...
Ahearn, Elizabeth A.
2010-01-01
Multiple linear regression equations for determining flow-duration statistics were developed to estimate select flow exceedances ranging from 25- to 99-percent for six 'bioperiods'-Salmonid Spawning (November), Overwinter (December-February), Habitat Forming (March-April), Clupeid Spawning (May), Resident Spawning (June), and Rearing and Growth (July-October)-in Connecticut. Regression equations also were developed to estimate the 25- and 99-percent flow exceedances without reference to a bioperiod. In total, 32 equations were developed. The predictive equations were based on regression analyses relating flow statistics from streamgages to GIS-determined basin and climatic characteristics for the drainage areas of those streamgages. Thirty-nine streamgages (and an additional 6 short-term streamgages and 28 partial-record sites for the non-bioperiod 99-percent exceedance) in Connecticut and adjacent areas of neighboring States were used in the regression analysis. Weighted least squares regression analysis was used to determine the predictive equations; weights were assigned based on record length. The basin characteristics-drainage area, percentage of area with coarse-grained stratified deposits, percentage of area with wetlands, mean monthly precipitation (November), mean seasonal precipitation (December, January, and February), and mean basin elevation-are used as explanatory variables in the equations. Standard errors of estimate of the 32 equations ranged from 10.7 to 156 percent with medians of 19.2 and 55.4 percent to predict the 25- and 99-percent exceedances, respectively. Regression equations to estimate high and median flows (25- to 75-percent exceedances) are better predictors (smaller variability of the residual values around the regression line) than the equations to estimate low flows (less than 75-percent exceedance). The Habitat Forming (March-April) bioperiod had the smallest standard errors of estimate, ranging from 10.7 to 20.9 percent. In
Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data
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.
Comparison of generalized Reynolds and Navier Stokes equations for flow of a power law fluid
Mullen, R. L.; Prekwas, A.; Braun, M. J.; Hendricks, R. C.
1987-01-01
This paper compares a finite element solution of a modified Reynolds equation with a finite difference solution of the Navier-Stokes equation for a power law fluid. Both the finite element and finite difference formulation are reviewed. Solutions to spiral flow in parallel and conical geometries are compared. Comparison with experimental results are also given. The effects of the assumptions used in the Reynolds equation are discussed.
The price of an exact, gauge-invariant RG-flow equation
International Nuclear Information System (INIS)
Branchina, Vincenzo; Meissner, Krzysztof A.; Veneziano, Gabriele
2003-01-01
We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky-De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to be paid for such a result is that both the action and the RGF equation depend explicitly upon the base point (in field space) needed for the VDW construction. We briefly discuss the complications originating from this fact and possible ways to overcome them
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.
Factorizable Schemes for the Equations of Fluid Flow
Sidilkover, David
1999-01-01
We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.
Designing a reservoir flow rate experiment for the GOM hydrate JIP leg 2 LWD drilling
Energy Technology Data Exchange (ETDEWEB)
Gullapalli, I.; Silpngarmlert, S.; Reik, B.; Kamal, M.; Jones, E. [Chevron Energy Technology Co., San Ramon, CA (United States); Moridis, G. [Lawrence Berkeley National Laboratories, CA (United States); Collett, T. [United States Geological Survey, Reston, VA (United States)
2008-07-01
Studies have indicated that the Gulf of Mexico may contain large deep sea hydrate deposits. This paper provided details of short-term production profiles obtained from a geological model of hydrate deposits located in the Gulf area. A well test analysis tool was used to obtain the production parameters. Pressure transients from numerical simulations of various well test designs were used to provide estimates of important flow parameters. The aim of the study was to determine the type and duration of a well test capable of providing data to support the accurate modeling of gas hydrate deposits. Parameters studied in the test included the effects of permeability and hydrate saturation as a function of the duration of the flow test. Results indicated that production using a constant bottom hole pressure is an appropriate method of impacting hydrate dissociation by depressurization. However, changes in transient pressure plots could not be characterized in order to identify regions of varying saturation levels. Results suggested that the rate of effective water to effective gas was higher than rates obtained from relative permeability relations due to low gas saturation levels. Fluid saturation regions were in areas of low confidence in relative permeability curves. However, it was not possible to calculate absolute permeability of the reservoir for systems with short production periods. Further studies are needed to determine effective permeability using history matching and a hydrate simulator. 8 refs., 4 tabs., 27 figs.
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
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.
Modified Saint-Venant equations for flow simulation in tidal rivers
Directory of Open Access Journals (Sweden)
Xiao-qin Zhang
2012-03-01
Full Text Available Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations (the SVN model are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal level was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton's second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers (the ISVN model was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.
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
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.
A generalised groundwater flow equation using the concept of non ...
African Journals Online (AJOL)
2006-01-01
Jan 1, 2006 ... K the hydraulic conductivity tensor of the aquifer. Ф(x,t) the piezometric head f(x,t) the strength of any sources or sinks, with x and t the usual spatial and time coordinates. V the gradient operator. ∂t the time derivative. This model showed that the dominant flow field in these aquifers is vertical and linear and ...
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.
Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces
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
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
International Nuclear Information System (INIS)
Vallepin, C.; Kowalewsky, H.
1989-01-01
Packages designed for the transport of radioactive materials are required by International and National regulations to restrict the possible loss of radioactive contents to very low levels under both Normal and Accident Conditions of Transport. The applicability of the equations used in the calculation of leak geometry and flow rates is assessed. Molecular, Laminar, Turbulent, and Choked flow may occur depending upon the leak geometry and pressure conditions. We present data from experimental work which used the flow models and equations to predict leakage rates through capillaries and gaps. National technical guides and computer codes for leak testing have been produced which give practical assistance in carrying out leak testing. The relationship between leak geometry and gas leakage rates can be described most appropriately and conservatively by the Knudsen flow equation for capillaries and in a slightly modified form for gaps
Modeling mode interactions in boundary layer flows via the Parabolized Floquet Equations
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...
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
The Soil Foam Drainage Equation - an alternative model for unsaturated flow in porous media
Assouline, Shmuel; Lehmann, Peter; Hoogland, Frouke; Or, Dani
2017-04-01
The analogy between the geometry and dynamics of wet foam drainage and gravity drainage of unsaturated porous media expands modeling capabilities for capillary flows and supplements the standard Richards equation representation. The governing equation for draining foam (or a soil variant termed the soil foam drainage equation - SFDE) obviates the need for macroscopic unsaturated hydraulic conductivity function by an explicit account of diminishing flow pathway sizes as the medium gradually drains. Potential advantages of the proposed drainage foam formalism include direct description of transient flow without requiring constitutive functions; evolution of capillary cross sections that provides consistent description of self-regulating internal fluxes (e.g., towards field capacity); and a more intuitive geometrical picture of capillary flow across textural boundaries. We will present new and simple analytical expressions for drainage rates and volumes from unsaturated porous media subjected to different boundary conditions that are in good agreement with the numerical solution of the SFDE and experimental results. The foam drainage methodology expands the range of tools available for describing and quantifying unsaturated flows and provides geometrically tractable links between evolution of liquid configuration and flow dynamics in unsaturated porous media. The resulting geometrical representation of capillary drainage could improve understanding of colloid and pathogen transport. The explicit geometrical interpretation of flow pathways underlying the hydraulic functions used by the Richards equation offers new insights that benefit both approaches.
Rheological equations in asymptotic regimes of granular flow
Chen, C.-L.; Ling, C.-H.
1998-01-01
This paper assesses the validity of the generalized viscoplastic fluid (GVF) model in light of the established constitutive relations in two asymptotic flow regimes, namely, the macroviscous and grain-inertia regimes. A comprehensive review of the literature on constitutive relations in both regimes reveals that except for some material constants, such as the coefficient of restitution, the normalized shear stress in both regimes varies only with the grain concentration, C. It is found that Krieger-Dougherty's relative viscosity, ??*(C), is sufficiently coherent among the monotonically nondecreasing functions of C used in describing the variation of the shear stress with C in both regimes. It not only accurately represents the C-dependent relative viscosity of a suspension in the macroviscous regime, but also plays a role of the radial distribution function that describes the statistics of particle collisions in the grain-inertia regime. Use of ??*(C) alone, however, cannot link the two regimes. Another parameter, the shear-rate number, N, is needed in modelling the rheology of neutrally buoyant granular flows in transition between the two asymptotic regimes. The GVF model proves compatible with most established relations in both regimes.
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.
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.
A Derivation of the Nonlocal Volume-Averaged Equations for Two-Phase Flow Transport
Directory of Open Access Journals (Sweden)
Gilberto Espinosa-Paredes
2012-01-01
Full Text Available In this paper a detailed derivation of the general transport equations for two-phase systems using a method based on nonlocal volume averaging is presented. The local volume averaging equations are commonly applied in nuclear reactor system for optimal design and safe operation. Unfortunately, these equations are limited to length-scale restriction and according with the theory of the averaging volume method, these fail in transition of the flow patterns and boundaries between two-phase flow and solid, which produce rapid changes in the physical properties and void fraction. The non-local volume averaging equations derived in this work contain new terms related with non-local transport effects due to accumulation, convection diffusion and transport properties for two-phase flow; for instance, they can be applied in the boundary between a two-phase flow and a solid phase, or in the boundary of the transition region of two-phase flows where the local volume averaging equations fail.
Kavvas, M. Levent; Tu, Tongbi; Ercan, Ali; Polsinelli, James
2017-10-01
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 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.
Low flows and reservoir management for the Durance River basin (Southern France) in the 2050s
Sauquet, Eric
2015-04-01
. A model of water management similar to the tools used by Electricité De France was calibrated to simulate the behavior of the three reservoirs Serre-Ponçon, Castillon, Sainte-Croix on present-day conditions. This model simulates water releases from reservoir under constraints imposed by rule curves, ecological flows downstream to the dams and water levels in summer for recreational purposes. The results demonstrate the relatively good performance of this simplified model and its ability to represent the influence of reservoir operations on the natural hydrological river flow regime, the decision-making involved in water management and the interactions at regional scale. Four territorial socio-economic scenarios have been also elaborated with the help of stake holders to project water needs in the 2050s for the area supplied with water from the Durance River basin. This presentation will focus on the specific tools developed within the project to simulate water management and water abstractions. The main conclusions related to the risk of water shortage in the 2050s and the level of satisfaction for each water use will be also discussed.
Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change
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.
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
Flow cytometric DNA analysis of ducks accumulating 137Cs on a reactor reservoir
International Nuclear Information System (INIS)
George, L.S.; Dallas, C.E.; Brisbin, I.L. Jr.; Evans, D.L.
1991-01-01
The objective of this study was to detect red blood cell (rbc) DNA abnormalities in male, game-farm mallard ducks as they ranged freely and accumulated 137Cs (radiocesium) from an abandoned nuclear reactor cooling reservoir. Prior to release, the ducks were tamed to enable recapture at will. Flow cytometric measurements conducted at intervals during the first year of exposure yielded cell cycle percentages of DNA (G0/G1, S, G2 + M phases) of rbc, as well as coefficients of variation (CV) in the G0/G1 phase. DNA histograms of exposed ducks were compared with two sets of controls which were maintained 30 and 150 miles from the study site. 137Cs live wholebody burdens were also measured in these animals in a parallel kinetics study, and an approximate steady-state equilibrium was attained after about 8 months. DNA histograms from 2 of the 14 contaminated ducks revealed DNA aneuploid-like patterns after 9 months exposure. These two ducks were removed from the experiment at this time, and when sampled again 1 month later, one continued to exhibit DNA aneuploidy. None of the control DNA histograms demonstrated DNA aneuploid-like patterns. There were no significant differences in cell cycle percentages at any time point between control and exposed animals. A significant increase in CV was observed at 9 months exposure, but after removal of the two ducks with DNA aneuploidy, no significant difference was detected in the group monitored after 12 months exposure. An increased variation in the DNA and DNA aneuploidy could, therefore, be detected in duck rbc using flow cytometric analysis, with the onset of these effects being related to the attainment of maximal levels of 137Cs body burdens in the exposed animals
Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology
Schaeffer, D. G.; Shearer, M.; Gray, J. M. N. T.
2017-01-01
Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too high or too low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions for well-posedness of partial differential equations that combine compressibility with I-dependent rheology. When the I-dependence comes from a specific friction coefficient μ(I), our results show that, with compressibility, the equations are well-posed for all deformation rates provided that μ(I) satisfies certain minimal, physically natural, inequalities. PMID:28588402
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)
On a modified form of navier-stokes equations for three-dimensional flows.
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.
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...
One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows
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.
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
THE METHOD OF ESTIMATION OF ACCEPTABLE DISCHARGE OF RADIONUCLIDES INTO FLOWING RESERVOIR
Directory of Open Access Journals (Sweden)
O. N. Prokof'ev
2008-01-01
Full Text Available Abroad and in Russia there exist the practices of discharge of liquids, which maintain radionuclides in reservoirs. In order to ensure radiation protection of environment and population such discharge must be carried out under control. For carrying out of the control it is necessary to determine the value of acceptable discharge of radionuclides into reservoir with consideration of specific conditions and to supervise the actual value of discharge. The value of acceptable discharge of radionuclide into reservoir depends on such parameters as its volume and rate of the water pour off.
International Nuclear Information System (INIS)
Stauber, T; Mielke, A
2003-01-01
To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different, initial Hamiltonians, a numerically solvable model is considered which is structurally similar to impurity models. By this we discuss the question of optimization for the first time. A general truncation scheme is established that produces good results for the Hamiltonian flow as well as for the operator flow. Nevertheless, it is also pointed out that a systematic and feasible scheme for the operator flow on the operator level is missing. For this, an explicit analysis of the operator flow is given for the first time. We observe that truncation of the series of the observable flow after the linear or bilinear terms does not yield satisfactory results for the entire parameter regime as - especially close to resonances - even high orders of the exact series expansion carry considerable weight
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.
Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation
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.
Turbulence equations in incompressible two-phase flow without mass transfer
International Nuclear Information System (INIS)
Lance, Michel; Marie, J.-L.; Charnay, Georges; Bataille, Jean
1979-01-01
In order to adapt the modelling methods of one-phase turbulence, the equations describing the evolution of the Reynolds stress tensor, of the dissipation and of the fluctuating pressure in each phase of an incompressible two-phase flow without mass transfer were established [fr
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)
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
Field Characterization of Reservoir Flow Paths Using Miscible and Immiscible Tracer Tests
Trautz, Robert C.; Freifeld, Barry M.; Doughty, Christine; Benson, Sally M.; Phelps, Tommy J.; McCallum, Scott D.
2005-01-01
Injection of supercritical CO2 into deep, brine-filled reservoirs may be used to slow the effect that greenhouse gas emissions have on global warming. During injection, the large contrast in fluid densities and viscosities causes immiscible displacement of the brine by CO2, resulting in a two-phase system. We performed a series of tracer tests during the Frio CO2 sequestration pilot program to study immiscible and miscible fluid displacement through the Frio sandstone, a deep saline reservoir...
MULTIDISCIPLINARY IMAGING OF ROCK PROPERTIES IN CARBONATE RESERVOIRS FOR FLOW-UNIT TARGETING
Energy Technology Data Exchange (ETDEWEB)
Stephen C. Ruppel
2004-07-20
Our analysis and imaging of reservoir properties at the Fullerton Clear Fork field (Figure 1) is in its final stages. Major accomplishments during the past 6 months include: (1) characterization of facies and cyclicity in cores, (2) correlation of cycles and sequences using core-calibrated wireline logs, (3) calculation and modeling of wireline porosity, (4) analysis of new cores for conventional and special core analysis data, (5) construction of full-field reservoir model, and (6) revision of 3D seismic inversion of reservoir porosity and permeability. One activity has been eliminated from the originally proposed tasks. Task 3 (Characterization and Modeling of Rock Mechanics and Fractures) has been deleted because we have determined that fractures are not significant contributing in the reservoir under study. A second project extension has been asked for to extend the project until 7/31/04. Remaining project activities are: (1) interpretation and synthesis of fieldwide data, (2) preparation of 3D virtual reality demonstrations of reservoir model and attributes, (3) transfer of working data sets to the operator for reservoir implementation and decision-making, and (4) preparation and distribution of final reports.
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
Analysis of Blasius Equation for Flat-Plate Flow with Infinite Boundary Value
DEFF Research Database (Denmark)
Miansari, M. O.; Miansari, M. E.; Barari, Amin
2010-01-01
This paper applies the homotopy perturbation method (HPM) to determine the well-known Blasius equation with infinite boundary value for Flat-plate Flow. We study here the possibility of reducing the momentum and continuity equations to ordinary differential equations by a similarity transformation...... and write the nonlinear differential equation in the state space format, and then solve the initial value problem instead of boundary value problem. The significance of linear part is a key factor in convergence. A first seen linear part may lead to an unstable solution, therefore an extra term is added...... to the linear part and deduced from the nonlinear section. The results reveal that HPM is very effective, convenient, and quite accurate to both linear and nonlinear problems. It is predicted that HPM can be widely applied in engineering. Some plots and numerical results are presented to show the reliability...
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...
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.
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.
Development of computational two-phase flow analysis code with interfacial area transport equation
International Nuclear Information System (INIS)
Bae, B.U.; Park, G.C.; Yoon, H.Y.; Euh, D.J.; Song, C.H.
2007-01-01
In the two-phase flow analysis with two-fluid model, interfacial area concentration (IAC) is a dominant factor governing the interfacial transfer of momentum and energy. In order to overcome the shortcomings of experimental correlation for IAC, such as the dependency on the flow regime, multi-dimensional computational fluid dynamics (CFD) code was developed with the interfacial area transport equation. The code is based on two-fluid model and simplified marker and cell (SMAC) algorithm using the finite volume method, and the conventional approach in single-phase flow has been modified in order to consider the term of phase change. Also, instead of a static one-dimensional correlation for IAC, the code adopted the one-group interfacial area transport equation which includes source terms with respect to the coalescence and breakup of bubbles, and the phase change such as evaporation or condensation. As benchmark problems of single-phase flow and two-phase flow, the natural convection in rectangular cavity and the subcooled boiling in vertical annulus channel were analyzed, respectively. In the calculation for single-phase flow, the developed code predicted reasonable behavior of buoyancy-driven flow depending on Rayleigh number, so that the robustness in calculation capability of each phase has been confirmed. In the analysis for the subcooled boiling experiment performed in Seoul National University, the calculation results represented the reasonable capability in predicting the multi-dimensional phenomena such as vapor generation and void propagation. (authors)
Development of computational two-phase flow analysis code with interfacial area transport equation
Energy Technology Data Exchange (ETDEWEB)
Bae, B.U.; Park, G.C. [Seoul National Univ., Dept. of Nuclear Engineering (Korea, Republic of); Yoon, H.Y.; Euh, D.J.; Song, C.H. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2007-07-01
In the two-phase flow analysis with two-fluid model, interfacial area concentration (IAC) is a dominant factor governing the interfacial transfer of momentum and energy. In order to overcome the shortcomings of experimental correlation for IAC, such as the dependency on the flow regime, multi-dimensional computational fluid dynamics (CFD) code was developed with the interfacial area transport equation. The code is based on two-fluid model and simplified marker and cell (SMAC) algorithm using the finite volume method, and the conventional approach in single-phase flow has been modified in order to consider the term of phase change. Also, instead of a static one-dimensional correlation for IAC, the code adopted the one-group interfacial area transport equation which includes source terms with respect to the coalescence and breakup of bubbles, and the phase change such as evaporation or condensation. As benchmark problems of single-phase flow and two-phase flow, the natural convection in rectangular cavity and the subcooled boiling in vertical annulus channel were analyzed, respectively. In the calculation for single-phase flow, the developed code predicted reasonable behavior of buoyancy-driven flow depending on Rayleigh number, so that the robustness in calculation capability of each phase has been confirmed. In the analysis for the subcooled boiling experiment performed in Seoul National University, the calculation results represented the reasonable capability in predicting the multi-dimensional phenomena such as vapor generation and void propagation. (authors)
A finite element formulation of Euler equations for the solution of steady transonic flows
Ecer, A.; Akay, H. U.
1982-01-01
The main objective of the considered investigation is related to the development of a relaxation scheme for the analysis of inviscid, rotational, transonic flow problems. To formulate the equations of motion for inviscid flows in a fixed coordinate system, an Eulerian type variational principle is required. The derivation of an Eulerian variational principle which is employed in the finite element formulation is discussed. The presented numerical method describes the mathematical formulation and the application of a numerical process for the direct solution of steady Euler equations. The development of the procedure as an extension of existing potential flow formulations provides the applicability of previous procedures, e.g., proper application of the artificial viscosity for supersonic elements, and the accurate modeling of the shock.
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)
Analysis of the Scramjet inlet flow field using two-dimensional Navier-Stokes equations
Kumar, A.; Tiwari, S. N.
1982-01-01
A computer code was developed to solve the full two dimensional Navier-Stokes equations in a scramjet inlet. The analysis uses a numerical coordinate transformation which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. A two-layer eddy viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with multiple struts in the flow field. Detailed results are presented for two model problems and two scramjet inlets with one and two struts. The application of the two dimensional analysis in the preliminary design of the actual scramjet inlet is briefly discussed.
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.
Khasani; Itoi, Ryuichi; Tanaka, Toshiaki; Fukuda, Michihiro
2004-01-01
The effects of initial water saturation on well characteristics in two-phase geothermal reservoirs were evaluated. A vertical wellbore model of uniform diameter coupled with a radial horizontal flow in a reservoir of uniform thickness was employed. The momentum equation for two-phase flow in a wellbore was numerically evaluated with a method introduced by Orkiszewski. The energy equation in the wellbore was assumed to be isenthalpic. Mass flow rate and pressure at a feed zone of the well were...
Fluid flow in porous media using image-based modelling to parametrize Richards' equation
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.
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)
Johnson-Segalman -- Saint-Venant equations for viscoelastic shallow flows in the elastic limit
Boyaval, Sébastien
2016-01-01
The shallow-water equations of Saint-Venant, often used to model the long-wave dynamics of free-surface flows driven by inertia and hydrostatic pressure, can be generalized to account for the elongational rheology of non-Newtonian fluids too. We consider here the $4 \\times 4$ shallow-water equations generalized to viscoelastic fluids using the Johnson-Segalman model in the elastic limit (i.e. at infinitely-large Deborah number, when source terms vanish). The system of nonlinear first-order eq...
A differential equation for the flow rate during silo discharge: Beyond the Beverloo rule
Directory of Open Access Journals (Sweden)
Madrid Marcos A.
2017-01-01
Full Text Available We present a differential equation for the flow rate of granular materials during the discharge of a silo. This is based in the energy balance of the variable mass system in contrast with the traditional derivations based on heuristic postulates such as the free fall arch. We show that this new equation is consistent with the well known Beverloo rule, providing an independent estimate for the universal Beverloo prefactor. We also find an analytic expression for the pressure under discharging conditions.
A study on the Wilkins and Forchheimer equations used in coarse granular media flow
Banerjee, Ashes; Pasupuleti, Srinivas; Singh, Mritunjay Kumar; Kumar, G. N. Pradeep
2018-02-01
Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy's law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.
Application of Reservoir Flow Simulation Integrated with Geomechanics in Unconventional Tight Play
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
A stochastic approach to the operative control of flood flows through a reservoir
Directory of Open Access Journals (Sweden)
Jaroš Lubomír
2016-03-01
Full Text Available The contribution focuses on the design of a control algorithm aimed at the operative control of runoff water from a reservoir during flood situations. Management is based on the stochastically specified forecast of water inflow into the reservoir. From a mathematical perspective, the solved task presents the control of a dynamic system whose predicted hydrological input (water inflow is characterised by significant uncertainty. The algorithm uses a combination of simulation model data, in which the position of the bottom outlets is sought via nonlinear optimisation methods, and artificial intelligence methods (adaptation and fuzzy model. The task is written in the technical computing language MATLAB using the Fuzzy Logic Toolbox.
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.
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
Directory of Open Access Journals (Sweden)
Giorgio Baiamonte
2010-03-01
Full Text Available This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed to investigate the effect of main parameter variability on the hillslope response. Particularly, the effect of hillslope geometry and rainfall intensity on the time to equilibrium is shown.
The effect of flow-through regimes zooplankton densities in a canyon-shaped dam reservoir
Czech Academy of Sciences Publication Activity Database
Seďa, Jaromír; Macháček, Jiří
1998-01-01
Roč. 83, Special Issue (1998), s. 477-484 ISSN 1434-2944. [International Conference on Reservoir Limnology and Water Quality /3./. České Budějovice, 11.08.1997-15.08.1997] R&D Projects: GA AV ČR IAA6017503 Subject RIV: DA - Hydrology ; Limnology Impact factor: 0.632, year: 1997
Heat-flow equation motivated by the ideal-gas shock wave.
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.
Heat-flow equation motivated by the ideal-gas shock wave
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.
An integro-partial differential equation for modeling biofluids flow in fractured biomaterials.
Sadegh Zadeh, Kouroush
2011-03-21
A novel mathematical model in the framework of a nonlinear integro-partial differential equation governing biofluids flow in fractured biomaterials is proposed, solved, verified, and evaluated. A semi-analytical solution is derived for the equation, verified by a mass-lumped Galerkin finite element method (FEM), and calibrated with two in vitro experimental datasets. The solution process uses separation of variables and results in explicit expression involving complete and incomplete beta functions. The proposed semi-analytical model shows reasonable agreements with the finite element simulator as well as with two in vitro experimental time series and can be successfully used to simulate biofluids (e.g. water, blood, oil, etc.) flow in natural and synthetic porous biomaterials. Copyright © 2010 Elsevier Ltd. All rights reserved.
Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow
Braun, M. J.; Wheeler, R. L., III; Hendricks, R. C.; Mullen, R. L.
An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.
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
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.
Energy Technology Data Exchange (ETDEWEB)
Tippie, D.B.; Kohlhaas, C.A.
1974-01-01
A semi-cylindrical sand-pack model of a cased-and-perforated completion was loaded with an overburden pressure and fluid flowed through the pack to simulate production. Flow rate was gradually increased in each test. Sand arches formed to stabilize sand movement. As reported previously by the same authors, arch size was a function of flow rate. Skin effect caused by arch formation, destruction, and size variation is also a function of flow rate. Minimum skin effects were noted for a particular flow rate. Potentiometric flow models were used to verify sand-pack results. Flow tests in a linear flow cell indicated a significant damage effect (permeability reduction) due to fines migration. The sand-pack completion model indicated that the fines migration and skin effect change are associated with sand instability.
Test of a new heat-flow equation for dense-fluid shock waves
Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon
2010-09-01
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.
Test of a new heat-flow equation for dense-fluid shock waves.
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.
Analytical equation for outflow along the flow in a perforated fluid distribution pipe.
Directory of Open Access Journals (Sweden)
Huanfang Liu
Full Text Available Perforated fluid distribution pipes have been widely used in agriculture, water supply and drainage, ventilation, the chemical industry, and other sectors. The momentum equation for variable mass flow with a variable exchange coefficient and variable friction coefficient was developed by using the momentum conservation method under the condition of a certain slope. The change laws of the variable momentum exchange coefficient and the variable resistance coefficient along the flow were analyzed, and the function of the momentum exchange coefficient was given. According to the velocity distribution of the power function, the momentum equation of variable mass flow was solved for different Reynolds numbers. The analytical solution contains components of pressure, gravity, friction and momentum and reflects the influence of various factors on the pressure distribution along the perforated pipe. The calculated results of the analytical solution were compared with the experimental values of the study by Jin et al. 1984 and Wang et al. 2001 with the mean errors 8.2%, 3.8% and 2.7%, and showed that the analytical solution of the variable mass momentum equation was qualitatively and quantitatively consistent with the experimental results.
Cervania, A.; Knack, I. M. W.
2017-12-01
The presence of woody debris (WD) jams in rivers and streams increases the risk of backwater flooding and reduces the navigability of a channel, but adds fish and macroinvertebrate habitat to the stream. When designing river engineering projects engineers use hydraulic models to predict flow behavior around these obstructions. However, the complexities of flow through and beneath WD jams are still poorly understood. By increasing the ability to predict flow behavior around WD jams, landowners and engineers are empowered to develop sustainable practices regarding the removal or placement of WD in rivers and flood plains to balance the desirable and undesirable effects to society and the environment. The objective of this study is to address some of this knowledge gap by developing a method to estimate the vertical velocity profile of flow under WD jams. When flow passes under WD jams, it becomes affected by roughness elements on all sides, similar to turbulent flows in pipe systems. Therefore, the method was developed using equations that define the velocity profiles of turbulent pipe flows: the law of the wall, the logarithmic law, and the velocity defect law. Flume simulations of WD jams were conducted and the vertical velocity profiles were measured along the centerline. A calculated velocity profile was fit to the measured profile through the calibration of eight parameters. An optimal value or range of values have been determined for several of these parameters using cross-validation techniques. The results indicate there may be some promise to using this method in hydraulic models.
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)
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.
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
Resolvent analysis of shear flows using One-Way Navier-Stokes equations
Rigas, Georgios; Schmidt, Oliver; Towne, Aaron; Colonius, Tim
2017-11-01
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, the One-Way Navier-Stokes (OWNS) equations permit a fast spatial marching procedure that results in a huge reduction in computational cost. Here, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The corresponding optimal response modes are validated against modes obtained in terms of global resolvent analysis. For laminar base flows, the optimal modes reveal modal and non-modal transition mechanisms. For turbulent base flows, they predict the evolution of coherent structures in a statistical sense. Results from the application of the method to three-dimensional laminar wall-bounded flows and turbulent jets will be presented. This research was supported by the Office of Naval Research (N00014-16-1-2445) and Boeing Company (CT-BA-GTA-1).
Study of magnetized accretion flow with variable Γ equation of state
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.
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
Active flow control insight gained from a modified integral boundary layer equation
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.
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)
Gong, J.; Rossen, W.R.
2014-01-01
Fracture network connectivity and aperture (or conductivity) distribution are two crucial features controlling the flow behavior of fractured formations. The effect of connectivity on flow properties is well documented. We focus here on the influence of fracture aperture distribution. We model a
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 equ...... 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.......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...
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)
Comparison of different notation for equations of motion of a body in a medium flow
Samsonov, V. A.; Selyutskii, Yu. D.
2008-02-01
In [1-6], a model of a nonstationary action of a medium flow on a body moving in this flow was constructed in the form of an associated dynamical system of second order. In the literature, the representation of the aerodynamic force in integral form with a Duhamel type integral is often used (e.g., see [7, 8]). In the present paper, we pay attention to the fact that a system of ODE is equivalent not to a single integro-differential equation but to a family of such equations. Therefore, it is necessary to discuss the problem of the correspondence between their solutions. The integro-differential representation of the aerodynamic force is reduced to a form convenient to realize the procedure of separation of motions. In this case, we single out the first two approximations with respect to a small parameter. It turns out that in the case of actual airfoils one can speak of "detached" rather than "attached" mass. In the problem on the forced drag of an airfoil in a flow, it is shown that for a sufficiently large acceleration the aerodynamic force can change its direction and turn from a drag force into an "accelerating" force for some time. At the same time, in the case of free drag of a sufficiently light plate, the "acceleration" effect is not observed, but in the course of deceleration the plate moves from it original position in the direction opposite to the initial direction of motion.
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.
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
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...... 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...... 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...
Prediction of Shock Wave Structure in Weakly Ionized Gas Flow by Solving MGD Equation
Deng, Z. T.; Oviedo-Rojas, Ruben; Chow, Alan; Litchford, Ron J.; Cook, Stephen (Technical Monitor)
2002-01-01
This paper reports the recent research results of shockwave structure predictions using a new developed code. The modified Rankine-Hugoniot relations across a standing normal shock wave are discussed and adopted to obtain jump conditions. Coupling a electrostatic body force to the Burnett equations, the weakly ionized flow field across the shock wave was solved. Results indicated that the Modified Rankine-Hugoniot equations for shock wave are valid for a wide range of ionization fraction. However, this model breaks down with small free stream Mach number and with large ionization fraction. The jump conditions also depend on the value of free stream pressure, temperature and density. The computed shock wave structure with ionization provides results, which indicated that shock wave strength may be reduced by existence of weakly ionized gas.
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)
Lid-driven cavity flow using a discrete velocity method for solving the Boltzmann equation
Sekaran, Aarthi; Varghese, Philip; Estes, Samuel; Goldstein, David
2016-11-01
We extend the discrete velocity method for solving the Boltzmann equation previously used for one-dimensional problems to two spatial dimensions. The collision integral is computed using collisions between velocity classes selected randomly using a Monte Carlo method. Arbitrary post-collision velocities are mapped back onto the grid using a projection scheme which conserves mass, momentum, and energy. In addition, a variance reduction scheme is implemented to decrease noise and further reduce computational effort. The convection part of the equation is computed using first order upwind finite differences. We apply this discrete velocity scheme to the 2D lid-driven square cavity flow problem with Ar as the fluid medium and explore the effect of the additional flexibility available in this quasi-particle based stochastic method on the accuracy and noise level in the solutions obtained.
Henn, J D; Bockor, L; Borille, R; Coldebella, A; Ribeiro, A M L; Kessler, A M
2015-09-01
The objective of this study was to determine the equation parameters of carbon (i.e., C) flow curves and to estimate C flow and carbon dioxide (i.e., CO2) emissions from the production of 1- to 49-day-old broilers from different genetic strains. In total, 384 1-day-old chicks were used, distributed into 4 groups: high-performance males (Cobb-M) and females (Cobb-F), and intermediate-performance males (C44-M) and females (C44-F), with 6 replicates/treatment according to a completely randomized study design. Carbon intake and retention were calculated based on diet and body C composition, and expired C was stoichiometrically estimated as digestible C intake-C retention-C in the urine. Litter C emission was estimated as initial litter C+C in the excreta-final litter C. Carbon flow curves were determined fitting data by nonlinear regression using the Gompertz function. Expired CO2 was calculated based on expired C. The applied nonlinear model presented goodness-of-fit for all responses (R2>0.99). Carbon dioxide production was highly correlated with growth rate. At 42 d age, CO2 expiration (g/bird) was 3,384.4 for Cobb-M, 2,947.9 for Cobb-F, 2,512.5 for C44-M, and 2185.1 for C44-F. Age also significantly affected CO2 production: to achieve 2.0 kg BW, CO2 expiration (g/bird) was 1,794.3 for Cobb-M, 2,016.5 for Cobb-F, 2617.7 for C44-M, and 3,092.3 for C44-F. The obtained equations present high predictability to estimate individual CO2 emissions in strains of Cobb and C44 broilers of any weight, or age, reared between 1 and 49 d age. © 2015 Poultry Science Association Inc.
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
Integral equation methods for Stokes flow and isotropic elasticity in the plane
International Nuclear Information System (INIS)
Greengard, L.; Kropinski, M.C.; Mayo, A.
1996-01-01
We present a class of integral equation methods for the solution of biharmonic boundary value problems, with applications to two-dimensional Stokes flow and isotropic elasticity. The domains may be multiply-connected and finite, infinite or semi-infinite in extent. Our analytic formulation is based on complex variables, and our fast multipole-based iterative solution procedure requires O(N) operations, where N is the number of nodes in the discretization of the boundary. The performance of the methods is illustrated with several large-scale numerical examples. 25 refs., 7 figs., 1 tab
Ohkitani, Koji
2015-09-01
We consider incompressible Euler flows in terms of the stream function in two dimensions and the vector potential in three dimensions. We pay special attention to the case with singular distributions of the vorticity, e.g., point vortices in two dimensions. An explicit equation governing the velocity potentials is derived in two steps. (i) Starting from the equation for the stream function [Ohkitani, Nonlinearity 21, T255 (2009)NONLE50951-771510.1088/0951-7715/21/12/T02], which is valid for smooth flows as well, we derive an equation for the complex velocity potential. (ii) Taking a real part of this equation, we find a dynamical equation for the velocity potential, which may be regarded as a refinement of Bernoulli theorem. In three-dimensional incompressible flows, we first derive dynamical equations for the vector potentials which are valid for smooth fields and then recast them in hypercomplex form. The equation for the velocity potential is identified as its real part and is valid, for example, flows with vortex layers. As an application, the Kelvin-Helmholtz problem has been worked out on the basis the current formalism. A connection to the Navier-Stokes regularity problem is addressed as a physical application of the equations for the vector potentials for smooth fields.
Tokunaga, Tetsu K.; Shen, Weijun; Wan, Jiamin; Kim, Yongman; Cihan, Abdullah; Zhang, Yingqi; Finsterle, Stefan
2017-11-01
Large volumes of water are used for hydraulic fracturing of low permeability shale reservoirs to stimulate gas production, with most of the water remaining unrecovered and distributed in a poorly understood manner within stimulated regions. Because water partitioning into shale pores controls gas release, we measured the water saturation dependence on relative humidity (rh) and capillary pressure (Pc) for imbibition (adsorption) as well as drainage (desorption) on samples of Woodford Shale. Experiments and modeling of water vapor adsorption into shale laminae at rh = 0.31 demonstrated that long times are needed to characterize equilibrium in larger (5 mm thick) pieces of shales, and yielded effective diffusion coefficients from 9 × 10-9 to 3 × 10-8 m2 s-1, similar in magnitude to the literature values for typical low porosity and low permeability rocks. Most of the experiments, conducted at 50°C on crushed shale grains in order to facilitate rapid equilibration, showed significant saturation hysteresis, and that very large Pc (˜1 MPa) are required to drain the shales. These results quantify the severity of the water blocking problem, and suggest that gas production from unconventional reservoirs is largely associated with stimulated regions that have had little or no exposure to injected water. Gravity drainage of water from fractures residing above horizontal wells reconciles gas production in the presence of largely unrecovered injected water, and is discussed in the broader context of unsaturated flow in fractures.
First-order flow equations for extremal and non-extremal black holes
International Nuclear Information System (INIS)
Perz, Jan; Vercnocke, Bert; Smyth, Paul; Van Riet, Thomas
2009-01-01
We derive a general form of first-order flow equations for extremal and non-extremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squares a la Bogomol'nyi, we identify the function governing the first-order gradient flow, the 'generalised superpotential', which reduces to the 'fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we present the condition for the existence of a generalised superpotential. We provide examples to illustrate the formalism in four and five spacetime dimensions.
Simulating variable-density flows with time-consistent integration of Navier-Stokes equations
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.
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
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.
The linearized pressure Poisson equation for global instability analysis of incompressible flows
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.
Further Development and Application of GEOFRAC-FLOW to a Geothermal Reservoir
Energy Technology Data Exchange (ETDEWEB)
Einstein, Herbert [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Vecchiarelli, Alessandra [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2014-05-01
GEOFRAC is a three-dimensional, geology-based, geometric-mechanical, hierarchical, stochastic model of natural rock fracture systems. The main characteristics of GEOFRAC are its use of statistical input representing fracture patterns in the field in form of the fracture intensity P32 (fracture area per volume) and the best estimate fracture size E(A). This information can be obtained from boreholes or scanlines on the surface, on the one hand, and from window sampling of fracture traces on the other hand. In the context of this project, “Recovery Act - Decision Aids for Geothermal Systems”, GEOFRAC was further developed into GEOFRAC-FLOW as has been reported in the reports, “Decision Aids for Geothermal Systems - Fracture Pattern Modelling” and “Decision Aids for Geothermal Systems - Fracture Flow Modeling”. GEOFRAC-FLOW allows one to determine preferred, interconnected fracture paths and the flow through them.
Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation
Leonard, Anthony
2017-11-01
Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions J+ 1 / 3 ,J- 1 / 3 ,J1 , and Y1 and their modified counterparts for any given wave speed c = ω /kx and k⊥ ,(k⊥2 =kx2 +kz2) . Of particular note to be discussed is a sequence i = 1 , 2 , . . . of homogeneous inviscid solutions with complex k⊥ i for each speed c, (0 < c <=Umax), in the downstream direction. These solutions for the velocity component normal to the wall v are localized in the plane parallel to the wall. In addition, for limited range of negative c, (- c * <= c <= 0) , we have found upstream-traveling homogeneous solutions with real k⊥(c) . In both cases the solutions for v serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall ωy.
International Nuclear Information System (INIS)
Bae, Byoung-Uhn; Park, Goon-Cherl; Yoon, Han-Young; Euh, Dong-Jin; Song, Chul-Hwa
2008-01-01
For a multidimensional analysis of a two-phase flow, a computational fluid dynamics (CFD) code was developed with the implementation of an interfacial area transport equation that is beneficial for dynamically estimating the interfacial area concentration (IAC). The code structure was based on the two-fluid model and the Simplified Marker and Cell (SMAC) algorithm. The SAMC algorithm was extended to a two-phase flow simulation with a phase change. Various well-known constitutive models regarding boiling, condensation, and nondrag forces have been implemented into the code. To verify the robustness of the code to predict wall boiling and void propagation phenomena, a subcooled boiling test in a vertical annulus channel was analyzed as a benchmark problem. As the analysis results, a model for bubble departure diameter on the heated wall was identified as the principal factor for subcooled boiling phenomena, and the limitation of the current departure diameter models under a low-pressure condition resulted in a deviation of the void fraction and IAC when compared with the results of the experiment. It is necessary that the research on the interfacial area transport equation focuses on modeling reliable source terms for the boiling mechanism as a future work. (author)
Infeld, E.; Rowlands, G.; Skorupski, A. A.
2014-10-01
We find a further class of exact solutions to the Lighthill-Whitham- Richards-Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either 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 not only that of Rowlands et al (2013 J. Phys. A: Math. Theor. 46 365202 (part I)) but also the two-soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates, etc, abound in the literature. However, we present an exact solution. These are few and far between, other than found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.
Directory of Open Access Journals (Sweden)
Abdulrauf Rasheed Adebayo
2017-01-01
Full Text Available The effect of gravity on vertical flow and fluids saturation, especially when flow is against gravity, is not often a subject of interest to researchers. This is because of the notion that flow in subsurface formations is usually in horizontal direction and that vertical flow is impossible or marginal because of the impermeable shales or silts overlying them. The density difference between two fluids (usually oil and water flowing in the porous media is also normally negligible; hence gravity influence is neglected. Capillarity is also often avoided in relative permeability measurements in order to satisfy some flow equations. These notions have guided most laboratory core flooding experiments to be conducted in horizontal flow orientation, and the data obtained are as good as what the experiments tend to mimic. However, gravity effect plays a major role in gas liquid systems such as CO2 sequestration and some types of enhanced oil recovery techniques, particularly those involving gases, where large density difference exists between the fluid pair. In such cases, laboratory experiments conducted to derive relative permeability curves should take into consideration gravity effects and capillarity. Previous studies attribute directional dependence of relative permeability and residual saturations to rock anisotropy. It is shown in this study that rock permeability, residual saturation, and relative permeability depend on the interplay between gravity, capillarity, and viscous forces and also the direction of fluid flow even when the rock is isotropic. Rock samples representing different lithology and wide range of permeabilities were investigated through unsteady-state experiments covering drainage and imbibition in both vertical and horizontal flow directions. The experiments were performed at very low flow rates to capture capillarity. The results obtained showed that, for each homogeneous rock and for the same flow path along the core length
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.
Brand, Andreas; Noss, Christian
2017-05-01
A bistatic high-resolution acoustic profiler was used in order to characterize the lowermost boundary layer of a run of the river reservoir. The profiler allows determining the statistics of the three-dimensional flow field at a single point (sweet spot) as well as the measurement of the time averaged flow velocity profiles at 1 mm resolution around the sweet spot. Therefore, in addition to the flow statistics provided by single point acoustic Doppler profilers, mixing coefficients as well as production of turbulent kinetic energy can be calculated using a single device. Fitting of semiempirical relations to observed cospectra allowed eliminating artifacts as they result from coordinate system rotation during calculation of Reynolds stress profiles at millimeter resolution. While most parameters showed characteristics of a constant stress layer, length scales indicated anisotropy of the turbulent flow. Under these anisotropic near wall conditions, we found that the use of the commonly accepted Kolmogorov constants for the determination of dissipation rates using the inertial dissipation method is not valid any more. Instead, these constants vary with distance from the sediment water interface. We provide evidence that coefficients determined by numerical simulations are the appropriate choice also in field applications. In addition we resolved the viscous boundary layer close to the sediment-water interface in high resolution (1 mm) profiles and identified a double logarithmic layer above 1.5 cm at one location. The discrepancy of the scales as well as the double logarithmic layer suggests the existence of roughness elements upstream of the measurement sites.
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)
Directory of Open Access Journals (Sweden)
M. Rehan Saleem
2018-03-01
Full Text Available 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. Keywords: Two-phase compressible flows, Non-conservative system, Shock discontinuities, Discontinuous Galerkin method, Central scheme
Time evolution of many-body localized systems with the flow equation approach
Thomson, S. J.; Schiró, M.
2018-02-01
The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling this interesting regime, here we develop a semianalytical flow equation approach to study the time evolution of strongly disordered interacting quantum systems. We apply this technique to a prototype model of interacting spinless fermions in a random on-site potential in both one and two dimensions. Key results include (i) an explicit construction of the local integrals of motion that characterize the many-body localized phase in one dimension, ultimately connecting the microscopic model to phenomenological descriptions, (ii) calculation of these quantities in two dimensions, and (iii) an investigation of the real-time dynamics in the localized phase which reveals the crucial role of l -bit interactions for enhancing dephasing and relaxation.
Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe
2018-02-01
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.
Converging shock flows for a Mie-Grüneisen equation of state
Ramsey, Scott D.; Schmidt, Emma M.; Boyd, Zachary M.; Lilieholm, Jennifer F.; Baty, Roy S.
2018-04-01
Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. The remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.
Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow
Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.
2018-03-01
We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0Navier-Stokes solution and the proposed expansion vanishes as the viscosity tends to zero in L^2(Ω ) uniformly in time, and remains bounded independently of viscosity in the space L^2([0,T];H^1(Ω )) . We make this construction both for a 3D channel domain and a smooth domain with a curved boundary. The zero-viscosity limit for LNSE, that is, the convergence of the LNSE solution to the solution of the linearized Euler equations around the same profile when viscosity vanishes, then naturally follows from the validity of this asymptotic expansion. This article generalizes and improves earlier works, such as Temam and Wang (Indiana Univ Math J 45(3):863-916, 1996), Xin and Yanagisawa (Commun Pure Appl Math 52(4):479-541, 1999), and Gie (Commun Math Sci 12(2):383-400, 2014).
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.
Li-hui, Zheng; Xiao-qing, He; Li-xia, Fu; Xiang-chun, Wang
2009-02-01
Water-based micro-bubble drilling fluid, which is used to exploit depleted reservoirs, is a complicated multiphase flow system that is composed of gas, water, oil, polymer, surfactants and solids. The gas phase is separate from bulk water by two layers and three membranes. They are "surface tension reducing membrane", "high viscosity layer", "high viscosity fixing membrane", "compatibility enhancing membrane" and "concentration transition layer of liner high polymer (LHP) & surfactants" from every gas phase centre to the bulk water. "Surface tension reducing membrane", "high viscosity layer" and "high viscosity fixing membrane" bond closely to pack air forming "air-bag", "compatibility enhancing membrane" and "concentration transition layer of LHP & surfactants" absorb outside "air-bag" to form "incompact zone". From another point of view, "air-bag" and "incompact zone" compose micro-bubble. Dynamic changes of "incompact zone" enable micro-bubble to exist lonely or aggregate together, and lead the whole fluid, which can wet both hydrophilic and hydrophobic surface, to possess very high viscosity at an extremely low shear rate but to possess good fluidity at a higher shear rate. When the water-based micro-bubble drilling fluid encounters leakage zones, it will automatically regulate the sizes and shapes of the bubbles according to the slot width of fracture, the height of cavern as well as the aperture of openings, or seal them by making use of high viscosity of the system at a very low shear rate. Measurements of the rheological parameters indicate that water-based micro-bubble drilling fluid has very high plastic viscosity, yield point, initial gel, final gel and high ratio of yield point and plastic viscosity. All of these properties make the multiphase flow system meet the requirements of petroleum drilling industry. Research on interface between gas and bulk water of this multiphase flow system can provide us with information of synthesizing effective agents to
Spectral SP: A New Approach to Mapping Reservoir Flow and Permeability
Energy Technology Data Exchange (ETDEWEB)
Thomas, Donald M. [Univ. of Hawaii, Honolulu, HI (United States). Hawaii Inst. of Geophysics; Lienert, Barry R. [Univ. of Hawaii, Honolulu, HI (United States). Hawaii Inst. of Geophysics; Wallin, Erin L. [Univ. of Hawaii, Honolulu, HI (United States); Gasperikova, Erika [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2014-05-27
Our objectives for the current project were to develop an innovative inversion and analysis procedure for magnetotelluric field data and time variable self-potentials that will enable us to map not only the subsurface resistivity structure of a geothermal prospect but to also delineate the permeability distribution within the field. Hence, the ultimate objective were to provide better targeting information for exploratory and development drilling of a geothermal prospect. Field data were collected and analyzed from the Kilauea Summit, Kilauea East Rift Zone, and the Humuula Saddle between Mauna Loa and Mauna Kea volcanoes. All of these areas were known or suspected to have geothermal activity of varying intensities. Our results provided evidence for significant long-term coordinated changes in spontaneous potential that could be associated with subsurface flows, significant interferences were encountered that arose from surface environmental changes (rainfall, temperature) that rendered it nearly impossible to unequivocally distinguish between deep fluid flow changes and environmental effects. Further, the analysis of the inferred spontaneous potential changes in the context of depth of the signals, and hence, permeability horizons, were unable to be completed in the time available.
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.
A sensitivity analysis of the mass balance equation terms in subcooled flow boiling
International Nuclear Information System (INIS)
Braz Filho, Francisco A.; Caldeira, Alexandre D.; Borges, Eduardo M.
2013-01-01
In a heated vertical channel, the subcooled flow boiling occurs when the fluid temperature reaches the saturation point, actually a small overheating, near the channel wall while the bulk fluid temperature is below this point. In this case, vapor bubbles are generated along the channel resulting in a significant increase in the heat flux between the wall and the fluid. This study is particularly important to the thermal-hydraulics analysis of Pressurized Water Reactors (PWRs). The computational fluid dynamics software FLUENT uses the Eulerian multiphase model to analyze the subcooled flow boiling. In a previous paper, the comparison of the FLUENT results with experimental data for the void fraction presented a good agreement, both at the beginning of boiling as in nucleate boiling at the end of the channel. In the region between these two points the comparison with experimental data was not so good. Thus, a sensitivity analysis of the mass balance equation terms, steam production and condensation, was performed. Factors applied to the terms mentioned above can improve the agreement of the FLUENT results to the experimental data. Void fraction calculations show satisfactory results in relation to the experimental data in pressures values of 15, 30 and 45 bars. (author)
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
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.
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.
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.
Hu, Fang Q; Pizzo, Michelle E; Nark, Douglas M
2017-12-01
It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source or sink points on solid surfaces. An alternative solid wall boundary condition, termed zero energy flux boundary condition, is proposed that conserves the acoustic energy and a time domain boundary integral equation is derived. Furthermore, stabilization of the integral equation by Burton-Miller type reformulation is presented. The stability is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the current formulation.
Flow equation of quantum Einstein gravity in a higher-derivative truncation
International Nuclear Information System (INIS)
Lauscher, O.; Reuter, M.
2002-01-01
Motivated by recent evidence indicating that quantum Einstein gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term (R 2 ). The beta functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the R 2 coupling are computed explicitly. The fixed point properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian fixed point predicted by the latter is found to generalize to a fixed point on the enlarged theory space. In order to test the reliability of the R 2 truncation near this fixed point we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a surprisingly high precision. Because of the consistency of the results it appears increasingly unlikely that the non-Gaussian fixed point is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and ''asymptotically safe.'' We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the R 2 truncation, the investigation of the fixed point is not afflicted with this problem. Also the Gaussian fixed point of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding fixed point on the enlarged theory space
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
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.
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
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.
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
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
African Journals Online (AJOL)
Calls have been made to the government through various media to assist its populace in combating this nagging problem. It was concluded that sediment maximum accumulation is experienced in reservoir during the periods of maximum flow. Keywords: reservoir model, siltation, sediment, catchment, sediment transport. 1.
On the Riemann solutions of the balance equations for steam and water flow in a porous medium
Lambert, W.; Marchesin, D.; Bruining, J.
2005-01-01
Conservation laws have been used to model a variety of physical phenomena and therefore the theory for this class of equations is well developed. However, in many problems, such as transport of hot fluids and gases undergoing mass transfer, balance laws are required to describe the flow. As an
Directory of Open Access Journals (Sweden)
Ahmed M. Elsayed
2013-01-01
Full Text Available Film cooling is vital to gas turbine blades to protect them from high temperatures and hence high thermal stresses. In the current work, optimization of film cooling parameters on a flat plate is investigated numerically. The effect of film cooling parameters such as inlet velocity direction, lateral and forward diffusion angles, blowing ratio, and streamwise angle on the cooling effectiveness is studied, and optimum cooling parameters are selected. The numerical simulation of the coolant flow through flat plate hole system is carried out using the “CFDRC package” coupled with the optimization algorithm “simplex” to maximize overall film cooling effectiveness. Unstructured finite volume technique is used to solve the steady, three-dimensional and compressible Navier-Stokes equations. The results are compared with the published numerical and experimental data of a cylindrically round-simple hole, and the results show good agreement. In addition, the results indicate that the average overall film cooling effectiveness is enhanced by decreasing the streamwise angle for high blowing ratio and by increasing the lateral and forward diffusion angles. Optimum geometry of the cooling hole on a flat plate is determined. In addition, numerical simulations of film cooling on actual turbine blade are performed using the flat plate optimal hole geometry.
Shi, Y.; Zhu, B.
2010-12-01
Coulomb failure assumption is used to evaluate the earthquake trigger, and pore pressures play an important part in triggering the earthquake slip. Based on the parallel CPU computation and GPU visualization technology, the relationship between the pore stress accumulation on Zipingpu reservoir and the trigging and propagation mechanism of the Longmenshan coseismic fault slip have been studied on different length scales [Scale I: 30.976E_31.105E, 103.45N_103.577N;Scale II: 30.7E_31.3E, 103.05N_103.76N; Scale III: 29E_33E, 101N_105N]. Longmenshan fault slip of 2008 Wenchuan Ms 8.0 earthquake is obtained by GPS & InSAR inversion technique, it composed with two slips and cross-wised Zipingpu reservoir zone. The relationship between the pore stress accumulation of Zipingpu reservoir and the trigging and propagation of the Longmenshan coseismic fault slip because very important for it direction effect the dynamic real-time security evaluation and monitor of Zipingpu key water control project. Zipingpu reservoir is located on the upstream of Minjiang river, the maximum reservoir storage capacity is 11×109 m3, the adjustable reservoir storage capacity is 8×109 m3, the normal impounded level is 877m, the dam top altitude is 894m and the dam bottom altitude is 728m.The key water control project began Mar.3.2001, stop flow time is Nov.1.2002, storage time is Dec.1.2004 and completed at Dec.1.2006. The total pore stress accumulation time before Wenchuan Ms 8.0 Earthquake (May.12.2008) is 3~4 years. In our physical model, we use the 15000 time steps (10 ts/day) to describe the effect of pore stress of reservoir to the Longmenshan fault slip. From the GPS&InSAR inversion technology, the Longmenshan earthquake fault slip is divided into 673 parts. The results show that the relationship between extended pore strain and stress on Zipingpu reservoir and Longmenshan coseismic fault slip on Scale I under 20000ts. The pore stress accumulation value level is 0.3Mp. The relationship
Pereira, F.; Girish, T. E.
2006-11-01
We have reported earlier some new results related to the seasonal and solar cycle changes in the north-south component of IMF (Bz) observed near 1 A.U. A relationship between geomagnetic activity and non-radial solar wind flows were reported recently. In this connection, we are planning some studies for IHY 2007. We propose to identify non-radial flow structures in the interplanetary medium using IPS observations and predict the associated IMF Bz structures. The effect of geomagnetic storms near magnetic equator associated with non-radial solar wind flows will be studied using magnetometer observations in Trivandrum.
A Note on Two-Equation Closure Modelling of Canopy Flow
DEFF Research Database (Denmark)
Sogachev, Andrey
2009-01-01
The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric...
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 (Saline (>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.
Hami, K.; Zeroual, I.
2017-12-01
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.
Directory of Open Access Journals (Sweden)
Donald P Bernstein
2010-01-01
, and more precisely, the electro-dynamic equivalent of peak aortic reduced average blood acceleration (PARABA, d
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.
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.
An analytical solution of the Navier-Stokes equation for internal flows
International Nuclear Information System (INIS)
Lyberg, Mats D; Tryggeson, Henrik
2007-01-01
This paper derives a solution to the Navier-Stokes equation by considering vorticity generated at system boundaries. The result is an explicit expression for the velocity. The Navier-Stokes equation is reformulated as a divergence and integrated, giving a tensor equation that splits into a symmetric and a skew-symmetric part. One equation gives an algebraic system of quadratic equations involving velocity components. A system of nonlinear partial differential equations is reduced to algebra. The velocity is then explicitly calculated and shown to depend on boundary conditions only. This removes the need to solve the Navier-Stokes equation by a 3D numerical computation, replacing it by computation of 2D surface integrals over the boundary. (fast track communication)
Staley, Dennis M.; Negri, Jacquelyn A.; Kean, Jason W.; Laber, Jayme L.; Tillery, Anne C.; Youberg, Ann M.
2016-06-30
Wildfire can significantly alter the hydrologic response of a watershed to the extent that even modest rainstorms can generate dangerous flash floods and debris flows. To reduce public exposure to hazard, the U.S. Geological Survey produces post-fire debris-flow hazard assessments for select fires in the western United States. We use publicly available geospatial data describing basin morphology, burn severity, soil properties, and rainfall characteristics to estimate the statistical likelihood that debris flows will occur in response to a storm of a given rainfall intensity. Using an empirical database and refined geospatial analysis methods, we defined new equations for the prediction of debris-flow likelihood using logistic regression methods. We showed that the new logistic regression model outperformed previous models used to predict debris-flow likelihood.
NMPC for Oil Reservoir Production Optimization
DEFF Research Database (Denmark)
Völcker, Carsten; Jørgensen, John Bagterp; Thomsen, Per Grove
2011-01-01
In this paper, we use nonlinear model predictive control (NMPC) to maximize secondary oil recovery from an oil reservoir by controlling two-phase subsurface porous flow using adjustable down-hole control valves. The resulting optimal control problem is nonlinear and large-scale. We solve...... this problem numerically using a single shooting sequential quadratic programming (SQP) based optimization method. Explicit singly diagonally implicit Runge-Kutta (ESDIRK) methods are used for integration of the stiff system of differential equations describing the two-phase flow, and the adjoint method...
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
Directory of Open Access Journals (Sweden)
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
Paniconi, C.; Troch, P.A.A.; Loon, van E.E.; Hilberts, A.G.J.
2003-01-01
The Boussinesq equation for subsurface flow in an idealized sloping aquifer of unit width has recently been extended to hillslopes of arbitrary geometry by incorporating the hillslope width function w(x) into the governing equation, where x is the flow distance along the length of the hillslope [
Energy Technology Data Exchange (ETDEWEB)
Ray A. Berry; Richard Saurel; Tamara Grimmett
2009-07-01
Typically, multiphase modeling begins with an averaged (or homogenized) system of partial differential equations (traditionally ill-posed) then discretizes this system to form a numerical scheme. Assuming that the ill-posedness problem is avoided by using a well-posed formulation such as the seven-equation model, this presents problems for the numerical approximation of non-conservative terms at discontinuities (interfaces, shocks) as well as unwieldy treatment of fluxes with seven waves. To solve interface problems without conservation errors and to avoid this questionable determination of average variables and the numerical approximation of the non-conservative terms associated with 2 velocity mixture flows we employ a new homogenization method known as the Discrete Equations Method (DEM). Contrary to conventional methods, the averaged equations for the mixture are not used, and this method directly obtains a (well-posed) discrete equation system from the single-phase system to produce a numerical scheme which accurately computes fluxes for arbitrary numbers of phases and solves non-conservative products. The method effectively uses a sequence of single phase Riemann equation solves. Phase interactions are accounted for by Riemann solvers at each interface. Flow topology can change with changing expressions for the fluxes. Non-conservative terms are correctly approximated. Some of the closure relations missing from the traditional approach are automatically obtained. Lastly, we can often times identify the continuous equation system, resulting from taking the continuous limit with weak wave assumptions, of the discrete equations. This can be very useful from a theoretical standpoint. As a first step toward implict integration of the DEM method in multidimensions, in this paper we construct a DEM model for the flow of two compressible phases in 1-D ducts of spatially varying cross-section to test this approach. To relieve time step size restrictions due to
Jung, Hojung; Singh, Gurpreet; Espinoza, D. Nicolas; Wheeler, Mary F.
2018-02-01
Subsurface CO2 injection and storage alters formation pressure. Changes of pore pressure may result in fault reactivation and hydraulic fracturing if the pressure exceeds the corresponding thresholds. Most simulation models predict such thresholds utilizing relatively homogeneous reservoir rock models and do not account for CO2 dissolution in the brine phase to calculate pore pressure evolution. This study presents an estimation of reservoir capacity in terms of allowable injection volume and rate utilizing the Frio CO2 injection site in the coast of the Gulf of Mexico as a case study. The work includes laboratory core testing, well-logging data analyses, and reservoir numerical simulation. We built a fine-scale reservoir model of the Frio pilot test in our in-house reservoir simulator IPARS (Integrated Parallel Accurate Reservoir Simulator). We first performed history matching of the pressure transient data of the Frio pilot test, and then used this history-matched reservoir model to investigate the effect of the CO2 dissolution into brine and predict the implications of larger CO2 injection volumes. Our simulation results -including CO2 dissolution- exhibited 33% lower pressure build-up relative to the simulation excluding dissolution. Capillary heterogeneity helps spread the CO2 plume and facilitate early breakthrough. Formation expansivity helps alleviate pore pressure build-up. Simulation results suggest that the injection schedule adopted during the actual pilot test very likely did not affect the mechanical integrity of the storage complex. Fault reactivation requires injection volumes of at least about sixty times larger than the actual injected volume at the same injection rate. Hydraulic fracturing necessitates much larger injection rates than the ones used in the Frio pilot test. Tested rock samples exhibit ductile deformation at in-situ effective stresses. Hence, we do not expect an increase of fault permeability in the Frio sand even in the presence of
Well testing in gas hydrate reservoirs
Kome, Melvin Njumbe
2015-01-01
Reservoir testing and analysis are fundamental tools in understanding reservoir hydraulics and hence forecasting reservoir responses. The quality of the analysis is very dependent on the conceptual model used in investigating the responses under different flowing conditions. The use of reservoir testing in the characterization and derivation of reservoir parameters is widely established, especially in conventional oil and gas reservoirs. However, with depleting conventional reserves, the ...
Efficient Computation of N-S Equation with Free Surface Flow Around an ACV on ShirazUCFD Grid
Sheikhalishahi, Seyyed Mehdi; Alizadehrad, Davood; Dastghaibyfard, Gholamhossein; Alishahi, Mohammad Mehdi; Nikseresht, Amir Hossein
This paper presents the application of a parallel high accuracy simulation code for Incompressible Navier-Stokes solution with free surface flow around an ACV (Air Cushion Vehicle) on ShirazUCFD Grid environment. The parallel finite volume code is developed for incompressible Navier-Stokes solver on general curvilinear coordinates system for modeling free surface flows. A single set of dimensionless equations is derived to handle both liquid and air phases in viscous incompressible free surface flow in general curvilinear coordinates. The volume of fluid (VOF) method with lagrangian propagation in computational domain for modeling the free surface flow is implemented. The parallelization approach uses a domain decomposition method for the subdivision of the numerical grid, the SPMD program model and MPICH-G2 as the message passing environment is used to obtain a portable application.
Wood, Brian; He, Xiaoliang; Apte, Sourabh
2017-11-01
Turbulent flows through porous media are encountered in a number of natural and engineered systems. Many attempts to close the Navier-Stokes equation for such type of flow have been made, for example using RANS models and double averaging. On the other hand, Whitaker (1996) applied volume averaging theorem to close the macroscopic N-S equation for low Re flow. In this work, the volume averaging theory is extended into the turbulent flow regime to posit a relationship between the macroscale velocities and the spatial velocity statistics in terms of the spatial averaged velocity only. Rather than developing a Reynolds stress model, we propose a simple algebraic closure, consistent with generalized effective viscosity models (Pope 1975), to represent the spatial fluctuating velocity and pressure respectively. The coefficients (one 1st order, two 2nd order and one 3rd order tensor) of the linear functions depend on averaged velocity and gradient. With the data set from DNS, performed with inertial and turbulent flows (pore Re of 300, 500 and 1000) through a periodic face centered cubic (FCC) unit cell, all the unknown coefficients can be computed and the closure is complete. The macroscopic quantity calculated from the averaging is then compared with DNS data to verify the upscaling. NSF Project Numbers 1336983, 1133363.
Clark, R. W.; James, R. M.
1981-01-01
A new approach to the solution of matrix equations resulting from integral equations is presented and applied to the solution of two-dimensional Neumann problems describing the inviscid, incompressible flow past an airfoil. The problem is reformulated in terms of a preselected set of mode functions giving an equivalent matrix equation to be solved for the mode-function expansion coefficients. Because of the inherent smoothness of the original problem, the coefficient problem can be solved approximately without significantly affecting the accuracy of the final solution. Very promising two-dimensional results are obtained and the extension of the method to three-dimensional problems is investigated. On the basis of these results it is shown that the computing time for the matrix solution for a large three-dimensional panel method calculation could be reduced by an order of magnitude compared with that required for a direct solution.
Directory of Open Access Journals (Sweden)
Pothanna N.
2017-12-01
Full Text Available In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.
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)
Cheng, H. K.; Wong, Eric Y.; Dogra, V. K.
1991-01-01
Grad's thirteen-moment equations are applied to the flow behind a bow shock under the formalism of a thin shock layer. Comparison of this version of the theory with Direct Simulation Monte Carlo calculations of flows about a flat plate at finite attack angle has lent support to the approach as a useful extension of the continuum model for studying translational nonequilibrium in the shock layer. This paper reassesses the physical basis and limitations of the development with additional calculations and comparisons. The streamline correlation principle, which allows transformation of the 13-moment based system to one based on the Navier-Stokes equations, is extended to a three-dimensional formulation. The development yields a strip theory for planar lifting surfaces at finite incidences. Examples reveal that the lift-to-drag ratio is little influenced by planform geometry and varies with altitudes according to a 'bridging function' determined by correlated two-dimensional calculations.
Asiri, Sharefa M.
2017-10-19
In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations of blood mass density. The method is described and its performance is assessed through some numerical simulations. The robustness of the method in presence of noise is also studied.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
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
Directory of Open Access Journals (Sweden)
ISAM M. Mahammed
2012-03-01
Full Text Available The objective of this research is to evaluate Method of Line (MOL used for solution of water flow equations through porous media using MATLAB package functions for solution of ordinary differential equations ODE,s , instead of writing long programs codes. sink & source term to MOL model were included. Then Comparing MOL model with another model that uses finite element method in solving water flow equations (FEM in one dimensional flow using computer program code in FORTRAN. Two cases were examined for evaluation and comparison of these two models. Firstly, infiltration phenomena using sandy soil was studied with the same parameter for both models. Results show that there is a divergence between the two models along time of 60 minutes of infiltration. Changes of moisture content with soil depth were sharp with FEM model. Second case, data of the volume of water content for wheat field where used taking irrigation and evaporation into account, along the growth period of wheat crop and different depths up to 100 cm. Results show that output of FEM model has high degree of agreement with the measured data for all depths and along all period of growth. Data given by MOL model were less in values than measured data for all depths and along all period of wheat growth time.
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.
Nelson, Kirk E.; Ginn, Timothy R.
2011-05-01
A new equation for the collector efficiency (η) of the colloid filtration theory (CFT) is developed via nonlinear regression on the numerical data generated by a large number of Lagrangian simulations conducted in Happel's sphere-in-cell porous media model over a wide range of environmentally relevant conditions. The new equation expands the range of CFT's applicability in the natural subsurface primarily by accommodating departures from power law dependence of η on the Peclet and gravity numbers, a necessary but as of yet unavailable feature for applying CFT to large-scale field transport (e.g., of nanoparticles, radionuclides, or genetically modified organisms) under low groundwater velocity conditions. The new equation also departs from prior equations for colloids in the nanoparticle size range at all fluid velocities. These departures are particularly relevant to subsurface colloid and colloid-facilitated transport where low permeabilities and/or hydraulic gradients lead to low groundwater velocities and/or to nanoparticle fate and transport in porous media in general. We also note the importance of consistency in the conceptualization of particle flux through the single collector model on which most η equations are based for the purpose of attaining a mechanistic understanding of the transport and attachment steps of deposition. A lack of sufficient data for small particles and low velocities warrants further experiments to draw more definitive and comprehensive conclusions regarding the most significant discrepancies between the available equations.
A review of reservoir desiltation
DEFF Research Database (Denmark)
Brandt, Anders
2000-01-01
physical geography, hydrology, desilation efficiency, reservoir flushing, density-current venting, sediment slucing, erosion pattern, downstream effects, flow characteristics, sedimentation......physical geography, hydrology, desilation efficiency, reservoir flushing, density-current venting, sediment slucing, erosion pattern, downstream effects, flow characteristics, sedimentation...
Energy Technology Data Exchange (ETDEWEB)
Fialova, M.; Fuerst, J.; Horak, J.; Kozel, K. [Czech Technical Univ., Faculty of Mechanical Engineering, Dept. of Technical Mathematics, Prague (Czech Republic)
1997-12-31
The work deals with numerical solution of 2D and 3D transonic flows using mathematical models of Euler and Navier-Stokes equations. For inviscid flows with a shock wave we tested modern TVD upwind and central methods. For computations of 2D and 3D compressible viscous laminar flows multistage Runge-Kutta methods were used. (orig.)
Bout, B.
2018-04-09
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 hydrological catchment model. We test the approach on the 4 km2 Scaletta catchment, North-Eastern Sicily, where the 1-10-2009 convective storm caused debris flooding after 395 shallow landslides. Validation is done based on the landslide inventory and photographic evidence from the days after the event. Results show that the model can recreate the impact of both shallow landslides, debris flow runout, and debris floods with acceptable accuracy (91 percent inventory overlap with a 0.22 Cohens Kappa). General patterns in slope failure and runout are well-predicted, leading to a fully physically based prediction of rainfall induced debris flood behavior in the downstream areas, such as the creation of a debris fan at the coastal outlet.
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)
Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods
Boronin, Ivan; Shevlyakov, Andrey
2018-03-01
Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.
Energy Technology Data Exchange (ETDEWEB)
Ramirez Sabag, Jetzabeth
1988-02-01
The proposed model has been developed to study the flow of tracers through naturally fractured geothermal reservoirs. The idealized system of the reservoir is made up of two regions: A movable region, where diffusion and convection mechanisms are present and a stagnant or immovable region where the diffusion and adsorption mechanisms are considered: in both regions the loss of mass by radioactive decay is considered. The solutions of the basic flow equations are in the Laplace space and for its numerical inversion the Stehfest algorithm was used. In spite of the numerical dispersion that these solutions involve, a well defined tendency to infer the system behavior under different flow conditions was found. It was found that, for practical purposes, the size of the matrix blocks does not have an influence on the concentration response, and the solution is reduced to the one presented by Tang and associates. Under these conditions, the system behavior can be described by two non-dimensional parameters: The Peclet number in fractures, P{sub e1}, and a parameter. The tracer response for the peak solution was also derived. An analytical solution limit was found for the case in which {alpha} tends to zero, which corresponds to the case of a homogenous system. It was verified that this limit solution is valid, for {alpha}<0.01. For the case of continuous injection, this solution is reduced to the one presented by Coasts and Smith. For the peak solution, it was found that the irruption time corresponding to the maximum concentration is directly related to the non-dimensional group. Therefore, it is possible to obtain the value of P{sub e1} for a given X{sub D}, or vice versa. A group of graphs of non-dimensional concentration in the fracture versus non-dimensional time, was developed. It was found that if P{sub e1} remains constant whereas {alpha} changes, the limit solution is the envelope of a family of curves in a graph of C{sub D} versus t{sub D}. In this figure P
International Nuclear Information System (INIS)
Foote, P.S.
1999-01-01
The City of Harrisburg, Pennsylvania, proposed to construct a new low-head hydroelectric project on the Susquehanna River in the central part of the state in 1986, about 108 km upstream of the river mouth. As part of the licensing process, the city was required by the Federal Energy Regulatory Commission to carry out studies that would forecast the impacts on riverine aquatic habitat as a result of construction of the proposed 13 km long by 1.5 km wide reservoir. The methodology selected by the city and its consultants was to use the IFIM to model the habitat conditions in the project reach both before and after construction of the proposed reservoir.The IFIM is usually used to model instream flow releases downstream of dams and diversions, and had not been used before to model habitat conditions within the proposed reservoir area. The study team hydraulically modelled the project reach using existing hydraulic data, and a HEC-2 backwater analysis to determine post-project water surface elevations. The IFG-4 model was used to simulate both pre- and post-project water velocities, by distributing velocities across transects based on known discharges and cell depth. Effects on aquatic habitat were determined using the IFIM PHABSIM program, in which criteria for several evaluation species and life stages were used to yield estimates of Weighted Usable Area. The analysis showed, based on trends in WUA from pre- and post-project conditions, that habitat conditions would improve for several species and life stages, and would be negatively affected for fewer life stages and species. Some agency concerns that construction of the proposed reservoir would have significant adverse effects on the resident and anadromous fish populations were responded to using these results
Yun, Keon-Young
For the computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen numbers (Kn) lie in continuum-transition regime, a set of extended three-dimensional hydrodynamic equations are required which are more accurate than the Navier-Stokes equations and computationally more efficient than the Direct Simulation Monte Carlo (DSMC) computations in this regime. In this thesis, the three-dimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn 2) and adding the augmented terms (linear third-order super Burnett terms with coefficients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances). The three-dimensional augmented Burnett equations are applied to compute the three-dimensional hypersonic blunt body flows for various range of Knudsen numbers and Mach numbers. An explicit time-stepping scheme with Steger-Warming flux vector splitting is employed to discretize the convective flux terms. Stress and heat flux terms are central differenced. For the wall boundary conditions, the first-order Maxwell-Smoluchowski slip boundary conditions are employed. The computational results are compared with the Navier-Stokes solutions, the existing augmented Burnett solutions of Zhong, and the available DSMC results. The comparisons show that the difference between the Navier-Stokes and the augmented Burnett solutions is very small at Knudsen numbers less than 0.01; the difference becomes significant as the Knudsen number increases. The comparisons also show that the augmented Burnett solutions are much closer to the DSMC results in the continuum-transition regime than the Navier-Stokes calculations.
Guan, Peng; Huang, Desheng; He, Miao; Shen, Tiefeng; Guo, Junqiao; Zhou, Baosen
2009-07-08
HFRS is a serious public health problem in China and the study on HFRS is important in China for its large population. The present study aimed to explore the impact of climatic variables and reservoir on the incidence of HFRS in Huludao City, an epidemic focus of the disease in northeastern China. Structure Equation Model (SEM), a statistical technique for testing and estimating causal relationships, was conducted based on climatic variables, virus-carrying index among rodents, and incidence of HFRS in the city during the period 1990 to 2006. The linear structural relationships (LISREL) software (Scientific Software International, Lincolnwood, IL) was used to fit SEMs. Temperature, precipitation, relative humidity and virus-carrying index among rodents have shown positive correlations with the monthly incidence of HFRS, while air pressure had a negative correlation with the incidence. The best-fit SEM model fitted well with the data-based correlation matrix, P value was more than 0.56, root mean square error of approximation (RMSEA) equaled to 0, goodness-of-fit index (GFI) was more than 0.99. Climate and reservoirs have affected the incidence of HFRS in Huludao City, located in northeastern China. Climate affects HFRS incidence mainly through the effect on reservoir in the study area. HFRS prevention and control should give more consideration to rodent control and climate variations.
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
A simplified approach to well test analysis of naturally fractured reservoirs
Energy Technology Data Exchange (ETDEWEB)
Aguilera, R. [Servipetrol Ltd., Calgary, AB (Canada)
2004-07-01
This paper presents a simplified equation for drawdown and well test analysis of naturally fractured reservoirs. It can also be used for conventional single porosity reservoirs. The proposed technique allows approximate solutions to determine parameters such as fracture, permeability, wellbore storage, skin, storativity ratio, interporosity flow coefficient, fracture spacing, number of fractures intercepted by the wellbore and the amount of secondary mineralization within fractures. The results are in reasonable agreement with more rigorous methods published in the literature which require specialized software. The proposed method was illustrated with actual data from fractured reservoirs. 13 refs., 2 tabs., 4 figs.
Zakharov equations for viscous flow and their use in the blood clot ...
Indian Academy of Sciences (India)
For theoretical study, blood can be regarded as a viscous electrically conducting fluid of negative ions and protons. Zakharov equations including viscosity are relevant for describing the behaviour of blood plasma. The dispersion formula is derived from the perturbation method and is solved numerically. It turns out that the ...
Non-isospectral flows of noncommutative differential-difference KP equation
International Nuclear Information System (INIS)
Huang, Lin; Ilangovane, R.; Tamizhmani, K.M.; Zhang, Da-jun
2013-01-01
We present master symmetries of noncommutative differential-difference KP equation by considering Sato approach, where the field variables are defined over associative algebras. The Lie algebraic structures of generalized and master symmetries are given. They form a Virasoro Lie algebraic structure
A modified SOR method for the Poisson equation in unsteady free-surface flow calculations.
Botta, E.F.F.; Ellenbroek, Marcellinus Hermannus Maria
1985-01-01
Convergence difficulties that sometimes occur if the successive overrelaxation (SOR) method is applied to the Poisson equation on a region with irregular free boundaries are analyzed. It is shown that these difficulties are related to the treatment of the free boundaries and caused by the appearance
Zakharov equations for viscous flow and their use in the blood clot ...
Indian Academy of Sciences (India)
Ai-Ping Zhou
2017-11-14
Nov 14, 2017 ... This would lead to the formation of blood clot. The viscous force can suppress the occurrence of instability and prevent thrombosis. One can find that the chaotic state of blood signals human health. Keywords. Blood plasma; Zakharov equations; viscosity; modulation instability. PACS Nos 52.27.–h; 52.35.
Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow
International Nuclear Information System (INIS)
Hammond, L A; Halliday, I; Care, C M; Stevens, A
2002-01-01
We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow
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.
Tian, Jun-Fang; Yuan, Zhen-Zhou; Jia, Bin; Fan, Hong-Qiang
2013-03-01
We investigate the phase transitions and the Korteweg-de Vries (KdV) equation in the density difference lattice hydrodynamic (DDLM) model, which shows a close connection with the gas-kinetic-based model and the microscopic car following model. The KdV equation near the neutral stability line is derived and the corresponding soliton solution describing the density waves is obtained. Numerical simulations are conducted in two aspects. On the one hand, under periodic conditions perturbations are applied to demonstrate the nonlinear analysis result. On the other hand, the open boundary condition with random fluctuations is designed to explore the empirical congested traffic patterns. The phase transitions among the free traffic (FT), widening synchronized flow pattern (WSP), moving localized cluster (MLC), oscillatory congested traffic (OCT) and homogeneous congested traffic (HCT) occur by varying the amplitude of the fluctuations. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce so many congested traffic patterns.
International Nuclear Information System (INIS)
Perez Guerrero, Jesus Salvador
1995-01-01
Laminar developing flow in channels of arbitrary geometry was studied by solving the Navier-Stokes equations in the stream function-only formulation through the Generalized Integral Transform Technique (GITT). The stream function is expanded in an infinite system based on eigenfunctions obtained by considering solely the diffusive terms of the original formulation. The Navier-Stokes equations are transformed into an infinite system of ordinary differential equations, by using the transformation and inversion formulae. For computational purposes, the infinite series is truncated, according to an automatic error control procedure. The ordinary differential is solved through well-established scientific subroutines from widely available mathematical libraries. The classical problem of developing flow between parallel-plates is analysed first, as for both uniform and irrotational inlet conditions. The effect of truncating the duct length in the accuracy of the obtained solution is studied. A convergence analysis of the results obtained by the GITT is performed and compared with results obtained by finite difference and finite element methods, for different values of Reynolds number. The problem of flow over a backward-facing step then follows. Comparisons with experimental results in the literature indicate an excellent agreement. The numerical co-validation was established for a test case, and perfect agreement is reached against results considered as benchmarks in the recent literature. The results were shown to be physically more reasonable than others obtained by purely numerical methods, in particular for situations where three-dimensional effects are identified. Finally, a test problem for an irregular by shoped duct was studied and compared against results found in the literature, with good agreement and excellent convergence rates for the stream function field along the whole channel, for different values of Reynolds number. (author)
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)
Directory of Open Access Journals (Sweden)
Xanming Wang
1996-01-01
Full Text Available A technique is developed for evaluation of eigenvalues in solution of the differential equation d2y/dr2+(1/rdy/dr+λ2(β−r2y=0 which occurs in the problem of heat convection in laminar flow through a circular tube with silp-flow (β>1. A series solution requires the expansions of coeffecients involving extremely large numbers. No work has been reported in the case of β>1, because of its computational complexity in the evaluation of the eigenvalues. In this paper, a matrix was constructed and a computational algorithm was obtained to calculate the first four eigenvalues. Also, an asymptotic formula was developed to generate the full spectrum of eigenvalues. The computational results for various values of β were obtained.
An efficient numerical technique for solving navier-stokes equations for rotating flows
International Nuclear Information System (INIS)
Haroon, T.; Shah, T.M.
2000-01-01
This paper simulates an industrial problem by solving compressible Navier-Stokes equations. The time-consuming tri-angularization process of a large-banded matrix, performed by memory economical Frontal Technique. This scheme successfully reduces the time for I/O operations even for as large as (40, 000 x 40, 000) matrix. Previously, this industrial problem can solved by using modified Newton's method with Gaussian elimination technique for the large matrix. In the present paper, the proposed Frontal Technique is successfully used, together with Newton's method, to solve compressible Navier-Stokes equations for rotating cylinders. By using the Frontal Technique, the method gives the solution within reasonably acceptance computational time. Results are compared with the earlier works done, and found computationally very efficient. Some features of the solution are reported here for the rotating machines. (author)
Energy Technology Data Exchange (ETDEWEB)
Aursand, Eskil, E-mail: eskil.aursand@sintef.no; Gjennestad, Magnus Aa.; Yngve Lervåg, Karl; Lund, Halvor
2016-03-15
A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base fluid. The magnetization model is based on statistical mechanics, taking into account non-uniform particle size distributions. An implementation of the proposed model is validated against experiments from the literature, and found to give good predictions for the thermomagnetic pumping performance. However, the results reveal a very large sensitivity to uncertainties in heat transfer coefficient predictions. - Highlights: • A multi-phase flow model for thermomagnetically pumped ferrofluid is proposed. • An implementation is validated against experiments from the literature. • Predicted thermomagnetic pumping effect agrees with experiments. • However, a very large sensitivity to heat transfer coefficient is revealed.
International Nuclear Information System (INIS)
Narvaez R, Paulo Cesar; Galeano P, Haiver
2002-01-01
Optimal design problem of liquid distribution systems has been viewed as the selection of pipe sizes and pumps, which will minimize overall costs, accomplishing the flow and pressure constraints. There is a set of methods for least cost design of liquids distribution networks (6). In the last years, some of them have been studied broadly: linear programming (1, 4, 5, 7], non-linear programming [8, 9], and genetic algorithms (3, 10, 13). This paper describes the development of a cost equation and the objective function for liquid distribution networks that together to the mathematical model and the solution method of the flow problem developed by Narvaez (11), were used by in a computer model that involves the application of an genetic algorithm to the problem of least cost design of liquids distribution networks
Afsar, Mohammed; Sescu, Adrian
2014-11-01
Transition in boundary layer flow over flat/curved surfaces and at moderate to high freestream disturbances or under the influence of various surface roughness elements often involves inviscid secondary instability. This stage in transition can be pictured as being a parametric resonance-type phenomena where a unstable primary flow saturates to a more-or-less steady-state, susceptible to infinitesimal three-dimensional wave-like instability modes that grow much faster than the primary. In decades of research on boundary layers, experimenters have relied upon an inflection point in the wall normal y and/or spanwise directions z of the primary as a pre-cursor to transition. This assertion, based on Rayleigh's theorem, does not however apply in transversely sheared flows. In this talk, we show that an alternative local criterion for inviscid secondary instability - sharing similarities to the original one-dimensional Rayleigh criterion - exists for a class of non-planar transversely sheared flows at long streamwise wavelength. Our general stability criterion is, remarkably, given by necessity of the surface U y , z possessing at least one saddle point in the plane. We analyze this saddle-point criterion numerically show its relevance to secondary instabilities. M.Z.A. would like to anknowledge financial support from Laminar Flow Control (LFC-UK) Research Program at Imperial College London and would like to thank Professor Philip Hall for motivating his interest in this problem.
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
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
Bakker, Mark; Kuhlman, Kristopher L.
2011-09-01
Two new approaches are presented for the accurate computation of the potential due to line elements that satisfy the modified Helmholtz equation with complex parameters. The first approach is based on fundamental solutions in elliptical coordinates and results in products of Mathieu functions. The second approach is based on the integration of modified Bessel functions. Both approaches allow evaluation of the potential at any distance from the element. The computational approaches are applied to model transient flow with the Laplace transform analytic element method. The Laplace domain solution is computed using a combination of point elements and the presented line elements. The time domain solution is obtained through a numerical inversion. Two applications are presented to transient flow fields, which could not be modeled with the Laplace transform analytic element method prior to this work. The first application concerns transient single-aquifer flow to wells near impermeable walls modeled with line-doublets. The second application concerns transient two-aquifer flow to a well near a stream modeled with line-sinks.
Kou, Jisheng
2017-12-06
In this paper, we consider a diffuse-interface gas-liquid two-phase flow model with inhomogeneous temperatures, in which we employ the Peng-Robinson equation of state and the temperature-dependent influence parameter instead of the van der Waals equation of state and the constant influence parameter used in the existing models. As a result, our model can characterize accurately the physical behaviors of numerous realistic gas-liquid fluids, especially hydrocarbons. Furthermore, we prove a relation associating the pressure gradient with the gradients of temperature and chemical potential, and thereby derive a new formulation of the momentum balance equation, which shows that gradients of the chemical potential and temperature become the primary driving force of the fluid motion. It is rigorously proved that the new formulations of the model obey the first and second laws of thermodynamics. To design efficient numerical methods, we prove that Helmholtz free energy density is a concave function with respect to the temperature under certain physical conditions. Based on the proposed modeling formulations and the convex-concave splitting of Helmholtz free energy density, we propose a novel thermodynamically stable numerical scheme. We rigorously prove that the proposed method satisfies the first and second laws of thermodynamics. Finally, numerical tests are carried out to verify the effectiveness of the proposed simulation method.
Otevrel, Marek; Klepárník, Karel
2002-10-01
The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
Frisch, Uriel; Villone, Barbara
2014-09-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to Göttingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation theorem was to be rediscovered independently by William Thomson (Kelvin) in 1869. Cauchy's invariants were only occasionally cited in the 19th century - besides Hankel, foremost by George Stokes and Maurice Lévy - and even less so in the 20th until they were rediscovered via Emmy Noether's theorem in the late 1960, but reattributed to Cauchy only at the end of the 20th century by Russian scientists.
Lee, T.-W.
2017-11-01
Recently, we developed a theoretical basis for determination of the Reynolds stress in canonical flows. Writing momentum balance for a control volume moving at the local mean velocity, along with a differential transform ∂/∂x =C1 U∂/∂y , a turbulence momentum balance is discovered which includes the Reynolds stress as a function of root turbulence parameters: ∂(u'v')/∂y = -C1 U∂u'2/∂y +νm∂2urms'/∂y2 . Then, the Reynolds stress can simply be computed by integrating in the y-direction using the right-hand side (RHS). This is obviously a far simplification of complex modeling of the Reynolds stress, but contains the correct physics, as borne out by comparisons with experimental and DNS data in canonical flows in our earlier works (e.g. in APS 2016). The RHS contains only two parameters, U and u'. In this work, we seek extensions of this solution to non-canonical flows such as wakes, flow over a step, and mixing layers. Comparisons with experimental and DNS data will be presented.
Sun, Shuyu
2012-09-01
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.
Icardi, Matteo
2014-09-01
The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier-Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries. © 2014 Elsevier Inc.
Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I
2016-04-01
Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it
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
Zakharov equations for viscous flow and their use in the blood clot formation
Zhou, Ai-Ping; Li, Xiao-Qing
2017-12-01
For theoretical study, blood can be regarded as a viscous electrically conducting fluid of negative ions and protons. Zakharov equations including viscosity are relevant for describing the behaviour of blood plasma. The dispersion formula is derived from the perturbation method and is solved numerically. It turns out that the imaginary part of one root of the perturbation frequency is greater than zero, and modulation instability occurs. This would lead to the formation of blood clot. The viscous force can suppress the occurrence of instability and prevent thrombosis. One can find that the chaotic state of blood signals human health.
Navier-Stokes Equation and Computational Scheme for Non-Newtonian Debris Flow
Directory of Open Access Journals (Sweden)
Ignazio Licata
2014-01-01
Full Text Available This paper proposes a computational approach to debris flow model. In recent years, the theoretical activity on the classical Herschel-Bulkley model (1926 has been very intense, but it was in the early 80s that the opportunity to explore the computational model has enabled considerable progress in identifying the subclasses of applicability of different sets of boundary conditions and their approximations. Here we investigate analytically the problem of the simulation of uniform motion for heterogeneous debris flow laterally confined taking into account mainly the geological data and methodological suggestions derived from simulation with cellular automata and grid systems, in order to propose a computational scheme able to operate a compromise between “global” predictive capacities and computing effort.
Normal Solutions of the Boltzmann Equation for Fourier and Couette Flow
Torczynski, J. R.
2005-11-01
Bird's Direct Simulation Monte Carlo (DSMC) method is used to simulate Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) for highly nonequilibrium conditions. The gas is confined between two parallel, fully-accommodating walls at unequal temperatures with opposite tangential velocities. For small system Knudsen numbers, the solution is normal in the central region of the domain (outside the Knudsen layers). For small heat-flux Knudsen numbers, the normal solution exhibits Chapman-Enskog (CE) behavior. More specifically, excellent agreement is observed between the DSMC and CE thermal conductivity, viscosity, and Sonine-polynomial coefficients of the molecular velocity distribution function. At larger heat-flux Knudsen numbers, the normal solution systematically departs from the CE solution. Under these conditions, the DSMC results for Maxwell molecules are in excellent agreement with the exact solution of Santos and co-workers, and the DSMC results for hard-sphere molecules exhibit similar trends. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Cuss, Robert; Harrington, Jon; Graham, Caroline
2013-04-01
Tight formations, such as shale, have a wide range of potential usage; this includes shale gas exploitation, hydrocarbon sealing, carbon capture & storage and radioactive waste disposal. Considerable research effort has been conducted over the last 20 years on the fundamental controls on gas flow in a range of clay-rich materials at the British Geological Survey (BGS) mainly focused on radioactive waste disposal; including French Callovo-Oxfordian claystone, Belgian Boom Clay, Swiss Opalinus Clay, British Oxford Clay, as well as engineered barrier material such as bentonite and concrete. Recent work has concentrated on the underlying physics governing fluid flow, with evidence of dilatancy controlled advective flow demonstrated in Callovo-Oxfordian claystone. This has resulted in a review of how advective gas flow is dealt with in Performance Assessment and the applicability of numerical codes. Dilatancy flow has been shown in Boom clay using nano-particles and is seen in bentonite by the strong hydro-mechanical coupling displayed at the onset of gas flow. As well as observations made at BGS, dilatancy flow has been shown by other workers on shale (Cuss et al., 2012; Angeli et al. 2009). As well as experimental studies using cores of intact material, fractured material has been investigated in bespoke shear apparatus. Experimental results have shown that the transmission of gas by fractures is highly localised, dependent on normal stress, varies with shear, is strongly linked with stress history, is highly temporal in nature, and shows a clear correlation with fracture angle. Several orders of magnitude variation in fracture transmissivity is seen during individual tests. Flow experiments have been conducted using gas and water, showing remarkably different behaviour. The radioactive waste industry has also noted a number of important features related to sample preservation. Differences in gas entry pressure have been shown across many laboratories and these may be
Xiong, Yuan
2014-04-28
Spurious current emerging in the vicinity of phase interfaces is a well-known disadvantage of the lattice Boltzmann equation (LBE) for two-phase flows. Previous analysis shows that this unphysical phenomenon comes from the force imbalance at discrete level inherited in LBE (Guo et al 2011 Phys. Rev. E 83 036707). Based on the analysis of the LBE free of checkerboard effects, in this work we further show that the force imbalance is caused by the different discretization stencils: the implicit one from the streaming process and the explicit one from the discretization of the force term. Particularly, the total contribution includes two parts, one from the difference between the intrinsically discretized density (or ideal gas pressure) gradient and the explicit ones in the force term, and the other from the explicit discretized chemical potential gradients in the intrinsically discretized force term. The former contribution is a special feature of LBE which was not realized previously.
Schmidt, J.; Piret, C.; Zhang, N.; Kadlec, B. J.; Liu, Y.; Yuen, D. A.; Wright, G. B.; Sevre, E. O.
2008-12-01
The faster growth curves in the speed of GPUs relative to CPUs in recent years and its rapidly gained popularity has spawned a new area of development in computational technology. There is much potential in utilizing GPUs for solving evolutionary partial differential equations and producing the attendant visualization. We are concerned with modeling tsunami waves, where computational time is of extreme essence, for broadcasting warnings. In order to test the efficacy of the GPU on the set of shallow-water equations, we employed the NVIDIA board 8600M GT on a MacBook Pro. We have compared the relative speeds between the CPU and the GPU on a single processor for two types of spatial discretization based on second-order finite-differences and radial basis functions. RBFs are a more novel method based on a gridless and a multi- scale, adaptive framework. Using the NVIDIA 8600M GT, we received a speed up factor of 8 in favor of GPU for the finite-difference method and a factor of 7 for the RBF scheme. We have also studied the atmospheric dynamics problem of swirling flows over a spherical surface and found a speed-up of 5.3 using the GPU. The time steps employed for the RBF method are larger than those used in finite-differences, because of the much fewer number of nodal points needed by RBF. Thus, in modeling the same physical time, RBF acting in concert with GPU would be the fastest way to go.
DEFF Research Database (Denmark)
Yang, Tian; Cao, Yingchang; Friis, Henrik
2017-01-01
The lacustrine deep-water gravity-flow sandstone reservoirs in the third member of the Shahejie Formation are the main exploration target for hydrocarbons in the Dongying Sag, Eastern China. Carbonate cementation is responsible for much of the porosity and permeability reduction in the lacustrine...
Haghi, A.; Asef, M.; Kharrat, R.
2010-12-01
Recently, rock mechanics and geophysics contribution in petroleum industry has been significantly increased. Wellbore stability analysis in horizontal wells, sand production problem while extracting hydrocarbon from sandstone reservoirs, land subsidence due to production induced reservoir compaction, reservoir management, casing shearing are samples of these contributions. In this context, determination of the magnitude and orientation of the in-situ stresses is an essential parameter. This paper is presenting new method to estimate the magnitude of in-situ stresses based on fracturing technology data. Accordingly, kirsch equations for the circular cavities and fracturing technology models in permeable formations have been used to develop an innovative Geomechanical Formulation (GFFT). GFFT introduces a direct reasonable relation between the reservoir stresses and the breakdown pressure of fracture, while the concept of effective stress was employed. Thus, this complex formula contains functions of some rock mechanic parameters such as poison ratio, Biot’s coefficient, Young’s modulus, rock tensile strength, depth of reservoir and breakdown/reservoir pressure difference. Hence, this approach yields a direct method to estimate maximum and minimum effective/insitu stresses in an oil field and improves minimum in-situ stress estimation compared to previous studies. In case of hydraulic fracturing; a new stress analysis method is developed based on well known Darcy equations for fluid flow in porous media which improves in-situ stress estimation using reservoir parameters such as permeability, and injection flow rate. The accuracy of the method would be verified using reservoir data of a case history. The concepts discussed in this research would eventually suggest an alternative methodology with sufficient accuracy to derive in-situ stresses in hydrocarbon reservoirs, while no extra experimental work is accomplished for this purpose.
Lacasse, David; Garon, Andre; Pelletier, Dominique
2007-02-01
This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.
Directory of Open Access Journals (Sweden)
Alex Braz Iacone Santos
2010-10-01
Full Text Available Changes in fish assemblage structure along a longitudinal gradient of the Paraíba do Sul River and Funil reservoir were studied to detect distribution patterns and the seasonal influence of the inflowing river. Fish were caught by gill nets in three zones (riverine, transition and lentic during two seasons (dry and wet. A total of 3,721 individuals were captured, comprising five orders, 14 families, 27 genera and 33 species. Five species were non-native and amounted to 17.7% of the total number of individuals. The 10 most abundant species were used to assess spatial-temporal patterns. Plagioscion squamosissimus (Heckel, 1840, Oligosarcus hepsetus (Curvier, 1829 and Metynnis maculatus (Kner, 1858 were widely distributed in both seasons. Astyanax bimaculatus (Linnaeus, 1758, Cichla kelberi Kullander & Ferreira, 2006 and Geophagus brasiliensis (Quoy & Gaimard, 1824 had higher abundance in the dry season, occurring mainly in the lentic zone. By contrast, the benthopelagics Pimelodus maculatus La Cèpede, 1803 and Astyanax parahybae (Eigenmann, 1908 and the benthics Hoplosternum littorale (Hancock, 1828 and Hypostomus auroguttatus Kner, 1854 had higher abundance in the wet season, with the two first species occurring mainly in the riverine zone, and latter two species in the transition zone. The highest diversity for both seasons was recorded in the transition zone, which is an ecotone that allows the co-existence of both riverine and lentic species. A major shift in assemblage structure occurred along the longitudinal gradient due to changes in discharge of the inflowing river, with increased fish abundance in the riverine zone caused by increased habitat availability in wet season, and the reverse of this situation in the dry season.
The Bernoulli-Poiseuille Equation.
Badeer, Henry S.; Synolakis, Costas E.
1989-01-01
Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)
Energy Technology Data Exchange (ETDEWEB)
D. D. Blackwell; K. W. Wisian; M. C. Richards; J. L. Steele
2000-04-01
Several activities related to geothermal resources in the western United States are described in this report. A database of geothermal site-specific thermal gradient and heat flow results from individual exploration wells in the western US has been assembled. Extensive temperature gradient and heat flow exploration data from the active exploration of the 1970's and 1980's were collected, compiled, and synthesized, emphasizing previously unavailable company data. Examples of the use and applications of the database are described. The database and results are available on the world wide web. In this report numerical models are used to establish basic qualitative relationships between structure, heat input, and permeability distribution, and the resulting geothermal system. A series of steady state, two-dimensional numerical models evaluate the effect of permeability and structural variations on an idealized, generic Basin and Range geothermal system and the results are described.
Multigrid Methods for Fully Implicit Oil Reservoir Simulation
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
Impact of Reservoir Operation to the Inflow Flood - a Case Study of Xinfengjiang Reservoir
Chen, L.
2017-12-01
Building of reservoir shall impact the runoff production and routing characteristics, and changes the flood formation. This impact, called as reservoir flood effect, could be divided into three parts, including routing effect, volume effect and peak flow effect, and must be evaluated in a whole by using hydrological model. After analyzing the reservoir flood formation, the Liuxihe Model for reservoir flood forecasting is proposed. The Xinfengjiang Reservoir is studied as a case. Results show that the routing effect makes peak flow appear 4 to 6 hours in advance, volume effect is bigger for large flood than small one, and when rainfall focus on the reservoir area, this effect also increases peak flow largely, peak flow effect makes peak flow increase 6.63% to 8.95%. Reservoir flood effect is obvious, which have significant impact to reservoir flood. If this effect is not considered in the flood forecasting model, the flood could not be forecasted accurately, particularly the peak flow. Liuxihe Model proposed for Xinfengjiang Reservoir flood forecasting has a good performance, and could be used for real-time flood forecasting of Xinfengjiang Reservoir.Key words: Reservoir flood effect, reservoir flood forecasting, physically based distributed hydrological model, Liuxihe Model, parameter optimization
Pore size determination using normalized J-function for different hydraulic flow units
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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.
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)
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
International Nuclear Information System (INIS)
Ishii, M.
1977-10-01
In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equation that specifies the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, shear stresses, and the interfacial momentum transfer, since these macroscopic effects govern the relative velocity between phases. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters shows a satisfactory agreement
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
Directory of Open Access Journals (Sweden)
Eric Aidan Letham
2018-01-01
Full Text Available The ability to quantify effective permeability at the various fluid saturations and stress states experienced during production from shale oil and shale gas reservoirs is required for efficient exploitation of the resources, but to date experimental challenges prevent measurement of the effective permeability of these materials over a range of fluid saturations. To work towards overcoming these challenges, we measured effective permeability of a suite of gas shales to gaseous ethane over a range of pore pressures up to the saturated vapour pressure. Liquid/semiliquid ethane saturation increases due to adsorption and capillary condensation with increasing pore pressure resulting in decreasing effective permeability to ethane gas. By how much effective permeability to ethane gas decreases with adsorption and capillary condensation depends on the pore size distribution of each sample and the stress state that effective permeability is measured at. Effective permeability decreases more at higher stress states because the pores are smaller at higher stress states. The largest effective permeability drops occur in samples with dominant pore sizes in the mesopore range. These pores are completely blocked due to capillary condensation at pore pressures near the saturated vapour pressure of ethane. Blockage of these pores cuts off the main fluid flow pathways in the rock, thereby drastically decreasing effective permeability to ethane gas.
Rathnaweera, T. D.; Ranjith, P. G.; Perera, M. S. A.
2016-01-01
Interactions between injected CO2, brine, and rock during CO2 sequestration in deep saline aquifers alter their natural hydro-mechanical properties, affecting the safety, and efficiency of the sequestration process. This study aims to identify such interaction-induced mineralogical changes in aquifers, and in particular their impact on the reservoir rock’s flow characteristics. Sandstone samples were first exposed for 1.5 years to a mixture of brine and super-critical CO2 (scCO2), then tested to determine their altered geochemical and mineralogical properties. Changes caused uniquely by CO2 were identified by comparison with samples exposed over a similar period to either plain brine or brine saturated with N2. The results show that long-term reaction with CO2 causes a significant pH drop in the saline pore fluid, clearly due to carbonic acid (as dissolved CO2) in the brine. Free H+ ions released into the pore fluid alter the mineralogical structure of the rock formation, through the dissolution of minerals such as calcite, siderite, barite, and quartz. Long-term CO2 injection also creates a significant CO2 drying-out effect and crystals of salt (NaCl) precipitate in the system, further changing the pore structure. Such mineralogical alterations significantly affect the saline aquifer’s permeability, with important practical consequences for the sequestration process. PMID:26785912
Energy Technology Data Exchange (ETDEWEB)
Fukushima, N.; Hyodo, M.; Shinohara, N.; Takasugi, S. [Geothermal Energy Research and Development Co. Ltd., Tokyo (Japan)
1996-05-01
This paper reports the result of a preliminary circulation test conducted in fiscal 1995 on a deep reservoir (at a depth of about 2200 m) in the Hijiori hot dry rock experimental field. One water injection well and two production wells were drilled to constitute a circulation loop, to which the circulation test was performed to investigate the flow characteristics thereof. The result revealed the following matters: total amount of injected water of 51500 m{sup 3} resulted in a total fluid recovery rate of about 40%; as a result of well stimulation given twice during the initial stage of the water injection, the continuity impedance in the vicinity of the injection well decreased largely (however, the continuity improvement upon the second attempt was considerably inferior to that from the first attempt); and increase in the water injection amount does not necessarily lead to increase in the production amount. The paper describes additionally that it is extremely difficult to interpret non-linearity between the injection and production amounts by using a model prepared previously with a main objective to analyze the Hijiori HDR circulation system. 1 ref., 9 figs., 1 tab.
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
Energy Technology Data Exchange (ETDEWEB)
Zou, Ling, E-mail: ling.zou@inl.gov; Zhao, Haihua; Zhang, Hongbin
2016-04-15
Highlights: • High-order spatial and fully implicit temporal numerical schemes in solving two-phase six-equation model. • Jacobian-free Newton–Krylov method was used to solve discretized nonlinear equations. • Realistic flow regimes and closure correlations were used. • Extensive code validation using experimental data, and benchmark with RELAP5-3D. - Abstract: This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. This in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.
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...
Energy Technology Data Exchange (ETDEWEB)
Fehler, Michael [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2017-04-19
The primary objective of this project was to improve our ability to predict performance of an Enhanced Geothermal System (EGS) reservoir over time by relating, in a quantitative manner, microseismic imaging with fluid and temperature changes within the reservoir. Historically, microseismic data have been used qualitatively to place bounds on the growth of EGS reservoirs created by large hydraulic fracturing experiments. Previous investigators used an experimentally based fracture opening relationship (fracture aperture as a function of pressure), the spatial extent of microseismic events, and some assumptions about fracture frequency to determine the size of an EGS reservoir created during large pumping tests. We addressed a number of issues (1) locating microearthquakes that occur during hydraulic fracturing, (2) obtaining more information about a reservoir than the microearthquake locations from the microearthquake data, for example, information about the seismic velocity structure of the reservoir or the scattering of seismic waves within the reservoir, (3) developing an improved methodology for estimating properties of fractures that intersect wellbores in a reservoir, and (4) developing a conceptual model for explaining the downward growth of observed seismicity that accompanies some hydraulic injections into geothermal reservoirs. We used two primary microseismic datasets for our work. The work was motivated by a dataset from the Salak Geothermal Field in Indonesia where seismicity accompanying a hydraulic injection was observed to migrate downward. We also used data from the Soultz EGS site in France. We also used Vertical Seismic Profiling data from a well in the United States. The work conducted is of benefit for characterizing reservoirs that are created by hydraulic fracturing for both EGS and for petroleum recovery.
International Nuclear Information System (INIS)
Constain Aragon, A.; Lemos Ruiz, R.
2011-01-01
It is very well known the basic equation of hydraulics discovered by Antoine de Chezy in 1769, which relates in a quadratic from the mean velocity of flow with the slope of energy line and the hydraulic radius, in a uniform regime. This equation has been the central axis of development of hydro metrics as science that faces the huge challenges of penetrating the knowledge of earths streams every time more contaminated. In virtue of that, its mathematical structure and the relationship with other related formulas have been carefully examined, despite the limitation due to constancy of velocity. Starting from chemical considerations rather than dynamic ones as was used to obtain chezys relationship it is possible to establish a second equation for mean velocity of fluid in a non uniform regime that corresponds to averaged movement of a solute poured to steam. This equation will go to relate in an accurate way several aspects hydraulics and mass transport, sight as a single thing, allowing a vital tool for a depth study of water contaminations. to arrive this equation it was reviewed the foundations of mass transport theory in flows, stating a time dependent nature for coefficient currently used in describing dispersion phenomena allowing to interpret properly certain inconsistencies detected long time ago in this theory. It is presented the detailed results of application of this new approach to a small steam and a larger river in Colombia. (Author) 23 refs.
Directory of Open Access Journals (Sweden)
Ramzi Othman
2015-01-01
Full Text Available In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5 to 5 × 104 s−1. This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.
Perakis, A C; Montarello, J K; Rosenthal, E; Boyd, E G; Yates, A K; Deverall, P B; Curry, P V; Sowton, E
1990-06-01
Aortic valve orifice area estimation in patients with aortic stenosis may be obtained non-invasively using several Doppler echocardiographic methods. Their validity has been established by correlation with catheterization data using the Gorlin formula, with its inherent limitations, and small discrepancies between the methods are present. To evaluate these differences further, 15 patients with severe aortic stenosis (mean transvalvular gradient 70, range 40-130 mmHg) had aortic valve area estimations by Doppler echocardiography using two variations of the continuity equation. The intact valves removed at valve replacement surgery were then mounted in a pulsatile model and the anatomical area was measured (mean 0.67 +/- 0.17 cm-2) from video recordings during flow at 5.4 l min-1. Aortic valve area calculated using the integrals of the velocity-time curves measured at the left ventricular outflow tract and aortic jet (mean 0.65 +/- 0.17 cm2) correlated best with the anatomical area (r = 0.87, P less than 0.001). The area derived by using the ratio of maximum velocities from the left ventricular outflow tract and aortic jet (mean 0.69 +/- 0.18 cm2) also correlated well with the anatomical area (r = 0.79, P less than 0.001). The index between the left ventricular outflow tract and aortic jet maximum velocities was less than or equal to 0.25 in all. In patients with severe aortic stenosis the aortic valve area can be reliably estimated using Doppler echocardiography.
Challenges of reservoir properties and production history matching in a CHOPS reservoir study
Energy Technology Data Exchange (ETDEWEB)
Alam, Mahbub [Department of Geoscience, University of Calgary (Canada)
2011-07-01
In order to meet increasing world energy demand, wells have to be drilled within very thin reservoir beds. This paper, we present one of the solutions for optimizing the reservoir characterization. Reservoir characterization is the process between the discovery of a property and the reservoir management phase. Principal data for reservoir modeling are: 4D Seismic interpretation, wireline log interpretation, core analysis, and petrophysical analysis. Reservoir conditions, perforation and completion technology are the key issues to the production rate of cold production. Reservoir modeling intends to minimize the risk factor, maximize production, and help determine the location for infill drillings. Cold heavy oil production with sand (CHOPS) is a method for enhancing primary production from heavy oil reservoirs. Gravitational forces, natural fluid pressure gradients and foamy oil flow phenomena are the major driving forces of the CHOPS mechanism. Finally, Reservoir characterization allows better understanding of permeability and porosity prediction.
Colombo, Maria
2017-01-01
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
DEFF Research Database (Denmark)
Jabbari, Masoud; Hattel, Jesper Henri
2014-01-01
and casting speed (belt velocity). In the present work, the flow in both doctor blade regions of a slurry is described with a steady state momentum equation in combination with a Bingham plastic constitutive equation, and this is integrated to a closed form analytical solution for both reservoirs based...
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)
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.
Directory of Open Access Journals (Sweden)
Jian Zhou
2016-09-01
Full Text Available Hydraulic fracturing is a useful tool for enhancing rock mass permeability for shale gas development, enhanced geothermal systems, and geological carbon sequestration by the high-pressure injection of a fracturing fluid into tight reservoir rocks. Although significant advances have been made in hydraulic fracturing theory, experiments, and numerical modeling, when it comes to the complexity of geological conditions knowledge is still limited. Mechanisms of fluid injection-induced fracture initiation and propagation should be better understood to take full advantage of hydraulic fracturing. This paper presents the development and application of discrete particle modeling based on two-dimensional particle flow code (PFC2D. Firstly, it is shown that the modeled value of the breakdown pressure for the hydraulic fracturing process is approximately equal to analytically calculated values under varied in situ stress conditions. Furthermore, a series of simulations for hydraulic fracturing in competent rock was performed to examine the influence of the in situ stress ratio, fluid injection rate, and fluid viscosity on the borehole pressure history, the geometry of hydraulic fractures, and the pore-pressure field, respectively. It was found that the hydraulic fractures in an isotropic medium always propagate parallel to the orientation of the maximum principal stress. When a high fluid injection rate is used, higher breakdown pressure is needed for fracture propagation and complex geometries of fractures can develop. When a low viscosity fluid is used, fluid can more easily penetrate from the borehole into the surrounding rock, which causes a reduction of the effective stress and leads to a lower breakdown pressure. Moreover, the geometry of the fractures is not particularly sensitive to the fluid viscosity in the approximate isotropic model.
Reservoir Simulations of Low-Temperature Geothermal Reservoirs
Bedre, Madhur Ganesh
The eastern United States generally has lower temperature gradients than the western United States. However, West Virginia, in particular, has higher temperature gradients compared to other eastern states. A recent study at Southern Methodist University by Blackwell et al. has shown the presence of a hot spot in the eastern part of West Virginia with temperatures reaching 150°C at a depth of between 4.5 and 5 km. This thesis work examines similar reservoirs at a depth of around 5 km resembling the geology of West Virginia, USA. The temperature gradients used are in accordance with the SMU study. In order to assess the effects of geothermal reservoir conditions on the lifetime of a low-temperature geothermal system, a sensitivity analysis study was performed on following seven natural and human-controlled parameters within a geothermal reservoir: reservoir temperature, injection fluid temperature, injection flow rate, porosity, rock thermal conductivity, water loss (%) and well spacing. This sensitivity analysis is completed by using ‘One factor at a time method (OFAT)’ and ‘Plackett-Burman design’ methods. The data used for this study was obtained by carrying out the reservoir simulations using TOUGH2 simulator. The second part of this work is to create a database of thermal potential and time-dependant reservoir conditions for low-temperature geothermal reservoirs by studying a number of possible scenarios. Variations in the parameters identified in sensitivity analysis study are used to expand the scope of database. Main results include the thermal potential of reservoir, pressure and temperature profile of the reservoir over its operational life (30 years for this study), the plant capacity and required pumping power. The results of this database will help the supply curves calculations for low-temperature geothermal reservoirs in the United States, which is the long term goal of the work being done by the geothermal research group under Dr. Anderson at
Energy Technology Data Exchange (ETDEWEB)
Richard C. Martineau; Ray A. Berry; Aurélia Esteve; Kurt D. Hamman; Dana A. Knoll; Ryosuke Park; William Taitano
2009-01-01
This report illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially-heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated body force, velocity, and divergence of velocity distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present. The results show that the use of
Asch, Th.W.J. van; Daehne, A.; Spickermann, A.; Travelletti, J.; Béguería-Portuguès, S.
2010-01-01
The kinematics of rapid and slow moving landslides is commonly described by equations of motion, which in case of a viscous component are based on the Navier-Stokes equation. They consist of inertial terms related to the change in velocity in time (local acceleration) and space (convective
Directory of Open Access Journals (Sweden)
Yonggang Shangguan
2017-11-01
Full Text Available The three equations involved in the time-temperature superposition (TTS of a polymer, i.e., Williams–Landel–Ferry (WLF, Vogel–Fulcher–Tammann–Hesse (VFTH and the Arrhenius equation, were re-examined, and the mathematical equivalence of the WLF form to the Arrhenius form was revealed. As a result, a developed WLF (DWLF equation was established to describe the temperature dependence of relaxation property for the polymer ranging from secondary relaxation to terminal flow, and its necessary criteria for universal application were proposed. TTS results of viscoelastic behavior for different polymers including isotactic polypropylene (iPP, high density polyethylene (HDPE, low density polyethylene (LDPE and ethylene-propylene rubber (EPR were well achieved by the DWLF equation at high temperatures. Through investigating the phase-separation behavior of poly(methyl methacrylate/poly(styrene-co-maleic anhydride (PMMA/SMA and iPP/EPR blends, it was found that the DWLF equation can describe the phase separation behavior of the amorphous/amorphous blend well, while the nucleation process leads to a smaller shift factor for the crystalline/amorphous blend in the melting temperature region. Either the TTS of polystyrene (PS and PMMA or the secondary relaxations of PMMA and polyvinyl chloride (PVC confirmed that the Arrhenius equation can be valid only in the high temperature region and invalid in the vicinity of glass transition due to the strong dependence of apparent activation energy on temperature; while the DWLF equation can be employed in the whole temperature region including secondary relaxation and from glass transition to terminal relaxation. The theoretical explanation for the universal application of the DWLF equation was also revealed through discussing the influences of free volume and chemical structure on the activation energy of polymer relaxations.
Energy Technology Data Exchange (ETDEWEB)
Rocha, Jussiê S., E-mail: jussie.soares@ifpi.edu.br [Instituto Federal do Piauí (IFPI), Valença, PI (Brazil); Maciel, Edisson Sávio de Góes, E-mail: edissonsavio@yahoo.com.br [Instituto Tecnológico de Aeronáutica (ITA), São José dos Campos, SP (Brazil); Lira, Carlos A.B.O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil); Sousa, Pedro A.S.; Neto, Raimundo N.C., E-mail: augusto.96pedro@gmail.com, E-mail: r.correia17@hotmail.com [Instituto Federal do Piauí (IFPI), Teresina, PI (Brazil)
2017-07-01
Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added security. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in using the DISSIPA2D{sub E}ULER code, to solve the Euler equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic flow along a ramp and diffusor configurations is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipation model linear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is obtain computational tools for flow analysis through the study the cited dissipation model and describe their characteristics in relation to the overall quality of the solution, as well as obtain preliminary results for the development of computational tools of dynamic analysis of helium gas flow in gas-cooled reactors. (author)
Kasperek, Regina
2011-01-01
The release of diclofenac sodium and papaverine hydrochloride from tablets and pellets using the flow-through cell apparatus was studied. The influence of excipients and of a size of the solid dosage forms on the amount of the released substances at the intervals of time using the different rates of flow of the dissolution medium was investigated. Physical parameters corresponding to the dissolution process as the mass transfer coefficient, the thickness of the boundary diffusion layer and the concentration of the saturated solution at this layer were calculated. The results of release were described by dimensionless equations.
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
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
Rodríguez de Castro, Antonio; Radilla, Giovanni
2017-02-01
The flow of shear-thinning fluids through unconsolidated porous media is present in a number of important industrial applications such as soil depollution, Enhanced Oil Recovery or filtration of polymeric liquids. Therefore, predicting the pressure drop-flow rate relationship in model porous media has been the scope of major research efforts during the last decades. Although the flow of Newtonian fluids through packs of spherical particles is well understood in most cases, much less is known regarding the flow of shear-thinning fluids as high molecular weight polymer aqueous solutions. In particular, the experimental data for the non-Darcian flow of shear-thinning fluids are scarce and so are the current approaches for their prediction. Given the relevance of non-Darcian shear-thinning flow, the scope of this work is to perform an experimental study to systematically evaluate the effects of fluid shear rheology on the flow rate-pressure drop relationships for the non-Darcian flow through different packs of glass spheres. To do so, xanthan gum aqueous solutions with different polymer concentrations are injected through four packs of glass spheres with uniform size under Darcian and inertial flow regimes. A total of 1560 experimental data are then compared with predictions coming from different methods based on the extension of widely used Ergun's equation and Forchheimer's law to the case of shear thinning fluids, determining the accuracy of these predictions. The use of a proper definition for Reynolds number and a realistic model to represent the rheology of the injected fluids results in the porous media are shown to be key aspects to successfully predict pressure drop-flow rate relationships for the inertial shear-thinning flow in packed beads.
WATER LOSS OF KOKA RESERVOIR, ETHIOPIA: COMMENTS ON
African Journals Online (AJOL)
ABSTRACT: Water balance evaluation of Koka Reservoir was attempted by different authors, and different leakage rates were estimated. However, the water balance equation that the previous authors used does not take into account ground. water inflow into the reservoir. Koka Reservoir is known to receive groundwater ...
Xu, Xianmin
2010-01-01
In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness becomes small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel and Cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition. The homogenization results are proved rigorously by the F-convergence theory. © 2010 Society for Industrial and Applied Mathematics.
Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli
2016-10-01
The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.
International Nuclear Information System (INIS)
Kolev, N.I.
1982-01-01
In the case of small leaks the description of a two-phase flow can be based on a change of the equilibrium state. Because of separation effects to be expected, however, it is necessary to take the inhomogeneity of the flow into account. A model of a transient inhomogeneous equilibrium two-phase flow is presented, which allows to modify already existing computer codes, describing the homogeneous two-phase flow in complex networks with distributed parameters, in such a way that they can be used for describing the inhomogeneity of the two-phase flow without changing the structure of the codes. (author)
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Rocha, Jussie Soares da, E-mail: jussie.soares@ifpi.edu.br [Instituto Federal de Educacao, Ciencia e Tecnologia do Piaui (IFPI), Valenca, PI (Brazil); Maciel, Edisson Savio de G., E-mail: edissonsavio@yahoo.com.br [Instituto Tecnologico de Aeronautica (ITA), Sao Paulo, SP (Brazil); Lira, Carlos A.B. de O., E-mail: cabol@ufpe.edu.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil)
2015-07-01
Very High Temperature Gas Cooled Reactors - VHTGRs are studied by several research groups for the development of advanced reactors that can meet the world's growing energy demand. The analysis of the flow of helium coolant around the various geometries at the core of these reactors through computational fluid dynamics techniques is an essential tool in the development of conceptual designs of nuclear power plants that provide added safety. This analysis suggests a close analogy with aeronautical cases widely studied using computational numerical techniques to solve systems of governing equations for the flow involved. The present work consists in solving the Navier-Stokes equations in a conservative form, in two-dimensional space employing a finite difference formulation for spatial discretization using the Euler method for explicit marching in time. The physical problem of supersonic laminar flow of helium gas along a ramp configuration is considered. For this, the Jameson and Mavriplis algorithm and the artificial dissipations models linear and nonlinear of Pulliam was implemented. A spatially variable time step is employed aiming to accelerate the convergence to the steady state solution. The main purpose of this work is to study the cited dissipation models and describe their characteristics in relation to the overall quality of the solution, aiming preliminary results for the development of computational tools of dynamic analysis of helium flow for the VHTGR core. (author)
DePaolo, D. J.; Steefel, C. I.; Bourg, I. C.
2013-12-01
This talk will review recent research relating to pore scale reactive transport effects done in the context of the Department of Energy-sponsored Energy Frontier Research Center led by Lawrence Berkeley National Laboratory with several other laboratory and University partners. This Center, called the Center for Nanoscale Controls on Geologic CO2 (NCGC) has focused effort on the behavior of supercritical CO2 being injected into and/or residing as capillary trapped-bubbles in sandstone and shale, with particular emphasis on the description of nanoscale to pore scale processes that could provide the basis for advanced simulations. In general, simulation of reservoir-scale behavior of CO2 sequestration assumes a number of mostly qualitative relationships that are defensible as nominal first-order descriptions of single-fluid systems, but neglect the many complications that are associated with a two-phase or three-phase reactive system. The contrasts in properties, and the mixing behavior of scCO2 and brine provide unusual conditions for water-rock interaction, and the NCGC has investigated the underlying issues by a combination of approaches including theoretical and experimental studies of mineral nucleation and growth, experimental studies of brine films, mineral wetting properties, dissolution-precipitation rates and infiltration patterns, molecular dynamic simulations and neutron scattering experiments of fluid properties for fluid confined in nanopores, and various approaches to numerical simulation of reactive transport processes. The work to date has placed new constraints on the thickness of brine films, and also on the wetting properties of CO2 versus brine, a property that varies between minerals and with salinity, and may also change with time as a result of the reactivity of CO2-saturated brine. Mineral dissolution is dependent on reactive surface area, which can be shown to vary by a large factor for various minerals, especially when correlated with
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.
A.R. Ansari; B. Hossain; B. Koren (Barry); G.I. Shishkin (Gregori)
2007-01-01
textabstractWe investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the flow is parallel to its axis. This problem is known to exhibit boundary layers. Also the problem does not have solutions in closed form, it is modelled by boundary-layer
Gartling, D. K.; Roache, P. J.
1978-01-01
The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.
An analytical thermohydraulic model for discretely fractured geothermal reservoirs
Fox, Don B.; Koch, Donald L.; Tester, Jefferson W.
2016-09-01
In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. The purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one-dimensional heat conduction perpendicular to the fracture, employing the Green's function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.
Data assimilation in reservoir management
Rommelse, J.R.
2009-01-01
The research presented in this thesis aims at improving computer models that allow simulations of water, oil and gas flows in subsurface petroleum reservoirs. This is done by integrating, or assimilating, measurements into physics-bases models. In recent years petroleum technology has developed
Ida, Masato; Taniguchi, Nobuyuki
2003-09-01
This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.
Cangioli, Filippo; Pennacchi, Paolo; Vannini, Giuseppe; Ciuchicchi, Lorenzo
2018-01-01
The influence of sealing components on the rotordynamic stability of turbomachinery has become a key topic because the oil and gas market is increasingly demanding high rotational speeds and high efficiency. This leads the turbomachinery manufacturers to design higher flexibility ratios and to reduce the clearance of the seals. Accurate prediction of the effective damping of seals is critical to avoid instability problems; in recent years, "negative-swirl" swirl brakes have been used to reverse the circumferential direction of the inlet flow, which changes the sign of the cross-coupled stiffness coefficients and generates stabilizing forces. Experimental tests for a teeth-on-stator labyrinth seal were performed by manufacturers with positive and negative pre-swirl values to investigate the pre-swirl effect on the cross-coupled stiffness coefficient. Those results are used as a benchmark in this paper. To analyse the rotor-fluid interaction in the seals, the bulk-flow numeric approach is more time efficient than computational fluid dynamics (CFD). Although the accuracy of the coefficients prediction in bulk-flow models is satisfactory for liquid phase application, the accuracy of the results strongly depends on the operating conditions in the case of the gas phase. In this paper, the authors propose an improvement in the state-of-the-art bulk-flow model by introducing the effect of the energy equation in the zeroth-order solution to better characterize real gas properties due to the enthalpy variation along the seal cavities. The consideration of the energy equation allows for a better estimation of the coefficients in the case of a negative pre-swirl ratio, therefore, it extend the prediction fidelity over a wide range of operating conditions. The numeric results are also compared to the state-of-the-art bulk-flow model, which highlights the improvement in the model.
International Nuclear Information System (INIS)
Clarisse, J.M.
2007-01-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
International Nuclear Information System (INIS)
Tariq, M.; Khan, I.A.
2003-01-01
A time dependent Finite Element simulation of penetration of a rigid cylindrical bar impacting on a copper plate is conducted, to demonstrate how material behavior appears to change when Johnson-Cook plasticity rule is employed along with a Gruneisen, equation of state with cubic shock velocity-particle relationship, and defining pressure both for compressed and expanded materials, as compared to the behavior when only isotropic strain-hardening model is employed. The bar impacts the plate with a velocity of 1000 m/s, and penetrates the plate, a portion of it coming out of the other side. Results are obtained and compared taking both an isotropic strain-hardening model, and a model incorporating Johnson-Cook flow rule along with Gruneisen equation of state. (author)
Yin, Xin-An; Yang, Zhi-Feng; Petts, Geoffrey E.; Kondolf, G. Mathias
2014-05-01
Riverine ecosystem protection requires the maintenance of natural flow and sediment regimes downstream from dams. In reservoir management schedules this requirement should be integrated with sedimentation control and human water supply. However, traditional eco-friendly reservoir operating methods have usually only considered the natural flow regime. This paper seeks to develop a reservoir operating method that accounts for both the natural flow and sediment regimes as well as optimizing the water supply allocations. Herein, reservoir water level (RWL), sediment-occupied ratio of reservoir volume (SOR) and rate of change of SOR (RCSOR) are adopted as three triggers of a drawdown-flushing-based sediment management policy. Two different groups of reservoir operating rule curves (RORCs) are designed for sediment-flushing and non-sediment-flushing years, and the three triggers, RWL, SOR and RCSOR, are used to change the “static” RORCs to “dynamic” ones. The approach is applied to the Wangkuai Reservoir, China to test its effectiveness. This shows that the approach can improve the flexibility of reservoir operators to balance the reservoir management, water supply management and the flow and sediment needs of the downstream riverine ecosystem.
Energy Technology Data Exchange (ETDEWEB)
Sotelo-Avila, G.; Gallegos-Silva, J. [Universidad Nacional Autonoma de Mexico, Mexico, D.F. (Mexico)
2002-03-01
The study of channel flow usually have its basis in the hydrostatic distribution of pressure and the rectilinear flow hypotheses. It is from this hypothesis that the main flow equations are obtained. However, this is not applicable to a vertically curved flow that is present in a curved bed channel. This kind of channel is used to join two different slopes or in ski jumps. This kind of flow presents several changes from the rectilinear flow as in the velocity and pressure distributions and even in the energy loses. The authors of this article propose an equation of gradually varied flow for vertically-curved bed rectangular channels that adds a coefficient to modify the velocity in the calculus of the local friction gradient. With these results is possible now to analyze flow profiles in vertically-curved bed channels where before were used the methods for straight channels and therefore, increase accuracy. [Spanish] Las hipotesis del movimiento rectilineo y de distribucion hidrostatica de la presion son ciertamente las mas importantes en la hidraulica de canales, y de ellas se derivan los principales modelos de flujo que usualmente emplean. Sin embargo, no es valido aplicar la misma hipotesis y metodos de analisis al flujo curvilineo, que ocurre cuando el canal adopta curvaturas verticales en el fondo, las cuales inducen cambios importantes en la distribucion de la velocidad, presion y hasta en la perdida d energia. Tal es el caso de canales que contienen curvas verticales para unir tramos de distintas pendientes y producir el cambio en la direccion del flujo en cubetas deflectoras y vertedores en tunel. Los autores de este articulo proponen una ecuacion de flujo gradualmente variado en canales rectangulares de fondo curvo, esta es de gran utilidad en la determinacion del perfil del flujo con dichas caracteristicas, donde se plantea la adicion de un factor de amplificacion de la velocidad en el calculo del gradiente local de friccion, para tomar en cuenta el
Directory of Open Access Journals (Sweden)
Ashes Banerjee
2018-02-01
Full Text Available Behaviour of flow resistance with velocity is still undefined for post-laminar flow through coarse granular media. This can cause considerable errors during flow measurements in situations like rock fill dams, water filters, pumping wells, oil and gas exploration, and so on. Keeping the non-deviating nature of Wilkins coefficients with the hydraulic radius of media in mind, the present study further explores their behaviour to independently varying media size and porosity, subjected to parallel post-laminar flow through granular media. Furthermore, an attempt is made to simulate the post-laminar flow conditions with the help of a Computational Fluid Dynamic (CFD Model in ANSYS FLUENT, since conducting large-scale experiments are often costly and time-consuming. The model output and the experimental results are found to be in good agreement. Percentage deviations between the experimental and numerical results are found to be in the considerable range. Furthermore, the simulation results are statistically validated with the experimental results using the standard ‘Z-test’. The output from the model advocates the importance and applicability of CFD modelling in understanding post-laminar flow through granular media.
A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow
Xu, Kun
1999-01-01
A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.
Ciccarelli, D.; El Mehtedi, M.; Jäger, A.; Spigarelli, S.
2015-12-01
The present study investigates the variation of flow stress and microstructural evolution with strain for ZK60 magnesium alloy. A new constitutive equation was used to model the flow stress with excellent results. This constitutive analysis and the microstructural studies carried out on strained samples revealed the existence of two different regimes. At temperatures above 300 °C, moderate grain growth and intragranular dislocation activity. Yet, the calculated value of the activation energy and the marked increase in the equivalent strain to fracture indicated grain boundary sliding as a dominant mechanism in this regime of strain rate and temperature, with dislocation motion playing an ancillary role. At lower temperatures, deformation was exclusively governed by dislocation motion, with the extensive occurrence of dynamic recrystallization, which started at low strains, and absence of grain growth.
Local Refinement of the Super Element Model of Oil Reservoir
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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
SIRIU RESERVOIR, BUZAU RIVER (ROMANIA
Directory of Open Access Journals (Sweden)
Daniel Constantin DIACONU
2008-06-01
Full Text Available Siriu reservoir, owes it`s creation to the dam built on the river Buzau, in the town which bears the same name. The reservoir has a hydro energetic role, to diminish the maximum flow and to provide water to the localities below. The partial exploitation of the lake, began in 1984; Since that time, the initial bed of the river began to accumulate large quantities of alluvia, reducing the retention capacity of the lake, which had a volume of 125 million m3. The changes produced are determined by many topographic surveys at the bottom of the lake.
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.
Moriasi, Daniel N; Gowda, Prasanna H; Arnold, Jeffrey G; Mulla, David J; Ale, Srinivasulu; Steiner, Jean L; Tomer, Mark D
2013-11-01
Subsurface tile drains in agricultural systems of the midwestern United States are a major contributor of nitrate-N (NO-N) loadings to hypoxic conditions in the Gulf of Mexico. Hydrologic and water quality models, such as the Soil and Water Assessment Tool, are widely used to simulate tile drainage systems. The Hooghoudt and Kirkham tile drain equations in the Soil and Water Assessment Tool have not been rigorously tested for predicting tile flow and the corresponding NO-N losses. In this study, long-term (1983-1996) monitoring plot data from southern Minnesota were used to evaluate the SWAT version 2009 revision 531 (hereafter referred to as SWAT) model for accurately estimating subsurface tile drain flows and associated NO-N losses. A retention parameter adjustment factor was incorporated to account for the effects of tile drainage and slope changes on the computation of surface runoff using the curve number method (hereafter referred to as Revised SWAT). The SWAT and Revised SWAT models were calibrated and validated for tile flow and associated NO-N losses. Results indicated that, on average, Revised SWAT predicted monthly tile flow and associated NO-N losses better than SWAT by 48 and 28%, respectively. For the calibration period, the Revised SWAT model simulated tile flow and NO-N losses within 4 and 1% of the observed data, respectively. For the validation period, it simulated tile flow and NO-N losses within 8 and 2%, respectively, of the observed values. Therefore, the Revised SWAT model is expected to provide more accurate simulation of the effectiveness of tile drainage and NO-N management practices. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
Kou, Jisheng
2018-02-25
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.
Joo, Young Ju; Oh, Eunjung; Kim, Su Mi
2015-01-01
The purpose of this study is to examine the structural relationships among self-efficacy, intrinsic value, test anxiety, instructional design, flow, and achievement among students at a Korean online university. To address research questions, the researchers administered online surveys to 963 college students at an online university in Korea…
Directory of Open Access Journals (Sweden)
A. M. Angulo
2011-01-01
Full Text Available This study revisits the utility of gravity models in the analysis of the principal determinants of exports. Traditional cross-sectional models are improved by considering the effect of omitted variables and/or the dynamic of trade flows through the use of spatial econometric techniques and panel data specification. This proposal is applied to the Tunisian olive oil exports during the period 2001-2009. The results provide evidence of the inertia found in export volumes, with trade relations anchored in the past likely to continue in the future. Also, we obtain evidence on the existence of a clear similarity in flows between neighbouring importing countries. On the other hand, the results show a positive, significant relationship between the importing country’s income level and imported olive oil volume. The effect of importers’ human development index is positive. The distance between countries has a negative impact on trade flow. On the contrary, sharing a common language increases olive oil trade flows. Finally, trade figures and results reflect a strong dependence of Tunisian olive oil production on precipitations
Reitz, Meredith; Sanford, Ward E.; Senay, Gabriel; Cazenas, J.
2017-01-01
This study presents new data-driven, annual estimates of the division of precipitation into the recharge, quick-flow runoff, and evapotranspiration (ET) water budget components for 2000-2013 for the contiguous United States (CONUS). The algorithms used to produce these maps ensure water budget consistency over this broad spatial scale, with contributions from precipitation influx attributed to each component at 800 m resolution. The quick-flow runoff estimates for the contribution to the rapidly varying portion of the hydrograph are produced using data from 1,434 gaged watersheds, and depend on precipitation, soil saturated hydraulic conductivity, and surficial geology type. Evapotranspiration estimates are produced from a regression using water balance data from 679 gaged watersheds and depend on land cover, temperature, and precipitation. The quick-flow and ET estimates are combined to calculate recharge as the remainder of precipitation. The ET and recharge estimates are checked against independent field data, and the results show good agreement. Comparisons of recharge estimates with groundwater extraction data show that in 15% of the country, groundwater is being extracted at rates higher than the local recharge. These maps of the internally consistent water budget components of recharge, quick-flow runoff, and ET, being derived from and tested against data, are expected to provide reliable first-order estimates of these quantities across the CONUS, even where field measurements are sparse.
International Nuclear Information System (INIS)
Khuri, S A; Sayfy, Ali
2013-01-01
This study is intended to provide a modified variational algorithm for the numerical solution of the third-order ordinary differential equation y″′ = y -2 which arises in the modeling of thin viscous films with surface tension. The resulting solution is used to solve a problem relevant to Tanner's Law for the speed of a moving three-phase contact line. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify and demonstrate the convergence and efficiency of the method.
DEFF Research Database (Denmark)
Corradi, Olivier; Hjorth, Poul G.; Starke, Jens
2012-01-01
a corridor where they are constrained by the walls of the corridor, and two crowds are aiming, from opposite directions, to pass through a narrowing doorway perpendicular to the corridor. We focus our investigation on the collective behavior of the model. As the width of the doorway is increased, we observe...... an onset of oscillations of the net pedestrian flux through the doorway, described by a Hopf bifurcation. An equation-free continuation of the Hopf point in the two parameters, door width and ratio of the pedestrian velocities of the two crowds, is performed. © 2012 Society for Industrial and Applied...
Reservoir Routing on Double-Peak Design Flood
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Andrea Gioia
2016-11-01
Full Text Available This work investigates the routing effect provided by an artificial reservoir to a double-peak flood of a given return period. The present paper introduces a dimensionless form of the reservoir balance equation that describes the hydrologic-hydraulic processes that may occur and allows for the evaluation of the reservoir routing coefficient (RC. Exploiting this equation, an extensive sensitivity analysis based on the use of two simple parametric indices that depend on the storage capacity (SC of the reservoir, the discharge capacity (DC of the spillway (with fixed-crest and the hydrologic behavior of the basin was performed.
Directory of Open Access Journals (Sweden)
F. Meunier
2017-12-01
Full Text Available In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil–root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact
Meunier, Félicien; Couvreur, Valentin; Draye, Xavier; Zarebanadkouki, Mohsen; Vanderborght, Jan; Javaux, Mathieu
2017-12-01
In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil-root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact of root maturation
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.
International Nuclear Information System (INIS)
Pellacani, F.; Macian, R.; Chiva, S.; Pena, C.
2011-01-01
In this paper upward, isothermal and turbulent bubbly flow in tubes is numerically modeled by using ANSYS CFX 12.1 with the aim of creating a basis for the reliable simulation of the flow along a vertical channel in a nuclear reactor as long term goal. Two approaches based on the mono-dispersed model and on the one-group Interfacial Area Transport Equation (IATE) model are used in order to maintain the computational effort as low as possible. This work represents the necessary step to implement a two-group interfacial area transport equation that will be able to dynamically represent the changes in interfacial structure in the transition region from bubbly to slug flow. The drag coefficient is calculated using the Grace model and the interfacial non-drag forces are also included. The Antal model is used for the calculation of the wall lubrication force coefficient. The lift force coefficient is obtained from the Tomiyama model. The turbulent dispersion force is taken into account and is modeled using the FAD (Favre averaged drag) approach, while the turbulence transfer is simulated with the Sato's model. The liquid velocity is in the range between 0.5 and 2 m/s and the average void fraction varies between 5 and 15%.The source and sink terms for break-up and coalescence needed for the calculation of the implemented Interfacial Area Density are those proposed by Yao and Morel. The model has been checked using experimental results by Mendez. Radial profile distributions of void fraction, interfacial area density and bubble mean diameter are shown at the axial position equivalent to z/D=56. The results obtained by the simulations have a good agreement with the experimental data but show also the need of a better study of the coalescence and breakup phenomena to develop more accurate interaction models. (author)
The Methane Hydrate Reservoir System
Flemings, P. B.; Liu, X.
2007-12-01
We use multi phase flow modeling and field examples (Hydrate Ridge, offshore Oregon and Blake Ridge, offshore North Carolina) to demonstrate that the methane hydrate reservoir system links traditional and non- traditional hydrocarbon system components: free gas flow is a fundamental control on this system. As in a traditional hydrocarbon reservoir, gas migrates into the hydrate reservoir as a separate phase (secondary migration) where it is trapped in a gas column beneath the base of the hydrate layer. With sufficient gas supply, buoyancy forces exceed either the capillary entry pressure of the cap rock or the fracture strength of the cap rock, and gas leaks into the hydrate stability zone, or cap rock. When gas enters the hydrate stability zone and forms hydrate, it becomes a very non traditional reservoir. Free gas forms hydrate, depletes water, and elevates salinity until pore water is too saline for further hydrate formation: salinity and hydrate concentration increase upwards from the base of the regional hydrate stability zone (RHSZ) to the seafloor and the base of the hydrate stability zone has significant topography. Gas chimneys couple the free gas zone to the seafloor through high salinity conduits that are maintained at the three-phase boundary by gas flow. As a result, significant amounts of gaseous methane can bypass the RHSZ, which implies a significantly smaller hydrate reservoir than previously envisioned. Hydrate within gas chimneys lie at the three-phase boundary and thus small increases in temperature or decreases in pressure can immediately transport methane into the ocean. This type of hydrate deposit may be the most economical for producing energy because it has very high methane concentrations (Sh > 70%) located near the seafloor, which lie on the three-phase boundary.
Southard, Rodney E.
2013-01-01
The weather and precipitation patterns in Missouri vary considerably from year to year. In 2008, the statewide average rainfall was 57.34 inches and in 2012, the statewide average rainfall was 30.64 inches. This variability in precipitation and resulting streamflow in Missouri underlies the necessity for water managers and users to have reliable streamflow statistics and a means to compute select statistics at ungaged locations for a better understanding of water availability. Knowledge of surface-water availability is dependent on the streamflow data that have been collected and analyzed by the U.S. Geological Survey for more than 100 years at approximately 350 streamgages throughout Missouri. The U.S. Geological Survey, in cooperation with the Missouri Department of Natural Resources, computed streamflow statistics at streamgages through the 2010 water year, defined periods of drought and defined methods to estimate streamflow statistics at ungaged locations, and developed regional regression equations to compute selected streamflow statistics at ungaged locations. Streamflow statistics and flow durations were computed for 532 streamgages in Missouri and in neighboring States of Missouri. For streamgages with more than 10 years of record, Kendall’s tau was computed to evaluate for trends in streamflow data. If trends were detected, the variable length method was used to define the period of no trend. Water years were removed from the dataset from the beginning of the record for a streamgage until no trend was detected. Low-flow frequency statistics were then computed for the entire period of record and for the period of no trend if 10 or more years of record were available for each analysis. Three methods are presented for computing selected streamflow statistics at ungaged locations. The first method uses power curve equations developed for 28 selected streams in Missouri and neighboring States that have multiple streamgages on the same streams. Statistical
International Nuclear Information System (INIS)
Sung, Chang Kyung; Chun, Moon Hyun
1996-01-01
A two-step approach has been used to obtain a new criterion for the onset of slug formation : (1) In the first step, a more general expression than the existing models for the onset of slug flow criterion has been derived from the analysis of singular points and neutral stability conditions of the transient one-dimensional two-phase flow equations of two-fluid model. (2) In the second step, introducing simplifications and incorporating a parameter into the general expression obtained in the first step to satisfy a number of physical conditions a priori specified, a new simple criterion for the onset of slug flow has been derived. Comparisons of the present model with existing models and experimental data show that the present model agree very closely with Taitel and Dukler's model and experimental data in horizontal pipes. In an inclined pipe (θ=50 deg ), however, the difference between the predictions of the present model and those of existing models is appreciably large and the present model gives the best agreement with Ohnuki et al.'s data. 17 refs., 5 figs., 1 tab. (author)
Salama, Amgad
2013-09-01
In this work the problem of flow in three-dimensional, axisymmetric, heterogeneous porous medium domain is investigated numerically. For this system, it is natural to use cylindrical coordinate system, which is useful in describing phenomena that have some rotational symmetry about the longitudinal axis. This can happen in porous media, for example, in the vicinity of production/injection wells. The basic feature of this system is the fact that the flux component (volume flow rate per unit area) in the radial direction is changing because of the continuous change of the area. In this case, variables change rapidly closer to the axis of symmetry and this requires the mesh to be denser. In this work, we generalize a methodology that allows coarser mesh to be used and yet yields accurate results. This method is based on constructing local analytical solution in each cell in the radial direction and moves the derivatives in the other directions to the source term. A new expression for the harmonic mean of the hydraulic conductivity in the radial direction is developed. Apparently, this approach conforms to the analytical solution for uni-directional flows in radial direction in homogeneous porous media. For the case when the porous medium is heterogeneous or the boundary conditions is more complex, comparing with the mesh-independent solution, this approach requires only coarser mesh to arrive at this solution while the traditional methods require more denser mesh. Comparisons for different hydraulic conductivity scenarios and boundary conditions have also been introduced. © 2013 Elsevier B.V.
Kim, Moon-Sang
A two-dimensional, axisymmetric, full Navier-Stokes solver has been developed with equilibrium and nonequilibrium air models. The effects of a real gas are investigated numerically in the hypersonic flow regime. The code employs several different upwind schemes to examine their effect on the accuracy and stability of the numerical solutions. A finite volume method is used with curvilinear coordinates, and the first-order, up wind schemes are extended to second-order accuracy in space. The steady-state solutions are obtained using an approximately factorized implicit scheme, including fully implicit boundary conditions, to accelerate the convergence. The numerical accuracy is improved by introducing the closed-control-volume concept in the metric quantity calculations. This idea is verified by a blunt-nosed flow case with a scrambled grid. In general, the fastest convergence in an implicit scheme is obtained when the same residual and correction operators are applied. A new simplified Jacobian matrix is derived for Roe's flux difference splitting scheme because of the complexity involved in deriving the full Jacobian matrix, and which yields a faster convergence compared to the use of a different correction operator such as Steger-Warming's.
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
International Nuclear Information System (INIS)
De Focatiis, Davide S. A.; Buckley, C. Paul; Embery, John
2008-01-01
This paper investigates the behaviour of a well-characterised monodisperse grade of entangled atactic polystyrene across a very wide temperature and strain rate range through linear and non-linear melt rheology and solid-state deformation. In an effort to construct a constitutive model for large deformations able to describe rheological response right across this wide timescale, two well-established rheological models are combined: the well known RoliePoly (RP) conformational melt model and the Oxford glass-rubber constitutive model for glassy polymers. Comparisons between experimental data and simulations from a numerical implementation of the model illustrate that the model can cope well with the range of deformations in which orientation is limited to length-scales longer than an entanglement length. One approach in which the model can be expanded to incorporate the effects of orientation on shorter length scales using anisotropic viscoplastic flow is briefly discussed
Physical Aspects in Upscaling of Fractured Reservoirs and Improved Oil Recovery Prediction
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
Discharge rating equation and hydraulic characteristics of standard Denil fishways
Odeh, M.
2003-01-01
This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables. A dimensionless discharge coefficient based only on the physical slope of the fishway is introduced. The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes. Hydraulic characteristics of flow inside these fishways are discussed. Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway. Engineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only. Discharge capacity was directly proportional to the fishway width and slope. The new equation is a design tool for engineers and field biologists, especially when designing a fishway based on flow availability in conjunction with the swimming capabilities of target fish species.
Akratos, Christos S; Papaspyros, John N E; Tsihrintzis, Vassilios A
2009-01-01
The aim of this paper is to examine if artificial neural networks (ANNs) can predict nitrogen removal in horizontal subsurface flow (HSF) constructed wetlands (CWs). ANN development was based on experimental data from five pilot-scale CW units. The proper selection of the components entering the ANN was achieved using principal component analysis (PCA), which identified the main factors affecting TN removal, i.e., porous media porosity, wastewater temperature and hydraulic residence time. Two neural networks were examined: the first included only the three factors selected from the PCA, and the second included in addition meteorological parameters (i.e., barometric pressure, rainfall, wind speed, solar radiation and humidity). The first model could predict TN removal rather satisfactorily (R(2)=0.53), and the second resulted in even better predictions (R(2)=0.69). From the application of the ANNs, a design equation was derived for TN removal prediction, resulting in predictions comparable to those of the ANNs (R(2)=0.47). For the validation of the results of the ANNs and of the design equation, available data from the literature were used and showed a rather satisfactory performance.
Düben, Peter D.; Dolaptchiev, Stamen I.
2015-08-01
Inexact hardware can reduce computational cost, due to a reduced energy demand and an increase in performance, and can therefore allow higher-resolution simulations of the atmosphere within the same budget for computation. We investigate the use of emulated inexact hardware for a model of the randomly forced 1D Burgers equation with stochastic sub-grid-scale parametrisation. Results show that numerical precision can be reduced to only 12 bits in the significand of floating-point numbers—instead of 52 bits for double precision—with no serious degradation in results for all diagnostics considered. Simulations that use inexact hardware on a grid with higher spatial resolution show results that are significantly better compared to simulations in double precision on a coarser grid at similar estimated computing cost. In the second half of the paper, we compare the forcing due to rounding errors to the stochastic forcing of the stochastic parametrisation scheme that is used to represent sub-grid-scale variability in the standard model setup. We argue that stochastic forcings of stochastic parametrisation schemes can provide a first guess for the upper limit of the magnitude of rounding errors of inexact hardware that can be tolerated by model simulations and suggest that rounding errors can be hidden in the distribution of the stochastic forcing. We present an idealised model setup that replaces the expensive stochastic forcing of the stochastic parametrisation scheme with an engineered rounding error forcing and provides results of similar quality. The engineered rounding error forcing can be used to create a forecast ensemble of similar spread compared to an ensemble based on the stochastic forcing. We conclude that rounding errors are not necessarily degrading the quality of model simulations. Instead, they can be beneficial for the representation of sub-grid-scale variability.
Mathematical models of a liquid filtration from reservoirs
Directory of Open Access Journals (Sweden)
Anvarbek Meirmanov
2014-02-01
Full Text Available This article studies the filtration from reservoirs into porous media under gravity. We start with the exact mathematical model at the microscopic level, describing the joint motion of a liquid in reservoir and the same liquid and the elastic solid skeleton in the porous medium. Then using a homogenization procedure we derive the chain of macroscopic models from the poroelasticity equations up to the simplest Darcy's law in the porous medium and hydraulics in the reservoir.
Impact of a Thermocline on Water Dynamics in Reservoirs – Dobczyce Reservoir Case
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Hachaj Paweł S.
2017-06-01
Full Text Available While modeling water dynamics in dam reservoirs, it is usually assumed that the flow involves the whole water body. It is true for shallow reservoirs (up to several meters of depth but may be false for deeper ones. The possible presence of a thermocline creates an inactive bottom layer that does not move, causing all the discharge to be carried by the upper strata. This study compares the results of hydrodydynamic simulations performed for the whole reservoir to the ones carried out for the upper strata only. The validity of a non-stratified flow approximation is then discussed.
Production Optimization of Oil Reservoirs
DEFF Research Database (Denmark)
Völcker, Carsten
With an increasing demand for oil and diculties in nding new major oil elds, research on methods to improve oil recovery from existing elds is more necessary now than ever. The subject of this thesis is to construct ecient numerical methods for simulation and optimization of oil recovery...... programming (SQP) with line-search and BFGS approximations of the Hessian, and the adjoint method for ecient computation of the gradients. We demonstrate that the application of NMPC for optimal control of smart-wells has the potential to increase the economic value of an oil reservoir....... 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...
Exploitation of subsea gas hydrate reservoirs
Janicki, Georg; Schlüter, Stefan; Hennig, Torsten; Deerberg, Görge
2016-04-01
Natural gas hydrates are considered to be a potential energy resource in the future. They occur in permafrost areas as well as in subsea sediments and are stable at high pressure and low temperature conditions. According to estimations the amount of carbon bonded in natural gas hydrates worldwide is two times larger than in all known conventional fossil fuels. Besides technical challenges that have to be overcome climate and safety issues have to be considered before a commercial exploitation of such unconventional reservoirs. The potential of producing natural gas from subsea gas hydrate deposits by various means (e.g. depressurization and/or injection of carbon dioxide) is numerically studied in the frame of the German research project »SUGAR«. The basic mechanisms of gas hydrate formation/dissociation and heat and mass transport in porous media are considered and implemented into a numerical model. The physics of the process leads to strong non-linear couplings between hydraulic fluid flow, hydrate dissociation and formation, hydraulic properties of the sediment, partial pressures and seawater solution of components and the thermal budget of the system described by the heat equation. This paper is intended to provide an overview of the recent development regarding the production of natural gas from subsea gas hydrate reservoirs. It aims at giving a broad insight into natural gas hydrates and covering relevant aspects of the exploitation process. It is focused on the thermodynamic principles and technological approaches for the exploitation. The effects occurring during natural gas production within hydrate filled sediment layers are identified and discussed by means of numerical simulation results. The behaviour of relevant process parameters such as pressure, temperature and phase saturations is described and compared for different strategies. The simulations are complemented by calculations for different safety relevant problems.
International Nuclear Information System (INIS)
Silva, S.S. De.
1990-01-01
At a workshop on reservoir fisheries research, papers were presented on the limnology of reservoirs, the changes that follow impoundment, fisheries management and modelling, and fish culture techniques. Separate abstracts have been prepared for three papers from this workshop
Miranda, Leandro E.; Bettoli, Phillip William
2010-01-01
Large impoundments, defined as those with surface area of 200 ha or greater, are relatively new aquatic ecosystems in the global landscape. They represent important economic and environmental resources that provide benefits such as flood control, hydropower generation, navigation, water supply, commercial and recreational fisheries, and various other recreational and esthetic values. Construction of large impoundments was initially driven by economic needs, and ecological consequences received little consideration. However, in recent decades environmental issues have come to the forefront. In the closing decades of the 20th century societal values began to shift, especially in the developed world. Society is no longer willing to accept environmental damage as an inevitable consequence of human development, and it is now recognized that continued environmental degradation is unsustainable. Consequently, construction of large reservoirs has virtually stopped in North America. Nevertheless, in other parts of the world construction of large reservoirs continues. The emergence of systematic reservoir management in the early 20th century was guided by concepts developed for natural lakes (Miranda 1996). However, we now recognize that reservoirs are different and that reservoirs are not independent aquatic systems inasmuch as they are connected to upstream rivers and streams, the downstream river, other reservoirs in the basin, and the watershed. Reservoir systems exhibit longitudinal patterns both within and among reservoirs. Reservoirs are typically arranged sequentially as elements of an interacting network, filter water collected throughout their watersheds, and form a mosaic of predictable patterns. Traditional approaches to fisheries management such as stocking, regulating harvest, and in-lake habitat management do not always produce desired effects in reservoirs. As a result, managers may expend resources with little benefit to either fish or fishing. Some locally
Mathematical and field analysis of longitudinal reservoir infill
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.
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.
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
Reservoirs in the United States
Harbeck, G. Earl
1948-01-01
Man has engaged in the control of flowing water since history began. Among his early recorded efforts were reservoirs for muncipal water-supplies constructed near ancient Jerusalem to store water which was brought there in masonry conduits. 1/ Irrigation was practiced in Egypt as early as 2000 B. C. There the "basin system" was used from ancient times until the 19th century. The land was divided , into basins of approximately 40,000 acres, separated by earthen dikes. 2/ Flood waters of the Nile generally inundated the basins through canals, many of which were built by the Pharaohs. Even then the economic consequences of a deficient annual flood were recognized. Lake Maeris, which according to Herodotus was an ancient storage reservoir, is said to have had an area of 30,000 acres. In India, the British found at the time of their occupancy of the Presidency of Madras about 50,000 reservoirs for irrigation, many believed to be of ancient construction. 3/ During the period 115-130 A. D. reservoirs were built to improve the water-supply of Athens. Much has been written concerning the elaborate collection and distribution system built to supply Rome, and parts of it remain to this day as monuments to the engineering skill employed by the Romans in solving the problem of large-scale municipal water-supplies.
Hydrocarbon Reservoir Parameter Estimation Using Production Data and Time-Lapse Seismic
Przybysz-Jarnut, J.K.
2010-01-01
The numerical simulation of hydrocarbon reservoir flow is necessarily an approximation of the flow in the real reservoir. The knowledge about the reservoir is limited and some of the processes occurring are either not taken into account or not described in an adequate way. The parameters influencing
Kinoshita, Masataka; Yamano, Makoto
1997-02-01
Detailed heat flow measurements revealed an enormous heat flow variation (102 to 105 mW m-2) in the Jade hydrothermal field (27°16'N, 127°05'E and water depth 1350 m) located on the slope of the Izena Hole in the Mid-Okinawa Trough. Within the Jade site, heat flow is higher than 1000 mW m-2 and decreases to ˜100 mW m-2 with a 1 km horizontal scale. Near the Jade black smoker, heat flow varies from >30,000 mW m-2 at a hydrothermally altered area to 1700 mW m-2 less than 100 m from it. A large-scale heat flow variation suggests that the base of the escarpment near the Jade site serves as a recharge area for the Jade site. Linear geotherms indicate that the upward Darcian flow within sediments is slower than ˜3 cm yr-1. Thus the fluid circulation pathways would basically be restricted in permeable channels. Estimated conductive heat output rate from the Jade site is 4-7 MW, which is comparable to heat output by a single black smoker vent (˜8 MW). One-dimensional thermal modeling predicts the existence of a boiling zone at ˜200 m beneath the Jade site, which may be overlain by a fractured impermeable layer. The normal chloride content of venting fluids from the black smoker may be explained either by upwelling of fluid which boiled at shallow depth but suffered no phase segregation, or by upwelling of fluid above the boiling interface.
Stream, Lake, and Reservoir Management.
Dai, Jingjing; Mei, Ying; Chang, Chein-Chi
2017-10-01
This review on stream, lake, and reservoir management covers selected 2016 publications on the focus of the following sections: Stream, lake, and reservoir management • Water quality of stream, lake, and reservoir • Reservoir operations • Models of stream, lake, and reservoir • Remediation and restoration of stream, lake, and reservoir • Biota of stream, lake, and reservoir • Climate effect of stream, lake, and reservoir.
FRACTURED PETROLEUM RESERVOIRS
Energy Technology Data Exchange (ETDEWEB)
Abbas Firoozabadi
1999-06-11
The four chapters that are described in this report cover a variety of subjects that not only give insight into the understanding of multiphase flow in fractured porous media, but they provide also major contribution towards the understanding of flow processes with in-situ phase formation. In the following, a summary of all the chapters will be provided. Chapter I addresses issues related to water injection in water-wet fractured porous media. There are two parts in this chapter. Part I covers extensive set of measurements for water injection in water-wet fractured porous media. Both single matrix block and multiple matrix blocks tests are covered. There are two major findings from these experiments: (1) co-current imbibition can be more efficient than counter-current imbibition due to lower residual oil saturation and higher oil mobility, and (2) tight fractured porous media can be more efficient than a permeable porous media when subjected to water injection. These findings are directly related to the type of tests one can perform in the laboratory and to decide on the fate of water injection in fractured reservoirs. Part II of Chapter I presents modeling of water injection in water-wet fractured media by modifying the Buckley-Leverett Theory. A major element of the new model is the multiplication of the transfer flux by the fractured saturation with a power of 1/2. This simple model can account for both co-current and counter-current imbibition and computationally it is very efficient. It can be orders of magnitude faster than a conventional dual-porosity model. Part II also presents the results of water injection tests in very tight rocks of some 0.01 md permeability. Oil recovery from water imbibition tests from such at tight rock can be as high as 25 percent. Chapter II discusses solution gas-drive for cold production from heavy-oil reservoirs. The impetus for this work is the study of new gas phase formation from in-situ process which can be significantly
Energy Technology Data Exchange (ETDEWEB)
1990-09-01
This is one in a series of status reports prepared by the Tennessee Valley Authority (TVA) for those interested in the conditions of TVA reservoirs. This overview of Wheeler Reservoir summarizes reservoir purposes and operation, reservoir and watershed characteristics, reservoir uses and use impairments, and water quality and aquatic biological conditions. The information presented here is from the most recent reports, publications, and original data available. If no recent data were available, historical data were summarized. If data were completely lacking, environmental professionals with special knowledge of the resource were interviewed. 12 refs., 2 figs.
Roure, F.; Andriessen, P.A.M.; Callot, J.P.; Ferket, H.; Gonzales, E.; Guilhaumou, N.; Hardebol, N.J.; Lacombe, O.; Malandain, J.; Mougin, P.; Muska, K.; Ortuno, S.; Sassi, W.; Swennen, R.; Vilasi, N.
2010-01-01
Basin modelling tools are now more efficient to reconstruct palinspastic structural cross sections and compute the history of temperature, pore-fluid pressure and fluid flow circulations in complex structural settings. In many cases and especially in areas where limited erosion occurred, the use of
Estimated cumulative sediment trapping in future hydropower reservoirs in Africa
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
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-04-01
This project has used a multi-disciplinary approach employing geology, geophysics, and engineering to conduct advanced reservoir characterization and management activities to design and implement an optimized infill drilling program at the North Robertson (Clearfork) Unit in Gaines County, Texas. The activities during the first Budget Period consisted of developing an integrated reservoir description from geological, engineering, and geostatistical studies, and using this description for reservoir flow simulation. Specific reservoir management activities were identified and tested. The geologically targeted infill drilling program currently being implemented is a result of this work. A significant contribution of this project is to demonstrate the use of cost-effective reservoir characterization and management tools that will be helpful to both independent and major operators for the optimal development of heterogeneous, low permeability shallow-shelf carbonate (SSC) reservoirs. The techniques that are outlined for the formulation of an integrated reservoir description apply to all oil and gas reservoirs, but are specifically tailored for use in the heterogeneous, low permeability carbonate reservoirs of West Texas.
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.
Crittenden, P. E.; Balachandar, S.
2018-03-01
The radial one-dimensional Euler equations are often rewritten in what is known as the geometric source form. The differential operator is identical to the Cartesian case, but source terms result. Since the theory and numerical methods for the Cartesian case are well-developed, they are often applied without modification to cylindrical and spherical geometries. However, numerical conservation is lost. In this article, AUSM^+ -up is applied to a numerically conservative (discrete) form of the Euler equations labeled the geometric form, a nearly conservative variation termed the geometric flux form, and the geometric source form. The resulting numerical methods are compared analytically and numerically through three types of test problems: subsonic, smooth, steady-state solutions, Sedov's similarity solution for point or line-source explosions, and shock tube problems. Numerical conservation is analyzed for all three forms in both spherical and cylindrical coordinates. All three forms result in constant enthalpy for steady flows. The spatial truncation errors have essentially the same order of convergence, but the rate constants are superior for the geometric and geometric flux forms for the steady-state solutions. Only the geometric form produces the correct shock location for Sedov's solution, and a direct connection between the errors in the shock locations and energy conservation is found. The shock tube problems are evaluated with respect to feature location using an approximation with a very fine discretization as the benchmark. Extensions to second order appropriate for cylindrical and spherical coordinates are also presented and analyzed numerically. Conclusions are drawn, and recommendations are made. A derivation of the steady-state solution is given in the Appendix.
DEFF Research Database (Denmark)
Knoop, Hans Henrik
2006-01-01
FLOW. Orden i hovedet på den fede måde Oplevelsesmæssigt er flow-tilstanden kendetegnet ved at man er fuldstændig involveret, fokuseret og koncentreret; at man oplever stor indre klarhed ved at vide hvad der skal gøres, og i hvilket omfang det lykkes; at man ved at det er muligt at løse opgaven...
Directory of Open Access Journals (Sweden)
Jing Lu
2010-01-01
Full Text Available For a bounded reservoir with no flow boundaries, the pseudo-steady-state flow regime is common at long-producing times. Taking a partially penetrating well as a uniform line sink in three dimensional space, by the orthogonal decomposition of Dirac function and using Green's function to three-dimensional Laplace equation with homogeneous Neumann boundary condition, this paper presents step-by-step derivations of a pseudo-steady-state productivity formula for a partially penetrating vertical well arbitrarily located in a closed anisotropic box-shaped drainage volume. A formula for calculating pseudo skin factor due to partial penetration is derived in detailed steps. A convenient expression is presented for calculating the shape factor of an isotropic rectangle reservoir with a single fully penetrating vertical well, for arbitrary aspect ratio of the rectangle, and for arbitrary position of the well within the rectangle.
Bezerra, F. H.; Cazarin, C. L.; Srivastava, N. K.
2017-12-01
This study investigates the diagenetic processes that generated secondary porosity-permeability in carbonates. Our study area is the Jandaira Formation, a post-rift unit, 50-700 m thick, which occurs over an area of 70 x 260 km in the Potiguar Basin, Equatorial margin of Brazil. The Jandaira Formation formed in the Turonian-Campanian and is the major exposed Cretaceous carbonate platform in the eastern continental margin of South America. Little folding and nearly flat-lying layers characterize this unit. We used a multidisciplinary approach, which included drone imagery, petrographic, petrophysical, petrological, and structural studies. Our results indicate that several levels of dissolution occurred in mudstone, grainstone, and wackestone facies along faults, fractures, and bedding planes. Fracture and faults provided vertical leaching pathways and sedimentary bedding provided horizontal pathways of increased secondary porosity and permeability. Dissolution resulted in a multi-scale karst system that could reach voids 5 m wide and 1 km long. Dissolution mostly affect the dolomitized sedimentary facies in the form of vugular, moldic, interparticular, and intercrystalline porosity. It also generated a new modified facies that we defined as karstified facies. Dissolution increased permeability in carbonate rocks from primary values of 0.0-0.94 mD to as much as 1370.11 mD. Micritization, lixiviation of evaporites, meteoric water infiltration and dolomitization during late diagenesis could have triggered dissolution processes. The Jandaira Formation serves as an analog of fractured and karstified carbonate reservoirs, where faults, joints, and bedding acted as pathways of high permeability.
Miles, Robin R [Danville, CA; Benett, William J [Livermore, CA; Coleman, Matthew A [Oakland, CA; Pearson, Francesca S [Livermore, CA; Nasarabadi, Shanavaz L [Livermore, CA
2011-03-08
A lateral flow strip assay apparatus comprising a housing; a lateral flow strip in the housing, the lateral flow strip having a receiving portion; a sample collection unit; and a reagent reservoir. Saliva and/or buccal cells are collected from an individual using the sample collection unit. The sample collection unit is immersed in the reagent reservoir. The tip of the lateral flow strip is immersed in the reservoir and the reagent/sample mixture wicks up into the lateral flow strip to perform the assay.
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
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
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.
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.
Stochastic Reservoir Characterization Constrained by Seismic Data
Energy Technology Data Exchange (ETDEWEB)
Eide, Alfhild Lien
1999-07-01
In order to predict future production of oil and gas from a petroleum reservoir, it is important to have a good description of the reservoir in terms of geometry and physical parameters. This description is used as input to large numerical models for the fluid flow in the reservoir. With increased quality of seismic data, it is becoming possible to extend their use from the study of large geologic structures such as seismic horizons to characterization of the properties of the reservoir between the horizons. Uncertainties because of the low resolution of seismic data can be successfully handled by means of stochastic modeling, and spatial statistics can provide tools for interpolation and simulation of reservoir properties not completely resolved by seismic data. This thesis deals with stochastic reservoir modeling conditioned to seismic data and well data. Part I presents a new model for stochastic reservoir characterization conditioned to seismic traces. Part II deals with stochastic simulation of high resolution impedance conditioned to measured impedance. Part III develops a new stochastic model for calcite cemented objects in a sandstone background; it is a superposition of a marked point model for the calcites and a continuous model for the background.
A volume-balance model for flow on porous media
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2015-11-01
Volume-balance models are used by petroleum engineers for simulating multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Numerical tests for phase separation under gravity are presented for multiphase three dimensional flow in heterogeneous porous media. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER grant number 42536 (DGAJ-SPI-34-170412-217).
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
Directory of Open Access Journals (Sweden)
Niculae Iulian TEODORESCU
2008-06-01
Full Text Available The Surduc reservoir was projected to ensure more water when water is scarce and to thus provide especially the city Timisoara, downstream of it with water.The accumulation is placed on the main affluent of the Bega river, Gladna in the upper part of its watercourse.The dam behind which this accumulation was created is of a frontal type made of enrochements with a masque made of armed concrete on the upstream part and protected/sustained by grass on the downstream. The dam is 130m long on its coping and a constructed height of 34 m. It is also endowed with spillway for high water and two bottom outlets formed of two conduits, at the end of which is the microplant. The second part of my paper deals with the hydrometric analysis of the Accumulation Surduc and its impact upon the flow, especially the maximum run-off. This influence is exemplified through the high flood from the 29th of July 1980, the most significant flood recorded in the basin with an apparition probability of 0.002%.
Constrained genetic algorithms for optimizing multi-use reservoir operation
Chang, Li-Chiu; Chang, Fi-John; Wang, Kuo-Wei; Dai, Shin-Yi
2010-08-01
To derive an optimal strategy for reservoir operations to assist the decision-making process, we propose a methodology that incorporates the constrained genetic algorithm (CGA) where the ecological base flow requirements are considered as constraints to water release of reservoir operation when optimizing the 10-day reservoir storage. Furthermore, a number of penalty functions designed for different types of constraints are integrated into reservoir operational objectives to form the fitness function. To validate the applicability of this proposed methodology for reservoir operations, the Shih-Men Reservoir and its downstream water demands are used as a case study. By implementing the proposed CGA in optimizing the operational performance of the Shih-Men Reservoir for the last 20 years, we find this method provides much better performance in terms of a small generalized shortage index (GSI) for human water demands and greater ecological base flows for most of the years than historical operations do. We demonstrate the CGA approach can significantly improve the efficiency and effectiveness of water supply capability to both human and ecological base flow requirements and thus optimize reservoir operations for multiple water users. The CGA can be a powerful tool in searching for the optimal strategy for multi-use reservoir operations in water resources management.
Investigation of gas flow in SAGD
Energy Technology Data Exchange (ETDEWEB)
Canas, C.; Kantzas, A. [Calgary Univ., AB (Canada); Edmunds, N. [Laricina Energy Ltd., Calgary, AB (Canada)
2009-07-01
Non-condensable gases play an important role in the thermal efficiency of steam assisted gravity drainage (SAGD) processes. The accurate characterization of gas flow in SAGD is needed in order to predicts its potential impact on process performance. This study used flow equations to describe viscous drag in a gas-water-oil system. A 3-phase flow analysis was used to predict the amount of gas produced by viscous drag in 2 geometries: (1) flow in a capillary tube; and (2) the flow of a descending film on a plate. The functionality analysis described the response of the dragged gas to changes in operating and reservoir conditions. A 12.6{sup 3} oil draining zone volume was modelled as a bundle of capillaries with a porosity of 0.35. Capillary length was 2 meters. Results of the study showed that a portion of the gas in the steam chamber flows downwards, and was caused by the viscous drag of the falling liquids. Momentum transfer was highly dependent on operational and reservoir conditions. It was concluded that amounts of gas that flow downwards will increase when operating temperatures increase in the SAGD chamber. 17 refs., 1 tab., 10 figs.
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.
Wang, Xuan; Hao, Guangling; Yang, Zhifeng; Liang, Peiyu; Cai, Yanpeng; Li, Chunhui; Sun, Lian; Zhu, Jie
2015-12-01
In this paper, the Mann-Kendall test and F-test were combined to analyze the annual and seasonal streamflow variations and aberrance points for the twin rivers from 1963 to 2011. The Tennant method was subsequently used to evaluate the ecological flow assurance and deficit. Finally, the Double Mass Curve method was applied to identifying the human activities affecting the streamflow variations. The results were as follows: (1) Three similar stages of the streamflow variations were found for the twin rivers: fluctuations before 1980, the tiny downward trends from the 1980s to the 1990s, and the notably downward trends in the 2000s. (2) The seasonal streamflow also decreased continuously and dramatically, especially in summer, by 80.9% for the Chaohe River and 86.0% for the Baihe River. (3) During the spawning season, 83.3% and 73.1% of streamflow was not at the appropriate level for the Chaohe and Baihe Rivers, respectively, which indicated that the ecological environment was not optimal for the reproduction and breeding of aquatic organisms. While in other periods, the ecological flow assurance was better than that in spawning seasons for the Chaohe and Baihe Rivers, respectively. This indicated that the streamflow regimes of the twin rivers were not always optimal and conducive to the development of the aquatic ecosystem. (4) The streamflow variations of the twin rivers were influenced by increasingly intensive human activities such as changes of land use and land cover, and excessive exploitation and utilization of water resources. These influences were cumulative and showed a gradually increasing tendency. This research is helpful for understanding the streamflow regime and for forecasting of the regional extreme climate, such as drought and floods, and can provide a basis for decision making and formulating adaptive ecological security countermeasures in response to climate changes and human activities. Copyright © 2015 Elsevier B.V. All rights reserved.
New boundary conditions for oil reservoirs with fracture
Andriyanova, Elena; Astafev, Vladimir
2017-06-01
Based on the fact that most of oil fields are on the late stage of field development, it becomes necessary to produce hard-to-extract oil, which can be obtained only by use of enhance oil recovery methods. For example many low permeable or shale formations can be developed only with application of massive hydraulic fracturing technique. In addition, modern geophysical researches show that mostly oil bearing formations are complicated with tectonic faults of different shape and permeability. These discontinuities exert essential influence on the field development process and on the well performance. For the modeling of fluid flow in the reservoir with some area of different permeability, we should determine the boundary conditions. In this article for the first time the boundary conditions for the problem of fluid filtration in the reservoir with some discontinuity are considered. This discontinuity represents thin but long area, which can be hydraulic fracturing of tectonic fault. The obtained boundary condition equations allow us to take into account pressure difference above and below the section and different values of permeability.
Reservoir characterization and enhanced oil recovery research
Energy Technology Data Exchange (ETDEWEB)
Lake, L.W.; Pope, G.A.; Schechter, R.S.
1992-03-01
The research in this annual report falls into three tasks each dealing with a different aspect of enhanced oil recovery. The first task strives to develop procedures for accurately modeling reservoirs for use as input to numerical simulation flow models. This action describes how we have used a detail characterization of an outcrop to provide insights into what features are important to fluid flow modeling. The second task deals with scaling-up and modeling chemical and solvent EOR processes. In a sense this task is the natural extension of task 1 and, in fact, one of the subtasks uses many of the same statistical procedures for insight into the effects of viscous fingering and heterogeneity. The final task involves surfactants and their interactions with carbon dioxide and reservoir minerals. This research deals primarily with phenomena observed when aqueous surfactant solutions are injected into oil reservoirs.
Acoustofluidics 1: Governing equations in microfluidics
DEFF Research Database (Denmark)
Bruus, Henrik
2011-01-01
Governing equations for microfluidics and basic flow solutions are presented. Equivalent circuit modeling for determining flow rates in microfluidic networks is introduced.......Governing equations for microfluidics and basic flow solutions are presented. Equivalent circuit modeling for determining flow rates in microfluidic networks is introduced....
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, ...
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 ...
Liquid oil production from shale gas condensate reservoirs
Energy Technology Data Exchange (ETDEWEB)
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.
Geomechanical production optimization in faulted and fractured reservoirs
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
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
Chyczewski, Thomas Stanley, Jr.
A national interest in High Speed Civil Transports (HSCT) coupled with strict airport noise regulations has prompted the scientific community to investigate new and improved noise prediction strategies. Meeting these airport regulations is considered to be a major design challenge for the HSCT. In light of this effort, a direct simulation strategy for predicting supersonic jet noise is developed in this thesis. Direct simulations are quickly becoming the method of choice due to their generality and ever decreasing expense associated with the development of parallel processors. Supersonic jet noise is known to be dominated by the growth and decay of large scale turbulent structures. The direct simulation approach used here consists of solving the full Navier Stokes equations using high order finite difference techniques to simulate the evolution of these structures and the noise they radiate to the acoustic near field. This near field solution is then extrapolated to the far field using a Kirchhoff method. The numerical algorithm uses a fourth order Runge -Kutta method for the time integration. The spatial derivatives are approximated by a sixth order central scheme. A sixth order filter is used at each interior mesh point to damp frequencies that cannot be resolved by the spatial scheme. Second order filtering is provided only where required for stability. It is found to be confined to specific locations in the jet core and should have no effect on the acoustic solution. Characteristic based nonreflecting conditions are used to minimize reflections at the far field boundaries and have proven to be effective. Additional boundary conditions are required in the form of it model for the nozzle exit flow. The characteristics of the nozzle exit flow can have a significant impact on the noise radiation. This dependence is unfortunate since comprehensive experimental data is not available in this region of the jet. A model is developed here that addresses a variety of
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...
Dynamic reservoir well interaction
Sturm, W.L.; Belfroid, S.P.C.; Wolfswinkel, O. van; Peters, M.C.A.M.; Verhelst, F.J.P.C.M.
2004-01-01
In order to develop smart well control systems for unstable oil wells, realistic modeling of the dynamics of the well is essential. Most dynamic well models use a semi-steady state inflow model to describe the inflow of oil and gas from the reservoir. On the other hand, reservoir models use steady
Reservoir Engineering Management Program
Energy Technology Data Exchange (ETDEWEB)
Howard, J.H.; Schwarz, W.J.
1977-12-14
The Reservoir Engineering Management Program being conducted at Lawrence Berkeley Laboratory includes two major tasks: 1) the continuation of support to geothermal reservoir engineering related work, started under the NSF-RANN program and transferred to ERDA at the time of its formation; 2) the development and subsequent implementation of a broad plan for support of research in topics related to the exploitation of geothermal reservoirs. This plan is now known as the GREMP plan. Both the NSF-RANN legacies and GREMP are in direct support of the DOE/DGE mission in general and the goals of the Resource and Technology/Resource Exploitation and Assessment Branch in particular. These goals are to determine the magnitude and distribution of geothermal resources and reduce risk in their exploitation through improved understanding of generically different reservoir types. These goals are to be accomplished by: 1) the creation of a large data base about geothermal reservoirs, 2) improved tools and methods for gathering data on geothermal reservoirs, and 3) modeling of reservoirs and utilization options. The NSF legacies are more research and training oriented, and the GREMP is geared primarily to the practical development of the geothermal reservoirs. 2 tabs., 3 figs.
Numerical simulation of hydraulic fracture propagation in heterogeneous unconventional reservoir
Liu, Chunting; Li, Mingzhong; Hao, Lihua; Hu, Hang
2017-10-01
The distribution of the unconventional reservoir fracture network is influenced by many factors. For the natural fracture undeveloped reservoir, the reservoir heterogeneity, construction factors (fracturing fluid flow rate, fluid viscosity, perforation clusters spacing), horizontal stress difference and stress different coefficient are the main factors that affect the fracture propagation. In the study, first, calculate the reservoir physics mechanics parameters that affect the fracture propagation on the base of the logging date from one actual horizontal well. Set the formation parameters according to the calculation that used to simulate the reservoir heterogeneity. Then, using damage mechanics method, the 2D fracture propagation model with seepage-stress-damage coupling of multi-fracture tight sand reservoir was established. Study the influences of different fracturing ways (open whole fracturing and oriented perforation fracturing) and the position of the perforation clusters to the fracture propagation for heterogeneity reservoir. Analyze the effects of flow rate, fracturing fluid viscosity, perforation clusters spacing, horizontal stress difference and stress different coefficient to fracture morphology for the heterogeneity reservoir and contrast with the homogeneous reservoir. The simulation results show that: the fracture morphology is more complexity formed by oriented perforation crack than open whole crack; For natural fracture undeveloped reservoir, as the flow rate or the fracturing fluid viscosity increases within a certain range, the fracture network tends to be more complexity and the effect is more obvious to heterogeneous reservoir than homogeneous reservoir; As the perforation clusters spacing decreases, the interaction of each fracture will increase, it tends to form more complexity fracture network but with short major fracture; If the horizontal stress difference and stress different coefficient is large (The stress different coefficient >0
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.
Top-Down, Intelligent Reservoir Model
Mohaghegh, Shahab
2010-05-01
Conventional reservoir simulation and modeling is a bottom-up approach. It starts with building a geological model of the reservoir that is populated with the best available petrophysical and geophysical information at the time of development. Engineering fluid flow principles are added and solved numerically so as to arrive at a dynamic reservoir model. The dynamic reservoir model is calibrated using the production history of multiple wells and the history matched model is used to strategize field development in order to improve recovery. Top-Down, Intelligent Reservoir Modeling approaches the reservoir simulation and modeling from an opposite angle by attempting to build a realization of the reservoir starting with the measured well production behavior (history). The production history is augmented by core, log, well test and seismic data in order to increase the accuracy of the Top-Down modeling technique. Although not intended as a substitute for the conventional reservoir simulation of large, complex fields, this novel approach to reservoir modeling can be used as an alternative (at a fraction of the cost) to conventional reservoir simulation and modeling in cases where performing conventional modeling is cost (and man-power) prohibitive. In cases where a conventional model of a reservoir already exists, Top-Down modeling should be considered as a compliment to, rather than a competition for the conventional technique, to provide an independent look at the data coming from the reservoir/wells for optimum development strategy and recovery enhancement. Top-Down, Intelligent Reservoir Modeling starts with well-known reservoir engineering techniques such as Decline Curve Analysis, Type Curve Matching, History Matching using single well numerical reservoir simulation, Volumetric Reserve Estimation and calculation of Recovery Factors for all the wells (individually) in the field. Using statistical techniques multiple Production Indicators (3, 6, and 9 months cum
Energy Technology Data Exchange (ETDEWEB)
Mullins, O.C.; Dong, C. [Schlumberger-Doll Research Center, Cambridge, MA (United States); Elshahawi, H. [Shell Exploration and Production Company, The Hague (Netherlands)
2008-07-01
This study emphasized the need for considering flow assurance for producing oil and gas, particularly in high cost areas such as deepwater. Phase behaviour studies, sticking propensities, and interfacial interactions have been investigated in many laboratory studies using asphaltenes, wax, hydrates, organic and inorganic scale, and even diamondoids. However, the spatial variation of reservoir fluids has received little attention, despite the fact that it is one of the most important factors affecting flow assurance. This issue was difficult to address in a systematic way in the past because of cost constraints. Today, reservoir fluid variation and flow assurance can be considered at the outset of a project given the technological advances in downhole fluid analysis. This study described the origins of reservoir fluid compositional variations and the controversies surrounding them. It also described the indispensable chemical analytical technology. The impact of these reservoir fluid compositional variations on flow assurance considerations was also discussed. A methodology that accounts for these variations at the outset in flow assurance evaluation was also presented.
Reservoir sizing using inert and chemically reacting tracers
Energy Technology Data Exchange (ETDEWEB)
Robinson, B.A.; Tester, J.W.; Brown, L.F.
1984-01-01
Non-reactive tracer tests in prototype hot dry rock (HDR) geothermal reservoirs indicate multiple fracture flow paths that show increases in volume due to energy extraction. Tracer modal volumes correlate roughly with estimated reservoir heat-transfer capacity. Chemically reactive tracers are proposed which will map the rate of advance of the cooled region of an HDR reservoir, providing advanced warning of thermal drawdown. Critical parameters are examined using a simplified reservoir model for screening purposes. Hydrolysis reactions are a promising class of reactions for this purpose.
Energy Technology Data Exchange (ETDEWEB)
Gastaldo, L
2007-11-15
We develop in this PhD thesis a simulation tool for bubbly flows encountered in some late phases of a core-melt accident in pressurized water reactors, when the flow of molten core and vessel structures comes to chemically interact with the concrete of the containment floor. The physical modelling is based on the so-called drift-flux model, consisting of mass balance and momentum balance equations for the mixture (Navier-Stokes equations) and a mass balance equation for the gaseous phase. First, we propose a pressure correction scheme for the compressible Navier-Stokes equations based on mixed non-conforming finite elements. An ad hoc discretization of the advection operator, by a finite volume technique based on a dual mesh, ensures the stability of the velocity prediction step. A priori estimates for the velocity and the pressure yields the existence of the solution. We prove that this scheme is stable, in the sense that the discrete entropy is decreasing. For the conservation equation of the gaseous phase, we build a finite volume discretization which satisfies a discrete maximum principle. From this last property, we deduce the existence and the uniqueness of the discrete solution. Finally, on the basis of these works, a conservative and monotone scheme which is stable in the low Mach number limit, is build for the drift-flux model. This scheme enjoys, moreover, the following property: the algorithm preserves a constant pressure and velocity through moving interfaces between phases (i.e. contact discontinuities of the underlying hyperbolic system). In order to satisfy this property at the discrete level, we build an original pressure correction step which couples the mass balance equation with the transport terms of the gas mass balance equation, the remaining terms of the gas mass balance being taken into account with a splitting method. We prove the existence of a discrete solution for the pressure correction step. Numerical results are presented; they
Model based management of a reservoir system
Energy Technology Data Exchange (ETDEWEB)
Scharaw, B.; Westerhoff, T. [Fraunhofer IITB, Ilmenau (Germany). Anwendungszentrum Systemtechnik; Puta, H.; Wernstedt, J. [Technische Univ. Ilmenau (Germany)
2000-07-01
The main goals of reservoir management systems consist of prevention against flood water damages, the catchment of raw water and keeping all of the quality parameters within their limits besides controlling the water flows. In consideration of these goals a system model of the complete reservoir system Ohra-Schmalwasser-Tambach Dietharz was developed. This model has been used to develop optimized strategies for minimization of raw water production cost, for maximization of electrical energy production and to cover flood situations, as well. Therefore a proper forecast of the inflow to the reservoir from the catchment areas (especially flooding rivers) and the biological processes in the reservoir is important. The forecast model for the inflow to the reservoir is based on the catchment area model of Lorent and Gevers. It uses area precipitation, water supply from the snow cover, evapotranspiration and soil wetness data to calculate the amount of flow in rivers. The other aim of the project is to ensure the raw water quality using quality models, as well. Then a quality driven raw water supply will be possible. (orig.)
Jhang, R.; Liou, T.
2013-12-01
Carbon capture and sequestration (CCS) is believed to be an economically feasible technology to mitigate global warming by capturing carbon dioxide (CO2), the major component of greenhouse gases, from the atmosphere and injecting it into deep geological formations.Several mechanisms can help trap CO2 in the pore space of a geological reservoir, stratigraphic and structural trapping, hydrodynamic trapping, and geochemical trapping.Besides these trapping mechanisms, another important issue that deserves careful attention is the risk of CO2 leakage. The common ';constant injection rate' scenario may induce high pressure buildup that will endanger the mechanical integrity as well as the sealing capability of the cap rock. Instead of injecting CO2 at a constant mass rate, CO2 can be injected into the reservoir by fixing the pressure (usually the bottom-hole pressure) in the injection borehole. By doing so, the inevitable pressure buildup associated with the constant injection scheme can be completely eliminated in the constant pressure injection scheme. In this paper, a semi-analytical solution for CO2 injection with constant pressure was developed. For simplicity, structural and geochemical trapping mechanisms were not considered. Therefore, a horizontal reservoir with infinite radial extent was considered. Prior to injection, the reservoir is fully saturated with the formation brine. It is assumed that CO2 does not mix with brine such that a sharp interface is formed once CO2 invades the brine-saturated pores. Because of the density difference between CO2 and brine, CO2 resides above the interface. Additional assumptions were also made when building up the brine and CO2 mass balance equations: (1) both of the fluids and the geological formations are incompressible, (2) capillary pressure is neglected, (3)there is no fluid flow in the vertical direction, and the horizontal flow satisfies the Darcy's law.In order to solve for the height of brine-CO2 interface, the two
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)
Energy Technology Data Exchange (ETDEWEB)
ECONOMY,KATHLEEN M.; HELTON,JON CRAIG; VAUGHN,PALMER
1999-10-01
The Waste Isolation Pilot Plant (WIPP), which is located in southeastern New Mexico, is being developed for the geologic disposal of transuranic (TRU) waste by the U.S. Department of Energy (DOE). Waste disposal will take place in panels excavated in a bedded salt formation approximately 2000 ft (610 m) below the land surface. The BRAGFLO computer program which solves a system of nonlinear partial differential equations for two-phase flow, was used to investigate brine and gas flow patterns in the vicinity of the repository for the 1996 WIPP performance assessment (PA). The present study examines the implications of modeling assumptions used in conjunction with BRAGFLO in the 1996 WIPP PA that affect brine and gas flow patterns involving two waste regions in the repository (i.e., a single waste panel and the remaining nine waste panels), a disturbed rock zone (DRZ) that lies just above and below these two regions, and a borehole that penetrates the single waste panel and a brine pocket below this panel. The two waste regions are separated by a panel closure. The following insights were obtained from this study. First, the impediment to flow between the two waste regions provided by the panel closure model is reduced due to the permeable and areally extensive nature of the DRZ adopted in the 1996 WIPP PA, which results in the DRZ becoming an effective pathway for gas and brine movement around the panel closures and thus between the two waste regions. Brine and gas flow between the two waste regions via the DRZ causes pressures between the two to equilibrate rapidly, with the result that processes in the intruded waste panel are not isolated from the rest of the repository. Second, the connection between intruded and unintruded waste panels provided by the DRZ increases the time required for repository pressures to equilibrate with the overlying and/or underlying units subsequent to a drilling intrusion. Third, the large and areally extensive DRZ void volumes is a
Physical modelling of the Akkajaure reservoir
Directory of Open Access Journals (Sweden)
J. Sahlberg
2003-01-01
Full Text Available This paper describes the seasonal temperature development in the Akkajaure reservoir, one of the largest Swedish reservoirs. It lies in the headwaters of the river Lulealven in northern Sweden; it is 60 km long and 5 km wide with a maximum depth of 92 m. The maximum allowed variation in surface water level is 30 m. The temperature field in the reservoir is important for many biochemical processes. A one-dimensional lake model of the Akkajaure reservoir is developed from a lake model by Sahlberg (1983 and 1988. The dynamic eddy viscosity is calculated by a two equation turbulence model, a k–ε model and the hypolimnic eddy diffusivity formulation which is a function of the stability frequency (Hondzo et al., 1993. A comparison between calculated and measured temperature profiles showed a maximum discrepancy of 0.5–1.0°C over the period 1999-2002. Except for a few days in summer, the water temperature is vertically homogeneous. Over that period of years, a weak stratification of temperature occurred on only one to two weeks a year on different dates in July and August. This will have biological consequences. Keywords: temperature profile,reservoir, 1-D lake model, stratification, Sweden
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.
Pressure Transient Analysis of Dual Fractal Reservoir
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2013-01-01
Full Text Available A dual fractal reservoir transient flow model was created by embedding a fracture system simulated by a tree-shaped fractal network into a matrix system simulated by fractal porous media. The dimensionless bottom hole pressure model was created using the Laplace transform and Stehfest numerical inversion methods. According to the model's solution, the bilogarithmic type curves of the dual fractal reservoirs are illustrated, and the influence of different fractal factors on pressure transient responses is discussed. This semianalytical model provides a practical and reliable method for empirical applications.
An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media
Lough, M. F.; Lee, S. H.; Kamath, J.
1998-07-01
In this paper we present a new model for flow in fractured porous media. We formulate our model in terms of a coupled system of boundary integral equations and present an efficient procedure for solving the equations using the boundary element method. In the new model, the flow in the matrix is governed by the usual Darcy law for porous media, with the fractures being treated as planar sources embedded in the matrix. The flow in an individual fracture is governed by a two-dimensional Darcy law (as in a Hele-Shaw cell), with an associated planar sink distribution. The essential feature of this approach is that the fractures are treated as special planes rather than narrow-gap voids. The error in the resulting system of equations is on the order of an intrinsic dimensionless parameter (the ratio of the fracture gap size to the scale of the volume under consideration). We also describe how we adapt the new model to compute effective grid block permeabilities. This was the principal motivation behind the development of the new model. Using effective grid block permeabilities to model flow in fractured oil and gas reservoirs is a much more efficient process than modeling the flow when every fracture is precisely represented. We present some numerical examples that illustrate the new flow model and how it is used to model flow in a reservoir.
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
International Nuclear Information System (INIS)
Satake, Masaaki; Yoneda, Kimitoshi; Fujiwara, Kazutoshi; Domae, Masafumi
2011-01-01
Flow accelerated corrosion (FAC) is one of the serious wall thinning problems when power plants are operating. FAC has been studied in water single-phase flow. The methods of evaluation of wall thinning rate in FAC are constructed from the results of these studies. On the other hand, FAC in water-steam two-phase flow has been hardly studied, so that methods of evaluation of wall thinning rate in it flow have not been constructed. In this report, a few researches about FAC in two-phase flow are investigated. From these researches, firstly FAC in two-phase flow is assumed to occur in annular flow. Secondly, liquid film velocity and liquid film thickness are dealt as the important hydrodynamic factors on FAC in the two phase flow. Besides, partition of pH control agent into water-vapor two phase flow is one of the water-chemical factors in the two phase flow. A water-air two phase annular flow is simulated. From the results, liquid film thicknesses in the simulation are under that of experimental results, and shear stresses are over that of experimental results. (author)
Reduction of infinite dimensional equations
Directory of Open Access Journals (Sweden)
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
Suspended-sediment inflows to Watts Bar Reservoir. Revision 1
Energy Technology Data Exchange (ETDEWEB)
Ewing, L.K.
1993-09-01
Suspended-sediment inflows to Watts Bar Reservoir are important data that are required in numerical modeling of transport and deposition of sediment in the reservoir. Acceptable numerical modeling requires sediment inflow rates and locations in order to be able to compute the location and quantity of sediment deposited within the reservoir. Therefore, the representativeness of modeling results is highly dependent on the characteristics of sediment input to the model. The following recommendations, that account for suspended-sediment inflows to be used in the numerical modeling of sediment transport and deposition in Watts Bar Reservoir, were developed through an evaluation of available watershed and sediment deposition data. (1) Use the suspended-sediment rating regression equations of Gaydos et al., for Emory River at Oakdale, TN, and for Poplar Creek near Oak Ridge, TN, to represent the suspended-sediment inflows into Watts Bar Reservoir from its tributaries; (2) Use a suspended-sediment rating regression equation that was derived from suspended-sediment and streamflow data of the Little Tennessee River at McGhee, TN, to represent sediment inflow from the Little Tennessee River for simulation of any historical year before the completion of Tellico Dam; (3) Check the appropriateness of any assumption for suspended-sediment inflows from upstream reservoirs by using its long-term relationship to local suspended-sediment inflows and to the suspended-sediment outflow through Watts Bar Dam; and (4) Focus refinements to suspended-sediment inflow rates on the Clinch arm of Watts Bar Reservoir.
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
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
Modeling Reservoir Formation Damage due to Water Injection for Oil Recovery
DEFF Research Database (Denmark)
Yuan, Hao
2010-01-01
The elliptic equation for non-Fickian transport of suspension in porous media is applied to simulate the reservoir formation damage due to water injection for oil recovery. The deposition release (erosion of reservoir formation) and the suspension deposition (pore plugging) are both taken...... into account. 1-D numerical simulations are carried out to reveal the erosion of reservoir formation due to water injection. 2-D numerical simulations are carried out to obtain the suspension and deposition profiles around the injection wells. These preliminary results indicate the non-Fickian behaviors...... of suspended reservoir fines and the corresponding formation damage due to erosion and relocation of reservoir fines....
Reservoir and injection technology and Heat Extraction Project
Energy Technology Data Exchange (ETDEWEB)
Horne, R.N.; Ramey, H.H. Jr.; Miller, F.G.; Brigham, W.E.; Kruger, P.
1989-12-31
For the Stanford Geothermal Program in the fiscal year 1989, the task areas include predictive modeling of reservoir behavior and tracer test interpretation and testing. Major emphasis is in reservoir technology, reinjection technology, and heat extraction. Predictive modeling of reservoir behavior consists of a multi-pronged approach to well test analysis under a variety of conditions. The efforts have been directed to designing and analyzing well tests in (1) naturally fractured reservoirs; (2) fractured wells; (3) complex reservoir geometries; and, (4) gas reservoirs including inertial and other effects. The analytical solutions for naturally fractured reservoirs are determined using fracture size distribution. In the study of fractured wells, an elliptical coordinate system is used to obtain semi-analytical solutions to finite conductivity fractures. Effort has also been directed to the modeling and creation of a user friendly computer program for steam/gas reservoirs including wellbore storage, skin and non-Darcy flow effects. This work has a complementary effort on modeling high flow rate wells including inertial effects in the wellbore and fractures. In addition, work on gravity drainage systems is being continued.
Multi Data Reservoir History Matching using the Ensemble Kalman Filter
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.
Are Geotehrmal Reservoirs Stressed Out?
Davatzes, N. C.; Laboso, R. C.; Layland-Bachmann, C. E.; Feigl, K. L.; Foxall, W.; Tabrez, A. R.; Mellors, R. J.; Templeton, D. C.; Akerley, J.
2017-12-01
Crustal permeability can be strongly influenced by developing connected networks of open fractures. However, the detailed evolution of a fracture network, its extent, and the persistence of fracture porosity are difficult to analyze. Even in fault-hosted geothermal systems, where heat is brought to the surface from depth along a fault, hydrothermal flow is heterogeneously distributed. This is presumably due to variations in fracture density, connectivity, and attitude, as well as variations in fracture permeability caused by sealing of fractures by precipitated cements or compaction. At the Brady Geothermal field in Nevada, we test the relationship between the modeled local stress state perturbed by dislocations representing fault slip or volume changes in the geothermal reservoir inferred from surface deformation measured by InSAR and the location of successful geothermal wells, hydrothermal activity, and seismicity. We postulate that permeability is favored in volumes that experience positive Coulomb stress changes and reduced compression, which together promote high densities of dilatant fractures. Conversely, permeability can be inhibited in locations where Coulomb stress is reduced, compression promotes compaction, or where the faults are poorly oriented in the stress field and consequently slip infrequently. Over geologic time scales spanning the development of the fault system, these local stress states are strongly influenced by the geometry of the fault network relative to the remote stress driving slip. At shorter time scales, changes in fluid pressure within the fracture network constituting the reservoir cause elastic dilations and contractions. We integrate: (1) direct observations of stress state and fractures in boreholes and the mapped geometry of the fault network; (2) evidence of permeability from surface hydrothermal features, production/injection wells and surface deformations related to pumping history; and (3) seismicity to test the
Indian Academy of Sciences (India)
limeters (blood flow in an artery) to maybe a few kilo- meters (wind systems in the atmosphere) ..... the road. It must be made clear that the flow is exactly the same in the two cases. Only the references or points of view are different. In steady flow the path of fluid particle will be along a streamline; and the streamline picture ...
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
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
Energy Technology Data Exchange (ETDEWEB)
Santos, Caio Graco Pereira; Clennell, Bennedict [Bahia Univ., Salvador, BA (Brazil). Curso de Pos-graduacao em Geofisica]. E-mail: cgps@cpgg.ufba.br; clennell@cpgg.ufba.br; Mato, Luiz Ferradans [PETROBRAS, Salvador, BA (Brazil). Exploracao e Producao]. E-mail: ferradans@petrobras.com.br
2003-07-01
The Namorado field is in the centre of the Campos Basin. The external geometry of the sand bodies is lenticular aligned in the direction NW/SE. In the study, the lithofacies were grouped on the basis of the reservoir characteristics and general rock type in order to simplify the discrimination function. The lithofacies were grouped into: conglomerates and conglomeratic, massive stratified and interfingering sands and clay, diamicitites, slumps and clay stones. Regarding reservoir quality, the lithofacies were grouped into: continuous and stratified reservoir, nonreservoir rocks and flow barriers. Data samples can form two or more groups of objects, and there is no a priori knowledge of the spatial arrangement of the objects or of the determining characteristics of the populations, from which the samples were taken. For application of multivariate analysis in the Namorado Field, it is first necessary to divide the lithologies into reservoir rocks and non-reservoir rocks. A linear equation was obtained that combines variables from log data. The binary discriminant, applied to logged intervals for winch core data was available was 80% successful i