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.
Master equation and two heat reservoirs.
Trimper, Steffen
2006-11-01
A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma-sigma and TT'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.
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.
The reservoir model: a differential equation model of psychological regulation.
Deboeck, Pascal R; Bergeman, C S
2013-06-01
Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
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.
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
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.
Energy Technology Data Exchange (ETDEWEB)
Nielsen, Bjoern Fredrik
1998-12-31
The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.
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
Numerical optimization using flow equations
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
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
Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs
Negara, Ardiansyah; Salama, Amgad; Sun, Shuyu; Elgassier, Mokhtar; Wu, Yu-Shu
2015-01-01
Shale gas resources have received great attention in the last decade due to the decline of the conventional gas resources. Unlike conventional gas reservoirs, the gas flow in shale formations involves complex processes with many mechanisms such as Knudsen diffusion, slip flow (Klinkenberg effect), gas adsorption and desorption, strong rock-fluid interaction, etc. Shale formations are characterized by the tiny porosity and extremely low-permeability such that the Darcy equation may no longer be valid. Therefore, the Darcy equation needs to be revised through the permeability factor by introducing the apparent permeability. With respect to the rock formations, several studies have shown the existence of anisotropy in shale reservoirs, which is an essential feature that has been established as a consequence of the different geological processes over long period of time. Anisotropy of hydraulic properties of subsurface rock formations plays a significant role in dictating the direction of fluid flow. The direction of fluid flow is not only dependent on the direction of pressure gradient, but it also depends on the principal directions of anisotropy. Therefore, it is very important to take into consideration anisotropy when modeling gas flow in shale reservoirs. In this work, the gas flow mechanisms as mentioned earlier together with anisotropy are incorporated into the dual-porosity dual-permeability model through the full-tensor apparent permeability. We employ the multipoint flux approximation (MPFA) method to handle the full-tensor apparent permeability. We combine MPFA method with the experimenting pressure field approach, i.e., a newly developed technique that enables us to solve the global problem by breaking it into a multitude of local problems. This approach generates a set of predefined pressure fields in the solution domain in such a way that the undetermined coefficients are calculated from these pressure fields. In other words, the matrix of coefficients
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...
International Nuclear Information System (INIS)
Crowe, C.T.
1975-01-01
General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources
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; Sun, Shuyu; Hoteit, Ibrahim; Katterbauer, Klemens
2016-01-01
Systems and methods for reservoir resistivity characterization are provided, in various aspects, an integrated framework for the estimation of Archie's parameters for a strongly heterogeneous reservoir utilizing the dynamics of the reservoir are provided. The framework can encompass a Bayesian estimation/inversion method for estimating the reservoir parameters, integrating production and time lapse formation conductivity data to achieve a better understanding of the subsurface rock conductivity properties and hence improve water saturation imaging.
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.
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.
Electrokinetic Flow in Microchannels with Finite Reservoir Size Effects
International Nuclear Information System (INIS)
Yan, D; Yang, C; Nguyen, N-T; Huang, X
2006-01-01
In electrokinetically-driven microfluidic applications, reservoirs are indispensable and have finite sizes. During operation processes, as the liquid level difference in reservoirs keeps changing as time elapses, the flow characteristics in a microchannel exhibit a combination of the electroosmotic flow and the time-dependent induced backpressure-driven flow. In this work, an assessment of the finite reservoir size effect on electroosmotic flows is presented theoretically and experimentally. A model is developed to describe the timedependent electrokinetic flow with finite reservoir size effects. The theoretical analysis shows that under certain conditions the finite reservoir size effect is significant. The important parameters that describe the effect of finite reservoir size on the flow characteristics are discussed. A new concept denoted as 'effective pumping period' is introduced to characterize the reservoir size effect. The proposed model clearly identifies the mechanisms of the finitereservoir size effects and is further confirmed by using micro-PIV technique. The results of this study can be used for facilitating the design of microfluidic devices
Enhanced Recovery in Tight Gas Reservoirs using Maxwell-Stefan Equations
Santiago, C. J. S.; Kantzas, A.
2017-12-01
Due to the steep production decline in unconventional gas reservoirs, enhanced recovery (ER) methods are receiving great attention from the industry. Wet gas or liquid rich reservoirs are the preferred ER candidates due to higher added value from natural gas liquids (NGL) production. ER in these reservoirs has the potential to add reserves by improving desorption and displacement of hydrocarbons through the medium. Nevertheless, analysis of gas transport at length scales of tight reservoirs is complicated because concomitant mechanisms are in place as pressure declines. In addition to viscous and Knudsen diffusion, multicomponent gas modeling includes competitive adsorption and molecular diffusion effects. Most models developed to address these mechanisms involve single component or binary mixtures. In this study, ER by gas injection is investigated in multicomponent (C1, C2, C3 and C4+, CO2 and N2) wet gas reservoirs. The competing effects of Knudsen and molecular diffusion are incorporated by using Maxwell-Stefan equations and the Dusty-Gas approach. This model was selected due to its superior properties on representing the physics of multicomponent gas flow, as demonstrated during the presented model validation. Sensitivity studies to evaluate adsorption, reservoir permeability and gas type effects are performed. The importance of competitive adsorption on production and displacement times is demonstrated. In the absence of adsorption, chromatographic separation is negligible. Production is merely dictated by competing effects between molecular and Knudsen diffusion. Displacement fronts travel rapidly across the medium. When adsorption effects are included, molecules with lower affinity to the adsorption sites will be produced faster. If the injected gas is inert (N2), an increase in heavier fraction composition occurs in the medium. During injection of adsorbing gases (CH4 and CO2), competitive adsorption effects will contribute to improved recovery of heavier
Design of a lube oil reservoir by using flow calculations
Energy Technology Data Exchange (ETDEWEB)
Rinkinen, J; Alfthan, A. [Institute of Hydraulics and Automation IHA, Tampere University of Technology, Tampere (Finland)] Suominen, J. [Institute of Energy and Process Engineering, Tampere University of Technology, Tampere (Finland); Airaksinen, A; Antila, K [R and D Engineer Safematic Oy, Muurame (Finland)
1998-12-31
The volume of usual oil reservoir for lubrication oil systems is designed by the traditional rule of thumb so that the total oil volume is theoretically changed in every 30 minutes by rated pumping capacity. This is commonly used settling time for air, water and particles to separate by gravity from the oil returning of the bearings. This leads to rather big volumes of lube oil reservoirs, which are sometimes difficult to situate in different applications. In this presentation traditionally sized lube oil reservoir (8 m{sup 3}) is modelled in rectangular coordinates and laminar oil flow is calculated by using FLUENT software that is based on finite difference method. The results of calculation are velocity and temperature fields inside the reservoir. The velocity field is used to visualize different particle paths through the reservoir. Particles that are studied by the model are air bubbles and water droplets. The interest of the study has been to define the size of the air bubbles that are released and the size of the water droplets that are separated in the reservoir. The velocity field is also used to calculate the modelled circulating time of the oil volume which is then compared with the theoretical circulating time that is obtained from the rated pump flow. These results have been used for designing a new lube oil reservoir. This reservoir has also been modelled and optimized by the aid of flow calculations. The best shape of the designed reservoir is constructed in real size for empirical measurements. Some results of the oil flow measurements are shown. (orig.) 7 refs.
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.
Afanasyev, Andrey
2017-04-01
Numerical modelling of multiphase flows in porous medium is necessary in many applications concerning subsurface utilization. An incomplete list of those applications includes oil and gas fields exploration, underground carbon dioxide storage and geothermal energy production. The numerical simulations are conducted using complicated computer programs called reservoir simulators. A robust simulator should include a wide range of modelling options covering various exploration techniques, rock and fluid properties, and geological settings. In this work we present a recent development of new options in MUFITS code [1]. The first option concerns modelling of multiphase flows in double-porosity double-permeability reservoirs. We describe internal representation of reservoir models in MUFITS, which are constructed as a 3D graph of grid blocks, pipe segments, interfaces, etc. In case of double porosity reservoir, two linked nodes of the graph correspond to a grid cell. We simulate the 6th SPE comparative problem [2] and a five-spot geothermal production problem to validate the option. The second option concerns modelling of flows in porous medium coupled with flows in horizontal wells that are represented in the 3D graph as a sequence of pipe segments linked with pipe junctions. The well completions link the pipe segments with reservoir. The hydraulics in the wellbore, i.e. the frictional pressure drop, is calculated in accordance with Haaland's formula. We validate the option against the 7th SPE comparative problem [3]. We acknowledge financial support by the Russian Foundation for Basic Research (project No RFBR-15-31-20585). References [1] Afanasyev, A. MUFITS Reservoir Simulation Software (www.mufits.imec.msu.ru). [2] Firoozabadi A. et al. Sixth SPE Comparative Solution Project: Dual-Porosity Simulators // J. Petrol. Tech. 1990. V.42. N.6. P.710-715. [3] Nghiem L., et al. Seventh SPE Comparative Solution Project: Modelling of Horizontal Wells in Reservoir Simulation
Reconstruction of dynamical equations for traffic flow
Kriso, S.; Friedrich, R.; Peinke, J.; Wagner, P.
2001-01-01
Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the fund...
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
International Nuclear Information System (INIS)
Penuela, G; Ordonez R, A; Bejarano, A
1998-01-01
A generalized material balance equation was presented at the Escuela de Petroleos de la Universidad Industrial de Santander for coal seam gas reservoirs based on Walsh's method, who worked in an analogous approach for oil and gas conventional reservoirs (Walsh, 1995). Our equation was based on twelve similar assumptions itemized by Walsh for his generalized expression for conventional reservoirs it was started from the same volume balance consideration and was finally reorganized like Walsh (1994) did. Because it is not expressed in terms of traditional (P/Z) plots, as proposed by King (1990), it allows to perform a lot of quantitative and qualitative analyses. It was also demonstrated that the existent equations are only particular cases of the generalized expression evaluated under certain restrictions. This equation is applicable to coal seam gas reservoirs in saturated, equilibrium and under saturated conditions, and to any type of coal beds without restriction on especial values of the constant diffusion
The model coupling fluid flow in reservoir with flow in horizontal wellbore
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiangping; Jiang, Zhixiang [RIPED-TEXACO Horizontal Well Technology Laboratory (United States)
1998-12-31
Three-dimensional pressure distributions of oil flow in a reservoir with horizontal well were derived, and a new formula to calculate pressure drop along the horizontal wellbore was developed based on the principle of conservation of matter and momentum. The formula considers the effect of influx into the horizontal wellbore from the reservoir on pressure drop in the wellbore. A mathematical model to couple fluid flow in the reservoir with flow in the horizontal wellbore is presented. Model results and experimental data showed good correspondence. Results showed the influence of pressure drop on well performance. 13 refs., 2 tabs., 7 figs.
International Nuclear Information System (INIS)
Gawusu, S.
2015-07-01
Oil extraction represents an important investment and the control of a rational exploitation of a field means mastering various scientific techniques including the understanding of the dynamics of fluids in place. This thesis presents a theoretical investigation of the dynamic behaviour of an oil reservoir during its exploitation. The study investigated the dynamics of fluid flow patterns in a homogeneous oil reservoir using the Radial Diffusivity Equation (RDE) as well as two phase oil-water flow equations. The RDE model was solved analytically and numerically for pressure using the Constant Terminal Rate Solution (CTRS) and the fully implicit Finite Difference Method (FDM) respectively. The mathematical derivations of the models and their solution procedures were presented to allow for easy utilization of the techniques for reservoir and engineering applications. The study predicted that the initial oil reservoir pressure will be able to do the extraction for a very long time before any other recovery method will be used to aid in the extraction process depending on the rate of production. Reservoir simulation describing a one dimensional radial flow of a compressible fluid in porous media may be adequately performed using ordinary laptop computers as revealed by the study. For the simulation of MATLAB, the case of the Jubilee Fields, Tano Basin was studied, an algorithm was developed for the simulation of pressure in the reservoir. It ensues from the analysis of the plots of pressure vrs time and space that the Pressure Transient Analysis (PTA) was duly followed. The approximate solutions of the analytical and numerical solutions to the Radial Diffusivity Equation (RDE) were in excellent agreement, thus the reservoir simulation model developed can be used to describe typical pressure-time relationships that are used in conventional Pressure Transient Analysis (PTA). The study was extended to two phase oil-water flow in reservoirs. The flow of fluids in multi
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.
Upscaling of Two-Phase Immiscible Flows in Communicating Stratified Reservoirs
DEFF Research Database (Denmark)
Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan
2011-01-01
A semi-analytical method for upscaling two-phase immiscible flows in heterogeneous porous media is described. This method is developed for stratified reservoirs with perfect communication between layers (the case of vertical equilibrium), in a viscous dominant regime, where the effects of capillary...... forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure...... and piston-like displacement, and it presumes non-zero exchange between layers. The method generalizes also the study of Yortsos (Transp Porous Media 18:107–129, 1995), taking into account in a more consistent way the interactions between the layers....
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.
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.
Triple-porosity/permeability flow in faulted geothermal reservoirs: Two-dimensional effects
Energy Technology Data Exchange (ETDEWEB)
Cesar Suarez Arriaga, M. [Michoacan Univ. & CFE, Mich. (Mexico); Samaniego Verduzco, F. [National Autonomous Univ. of Mexico, Coyoacan (Mexico)
1995-03-01
An essential characteristic of some fractured geothermal reservoirs is noticeable when the drilled wells intersect an open fault or macrofracture. Several evidences observed, suggest that the fluid transport into this type of systems, occurs at least in three stages: flow between rock matrix and microfractures, flow between fractures and faults and flow between faults and wells. This pattern flow could define, by analogy to the classical double-porosity model, a triple-porosity, triple-permeability concept. From a mathematical modeling point of view, the non-linearity of the heterogeneous transport processes, occurring with abrupt changes on the petrophysical properties of the rock, makes impossible their exact or analytic solution. To simulate this phenomenon, a detailed two-dimensional geometric model was developed representing the matrix-fracture-fault system. The model was solved numerically using MULKOM with a H{sub 2}O=CO{sub 2} equation of state module. This approach helps to understand some real processes involved. Results obtained from this study, exhibit the importance of considering the triple porosity/permeability concept as a dominant mechanism producing, for example, strong pressure gradients between the reservoir and the bottom hole of some wells.
Dong, Xiaohua; Dohmen-Janssen, Catarine M.; Booij, Martijn J.; Hulscher, Suzanne J.M.H.
2006-01-01
This paper presents a methodology to determine the effect of flow forecasting quality on the benefits of reservoir operation. The benefits are calculated in terms of the electricity generated, and the quality of the flow forecasting is defined in terms of lead time and accuracy of the forecasts. In
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.
The flow equation approach to many-particle systems
Kehrein, Stefan; Fujimori, A; Varma, C; Steiner, F
2006-01-01
This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate- level solid-state theory.
Fluid flow in gas condensate reservoirs. The interplay of forces and their relative strengths
Energy Technology Data Exchange (ETDEWEB)
Ursin, Jann-Rune [Stavanger University College, Department of Petroleum Engineering, PO Box 8002, Stavanger, 4068 (Norway)
2004-02-01
Natural production from gas condensate reservoirs is characterized by gas condensation and liquid dropout in the reservoir, first in the near wellbore volume, then as a cylindrical shaped region, dynamically developing into the reservoir volume. The effects of liquid condensation are reduced productivity and loss of production. Successful forecast of well productivity and reservoir production depends on detailed understanding of the effect of various forces acting on fluid flow in time and space. The production form gas condensate reservoirs is thus indirectly related to the interplay of fundamental forces, such as the viscosity, the capillary, the gravitational and the inertial force and their relative strengths, demonstrated by various dimensionless numbers. Dimensionless numbers are defined and calculated for all pressure and space coordinates in a test reservoir. Various regions are identified where certain forces are more important than others. Based on reservoir pressure development, liquid condensation and the numerical representation of dimensionless numbers, a conceptual understanding of a varying reservoir permeability has been reached.The material balance, the reservoir fluid flow and the wellbore flow calculations are performed on a cylindrical reservoir model. The ratios between fundamental forces are calculated and dimensionless numbers defined. The interplay of forces, demonstrated by these numbers, are calculated as function of radial dimension and reservoir pressure.
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.
A generalised groundwater flow equation using the concept of non ...
African Journals Online (AJOL)
The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of ...
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
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
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.
Macroscopic balance equations for two-phase flow models
International Nuclear Information System (INIS)
Hughes, E.D.
1979-01-01
The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)
Cross-flow analysis of injection wells in a multilayered reservoir
Directory of Open Access Journals (Sweden)
Mohammadreza Jalali
2016-09-01
Natural and forced cross-flow is modeled for some injection wells in an oil reservoir located at North Sea. The solution uses a transient implicit finite difference approach for multiple sand layers with different permeabilities separated by impermeable shale layers. Natural and forced cross-flow rates for each reservoir layer during shut-in are calculated and compared with different production logging tool (PLT measurements. It appears that forced cross-flow is usually more prolonged and subject to a higher flow rate when compared with natural cross-flow, and is thus worthy of more detailed analysis.
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.
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
Statistically derived conservation equations for fluid particle flows
International Nuclear Information System (INIS)
Reyes, J.N. Jr.
1989-01-01
The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior
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.
Flow visualization via partial differential equations
Preusser, T.; Rumpf, M.; Telea, A.C.; Möller, T.; Hamann, B.; Russell, R.D.
2009-01-01
The visualization of stationary and time-dependent flow is an important and chaltenging topic in scientific visualization. lts aim is 10 represent transport phenomena govemed by vector fjelds in an intuitively understandable way. In this paper. we review the use of methods based on partial
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.
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 ...
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.
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
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)
THE STATEMENT OF CASH FLOWS USING FINANCIAL STATEMENT EQUATIONS
Harold Fletcher; Thomas Ulrich
2010-01-01
This paper addresses one of the more difficult topics in teaching MBA level financial management, the statement of cash flows. By employing financial statement equations in preparing the statement of cash flows, students: (1) are employing tools that they are more familiar and comfortable with which mitigates their anxiety and enhances their understanding, (2) are better able to understand the logic of the statement of cash flows and the relationships that exist between it and the income stat...
Coupled equations for transient water flow, heat flow, and ...
Indian Academy of Sciences (India)
interacting processes, including flow of fluids, deformation of porous materials, chemical reactions, and transport of ... systems involving the flow of water, heat, and deformation. Such systems are ..... Defined thus, αI is independent of boundary con- ditions in an ... perature change with free deformation at constant total stress ...
Exactly averaged equations for flow and transport in random media
International Nuclear Information System (INIS)
Shvidler, Mark; Karasaki, Kenzi
2001-01-01
It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)
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
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
Diagonalizing quadratic bosonic operators by non-autonomous flow equations
Bach, Volker
2016-01-01
The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocketâe"Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.
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.
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 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.
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.
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.
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.
Oil-water flows in wells with powerful fracture reservoirs
Energy Technology Data Exchange (ETDEWEB)
Ivanov, N.P.
1979-01-01
The character of two phase liquid flows from powerful layer fractures to bottom holes in Starogrodnen and Malgobek-Voznesenskiy fields in the Chechen-Ingush ASSR found in the late stage of operation. The studies were done with the electrothermometer TEG-36, the manometer MGN-2, the remote control thermal flow meter T-4, the remote control moisture meter VBST-1, the density meter GGP-1M, whose accuracy class is 1.0 and whose working limits are: temperature, up to 150/sup 0/C and pressure, up to 1000 kGs/cm/sup 2/. The breakdown of the linear filtration law and the gravitational division of the water-oil mixture phase occurred during fieldwork. The oil and water, etc., flow intervals were defined. The data from the moisture meter and the gamma density meter coincided.
Hazard Assessment of Debris Flows in the Reservoir Region of Wudongde Hydropower Station in China
Directory of Open Access Journals (Sweden)
Cencen Niu
2015-11-01
Full Text Available The outbreak of debris flows in a reservoir region can affect the stability of hydropower stations and threaten the lives of the people living downstream of dams. Therefore, determining the hazard degree of debris flows in a reservoir region is of great importance. SPOT5 remote sensing images and digital elevation models are introduced to determine the characteristics of debris-flow catchments. The information is acquired through comprehensive manual investigation and satellite image interpretation. Ten factors that influence debris flow are extracted for the hazard assessment. The weight of these factors is determined using the analytic hierarchy process method. As a multi-criterion decision analysis method, fuzzy synthetic evaluation is applied for hazard assessment.
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
International Nuclear Information System (INIS)
Guzman, Juan; Maximov, Serguei; Escarela-Perez, Rafael; López-García, Irvin; Moranchel, Mario
2015-01-01
The diffusion and distribution coefficients are important parameters in the design of barrier systems used in radioactive repositories. These coefficients can be determined using a two-reservoir configuration, where a saturated porous medium is allocated between two reservoirs filled by stagnant water. One of the reservoirs contains a high concentration of radioisotopes. The goal of this work is to obtain an analytical solution for the concentration of all radioisotopes in the decay chain of a two-reservoir configuration. The analytical solution must be obtained by taking into account the diffusion and sorption processes. Concepts such as overvalued concentration, diffusion and decay factors are employed to this end. It is analytically proven that a factor of the solution is identical for all chains (considering a time scaling factor), if certain parameters do not change. In addition, it is proven that the concentration sensitivity, due to the distribution coefficient variation, depends of the porous medium thickness, which is practically insensitive for small porous medium thicknesses. The analytical solution for the radioisotope concentration is compared with experimental and numerical results available in literature. - Highlights: • Saturated porous media allocated between two reservoirs. • Analytical solution of the isotope transport equation. • Transport considers diffusion, sorption and decay chain
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
Constitutive Equation with Varying Parameters for Superplastic Flow Behavior
Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui
2014-03-01
In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.
CO2 interfacial properties: application to multiphase flow at reservoir conditions
International Nuclear Information System (INIS)
Chalbaud, C.
2007-07-01
In this work we deal with the interfacial properties of CO 2 at reservoir conditions with a special interest on deep saline aquifers. Each chapter of this dissertation represents a different physical scale studied with different experimental devices and simulation tools. The results obtained in the first part of this study represent a complete data set of brine-CO 2 interfacial tension at reservoir conditions. A semi-analytical equation is proposed in order to facilitate the work of reservoir engineers. The second deals with the interfacial properties at the pore scale using glass micro-models at different wettability conditions. This part shows the wetting behavior of CO 2 on hydrophobic or oil-wet solid surfaces. A pore network model was used for the interpretation and exploitation of these results. The third part corresponds to two different experimental approaches at the core scale at different wettability conditions associated to a modelling at flue Darcy scale. This part is a significant contribution to the validation of COORES compositional reservoir simulator developed by IFP. It has also allow us to estimate multiphase properties, Pc and kr, for brine-CO 2 systems at reservoir conditions. This study presents the necessary scales to model CO 2 storage in deep saline aquifers. (author)
International Nuclear Information System (INIS)
Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming
2013-01-01
Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)
Irregular conformal block, spectral curve and flow equations
International Nuclear Information System (INIS)
Choi, Sang Kwan; Rim, Chaiho; Zhang, Hong
2016-01-01
Irregular conformal block is motivated by the Argyres-Douglas type of N=2 super conformal gauge theory. We investigate the classical/NS limit of irregular conformal block using the spectral curve on a Riemann surface with irregular punctures, which is equivalent to the loop equation of irregular matrix model. The spectral curve is reduced to the second order (Virasoro symmetry, SU(2) for the gauge theory) and third order (W_3 symmetry, SU(3)) differential equations of a polynomial with finite degree. The conformal and W symmetry generate the flow equations in the spectral curve and determine the irregular conformal block, hence the partition function of the Argyres-Douglas theory ala AGT conjecture.
Improved coupling of the conduction and flow equations in TRAC
International Nuclear Information System (INIS)
Addessio, F.L.
1981-01-01
Recent nuclear-reactor-systems modeling efforts have been directed toward the development of computer codes capable of simulating transients in short computational times. For this reason, a stability enhancing two-stem method (SETS) has been applied to the two-phase flow equations in the Transient Reactor Analysis Code (TRAC) allowing the Courant limit to be violated. Unfortunately, the coupling between the wall conduction equation and the fluid-dynamics equations is performed semi-implicitly, that is, the wall-heat transfer term, is evaluated using old-time heat-transfer coefficients and wall temperatures and new-time coolant temperatures. This coupling may lead to numerical instabilities at large time steps because of large variations in the heat-transfer coefficient in certain regimes of the boiling curve. Consequently, simply using new-time wall temperatures is not sufficient. A technique that also incorporates new-time heat-transfer coefficients must be used
Perturbative renormalization of composite operators via flow equations. Pt. 2
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1993-01-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ 4 4 . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.)
Ill-posedness of Dynamic Equations of Compressible Granular Flow
Shearer, Michael; Gray, Nico
2017-11-01
We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.
A Novel 3D Viscoelastic Acoustic Wave Equation Based Update Method for Reservoir History Matching
Katterbauer, Klemens
2014-01-01
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
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
River Stream-Flow and Zayanderoud Reservoir Operation Modeling Using the Fuzzy Inference System
Directory of Open Access Journals (Sweden)
Saeed Jamali
2007-12-01
Full Text Available The Zayanderoud basin is located in the central plateau of Iran. As a result of population increase and agricultural and industrial developments, water demand on this basin has increased extensively. Given the importance of reservoir operation in water resource and management studies, the performance of fuzzy inference system (FIS for Zayanderoud reservoir operation is investigated in this paper. The model of operation consists of two parts. In the first part, the seasonal river stream-flow is forecasted using the fuzzy rule-based system. The southern oscillated index, rain, snow, and discharge are inputs of the model and the seasonal river stream-flow its output. In the second part, the operation model is constructed. The amount of releases is first optimized by a nonlinear optimization model and then the rule curves are extracted using the fuzzy inference system. This model operates on an "if-then" principle, where the "if" is a vector of fuzzy permits and "then" is the fuzzy result. The reservoir storage capacity, inflow, demand, and year condition factor are used as permits. Monthly release is taken as the consequence. The Zayanderoud basin is investigated as a case study. Different performance indices such as reliability, resiliency, and vulnerability are calculated. According to results, FIS works more effectively than the traditional reservoir operation methods such as standard operation policy (SOP or linear regression.
High resolution solutions of the Euler equations for vortex flows
International Nuclear Information System (INIS)
Murman, E.M.; Powell, K.G.; Rizzi, A.; Tel Aviv Univ., Israel)
1985-01-01
Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research. 16 references
Chemical-potential flow equations for graphene with Coulomb interactions
Fräßdorf, Christian; Mosig, Johannes E. M.
2018-06-01
We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results are consistent with a charge carrier-independent Fermi velocity v (k ) for small densities n ≲k2/π , supporting the comparison of the zero-density fRG calculation of Bauer et al. [Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409], with the experiment of Elias et al. [Nat. Phys. 7, 701 (2011), 10.1038/nphys2049].
Ye, LvZhou; Zhang, Hou-Dao; Wang, Yao; Zheng, Xiao; Yan, YiJing
2017-08-21
An efficient low-frequency logarithmic discretization (LFLD) scheme for the decomposition of fermionic reservoir spectrum is proposed for the investigation of quantum impurity systems. The scheme combines the Padé spectrum decomposition (PSD) and a logarithmic discretization of the residual part in which the parameters are determined based on an extension of the recently developed minimum-dissipaton ansatz [J. J. Ding et al., J. Chem. Phys. 145, 204110 (2016)]. A hierarchical equations of motion (HEOM) approach is then employed to validate the proposed scheme by examining the static and dynamic system properties in both the Kondo and noninteracting regimes. The LFLD scheme requires a much smaller number of exponential functions than the conventional PSD scheme to reproduce the reservoir correlation function and thus facilitates the efficient implementation of the HEOM approach in extremely low temperature regimes.
Analysis of Flow Behavior for Acid Fracturing Wells in Fractured-Vuggy Carbonate Reservoirs
Directory of Open Access Journals (Sweden)
Mingxian Wang
2018-01-01
Full Text Available This study develops a mathematical model for transient flow analysis of acid fracturing wells in fractured-vuggy carbonate reservoirs. This model considers a composite system with the inner region containing finite number of artificial fractures and wormholes and the outer region showing a triple-porosity medium. Both analytical and numerical solutions are derived in this work, and the comparison between two solutions verifies the model accurately. Flow behavior is analyzed thoroughly by examining the standard log-log type curves. Flow in this composite system can be divided into six or eight main flow regimes comprehensively. Three or two characteristic V-shaped segments can be observed on pressure derivative curves. Each V-shaped segment corresponds to a specific flow regime. One or two of the V-shaped segments may be absent in particular cases. Effects of interregional diffusivity ratio and interregional conductivity ratio on transient responses are strong in the early-flow period. The shape and position of type curves are also influenced by interporosity coefficients, storativity ratios, and reservoir radius significantly. Finally, we show the differences between our model and the similar model with single fracture or without acid fracturing and further investigate the pseudo-skin factor caused by acid fracturing.
Franz, Delbert D.; Melching, Charles S.
1997-01-01
The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The
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
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
Bones and oil reservoirs : bioengineers use oilpatch technology to study fluid flow in bones
Energy Technology Data Exchange (ETDEWEB)
Marsters, S.
2003-06-01
The fact that porosity and the presence of channels are qualities that are common to oil reservoirs and bones, led to the use of reservoir modelling technology in investigating bone disorders and to the discovery of dramatic changes in the structure and blood supply of osteoarthritic bones that lie under degenerating cartilage. CMG (Computer Modelling Group) Ltd., developers of reservoir simulation software claim that their software packages can help with the modelling of cellular responses to strains and deformations that occur as fluid flows through bone after a traumatic event such as a tear in the anterior cruciate ligament, a common sports-related injury. Researchers at the University of Calgary expect that by looking at the changes in blood and fluid flow within the bone, they can attain a better understanding of the chain of events that leads to osteoarthritis. Better understanding of the progression of the disease could eventually lead to more precise administration of drugs to deal with osteoarthritic pain, and even to the prevention of painful arthritic joints.
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
Numerical solution of compressible flow equations inside an ejector
International Nuclear Information System (INIS)
Omid khah, M. R.; Navid Famili, M. H.; Jalili Keshtiban, E.
2002-01-01
Ejector is important equipment in the chemical industry. It is mainly used for vaccuming and mixing of flows. In the present work a computer modeling of the flow inside an ejector is used to give a better understanding of the principle of the operation of an ejector. Since the fluid inside an ejector passes through subsonic, sonic and supersonic regimens, the pressure field is used as the controlling variable and the density is found through the constitutive equations. The control volume method with a co-location grid, attached to the boundary is used to discretize the domain. The overall solution is obtained by the SIMPLEC method and to dissociate the pressure and the velocity grid Rhie-Chow interpolation method is employed. A central difference approximation method is used to approximate the density on the elements borders and the upwind approximation is used to correct the density correction factors. Both upwind, quick and minimum gradient methods were used to approximate the momentum variables on the control volumes. The resultant matrices are solved with the tri-diagonal method. The accuracy of the model is checked by simulating a flow regiment in a converging-diverging nozzle, and comparing the results with the available experimental data. The results show that for an inviscid the first order approximation produce as an accurate results as the higher order approximations while it has a better stability. However, for the viscous fluid the second order approximation produces a better understanding of the physics of the problem. The solution also showes that the flow field inside an ejector is a complex one and the shock wave has a great influence on the pressure field especially close to the walls. The upper convective quick method did not converge well in the shock calculations while the slowest descent method had a very stable behavior in the analysis of the shock behavior
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.
Five easy equations for patient flow through an emergency department.
Madsen, Thomas Lill; Kofoed-Enevoldsen, Allan
2011-10-01
Queue models are effective tools for framing management decisions and Danish hospitals could benefit from awareness of such models. Currently, as emergency departments (ED) are under reorganization, we deem it timely to empirically investigate the applicability of the standard "M/M/1" queue model in order to document its relevance. We compared actual versus theoretical distributions of hourly patient flow from 27,000 patient cases seen at Frederiksberg Hospital's ED. Formulating equations for arrivals and capacity, we wrote and tested a five equation simulation model. The Poisson distribution fitted arrivals with an hour-of-the-day specific parameter. Treatment times exceeding 15 minutes were well-described by an exponential distribution. The ED can be modelled as a black box with an hourly capacity that can be estimated either as admissions per hour when the ED operates full hilt Poisson distribution or from the linear dependency of waiting times on queue number. The results show that our ED capacity is surprisingly constant despite variations in staffing. These findings led to the formulation of a model giving a compact framework for assessing the behaviour of the ED under different assumptions about opening hours, capacity and workload. The M/M/1 almost perfectly fits our. Thus modeling and simulations have contributed to the management process. not relevant. not relevant.
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.
Scaling properties reveal regulation of river flows in the Amazon through a forest reservoir
Directory of Open Access Journals (Sweden)
J. F. Salazar
2018-03-01
Full Text Available Many natural and social phenomena depend on river flow regimes that are being altered by global change. Understanding the mechanisms behind such alterations is crucial for predicting river flow regimes in a changing environment. Here we introduce a novel physical interpretation of the scaling properties of river flows and show that it leads to a parsimonious characterization of the flow regime of any river basin. This allows river basins to be classified as regulated or unregulated, and to identify a critical threshold between these states. We applied this framework to the Amazon river basin and found both states among its main tributaries. Then we introduce the forest reservoir hypothesis to describe the natural capacity of river basins to regulate river flows through land–atmosphere interactions (mainly precipitation recycling that depend strongly on the presence of forests. A critical implication is that forest loss can force the Amazonian river basins from regulated to unregulated states. Our results provide theoretical and applied foundations for predicting hydrological impacts of global change, including the detection of early-warning signals for critical transitions in river basins.
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.
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
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.
Flow Equation Approach to the Statistics of Nonlinear Dynamical Systems
Marston, J. B.; Hastings, M. B.
2005-03-01
The probability distribution function of non-linear dynamical systems is governed by a linear framework that resembles quantum many-body theory, in which stochastic forcing and/or averaging over initial conditions play the role of non-zero . Besides the well-known Fokker-Planck approach, there is a related Hopf functional methodootnotetextUriel Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995) chapter 9.5.; in both formalisms, zero modes of linear operators describe the stationary non-equilibrium statistics. To access the statistics, we investigate the method of continuous unitary transformationsootnotetextS. D. Glazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993); Phys. Rev. D 49, 4214 (1994). (also known as the flow equation approachootnotetextF. Wegner, Ann. Phys. 3, 77 (1994).), suitably generalized to the diagonalization of non-Hermitian matrices. Comparison to the more traditional cumulant expansion method is illustrated with low-dimensional attractors. The treatment of high-dimensional dynamical systems is also discussed.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Boerresen, Knut Arne
1997-12-31
Hydrocarbon recovery from subsurface reservoirs has become increasingly dependent on advanced recovery techniques that require improved understanding of the physics of fluid flow within and across geological units including small-scale heterogeneities and fractures. In this thesis, impacts from heterogeneities on local fluid flow are studied experimentally by means of imaging techniques to visualize fluid flow in two dimensions during flooding of larger reservoir models. Part 1 reflects the multi-disciplinary collaboration, by briefly introducing the relevant geology, the literature on experiments on fluid flow in bedded structures, and outlining the applied numerical simulator and imaging techniques applied to visualize fluid flow. The second part contains a synopsis of displacement experiments in naturally laminated sandstones and in crossbed laboratory models, and of the impact from incipient shear fractures on oil recovery. The detailed results obtained from the experiments and simulations are described in six papers, all included. 215 refs., 108 figs., 16 tabs.
Directory of Open Access Journals (Sweden)
Yifeng Chen
2016-08-01
Full Text Available Even though a large number of large-scale arch dams with height larger than 200 m have been built in the world, the transient groundwater flow behaviors and the seepage control effects in the dam foundations under difficult geological conditions are rarely reported. This paper presents a case study on the transient groundwater flow behaviors in the rock foundation of Jinping I double-curvature arch dam, the world's highest dam of this type to date that has been completed. Taking into account the geological settings at the site, an inverse modeling technique utilizing the time series measurements of both hydraulic head and discharge was adopted to back-calculate the permeability of the foundation rocks, which effectively improves the uniqueness and reliability of the inverse modeling results. The transient seepage flow in the dam foundation during the reservoir impounding was then modeled with a parabolic variational inequality (PVI method. The distribution of pore water pressure, the amount of leakage, and the performance of the seepage control system in the dam foundation during the entire impounding process were finally illustrated with the numerical results.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu
2017-01-01
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.
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.
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 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.
Basic equations of interfacial area transport in gas-liquid two-phase flow
International Nuclear Information System (INIS)
Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.
2011-01-01
The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)
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.
DEFF Research Database (Denmark)
Riaz, Muhammad; Kontogeorgis, Georgios; Stenby, Erling Halfdan
2011-01-01
This work presents new experimental phase equilibrium data of binary MEG-reservoir fluid and ternary MEG-water-reservoir fluid systems at temperatures 275-326 K and at atmospheric pressure. The reservoir fluid consists of a natural gas condensate from a Statoil operated gas field in the North Sea...... compounds. It has also been extended to reservoir fluids in presence of water and polar chemicals using a Pedersen like characterization method with modified correlations for critical temperature, pressure and acentric factor. In this work CPA is applied to the prediction of mutual solubility of reservoir...
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 ...
Coupling a fluid flow simulation with a geomechanical model of a fractured reservoir
Segura Segarra, José María; Paz, C.M.; de Bayser, M.; Zhang, J.; Bryant, P.W.; Gonzalez, Nubia Aurora; Rodrigues, E.; Vargas, P.E.; Carol, Ignacio; Lakshmikantha, Ramasesha Mookanahallipatna; Das, K. C.; Sandha, S.S.; Cerqueira, R.; Mello,, U.
2013-01-01
Improving the reliability of integrated reservoir development planning and addressing subsidence, fault reactivation and other environmental impacts, requires increasingly sophisticated geomechanical models, especially in the case of fractured reservoirs where fracture deformation is strongly coupled with its permeability change. Reservoir simulation has historically treated any geomechanical effects by means of a rock compressibility term/table, which can be improved by simulating the actual...
Cowton, L. R.; Neufeld, J. A.; Bickle, M.; White, N.; White, J.; Chadwick, A.
2017-12-01
Vertically-integrated gravity current models enable computationally efficient simulations of CO2 flow in sub-surface reservoirs. These simulations can be used to investigate the properties of reservoirs by minimizing differences between observed and modeled CO2 distributions. At the Sleipner project, about 1 Mt yr-1 of supercritical CO2 is injected at a depth of 1 km into a pristine saline aquifer with a thick shale caprock. Analysis of time-lapse seismic reflection surveys shows that CO2 is distributed within 9 discrete layers. The trapping mechanism comprises a stacked series of 1 m thick, impermeable shale horizons that are spaced at 30 m intervals through the reservoir. Within the stratigraphically highest reservoir layer, Layer 9, a submarine channel deposit has been mapped on the pre-injection seismic survey. Detailed measurements of the three-dimensional CO2 distribution within Layer 9 have been made using seven time-lapse surveys, providing a useful benchmark against which numerical flow simulations can be tested. Previous simulations have, in general, been largely unsuccessful in matching the migration rate of CO2 in this layer. Here, CO2 flow within Layer 9 is modeled as a vertically-integrated gravity current that spreads beneath a structurally complex caprock using a two-dimensional grid, considerably increasing computational efficiency compared to conventional three-dimensional simulators. This flow model is inverted to find the optimal reservoir permeability in Layer 9 by minimizing the difference between observed and predicted distributions of CO2 as a function of space and time. A three parameter inverse model, comprising reservoir permeability, channel permeability and channel width, is investigated by grid search. The best-fitting reservoir permeability is 3 Darcys, which is consistent with measurements made on core material from the reservoir. Best-fitting channel permeability is 26 Darcys. Finally, the ability of this simplified numerical model
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
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
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.
16 reference population equations using peak expiratory flow meters
African Journals Online (AJOL)
DR. AMINU
equations in current use are based on linear statistical models which are subject to change and they did not ... assess risks of surgery and to assist in evaluations performed ... identify and quantify pulmonary involvement incases of asthma.
A generalised groundwater flow equation using the concept of non ...
African Journals Online (AJOL)
2006-01-01
Jan 1, 2006 ... 2 Institute for Groundwater Studies, University of the Free State, PO Box 339, Bloemfontein, South Africa. Abstract ... Keywords: porous media, Darcy Law, integro-differential equations .... f(x) satisfies the boundary conditions.
Directory of Open Access Journals (Sweden)
Farhang Azarang
2017-06-01
Full Text Available Introduction: The critical role of the rivers in supplying water for various needs of life has led to engineering identification of the hydraulic regime and flow condition of the rivers. Hydraulic structures such dams have inevitable effects on their downstream that should be well investigated. The reservoir dams are the most important hydraulic structures which are the cause of great changes in river flow conditions. Materials and Methods: In this research, an accurate assessment was performed to study the flow regime of Karkheh river at downstream of Karkheh Reservoir Dam as the largest dam in Middle East. Karkheh River is the third waterful river of Iran after Karun and Dez and the third longest river after the Karun and Sefidrud. The Karkheh Dam is a large reservoir dam built in Iran on the Karkheh River in 2000. The Karkheh Reservoir Dam is on the Karkheh River in the Northwestern Khouzestan Province, the closest city being Andimeshk to the east. The part of Karkheh River, which was studied in this research is located at downstream of Karkheh Reservoir Dam. This interval is approximately 94 km, which is located between PayePol and Abdolkhan hydrometric stations. In this research, 138 cross sections were used along Karkheh River. Distance of cross sections from each other was 680m in average. The efficient model of HEC-RAS has been utilized to simulate the Karkheh flow conditions before and after the reservoir dam construction using of hydrometric stations data included annually and monthly mean discharges, instantaneous maximum discharges, water surface profiles and etc. Three defined discharges had been chosen to simulate the Karkheh River flow; maximum defined discharge, mean defined discharge and minimum defined discharge. For each of these discharges values, HEC-RAS model was implemented as a steady flow of the Karkheh River at river reach of study. Water surface profiles of flow, hydraulic parameters and other results of flow regime in
Explicit flow equations and recursion operator of the ncKP hierarchy
International Nuclear Information System (INIS)
He, Jingsong; Wang, Lihong; Tu, Junyi; Li, Xiaodong
2011-01-01
The explicit expression of the flow equations of the noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy is derived. Compared with the flow equations of the KP hierarchy, our result shows that the additional terms in the flow equations of the ncKP hierarchy indeed consist of commutators of dynamical coordinates {u i }. The recursion operator for the flow equations under n-reduction is presented. Further, under 2-reduction, we calculate a nonlocal recursion operator Φ(2) of the noncommutative Korteweg–de Vries(ncKdV) hierarchy, which generates a hierarchy of local, higher-order flows. Thus we solve the open problem proposed by Olver and Sokolov (1998 Commun. Math. Phys. 193 245–68)
DEFF Research Database (Denmark)
Yan, Wei; Kontogeorgis, Georgios; Stenby, Erling Halfdan
2009-01-01
to reservoir fluids in presence of water and polar chemical Such as methanol and monoethylene glycol. With a minimum number of adjustable parameters from binary pairs, satisfactory results have been obtained for different types of phase equilibria in reservoir fluid systems and several relevant model......The complex phase equilibrium between reservoir fluids and associating compounds like water, methanol and glycols has become more and more important as the increasing global energy demand pushes the oil industry to target reservoirs with extreme or complicated conditions, such as deep or offshore...
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.
Kwon, Young-Sam; Lin, Ying-Chieh; Su, Cheng-Fang
2018-04-01
In this paper, we consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the rotational compressible magnetohydrodynamic flows with the well-prepared initial data. It is a first derivation of quasi-geostrophic equation governed by the magnetic field, and the tool is based on the relative entropy method. This paper covers two results: the existence of the unique local strong solution of quasi-geostrophic equation with the good regularity and the derivation of a quasi-geostrophic equation.
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
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
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......-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...
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.
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.
On the One-Dimensional Steady and Unsteady Porous Flow Equation
DEFF Research Database (Denmark)
Andersen, O. H.; Burcharth, H. F.
1995-01-01
Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative...... derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow...... resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available....
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.
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
Directory of Open Access Journals (Sweden)
I. Pal
2013-06-01
Full Text Available Snowmelt-dominated streamflow of the Western Himalayan rivers is an important water resource during the dry pre-monsoon spring months to meet the irrigation and hydropower needs in northern India. Here we study the seasonal prediction of melt-dominated total inflow into the Bhakra Dam in northern India based on statistical relationships with meteorological variables during the preceding winter. Total inflow into the Bhakra Dam includes the Satluj River flow together with a flow diversion from its tributary, the Beas River. Both are tributaries of the Indus River that originate from the Western Himalayas, which is an under-studied region. Average measured winter snow volume at the upper-elevation stations and corresponding lower-elevation rainfall and temperature of the Satluj River basin were considered as empirical predictors. Akaike information criteria (AIC and Bayesian information criteria (BIC were used to select the best subset of inputs from all the possible combinations of predictors for a multiple linear regression framework. To test for potential issues arising due to multicollinearity of the predictor variables, cross-validated prediction skills of the best subset were also compared with the prediction skills of principal component regression (PCR and partial least squares regression (PLSR techniques, which yielded broadly similar results. As a whole, the forecasts of the melt season at the end of winter and as the melt season commences were shown to have potential skill for guiding the development of stochastic optimization models to manage the trade-off between irrigation and hydropower releases versus flood control during the annual fill cycle of the Bhakra Reservoir, a major energy and irrigation source in the region.
On the scarcity of solutions of the equations of magnetohydrodynamic equilibria with flow
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)], E-mail: mnjmhd@am.uva.es
2008-06-16
While particular analytic solutions to the equations of axisymmetric MHD equilibria with flow are known, it is not clear what possible choosing of the free parameters of the equation of the magnetic flux will yield a solution. The most important of these is the poloidal stream function. We show that for a given flow to be able to yield an equilibrium, the flow itself must satisfy an analogous equation to the generalized Grad-Shafranov one. The problem therefore turns out to be how common are solutions to this type of equations. It is shown that in a natural space of functions, the set of these solutions is contained within a manifold of infinite codimension: extremely small by any criteria. Hence the class of flows for which an equilibrium, even defined only locally and irrespective of boundary conditions, may be found, is highly constrained.
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.
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.
Assessment of consistent two-equation closure for forest flows
DEFF Research Database (Denmark)
Sogachev, Andrey; Cavar, Dalibor; Bechmann, Andreas
of grid turbulence and wall-bounded flow, the closure suggested is also valid for homogeneous shear flows commonly observed inside tall vegetative canopies. The present work assess the plant drag closure by comparing results of two different CFD models against observations derived over the forested area...... and can be applied for any twoequation closure. Results derived by different CFD models with k-epsilon and k-omega closure are similar and in good comparison with observations. Overall, numerical results show that the closure performs well, opening new possibilities for application to tasks related...... to the atmospheric boundary layer—where it is important to adequately account for the influences of vegetation....
PREDICTION OF RESERVOIR FLOW RATE OF DEZ DAM BY THE PROBABILITY MATRIX METHOD
Directory of Open Access Journals (Sweden)
Mohammad Hashem Kanani
2012-12-01
Full Text Available The data collected from the operation of existing storage reservoirs, could offer valuable information for the better allocation and management of fresh water rates for future use to mitigation droughts effect. In this paper the long-term Dez reservoir (IRAN water rate prediction is presented using probability matrix method. Data is analyzed to find the probability matrix of water rates in Dez reservoir based on the previous history of annual water entrance during the past and present years(40 years. The algorithm developed covers both, the overflow and non-overflow conditions in the reservoir. Result of this study shows that in non-overflow conditions the most exigency case is equal to 75%. This means that, if the reservoir is empty (the stored water is less than 100 MCM this year, it would be also empty by 75% next year. The stored water in the reservoir would be less than 300 MCM by 85% next year if the reservoir is empty this year. This percentage decreases to 70% next year if the water of reservoir is less than 300 MCM this year. The percentage also decreases to 5% next year if the reservoir is full this year. In overflow conditions the most exigency case is equal to 75% again. The reservoir volume would be less than 150 MCM by 90% next year, if it is empty this year. This percentage decreases to 70% if its water volume is less than 300 MCM and 55% if the water volume is less than 500 MCM this year. Result shows that too, if the probability matrix of water rates to a reservoir is multiplied by itself repeatedly; it converges to a constant probability matrix, which could be used to predict the long-term water rate of the reservoir. In other words, the probability matrix of series of water rates is changed to a steady probability matrix in the course of time, which could reflect the hydrological behavior of the watershed and could be easily used for the long-term prediction of water storage in the down stream reservoirs.
Inversion of collective matter flow and equation of state
International Nuclear Information System (INIS)
Peter, J.
1992-03-01
The multidetector array Mur + Tonneau has been used to perform a 4π detection of charged particles and fragments emitted in reactions at energies ranging from 25 to 95 MeV/u. The collective transverse momentum in the reaction plane (sidewards flow parameter) is observed to strongly vary as a function of impact parameter and incident energy. The measured values have to be corrected for the effects due to the error on the reaction plane determination and to the detector limitations. Those limitations caused by the method itself are more important than those caused by the detector. The flow value changes from negative values (negative scattering at low energies). The inversion (or balance) energy is in the range 50-100 MeV/u, depending on the system and impact parameter value. Comparisons between experimental data and theoretical values are shown for the system 40 Ar + 27 Al. These studies (BUU, Landau-Vlasov, QMD) show that the flow, and especially the inversion energy, is sensitive to the nucleon-nucleon cross section σNN in medium. The data indicate that a momentum dependent effective interaction should be used. Then, the flow value is not much sensitive to the incompressibility modulus K, but possibly in peripheral collisions. Additional observables should be used. The azimuthal distribution of mid-rapidity particles indicates a rotation-like behaviour of the interaction region
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.
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
Directory of Open Access Journals (Sweden)
FU Ping
2017-08-01
Full Text Available The flow stress behavior of 5083 aluminum alloy was investigated under hot compression deformation at 523-723K,strain rates of 0.01-10s-1 and true strains of 0-0.7 with Gleeble-3800 thermal simulator. Based on the heat transfer effect on alloy deformation heat effect, the flow stress curves were corrected. The results show that influence of heat conduction can not be neglected and becomes more obvious with the increase of true strain. The corrected flow stress has little influence on the peak stress, but the steady flow stress softening trends to be diminished to some degree. The flow stress can be predicted by the Zener-Hollomon parameters in the constitutive equation. The corrected measured value exhibits a good agreement with the flow stress predicted by the constitutive equation, and the average relative error is only 5.21%.
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
Directory of Open Access Journals (Sweden)
N. Eriyagama
2018-06-01
Full Text Available Storage of surface water is widely regarded as a form of insurance against rainfall variability. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The issues of optimal size, placement and the number of reservoirs in a river basin – which maximizes sustainable benefits from storage – remain subjects for debate. This study examines the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. The study produced multiple surface storage development pathways for the basin under different scenarios of environmental flow (EF releases and reservoir network configurations. The EF scenarios ranged from zero to very healthy releases. It is shown that if the middle ground between the two extreme EF scenarios is considered, the theoretical maximum safe yield from surface storage is about 65–70 % of the mean annual runoff (MAR of the basin. It is also identified that although distribution of reservoirs in the river network reduces the cumulative yield from the basin, this cumulative yield is maximized if the ratio among the storage capacities placed in each sub drainage basin is equivalent to the ratio among their MAR. The study suggests a framework to identify drainage regions having higher surface storage potential, to plan for the right distribution of storage capacity within a river basin, as well as to plan for EF allocations.
Eriyagama, Nishadi; Smakhtin, Vladimir; Udamulla, Lakshika
2018-06-01
Storage of surface water is widely regarded as a form of insurance against rainfall variability. However, creation of surface storage often endanger the functions of natural ecosystems, and, in turn, ecosystem services that benefit humans. The issues of optimal size, placement and the number of reservoirs in a river basin - which maximizes sustainable benefits from storage - remain subjects for debate. This study examines the above issues through the analysis of a range of reservoir configurations in the Malwatu Oya river basin in the dry zone of Sri Lanka. The study produced multiple surface storage development pathways for the basin under different scenarios of environmental flow (EF) releases and reservoir network configurations. The EF scenarios ranged from zero to very healthy releases. It is shown that if the middle ground between the two extreme EF scenarios is considered, the theoretical maximum safe yield from surface storage is about 65-70 % of the mean annual runoff (MAR) of the basin. It is also identified that although distribution of reservoirs in the river network reduces the cumulative yield from the basin, this cumulative yield is maximized if the ratio among the storage capacities placed in each sub drainage basin is equivalent to the ratio among their MAR. The study suggests a framework to identify drainage regions having higher surface storage potential, to plan for the right distribution of storage capacity within a river basin, as well as to plan for EF allocations.
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...
Zhang, Rui-Han; Zhang, Lie-Hui; Wang, Rui-He; Zhao, Yu-Long; Huang, Rui
2018-06-01
Reservoir development for unconventional resources such as tight gas reservoirs is in increasing demand due to the rapid decline of production in conventional reserves. Compared with conventional reservoirs, fluid flow in water-bearing tight gas reservoirs is subject to more nonlinear multiphase flow and gas slippage in nano/micro matrix pores because of the strong collisions between rock and gas molecules. Economic gas production from tight gas reservoirs depends on extensive application of water-based hydraulic fracturing of horizontal wells, associated with non-Darcy flow at a high flow rate, geomechanical stress sensitivity of un-propped natural fractures, complex flow geometry and multiscale heterogeneity. How to efficiently and accurately predict the production performance of a multistage fractured horizontal well (MFHW) is challenging. In this paper, a novel multicontinuum, multimechanism, two-phase simulator is established based on unstructured meshes and the control volume finite element method to analyze the production performance of MFHWs. The multiple interacting continua model and discrete fracture model are coupled to integrate the unstimulated fractured reservoir, induced fracture networks (stimulated reservoir volumes, SRVs) and irregular discrete hydraulic fractures. Several simulations and sensitivity analyses are performed with the developed simulator for determining the key factors affecting the production performance of MFHWs. Two widely applied fracturing models, classic hydraulic fracturing which generates long double-wing fractures and the volumetric fracturing aimed at creating large SRVs, are compared to identify which of them can make better use of tight gas reserves.
Turnbull, S. J.
2017-12-01
Within the US Army Corps of Engineers (USACE), reservoirs are typically operated according to a rule curve that specifies target water levels based on the time of year. The rule curve is intended to maximize flood protection by specifying releases of water before the dominant rainfall period for a region. While some operating allowances are permissible, generally the rule curve elevations must be maintained. While this operational approach provides for the required flood control purpose, it may not result in optimal reservoir operations for multi-use impoundments. In the Russian River Valley of California a multi-agency research effort called Forecast-Informed Reservoir Operations (FIRO) is assessing the application of forecast weather and streamflow predictions to potentially enhance the operation of reservoirs in the watershed. The focus of the study has been on Lake Mendocino, a USACE project important for flood control, water supply, power generation and ecological flows. As part of this effort the Engineer Research and Development Center is assessing the ability of utilizing the physics based, distributed watershed model Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model to simulate stream flows, reservoir stages, and discharges while being driven by weather forecast products. A key question in this application is the effect of watershed model resolution on forecasted stream flows. To help resolve this question, GSSHA models of multiple grid resolutions, 30, 50, and 270m, were developed for the upper Russian River, which includes Lake Mendocino. The models were derived from common inputs: DEM, soils, land use, stream network, reservoir characteristics, and specified inflows and discharges. All the models were calibrated in both event and continuous simulation mode using measured precipitation gages and then driven with the West-WRF atmospheric model in prediction mode to assess the ability of the model to function in short term, less than one week
Transition flow ion transport via integral Boltzmann equation
International Nuclear Information System (INIS)
Darcie, T.E.
1983-10-01
A new approach is developed to solve the Integral Boltzmann Equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion/neutral mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion beam extractions from high pressure sources. Theoretical predictions are tested through an experiment in which an atmospheric pressure ion source is coupled to a high vacuum energy analyser. Excellent agreement results for configurations in which the radial velocity remains small. Velocity distributions are applied to predicting the efficiency of coupling an atmospheric pressure ion source to a quadrupole mass spectrometer and results clearly indicate the most desirable extracting configuration. A method is devised to calculate ion-molecule hard sphere collision cross sections for easily fragmented organic ions
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.
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.
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.
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.
Wilcox, Andrew C.; O'Connor, James E.; Major, Jon J.
2014-01-01
Condit Dam on the White Salmon River, Washington, a 38 m high dam impounding a large volume (1.8 million m3) of fine-grained sediment (60% sand, 35% silt and clay, and 5% gravel), was rapidly breached in October 2011. This unique dam decommissioning produced dramatic upstream and downstream geomorphic responses in the hours and weeks following breaching. Blasting a 5 m wide hole into the base of the dam resulted in rapid reservoir drawdown, abruptly releasing ~1.6 million m3 of reservoir water, exposing reservoir sediment to erosion, and triggering mass failures of the thickly accumulated reservoir sediment. Within 90 min of breaching, the reservoir's water and ~10% of its sediment had evacuated. At a gauging station 2.3 km downstream, flow increased briefly by 400 m3 s−1during passage of the initial pulse of released reservoir water, followed by a highly concentrated flow phase—up to 32% sediment by volume—as landslide-generated slurries from the reservoir moved downstream. This hyperconcentrated flow, analogous to those following volcanic eruptions or large landslides, draped the downstream river with predominantly fine sand. During the ensuing weeks, suspended-sediment concentration declined and sand and gravel bed load derived from continued reservoir erosion aggraded the channel by >1 m at the gauging station, after which the river incised back to near its initial elevation at this site. Within 15 weeks after breaching, over 1 million m3 of suspended load is estimated to have passed the gauging station, consistent with estimates that >60% of the reservoir's sediment had eroded. This dam removal highlights the influence of interactions among reservoir erosion processes, sediment composition, and style of decommissioning on rate of reservoir erosion and consequent downstream behavior of released sediment.
Directory of Open Access Journals (Sweden)
M. L. Kavvas
2017-10-01
Full Text Available Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.
Welch, N.; Crawshaw, J.; Boek, E.
2014-12-01
The successful storage of carbon dioxide in geologic formations requires an in-depth understanding of all reservoir characteristics and morphologies. An intact and substantial seal formation above a storage reservoir is required for a significant portion of the initial sealing mechanisms believed to occur during carbon dioxide storage operations. Shales are a common seal formation rock types found above numerous hydrocarbon reservoirs, as well as potential saline aquifer storage locations. Shales commonly have very low permeability, however they also have the tendency to be quite fissile, and the formation of fractures within these seals can have a significant detrimental effect on the sealing potential of a reservoir and amount to large areas of high permeability and low capillary pressures compared to the surrounding intact rock. Fractured shales also have an increased current interest due to the increasing development of shale gas reservoirs using hydraulic fracturing techniques. This work shows the observed changes that occur within fractured pieces of reservoir seal shale samples, along with quarry analogues, using an in-situ micro-CT fluid flow imaging apparatus with a Hassler type core holder. Changes within the preferential flow path under different stress regimes as well as physical changes to the fracture geometry are reported. Lattice Boltzmann flow simulations were then performed on the extracted flow paths and compared to experiment permeability measurements. The preferential flow path of carbon dioxide through the fracture network is also observed and compared to the results two-phase Lattice Boltzmann fluid flow simulations.
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
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.
International Nuclear Information System (INIS)
Kovscek, A.R.; Wang, Y.
2005-01-01
Carbon dioxide (CO 2 ) is already injected into a limited class of reservoirs for oil recovery purposes; however, the engineering design question for simultaneous oil recovery and storage of anthropogenic CO 2 is significantly different from that of oil recovery alone. Currently, the volumes of CO 2 injected solely for oil recovery are minimized due to the purchase cost of CO 2 . If and when CO 2 emissions to the atmosphere are managed, it will be necessary to maximize simultaneously both economic oil recovery and the volumes of CO 2 emplaced in oil reservoirs. This process is coined 'cooptimization'. This paper proposes a work flow for cooptimization of oil recovery and geologic CO 2 storage. An important component of the work flow is the assessment of uncertainty in predictions of performance. Typical methods for quantifying uncertainty employ exhaustive flow simulation of multiple stochastic realizations of the geologic architecture of a reservoir. Such approaches are computationally intensive and thereby time consuming. An analytic streamline based proxy for full reservoir simulation is proposed and tested. Streamline trajectories represent the three-dimensional velocity field during multiphase flow in porous media and so are useful for quantifying the similarity and differences among various reservoir models. The proxy allows rational selection of a representative subset of equi-probable reservoir models that encompass uncertainty with respect to true reservoir geology. The streamline approach is demonstrated to be thorough and rapid
Vibrational energy flow in the villin headpiece subdomain: Master equation simulations
International Nuclear Information System (INIS)
Leitner, David M.; Buchenberg, Sebastian; Brettel, Paul; Stock, Gerhard
2015-01-01
We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water
Vibrational energy flow in the villin headpiece subdomain: Master equation simulations
Energy Technology Data Exchange (ETDEWEB)
Leitner, David M., E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557 (United States); Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Buchenberg, Sebastian; Brettel, Paul [Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany); Stock, Gerhard, E-mail: dml@unr.edu, E-mail: stock@physik.uni-freiburg.de [Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Freiburg (Germany); Biomolecular Dynamics, Institute of Physics, University of Freiburg, Freiburg (Germany)
2015-02-21
We examine vibrational energy flow in dehydrated and hydrated villin headpiece subdomain HP36 by master equation simulations. Transition rates used in the simulations are obtained from communication maps calculated for HP36. In addition to energy flow along the main chain, we identify pathways for energy transport in HP36 via hydrogen bonding between residues quite far in sequence space. The results of the master equation simulations compare well with all-atom non-equilibrium simulations to about 1 ps following initial excitation of the protein, and quite well at long times, though for some residues we observe deviations between the master equation and all-atom simulations at intermediate times from about 1–10 ps. Those deviations are less noticeable for hydrated than dehydrated HP36 due to energy flow into the water.
BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows
Shaing, K. C.
2010-07-01
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.
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)
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
Kinetic equations for clean superconductors: Application to the flux flow hall effect
International Nuclear Information System (INIS)
Kopnin, N.B.
1994-01-01
The kinetic equations for clean superconductors (l>>ζ) are derived. expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℎE F /Δ 2 . The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of 3 He
A reduced set of gyrofluid equations for plasma flow in a diverging magnetic field
International Nuclear Information System (INIS)
Robertson, Scott
2016-01-01
Plasmas are often generated in a small diameter source with a strong magnetic field and subsequently flow into a region with greater diameter and smaller field. The magnetic mirror force that accelerates plasma in a diverging magnetic field appears in the gyrofluid equations developed for applications to toroidal devices, but this force is often absent from fluid equations. A set of gyrofluid equations with reduced complexity is developed in which drifts are assumed negligible and the mirror force is retained. The Chew–Goldberger–Low equations of state are used for a simple closure. These reduced gyrofluid equations are applied to plasma equilibrium in a magnetic mirror, to acceleration of plasma in a magnetic nozzle, and to space charge neutralization of an ion beam by electrons in a diverging magnetic field. The results from gyrofluid theory are compared with results from drift kinetic theory to find the accuracy of the gyrofluid approximation in these applications.
International Nuclear Information System (INIS)
Chen Yunyun; Li Zhenhua; Song Yang; He Anzhi
2009-01-01
An extended model of the original Gladstone-Dale (G-D) equation is proposed for optical computerized tomography (OCT) diagnosis of flame flow fields. For the purpose of verifying the newly established model, propane combustion is used as a practical example for experiment, and moire deflection tomography is introduced with the probe wavelength 808 nm. The results indicate that the temperature based on the extended model is more accurate than that based on the original G-D equation. In a word, the extended model can be suitable for all kinds of flame flow fields whatever the components, temperature, and ionization are.
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...
Directory of Open Access Journals (Sweden)
Nadjafikhah M.
2017-07-01
Full Text Available Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.
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.
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.
Governing equations for a seriated continuum: an unequal velocity model for two-phase flow
International Nuclear Information System (INIS)
Solbrig, C.W.; Hughes, E.D.
1975-05-01
The description of the flow of two-phase fluids is important in many engineering devices. Unexpected transient conditions which occur in these devices cannot, in general, be treated with single-component momentum equations. Instead, the use of momentum equations for each phase is necessary in order to describe the varied transient situations which can occur. These transient conditions can include phases moving in the opposite directions, such as steam moving upward and liquid moving downward, as well as phases moving in the same direction. The derivation of continuity and momentum equations for each phase and an overall energy equation for the mixture are presented. Terms describing interphase forces are described. A seriated (series of) continuum is distinguished from an interpenetrating medium by the representation of interphase friction with velocity differences in the former and velocity gradients in the latter. The seriated continuum also considers imbedded stationary solid surfaces such as occur in nuclear reactor cores. These stationary surfaces are taken into account with source terms. Sufficient constitutive equations are presented to form a complete set of equations. Methods are presented to show that all these coefficients are determinable from microscopic models and well known experimental results. Comparison of the present deviation with previous work is also given. The equations derived here may also be employed in certain multiphase, multicomponent flow applications. (U.S.)
Ladiges, Daniel R.; Sader, John E.
2018-05-01
Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969), 10.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two canonical flow problems: oscillatory Couette flow and Stokes' second problem. Approximate analytical formulas giving the bulk velocity and shear stress, valid for arbitrary oscillation frequency, are obtained for Couette flow. For Stokes' second problem, a simple system of ordinary differential equations is derived which may be solved to obtain the desired flow fields. Using this framework, a simple and accurate formula is provided for the shear stress at the oscillating boundary, again for arbitrary frequency, which may prove useful in application. These solutions are easily implemented on any symbolic or numerical package, such as Mathematica or matlab, facilitating the characterization of flows produced by nanomechanical devices and providing insight into the underlying flow physics.
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
Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions
Walters, Robert W.; Dwoyer, Douglas L.
1987-01-01
A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.
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.
Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations
International Nuclear Information System (INIS)
Anco, Stephen C
2006-01-01
Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps
Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations
Energy Technology Data Exchange (ETDEWEB)
Anco, Stephen C [Department of Mathematics, Brock University, St Catharines, ON (Canada)
2006-03-03
Moving frames of various kinds are used to derive bi-Hamiltonian operators and associated hierarchies of multi-component soliton equations from group-invariant flows of non-stretching curves in constant-curvature manifolds and Lie-group manifolds. The hierarchy in the constant-curvature case consists of a vector mKdV equation coming from a parallel frame, a vector potential mKdV equation coming from a covariantly constant frame, and higher order counterparts generated by an underlying vector mKdV recursion operator. In the Lie-group case, the hierarchy comprises a group-invariant analogue of the vector NLS equation coming from a left-invariant frame, along with higher order counterparts generated by a recursion operator that is like a square root of the mKdV one. The corresponding respective curve flows are found to be given by geometric nonlinear PDEs, specifically mKdV and group-invariant analogues of Schroedinger maps. In all cases the hierarchies also contain variants of vector sine-Gordon equations arising from the kernel of the respective recursion operators. The geometric PDEs that describe the corresponding curve flows are shown to be wave maps.
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.
Boek, E.S.; Padding, J.T.; Anderson, V.J.; Tardy, P.M.J.; Crawshaw, J.P.; Pearson, J.R.A.
2005-01-01
We carry out a stability analysis of the Bautista-Manero (B-M) constitutive equations for extensional flow of wormlike micelles. We show that all solutions for the steady-state extensional viscosity ¿E are unstable when the elongational rates e exceed some critical value. In some cases the only real
Pole dynamics for the Flierl-Petvishvili equation and zonal flow
International Nuclear Information System (INIS)
Spineanu, F.; Vlad, M.; Itoh, K.; Sanuki, H.; Itoh, S.-I.
2003-09-01
We use a systematic method which allows us to identify a class of exact solutions of the Flierl-Petvishvili equation. The solutions are periodic and have one dimensional geometry. We examine the physical properties and find that these structures can have a significant effect on the zonal flow generation. (author)
Transverse momentum spectra and elliptic flow: Hydrodynamics with QCD-based equations of state
Bluhm, M; Heinz, U
2008-01-01
We present a family of equations of state within a quasiparticle model adjusted to lattice QCD and study the impact on azimuthal flow anisotropies and transverse momentum spectra within hydrodynamic simulations for heavy-ion collisions at energies relevant for LHC.
Adjustment of pipe flow explicit friction factor equations for application to tube bundles
International Nuclear Information System (INIS)
Wiltz, Christopher L.; Bowen, Mike D.; Von Olnhausen, Wayne A.
2005-01-01
Full text of publication follows: The accurate determination of single phase friction losses or friction pressure drop in tube bundles is essential in the thermal-hydraulic analyses of components such as nuclear fuel assemblies, heat exchangers and steam generators. Such friction losses are normally calculated using a friction factor, f, along with the experimental observation that the friction pressure drop in a pipe is proportional to the dynamic pressure (1/2 ρV 2 ) of the flow: ΔP = 1/2 ρV 2 (fL/D). In this equation L is the pipe or tube bundle length and D is the hydraulic diameter of the pipe or tube bundle. The friction factor is normally calculated using one of a number of explicit friction factor equations. A significant amount of work has been accomplished in developing explicit friction factor equations. These explicit equations range from approximations, which were developed for ease of numerical evaluation, to those which are mathematically complex but yield very good fits to the test data. These explicit friction factor equations are based on a large experimental data base, nearly all of which comes from pipe flow geometry information, and have been historically applied to tube bundles. This paper presents an adjustment method which may be applied to various explicit friction factor equations developed for pipe flow to accurately predict the friction factor for tube bundles. The characteristic of the adjustment is based on experimental friction pressure loss data obtained by Framatome ANP through flow testing of a nuclear fuel assembly (tube bundle) at its Richland Test Facility (RTF). Through adjustment of previously developed explicit friction factor equations for pipe flow, the vast amount of historical development and experimentation in the area of single phase pipe flow friction loss may be incorporated into the evaluation of single phase friction losses within tube bundles. Comparisons of the application of one or more of the previously
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
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)
Nuclear stimulation of oil-reservoirs
Energy Technology Data Exchange (ETDEWEB)
Delort, F; Supiot, F [Commissariat a l' Energie Atomique, Centre d' Etudes de Bruyere-le-Chatel (France)
1970-05-01
Underground nuclear explosions in the Hoggar nuclear test site have shown that the geological effects may increase the production of oil or gas reservoirs. By studying the permanent liquid flow-rate with approximate DUPUIT's equation, or with a computer code, it is shown that the conventional well flow-rate may be increased by a factor between 3 and 50, depending on the medium and explosion conditions. (author)
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
Bout, B.; Lombardo, Luigi; van Westen, C.J.; Jetten, V.G.
2018-01-01
An integrated, modeling method for shallow landslides, debris flows and catchment hydrology is developed and presented in this paper. Existing two-phase debris flow equations and an adaptation on the infinite slope method are coupled with a full
Field differential equations for a potential flow from a Hamilton type variational principle
International Nuclear Information System (INIS)
Fierros Palacios, A.
1992-01-01
The same theoretical frame that was used to solve the problem of the field equations for a viscous fluid is utilized in this work. The purpose is to obtain the differential field equations for a potential flow from the Lagrangian formalism as in classical field theory. An action functional is introduced as a space-time integral over a region of three-dimensional Euclidean space, of a Lagrangian density as a function of certain field variables. A Hamilton type extremum action principle is postulated with adequate boundary conditions, and a set of differential field equations is derived. A particular Lagrangian density of the T-V type leads to the wave equation for the velocity potential. (Author)
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...
Flow behavior of N2 huff and puff process for enhanced oil recovery in tight oil reservoirs.
Lu, Teng; Li, Zhaomin; Li, Jian; Hou, Dawei; Zhang, Dingyong
2017-11-16
In the present work, the potential of N 2 huff and puff process to enhance the recovery of tight oil reservoir was evaluated. N 2 huff and puff experiments were performed in micromodels and cores to investigate the flow behaviors of different cycles. The results showed that, in the first cycle, N 2 was dispersed in the oil, forming the foamy oil flow. In the second cycle, the dispersed gas bubbles gradually coalesced into the continuous gas phase. In the third cycle, N 2 was produced in the form of continuous gas phase. The results from the coreflood tests showed that, the primary recovery was only 5.32%, while the recoveries for the three N 2 huff and puff cycles were 15.1%, 8.53% and 3.22%, respectively.The recovery and the pressure gradient in the first cycle were high. With the increase of huff and puff cycles, and the oil recovery and the pressure gradient rapidly decreased. The oil recovery of N 2 huff and puff has been found to increase as the N 2 injection pressure and the soaking time increased. These results showed that, the properly designed and controlled N 2 huff and puff process can lead to enhanced recovery of tight oil reservoirs.
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.
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.
Exact solutions of the Navier-Stokes equations generalized for flow in porous media
Daly, Edoardo; Basser, Hossein; Rudman, Murray
2018-05-01
Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.
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)
Fixation of waste materials in grouts: Part 3, Equation for critical flow rate
International Nuclear Information System (INIS)
Tallent, O.K.; McDaniel, E.W.; Spence, R.D.; Godsey, T.T.; Dodson, K.E.
1986-12-01
Critical flow rate data for grouts prepared from three distinctly different nuclear waste materials have been correlated. The wastes include Oak Ridge National Laboratory (ORNL) low-level waste (LLW) solution, Hanford Facility waste (HFW) solution, and cladding removal waste (CRW) slurry. Data for the three wastes have been correlated with a 0.96 coefficient of correlation by the following equation: log V/sub E/ = 0.289 + 0.707 log μ/sub E/, where V/sub E/ and μ/sub E/ denote critical flow rate in m 3 /min and apparent viscosity in Pa.s, respectively. The equation may be used to estimate critical flow rate for grouts prepared within the compositional range of the investigation. 5 refs., 4 figs., 7 tabs
Calibration of the 7—Equation Transition Model for High Reynolds Flows at Low Mach
Colonia, S.; Leble, V.; Steijl, R.; Barakos, G.
2016-09-01
The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients that need tuning. In this paper, the γ—equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. An aerofoil is used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solutions for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
International Nuclear Information System (INIS)
Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
Energy Technology Data Exchange (ETDEWEB)
Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires
1968-12-01
This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental
Energy Technology Data Exchange (ETDEWEB)
Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires
1968-12-01
This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental
Rarefied gas flows through a curved channel: Application of a diffusion-type equation
Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki
2010-11-01
Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.
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.
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
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)
Sohn, J. L.; Heinrich, J. C.
1990-01-01
The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
Applicability of Voce equation for tensile flow and work hardening behaviour of P92 ferritic steel
International Nuclear Information System (INIS)
Sainath, G.; Choudhary, B.K.; Christopher, J.; Isaac Samuel, E.; Mathew, M.D.
2015-01-01
Detailed analysis of true stress (σ)-true plastic strain (ε) data indicated that tensile flow behaviour of P92 ferritic steel can be adequately described by Voce equation at strain rates ranging from 3.16 × 10 −5 to 1.26 × 10 −3 s −1 over a temperature range 300–923 K. The steel exhibited two-stage work hardening in the variations of instantaneous work hardening rate (θ = dσ/dε) with stress. At all the strain rates, the variations in σ-ε, θ-σ and work hardening parameters associated with Voce equation with temperature exhibited three distinct temperature regimes. At intermediate temperatures, the variations in σ-ε, θ-σ and work hardening parameters with temperature and strain rate exhibited anomalous behaviour due to the occurrence of dynamic strain ageing in the steel. The shift in θ-σ towards low stresses, and rapid decrease in flow stress and work hardening parameters with increasing temperature and decreasing strain rate suggested dominance of dynamic recovery at high temperatures. - Highlights: • Tensile flow and work hardening behaviour of P92 steel has been examined. • Applicability of Voce equation to P92 steel is demonstrated. • Three temperature regimes in flow and work hardening has been observed. • Good match between predicted and the experimental tensile properties has been shown
International Nuclear Information System (INIS)
McCarthy, K.A.; Abdou, M.A.
1991-01-01
A computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics. The method which has been developed is an 'iterative' method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error. The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. (orig./AH)
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
Numerical simulation of single-phase and multiphase non-Darcy flowin porous and fractured reservoirs
Energy Technology Data Exchange (ETDEWEB)
Wu, Yu-Shu
2000-06-02
A numerical method as well as a theoretical study of non-Darcy fluid flow of through porous and fractured reservoirs is described. The non-Darcy flow is handled in a three-dimensional, multiphase flow reservoir simulator, while the model formulation incorporates the Forchheimer equation for describing single-phase or multiphase non-Darcy flow and displacement. The numerical scheme has been verified by comparing its results against those of analytical methods. Numerical solutions are used to obtain some insight into the physics of non-Darcy flow and displacement in reservoirs. In addition, several type curves are provided for well-test analyses of non-Darcy flow to demonstrate a methodology for modeling this type of flow in porous and fractured rocks, including flow in geothermal reservoirs.
M. L. Kavvas; T. Tu; A. Ercan; J. Polsinelli
2017-01-01
Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally...
Directory of Open Access Journals (Sweden)
Mohammad Amin Dezfoolian
2013-07-01
Full Text Available This study presents an intelligent model based on probabilistic neural networks (PNN to produce a quantitative formulation between seismic attributes and hydraulic flow units (HFUs. Neural networks have been used for the last several years to estimate reservoir properties. However, their application for hydraulic flow unit estimation on a cube of seismic data is an interesting topic for research. The methodology for this application is illustrated using 3D seismic attributes and petrophysical and core data from 6 wells from the Kangan and Dalan gas reservoirs in the Persian Gulf basin. The methodology introduced in this study estimates HFUs from a large volume of 3D seismic data. This may increase exploration success rates and reduce costs through the application of more reliable output results in hydrocarbon exploration programs. 4 seismic attributes, including acoustic impedance, dominant fre- quency, amplitude weighted phase and instantaneous phase, are considered as the optimal inputs for pre- dicting HFUs from seismic data. The proposed technique is successfully tested in a carbonate sequence of Permian-Triassic rocks from the studied area. The results of this study demonstrate that there is a good agreement between the core and PNN-derived flow units. The PNN used in this study is successful in modeling flow units from 3D seismic data for which no core data or well log data are available. Resumen Este estudio presenta un modelo inteligente basado en redes neuronales probabilísticas (PNN para pro- ducir una formulación cuantitativa entre atributos sísmicos y unidades de flujo hidráulico (HFU. Las redes neuronales han sido utilizadas durante los últimos años para estimar las propiedades de reserva. Sin embargo, su aplicación para estimación de unidades de flujo hidráulico en un cubo de datos sísmicos es un tema importante de investigación. La metodología para esta aplicación está ilustrada a partir de datos tridimensionales y
A non-hybrid method for the PDF equations of turbulent flows on unstructured grids
International Nuclear Information System (INIS)
Bakosi, J.; Franzese, P.; Boybeyi, Z.
2008-01-01
In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. In the vicinity of walls the flow is resolved by an elliptic relaxation technique down to the viscous sublayer, explicitly modeling the high anisotropy and inhomogeneity of the low-Reynolds-number wall region without damping or wall-functions. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (i.e., the mean pressure and the elliptic relaxation tensor) and to track particles. All three aspects regarding the grid make use of the finite element method employing the simplest linear shapefunctions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean (IECM) model is adopted. An adaptive algorithm to compute the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory
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.
Isentropic Gas Flow for the Compressible Euler Equation in a Nozzle
Tsuge, Naoki
2013-08-01
We study the motion of isentropic gas in a nozzle. Nozzles are used to increase the thrust of engines or to accelerate a flow from subsonic to supersonic. Nozzles are essential parts for jet engines, rocket engines and supersonicwind tunnels. In the present paper, we consider unsteady flow, which is governed by the compressible Euler equation, and prove the existence of global solutions for the Cauchy problem. For this problem, the existence theorem has already been obtained for initial data away from the sonic state, (Liu in Commun Math Phys 68:141-172, 1979). Here, we are interested in the transonic flow, which is essential for engineering and physics. Although the transonic flow has recently been studied (Tsuge in J Math Kyoto Univ 46:457-524, 2006; Lu in Nonlinear Anal Real World Appl 12:2802-2810, 2011), these papers assume monotonicity of the cross section area. Here, we consider the transonic flow in a nozzle with a general cross section area. When we prove global existence, the most difficult point is obtaining a bounded estimate for approximate solutions. To overcome this, we employ a new invariant region that depends on the space variable. Moreover, we introduce a modified Godunov scheme. The corresponding approximate solutions consist of piecewise steady-state solutions of an auxiliary equation, which yield a desired bounded estimate. In order to prove their convergence, we use the compensated compactness framework.
Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.
International Nuclear Information System (INIS)
Naumann, U.
2002-01-01
The fast computation of gradients in reverse mode Automatic Differentiation (AD) requires the generation of adjoint versions of every statement in the original code. Due to the resulting reversal of the control flow certain intermediate values have to be made available in reverse order to compute the local partial derivatives. This can be achieved by storing these values or by recomputing them when they become required. In any case one is interested in minimizing the size of this set. Following an extensive introduction of the ''To-Be-Recorded'' (TBR) problem the authors present flow equations for propagating the TBR status of variables in the context of reverse mode AD of structured programs
Energy Technology Data Exchange (ETDEWEB)
Kafka, P; Meszaros, P [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany, F.R.)
1976-11-01
Stationary spherically symmetric solutions of the equations for accretion of large mass flows onto a black hole, including the interaction of matter and radiation due to Thomson scattering in diffusion approximation are constructed. The relevance of these solutions is discussed with respect to the question of whether the limitation of the luminosity (Eddington limit) also implies an upper bound to the possible rate of mass flow. The question remains open until all instabilities have been studied. At the moment a negative answer is favoured.
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.
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann
2003-01-01
This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1993-04-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive [Phi][sub 4][sup 4]. The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.).
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
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
framework to increase the production and economic value of an oil reservoir. Wether the objective is to maximize recovery or some financial measure like Net Present Value, the increased production is achieved by manipulation of the well rates and bottom-hole pressures of the injection and production wells....... The optimal water injection rates and production well bottom-hole pressures are computed by solution of a large-scale constrained optimal control problem. The objective is to maximize production by manipulating the well rates and bottom hole pressures of injection and production wells. Optimal control...... settings of injection and production wells are computed by solution of a large scale constrained optimal control problem. We describe a gradient based method to compute the optimal control strategy of the water flooding process. An explicit singly diagonally implicit Runge-Kutta (ESDIRK) method...
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.
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.
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.
Is the kinetic equation for turbulent gas-particle flows ill posed?
Reeks, M; Swailes, D C; Bragg, A D
2018-02-01
This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.
Becker, Carol J.
2001-01-01
Fort Cobb Reservoir in northwest Caddo County Oklahoma is managed by the Bureau of Reclamation for water supply, recreation, flood control, and wildlife. Excessive amounts of nitrogen in the watershed have the potential to cause long-term eutrophication of the reservoir and increase already elevated concentrations of nitrogen in the Rush Springs aquifer. The U.S. Geological Survey in cooperation with the Bureau of Reclamation studied ground water in the area surrounding a swine feeding operation located less than 2 miles upgradient from Fort Cobb Reservoir in Caddo County, Oklahoma. Objectives of the study were to (1) determine if the operation was contributing nitrogen to the ground water and (2) measure changes in ground-water levels and determine the local ground-water flow direction in the area surrounding the swine feeding operation. Nitrate concentrations (28.1 and 31.5 milligrams per liter) were largest in two ground-water samples from a well upgradient of the wastewater lagoon. Nitrate concentrations ranged from 4.30 to 8.20 milligrams per liter in samples from downgradient wells. Traces of ammonia and nitrite were detected in a downgradient well, but not in upgradient wells. d15N values indicate atmospheric nitrogen, synthetic fertilizer, or plants were the predominate sources of nitrate in ground water from the downgradient wells. The d15N values in these samples are depleted in nitrogen-15, indicating that animal waste was not a significant contributor of nitrate. Manganese concentrations (1,150 and 965 micrograms per liter) in samples from a downgradient well were substantially larger than concentrations in samples from other wells, exceeding the secondary drinking-water standard of 50 micrograms per liter. Larger concentrations of bicarbonate, magnesium, fluoride, and iron and a higher pH were also measured in water from a downgradient well. Ground-water levels in an observation well were higher from April to mid-July and lower during the late summer
DEFF Research Database (Denmark)
Yuan, Hao; Shapiro, Alexander; Stenby, Erling Halfdan
Modeling transport of reservoir fines is of great importance for evaluating the damage of production wells and infectivity decline. The conventional methodology accounts for neither the formation heterogeneity around the wells nor the reservoir fines’ heterogeneity. We have developed an integral...... dispersion equation in modeling the transport and the deposition of reservoir fines. It successfully predicts the unsymmetrical concentration profiles and the hyperexponential deposition in experiments....
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.
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.
International Nuclear Information System (INIS)
Leung Shingyu; Qian Jianliang
2010-01-01
We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.
SGS Modeling of the Internal Energy Equation in LES of Supersonic Channel Flow
Raghunath, Sriram; Brereton, Giles
2011-11-01
DNS of fully-developed turbulent supersonic channel flows (Reτ = 190) at up to Mach 3 indicate that the turbulent heat fluxes depend only weakly on Mach number, while the viscous dissipation and pressure dilatation do so strongly. Moreover, pressure dilatation makes a significant contribution to the internal energy budget at Mach 3 and higher. The balance between these terms is critical to determining the temperature (and so molecular viscosity) from the internal energy equation and so, in LES of these flows, it is essential to use accurate SGS models for the viscous dissipation and the pressure dilatation. In this talk, we present LES results for supersonic channel flow, using SGS models for these terms that are based on the resolved-scale dilatation, an inverse timescale, and SGS momentum fluxes, which intrinsically represent this Mach number effect.
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
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.
Multigrid methods for fully implicit oil reservoir simulation
Energy Technology Data Exchange (ETDEWEB)
Molenaar, J.
1995-12-31
In this paper, the authors consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations the material balance or continuity equations, and the equation of motion (Darcy`s law). For the numerical solution of this system of nonlinear partial differential equations, there are two approaches: the fully implicit or simultaneous solution method, and the sequential solution method. In this paper, the authors consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations.
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
Simon, Moritz; Ulbrich, Michael
2014-01-01
is to maximize the amount of trapped CO2 in an underground reservoir after a fixed period of CO2 injection, while time-dependent injection rates in multiple wells are used as control parameters. We describe the governing two-phase two-component Darcy flow PDE
Ferket, H.; Swennen, R.; Ortuno-Arzate, S.; Roure, F.
2006-01-01
This paper discusses the fluid flow evolution in the Veracruz petroleum province of eastern Mexico based on results of an integrated diagenetic, sedimentological and structural analysis. The area progressively changed from passive foreland towards an active fold-and-thrust belt into a passive belt
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.
Chen, Gui-Qiang G.; Schrecker, Matthew R. I.
2018-04-01
We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).
International Nuclear Information System (INIS)
Green, B I; Vedula, Prakash
2013-01-01
An alternative approach for solution of the collisional Boltzmann equation for a lattice architecture is presented. In the proposed method, termed the collisional lattice Boltzmann method (cLBM), the effects of spatial transport are accounted for via a streaming operator, using a lattice framework, and the effects of detailed collisional interactions are accounted for using the full collision operator of the Boltzmann equation. The latter feature is in contrast to the conventional lattice Boltzmann methods (LBMs) where collisional interactions are modeled via simple equilibrium based relaxation models (e.g. BGK). The underlying distribution function is represented using weights and fixed velocity abscissas according to the lattice structure. These weights are evolved based on constraints on the evolution of generalized moments of velocity according to the collisional Boltzmann equation. It can be shown that the collision integral can be reduced to a summation of elementary integrals, which can be analytically evaluated. The proposed method is validated using studies of canonical microchannel Couette and Poiseuille flows (both body force and pressure driven) and the results are found to be in good agreement with those obtained from conventional LBMs and experiments where available. Unlike conventional LBMs, the proposed method does not involve any equilibrium based approximations and hence can be useful for simulation of highly nonequilibrium flows (for a range of Knudsen numbers) using a lattice framework. (paper)
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)
Relations between the kinetic equation and the Langevin models in two-phase flow modelling
International Nuclear Information System (INIS)
Minier, J.P.; Pozorski, J.
1997-05-01
The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)
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)
Some exact solutions to the Lighthill–Whitham–Richards–Payne traffic flow equations
International Nuclear Information System (INIS)
Rowlands, G; Infeld, E; Skorupski, A A
2013-01-01
We find a class of exact solutions to the Lighthill–Whitham–Richards–Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg–de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end. (paper)
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.
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
fluctuations of virial and potential energy. Such systems have good isomorphs (curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units). The SLLOD equations of motion were used to simulate Couette shear flows......Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to have strong correlations between equilibrium thermal...... of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of strain rates were simulated to test for the predicted invariance, covering both the linear...
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)
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.
Adem, Abdullahi Rashid; Moawad, Salah M.
2018-05-01
In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.
Spectral and evolutionary analysis of advection-diffusion equations and the shear flow paradigm
International Nuclear Information System (INIS)
Thyagaraja, A.; Loureiro, N.; Knight, P.J.
2002-01-01
Advection-diffusion equations occur in a wide variety of fields in many contexts of active and passive transport in fluids and plasmas. The effects of sheared advective flows in the presence of irreversible processes such as diffusion and viscosity are of considerable current interest in tokamak and astrophysical contexts, where they are thought to play a key role in both transport and the dynamical structures characteristic of electromagnetic plasma turbulence. In this paper we investigate the spectral and evolutionary properties of relatively simple, linear, advection-diffusion equations. We apply analytical approaches based on standard Green's function methods to obtain insight into the nature of the spectra when the advective and diffusive effects occur separately and in combination. In particular, the physically interesting limit of small (but finite) diffusion is studied in detail. The analytical work is extended and supplemented by numerical techniques involving a direct solution of the eigenvalue problem as well as evolutionary studies of the initial value problem using a parallel code, CADENCE. The three approaches are complementary and entirely consistent with each other when appropriate comparison is made. They reveal different aspects of the properties of the advection-diffusion equation, such as the ability of sheared flows to generate a direct cascade to high wave numbers transverse to the advection and the consequent enhancement of even small amounts of diffusivity. The invariance properties of the spectra in the low diffusivity limit and the ability of highly sheared, jet-like flows to 'confine' transport to low shear regions are demonstrated. The implications of these properties in a wider context are discussed and set in perspective. (author)
Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed
2012-01-01
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
Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem
2017-01-01
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
Daivis, Peter J; Todd, B D
2006-05-21
We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.
International Nuclear Information System (INIS)
Zheng Lihui; He Xiaoqing; Wang Xiangchun; Fu Lixia
2009-01-01
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) and 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 and 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
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.
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.
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
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.
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.
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.
Birdsell, D.; Karra, S.; Rajaram, H.
2017-12-01
The governing equations for subsurface flow codes in deformable porous media are derived from the fluid mass balance equation. One class of these codes, which we call general subsurface flow (GSF) codes, does not explicitly track the motion of the solid porous media but does accept general constitutive relations for porosity, density, and fluid flux. Examples of GSF codes include PFLOTRAN, FEHM, STOMP, and TOUGH2. Meanwhile, analytical and numerical solutions based on the groundwater flow equation have assumed forms for porosity, density, and fluid flux. We review the derivation of the groundwater flow equation, which uses the form of Darcy's equation that accounts for the velocity of fluids with respect to solids and defines the soil matrix compressibility accordingly. We then show how GSF codes have a different governing equation if they use the form of Darcy's equation that is written only in terms of fluid velocity. The difference is seen in the porosity change, which is part of the specific storage term in the groundwater flow equation. We propose an alternative definition of soil matrix compressibility to correct for the untracked solid velocity. Simulation results show significantly less error for our new compressibility definition than the traditional compressibility when compared to analytical solutions from the groundwater literature. For example, the error in one calculation for a pumped sandstone aquifer goes from 940 to <70 Pa when the new compressibility is used. Code users and developers need to be aware of assumptions in the governing equations and constitutive relations in subsurface flow codes, and our newly-proposed compressibility function should be incorporated into GSF codes.
Radiant heating of petroleum reservoirs; Aquecimento radiante de reservatorios petroliferos
Energy Technology Data Exchange (ETDEWEB)
Sidrim, Fernando A.C.
1990-12-31
This work presents a proposal of a simplified model for the enhanced oil recovery process through radiant heating of oil reservoirs. The resulting continuity, energy and motion equations were solved analytically for the prediction of the increase in well flow rates. The heat loss to adjacent formations and the necessary for the establishment of the temperature profile,which are transient terms of energy equation, have been neglected. Also, no temperature gradient in the axial direction has been modelled as a cylindrical wave propagating in a loss medium. It is concluded that: the inclusion of a radial conduction term in the energy equation led to higher flow rates than the ones predicted by the literature existing solution; if the absorption coefficient is too large, it is profitable to dry the reservoir around the well bore; the transient terms in the energy equation are significant for extended periods of well production. 47 refs., 18 figs., 4 tabs.
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.
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
Prediction of adiabatic bubbly flows in TRACE using the interfacial area transport equation
International Nuclear Information System (INIS)
Talley, J.; Worosz, T.; Kim, S.; Mahaffy, J.; Bajorek, S.; Tien, K.
2011-01-01
The conventional thermal-hydraulic reactor system analysis codes utilize a two-field, two-fluid formulation to model two-phase flows. To close this model, static flow regime transition criteria and algebraic relations are utilized to estimate the interfacial area concentration (a i ). To better reflect the continuous evolution of two-phase flow, an experimental version of TRACE is being developed which implements the interfacial area transport equation (IATE) to replace the flow regime based approach. Dynamic estimation of a i is provided through the use of mechanistic models for bubble coalescence and disintegration. To account for the differences in bubble interactions and drag forces, two-group bubble transport is sought. As such, Group 1 accounts for the transport of spherical and distorted bubbles, while Group 2 accounts for the cap, slug, and churn-turbulent bubbles. Based on this categorization, a two-group IATE applicable to the range of dispersed two-phase flows has been previously developed. Recently, a one-group, one-dimensional, adiabatic IATE has been implemented into the TRACE code with mechanistic models accounting for: (1) bubble breakup due to turbulent impact of an eddy on a bubble, (2) bubble coalescence due to random collision driven by turbulent eddies, and (3) bubble coalescence due to the acceleration of a bubble in the wake region of a preceding bubble. To demonstrate the enhancement of the code's capability using the IATE, experimental data for a i , void fraction, and bubble velocity measured by a multi-sensor conductivity probe are compared to both the IATE and flow regime based predictions. In total, 50 air-water vertical co-current upward and downward bubbly flow conditions in pipes with diameters ranging from 2.54 to 20.32 cm are evaluated. It is found that TRACE, using the conventional flow regime relation, always underestimates a i . Moreover, the axial trend of the a i prediction is always quasi-linear because a i in the
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
Veldman, A.E.P.
1973-01-01
A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag
Energy Technology Data Exchange (ETDEWEB)
NONE
1999-03-01
This R and D are aimed at establishing technology to support the reservoir modeling work required for predicting the reservoir variation from the geological/geochemical side. The contents of the development are (1) establishment of the practical measuring system for core fracture system, and (2) establishment of new modeling support technology. In (1), as the core fraction system measuring system, the measurement of fluid inclusion homogenization temperature and melting point and laser Raman spectroscopy were applied to the Wasabizawa area to obtain the results. In (2), the R and D were conducted of a rapid age measuring method for altered rock/unaltered rock and an analytical method for fluid flow using trace chemical components of hydrothermal minerals. In the former, 3-D thermoluminescent intensity of the age-known quartz was measured. The TL age of weak altered rock of Kijiyama dacite in the Wasabizawa area was 320Ka, almost the same result as 320Ka already reported. In the latter, trace components of quartz were measured at each well, and changes in the depth direction were made clear. It was made clear that the variation of Na/K ratio is large around the lost circulation stratum. The geothermal fluid flow was made clear by the analysis of similarity of the intensity ratio. (NEDO)
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)
Engle, Mark A.; Reyes, Francisco R.; Varonka, Matthew S.; Orem, William H.; Lin, Ma; Ianno, Adam J.; Westphal, Tiffani M.; Xu, Pei; Carroll, Kenneth C.
2016-01-01
Despite being one of the most important oil producing provinces in the United States, information on basinal hydrogeology and fluid flow in the Permian Basin of Texas and New Mexico is lacking. The source and geochemistry of brines from the basin were investigated (Ordovician- to Guadalupian-age reservoirs) by combining previously published data from conventional reservoirs with geochemical results for 39 new produced water samples, with a focus on those from shales. Salinity of the Ca–Cl-type brines in the basin generally increases with depth reaching a maximum in Devonian (median = 154 g/L) reservoirs, followed by decreases in salinity in the Silurian (median = 77 g/L) and Ordovician (median = 70 g/L) reservoirs. Isotopic data for B, O, H, and Sr and ion chemistry indicate three major types of water. Lower salinity fluids (100 g/L), isotopically heavy (O and H) water in Leonardian [Permian] to Pennsylvanian reservoirs (2–3.2 km depth) is evaporated, Late Permian seawater. Water from the Permian Wolfcamp and Pennsylvanian “Cline” shales, which are isotopically similar but lower in salinity and enriched in alkalis, appear to have developed their composition due to post-illitization diffusion into the shales. Samples from the “Cline” shale are further enriched with NH4, Br, I and isotopically light B, sourced from the breakdown of marine kerogen in the unit. Lower salinity waters (3 km depth), which plot near the modern local meteoric water line, are distinct from the water in overlying reservoirs. We propose that these deep meteoric waters are part of a newly identified hydrogeologic unit: the Deep Basin Meteoric Aquifer System. Chemical, isotopic, and pressure data suggest that despite over-pressuring in the Wolfcamp shale, there is little potential for vertical fluid migration to the surface environment via natural conduits.
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], 0Math 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)
Hung, P.C.; Irwin, G.; Kee, R.; McLoone, S.
2005-01-01
Thermocouples are one of the most popular devices for temperature measurement due to their robustness, ease of manufacture and installation, and low cost. However, when used in certain harsh environments, for example, in combustion systems and engine exhausts, large wire diameters are required, and consequently the measurement bandwidth is reduced. This article discusses a software compensation technique to address the loss of high frequency fluctuations based on measurements from two thermocouples. In particular, a difference equation (DE) approach is proposed and compared with existing methods both in simulation and on experimental test rig data with constant flow velocity. It is found that the DE algorithm, combined with the use of generalized total least squares for parameter identification, provides better performance in terms of time constant estimation without any a priori assumption on the time constant ratios of the thermocouples
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.
Frost, W.; Harper, W. L.
1975-01-01
Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.
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.
DEFF Research Database (Denmark)
Lerch, Dariusz Michal; Völcker, Carsten; Capolei, Andrea
2012-01-01
in the reservoir. A promising decrease of these remained resources can be provided by smart wells applying water injections to sustain satisfactory pressure level in the reservoir throughout the whole process of oil production. Basically to enhance secondary recovery of the remaining oil after drilling, water...... is injected at the injection wells of the down-hole pipes. This sustains the pressure in the reservoir and drives oil towards production wells. There are however, many factors contributing to the poor conventional secondary recovery methods e.g. strong surface tension, heterogeneity of the porous rock...... fields, or closed loop optimisation, can be used for optimising the reservoir performance in terms of net present value of oil recovery or another economic objective. In order to solve an optimal control problem we use a direct collocation method where we translate a continuous problem into a discrete...
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
A filtering technique for solving the advection equation in two-phase flow problems
International Nuclear Information System (INIS)
Devals, C.; Heniche, M.; Bertrand, F.; Tanguy, P.A.; Hayes, R.E.
2004-01-01
The aim of this work is to develop a numerical strategy for the simulation of two-phase flow in the context of chemical engineering applications. The finite element method has been chosen because of its flexibility to deal with complex geometries. One of the key points of two-phase flow simulation is to determine precisely the position of the interface between the two phases, which is an unknown of the problem. In this case, the interface can be tracked by the advection of the so-called color function. It is well known that the solution of the advection equation by most numerical schemes, including the Streamline Upwind Petrov-Galerkin (SUPG) method, may exhibit spurious oscillations. This work proposes an approach to filter out these oscillations by means of a change of variable that is efficient for both steady state and transient cases. First, the filtering technique will be presented in detail. Then, it will be applied to two-dimensional benchmark problems, namely, the advection skew to the mesh and the Zalesak's problems. (author)
Energy Technology Data Exchange (ETDEWEB)
Sari, Salih [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey); Erguen, Sule [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey); Barik, Muhammet; Kocar, Cemil; Soekmen, Cemal Niyazi [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey)
2009-03-15
In this study, isothermal turbulent bubbly flow is mechanistically modeled. For the modeling, Fluent version 6.3.26 is used as the computational fluid dynamics solver. First, the mechanistic models that simulate the interphase momentum transfer between the gas (bubbles) and liquid (continuous) phases are investigated, and proper models for the known flow conditions are selected. Second, an interfacial area transport equation (IATE) solution is added to Fluent's solution scheme in order to model the interphase momentum transfer mechanisms. In addition to solving IATE, bubble number density (BND) approach is also added to Fluent and this approach is also used in the simulations. Different source/sink models derived for the IATE and BND models are also investigated. The simulations of experiments based on the available data in literature are performed by using IATE and BND models in two and three-dimensions. The results show that the simulations performed by using IATE and BND models agree with each other and with the experimental data. The simulations performed in three-dimensions give better agreement with the experimental data.
International Nuclear Information System (INIS)
Sari, Salih; Erguen, Sule; Barik, Muhammet; Kocar, Cemil; Soekmen, Cemal Niyazi
2009-01-01
In this study, isothermal turbulent bubbly flow is mechanistically modeled. For the modeling, Fluent version 6.3.26 is used as the computational fluid dynamics solver. First, the mechanistic models that simulate the interphase momentum transfer between the gas (bubbles) and liquid (continuous) phases are investigated, and proper models for the known flow conditions are selected. Second, an interfacial area transport equation (IATE) solution is added to Fluent's solution scheme in order to model the interphase momentum transfer mechanisms. In addition to solving IATE, bubble number density (BND) approach is also added to Fluent and this approach is also used in the simulations. Different source/sink models derived for the IATE and BND models are also investigated. The simulations of experiments based on the available data in literature are performed by using IATE and BND models in two and three-dimensions. The results show that the simulations performed by using IATE and BND models agree with each other and with the experimental data. The simulations performed in three-dimensions give better agreement with the experimental data
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)
Di Nucci, Carmine
2018-05-01
This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.
International Nuclear Information System (INIS)
Bessho, Y.; Uchikawa, S.
1985-01-01
A subchannel analysis program, MENUETT, is developed for evaluation of thermal-hydraulic characteristics in boiling water reactor fuel bundles. This program is based on five conservation equations of two-phase flow with the drift-flux correlation. The cross flows are calculated separately for liquid and vapor phases from the lateral momentum conservation equation. The effects of turbulent mixing and void drift are accounted for in the program. The conservation equations are implicitly differentiated with the convective terms by the donor-cell method, and are solved iteratively in the axial and lateral directions. Data of the 3 X 3 rod bundle experiments are used for program verification. The lateral distributions of equilibrium quality and mass flow rate at the bundle exit calculated by the program compare satisfactorily with the experimental results
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.
Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan
2016-01-01
Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.
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.
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
Zhang, Penghui; Zhang, Jinliang; Wang, Jinkai; Li, Ming; Liang, Jie; Wu, Yingli
2018-05-01
Flow units classification can be used in reservoir characterization. In addition, characterizing the reservoir interval into flow units is an effective way to simulate the reservoir. Paraflow units (PFUs), the second level of flow units, are used to estimate the spatial distribution of continental clastic reservoirs at the detailed reservoir description stage. In this study, we investigate a nonroutine methodology to predict the external and internal distribution of PFUs. The methodology outlined enables the classification of PFUs using sandstone core samples and log data. The relationships obtained between porosity, permeability and pore throat aperture radii (r35) values were established for core and log data obtained from 26 wells from the Funing Formation, Gaoji Oilfield, Subei Basin, China. The present study refines predicted PFUs at logged (0.125-m) intervals, whose scale is much smaller than routine methods. Meanwhile, three-dimensional models are built using sequential indicator simulation to characterize PFUs in wells. Four distinct PFUs are classified and located based on the statistical methodology of cluster analysis, and each PFU has different seepage ability. The results of this study demonstrate the obtained models are able to quantify reservoir heterogeneity. Due to different petrophysical characteristics and seepage ability, PFUs have a significant impact on the distribution of the remaining oil. Considering these allows a more accurate understanding of reservoir quality, especially within non-marine sandstone reservoirs.
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.
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations
Energy Technology Data Exchange (ETDEWEB)
Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)
2016-06-01
Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region
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
Large CYBER-205-model of the Euler equations for vortex-stretched turbulent flow around Delta wings
International Nuclear Information System (INIS)
Rizzi, A.; Purcell, C.J.
1985-01-01
The large-scale numerical simulation of fluid flow is described as a discipline within the field of software engineering. As an example of such work, a vortex flow field is analyzed for its essential physical flow features, an appropriate mathematical description is presented (the Euler equations with an artificial viscosity model), a numerical algorithm to solve mathematical equations is described, and the programming methodology which allows us to attain a very high degree of vectorization on the CYBER 205 is discussed. Four simulated flowfields with vorticity shed from wing edges are computed with up to as many as one million grid points and verify the realism of the simulation model. The computed solutions show all of the qualitative features that are expected in these flows. The twisted cranked-and-cropped delta case is one where the leading-edge vortex is highly stretched and unstable, displaying ultimately inviscid large-scale turbulent-like phenomena
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.
International Nuclear Information System (INIS)
Criado-Sancho, M.; Casas-Vazquez, J.; Jou, D.
1997-01-01
In the literature, the shift of the spinodal line of polymer solutions under flow is attributed either to an actual shift of the spinodal due to a nonequilibrium modification of the equation of state for the chemical potential, or to an apparent shift due to an increase of hydrodynamic fluctuations owing to the flow. Here we see that both approaches are compatible and that both effects add up. copyright 1997 The American Physical Society
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
International Nuclear Information System (INIS)
Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.
2003-01-01
This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)
Directory of Open Access Journals (Sweden)
Hożejowska Sylwia
2017-01-01
Full Text Available This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.
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
Energy Technology Data Exchange (ETDEWEB)
Zhang Shijie [Tsinghua University, Beijing (China). School of Architecture; Yuan Xin; Ye Dajun [Tsinghua University, Beijing (China). Dept. of Thermal Engineering
2001-07-01
Numerical simulations of the turbulent flow fields at stall conditions are presented for the NREL (National Renewable Energy Laboratory) S809 airfoil. The flow is modelled as compressible, viscous, steady/unsteady and turbulent. Four two-equation turbulence models (isotropic {kappa}-{epsilon} and q-{omega} models, anisotropic {kappa}-{epsilon} and -{omega} models), are applied to close the Reynolds-averaged Navier-Stokes equations, respectively. The governing equations are integrated in time by a new LU-type implicit scheme. To accurately model the convection terms in the mean-flow and turbulence model equations, a modified fourth-order high resolution MUSCL TVD scheme is incorporated. The large-scale separated flow fields and their losses at the stall and post-stall conditions are analyzed for the NREL S809 airfoil at various angles of attack ({alpha}) from 0 to 70 degrees. The numerical results show excellent to fairly good agreement with the experimental data. The feasibility of the present numerical method and the influence of the four turbulence models are also investigated. (author)
International Nuclear Information System (INIS)
Narvaez, Paulo Cesar
1999-01-01
The dimension of nets of distribution of gases is a complex problem, so much for the diversity of the phenomena that they are presented, like for the variation of the properties of the fluids, especially, the density for effect of the changes in the pressure along the net. This work presents a model for its simulation starting from the deduction of the general equation of flow in stable and isothermal state, its inclusion in the pattern of balance of nodes and the solution of this for the method of linealization of equations. Additionally, a summary of the empiric equations more used is made for the calculation of the fall of pressure for gases flowing in pipes and an example that it illustrates the application of the pattern and the developed method
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
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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.
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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.
International Nuclear Information System (INIS)
Wang, Xia; Sun, Xiaodong
2014-01-01
Highlights: • Two-group interfacial area transport equation was implemented into a three-field two-fluid model in Fluent. • Numerical model was developed for cap-bubbly flows in a narrow rectangular flow channel. • Numerical simulations were performed for cap-bubbly flows with uniform void inlets and with central peaked void inlets. • Code simulations showed a significant improve over the conventional two-fluid model. - Abstract: Knowledge of cap-bubbly flows is of great interest due to its role in understanding of the flow regime transition from bubbly to slug or churn-turbulent flows. One of the key characteristics of such flows is the existence of bubbles in different sizes and shapes associated with their distinctive dynamic natures. This important feature is, however, generally not well captured by many available two-phase flow modeling approaches. In this study, a modified two-fluid model, namely a three-field, two-fluid model, is proposed. In this model, bubbles are categorized into two groups, i.e., spherical/distorted bubbles as Group-1 while cap/churn-turbulent bubbles as Group-2. A two-group interfacial area transport equation (IATE) is implemented to describe dynamic changes of interfacial structure in each bubble group, resulting from intra- and inter-group interactions and phase changes due to evaporation and condensation. Attention is also paid to appropriate constitutive relations of the interfacial transfers due to mechanical and thermal non-equilibrium between the different fields. The proposed three-field, two-fluid model is used to predict the phase distributions of adiabatic air–water flows in a confined rectangular duct. Good agreement between the simulation results from the proposed model and relevant experimental data indicates that the proposed model is promising as an improved computational tool for two-phase cap-bubbly flow simulations in rectangular flow ducts
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Donald P Bernstein
2010-01-01
, and more precisely, the electro-dynamic equivalent of peak aortic reduced average blood acceleration (PARABA, d
Ogata, K.; Senger, K.; Braathen, A.; Tveranger, J.; Petrie, E.; Evans, J.P.
2012-01-01
Fault- And fold-related fractures influence the fluid circulation in the subsurface, thus being of high importance for CO2 storage site assessment, especially in terms of reservoir connectivity and leakage. In this context, discrete regions of concentrated sub-parallel fracturing known as fracture
Directory of Open Access Journals (Sweden)
Hami K.
2017-12-01
Full Text Available In the present research, simulations have been conducted to determine numerically the dynamic behaviour of the flow of underground water fed by a river. The basic equations governing the problem studied are those of Navier–Stokes equations of conservation of momentum (flows between pores, coupled by the Darcy–Forchheimer equations (flows within these pores. To understand the phenomena involved, we first study the impact of flow rate on the pressure and the filtration velocity in the underground medium, the second part is devoted to the calculation of the elevation effect of the river water on the flow behaviour in the saturated and unsaturated zone of the aquifer.
On the validity of the Navier-Stokes equations for nanoscale liquid flows: The role of channel size
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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.
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.
Impact of higher-order flows in the moment equations on Pfirsch-Schlüter friction coefficients
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Honda, M., E-mail: honda.mitsuru@jaea.go.jp [Japan Atomic Energy Agency, Naka, Ibaraki 311-0193 (Japan)
2014-09-15
The impact of the higher-order flows in the moment approach on an estimate of the friction coefficients is numerically examined. The higher-order flows are described by the lower-order hydrodynamic flows using the collisional plasma assumption. Their effects have not been consistently taken into account thus far in the widely used neoclassical transport codes based on the moment equations in terms of the Pfirsch-Schlüter flux. Due to numerically solving the friction-flow matrix without using the small-mass ratio expansion, it is clearly revealed that incorporating the higher-order flow effects is of importance especially for plasmas including multiple hydrogenic ions and other lighter species with similar masses.
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.
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)
The flow behavior and constitutive equation in isothermal compression of FGH4096-GH4133B dual alloy
International Nuclear Information System (INIS)
Liu, Yanhui; Yao, Zekun; Ning, Yongquan; Nan, Yang; Guo, Hongzhen; Qin, Chun; Shi, Zhifeng
2014-01-01
Highlights: • Hot compression behaviors of the FGH4096-GH4133B dual alloy were investigated. • Constitutive equation also represented deformation behavior of a dual alloy. • The effects of deformation activation energy on the microstructures were discussed. • Constitutive equation represented an accurate and precise estimate of flow stress. - Abstract: The electron beam welding of superalloy FGH4096 and GH4133B was conducted, and the cylindrical compression specimens were machined from the central part of the electron beam weldments. Isothermal compression tests were carried out on electron beam weldments FGH4096-GH4133B alloy at the temperatures of 1020–11140 °C (the nominal γ′-transus temperature is about 1080 °C) and the strain rates of 0.001–1.0 s −1 with the height reduction of 50%. True stress–true strain curves are sensitive to the deformation temperature and strain rate, and the flow stress decreases with the increasing deformation temperature and the decreasing strain rate. The true stress–true strain curves can indicate the intrinsic relationship between the flow stress and the thermal-dynamic behavior. The apparent activation energy of deformation at the strain of 0.6 was calculated to be 550 kJ/mol, and the apparent activation energy has a great effect on the microstructure. The constitutive equation that describes the flow stress as a function of strain rate and deformation temperature was proposed for modeling the hot deformation process of FGH4096-GH4133B electron beam weldments. The constitutive equation at the strain of 0.6 was established using the hyperbolic law. The relationship between the strain and the values of parameters was studied, and the cubic functions were built. The constitutive equation during the whole process can be obtained based on the parameters under different strains. Comparing the experimental flow stress and the calculated flow stress, the constitutive equation obtained in this paper can be very good
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
International Nuclear Information System (INIS)
Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo
2015-01-01
This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.
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
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)
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.
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
International Nuclear Information System (INIS)
Satter, A.; Varnon, J.E.; Hoang, M.T.
1992-01-01
A reservoir's life begins with exploration leading to discovery followed by delineation of the reservoir, development of the field, production by primary, secondary and tertiary means, and finally to abandonment. Sound reservoir management is the key to maximizing economic operation of the reservoir throughout its entire life. Technological advances and rapidly increasing computer power are providing tools to better manage reservoirs and are increasing the gap between good and neural reservoir management. The modern reservoir management process involves goal setting, planning, implementing, monitoring, evaluating, and revising plans. Setting a reservoir management strategy requires knowledge of the reservoir, availability of technology, and knowledge of the business, political, and environmental climate. Formulating a comprehensive management plan involves depletion and development strategies, data acquisition and analyses, geological and numerical model studies, production and reserves forecasts, facilities requirements, economic optimization, and management approval. This paper provides management, engineers, geologists, geophysicists, and field operations staff with a better understanding of the practical approach to reservoir management using a multidisciplinary, integrated team approach
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
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.
Effects of water-supply reservoirs on streamflow in Massachusetts
Levin, Sara B.
2016-10-06
State and local water-resource managers need modeling tools to help them manage and protect water-supply resources for both human consumption and ecological needs. The U.S. Geological Survey, in cooperation with the Massachusetts Department of Environmental Protection, has developed a decision-support tool to estimate the effects of reservoirs on natural streamflow. The Massachusetts Reservoir Simulation Tool is a model that simulates the daily water balance of a reservoir. The reservoir simulation tool provides estimates of daily outflows from reservoirs and compares the frequency, duration, and magnitude of the volume of outflows from reservoirs with estimates of the unaltered streamflow that would occur if no dam were present. This tool will help environmental managers understand the complex interactions and tradeoffs between water withdrawals, reservoir operational practices, and reservoir outflows needed for aquatic habitats.A sensitivity analysis of the daily water balance equation was performed to identify physical and operational features of reservoirs that could have the greatest effect on reservoir outflows. For the purpose of this report, uncontrolled releases of water (spills or spillage) over the reservoir spillway were considered to be a proxy for reservoir outflows directly below the dam. The ratio of average withdrawals to the average inflows had the largest effect on spillage patterns, with the highest withdrawals leading to the lowest spillage. The size of the surface area relative to the drainage area of the reservoir also had an effect on spillage; reservoirs with large surface areas have high evaporation rates during the summer, which can contribute to frequent and long periods without spillage, even in the absence of water withdrawals. Other reservoir characteristics, such as variability of inflows, groundwater interactions, and seasonal demand patterns, had low to moderate effects on the frequency, duration, and magnitude of spillage. The
International Nuclear Information System (INIS)
Lim, S.C.; Lee, K.J.
1993-01-01
The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)
Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka
2017-06-01
The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.
Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen
2015-04-01
This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive
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)
Wajs Jan; Mikielewicz Dariusz
2017-01-01
Detailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged that any discrepancy in determination of deposition and entrainmen...
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.
Directory of Open Access Journals (Sweden)
Li-ren Yu
2012-03-01
Full Text Available This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k˜−ε˜,k˜−w˜, and k˜−ω˜ , were used to close the non-simplified quasi-three dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k˜−ω˜ model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.
Correlations and the Ring-Kinetic Equation in Dense Sheared Granular Flows
Kumaran, V.
A formal way of deriving fluctuation-correlation relations in densesheared granular media, starting with the Enskog approximation for the collision integral in the Chapman-Enskog theory, is discussed. The correlation correction to the viscosity is obtained using the ring-kinetic equation, in terms of the correlations in the hydrodynamic modes of the linearised Enskog equation. It is shown that the Green-Kubo formula for the shear viscosity emerges from the two-body correlation function obtained from the ring-kinetic equation.
Parallel Numerical Simulations of Water Reservoirs
Torres, Pedro; Mangiavacchi, Norberto
2010-11-01
The study of the water flow and scalar transport in water reservoirs is important for the determination of the water quality during the initial stages of the reservoir filling and during the life of the reservoir. For this scope, a parallel 2D finite element code for solving the incompressible Navier-Stokes equations coupled with scalar transport was implemented using the message-passing programming model, in order to perform simulations of hidropower water reservoirs in a computer cluster environment. The spatial discretization is based on the MINI element that satisfies the Babuska-Brezzi (BB) condition, which provides sufficient conditions for a stable mixed formulation. All the distributed data structures needed in the different stages of the code, such as preprocessing, solving and post processing, were implemented using the PETSc library. The resulting linear systems for the velocity and the pressure fields were solved using the projection method, implemented by an approximate block LU factorization. In order to increase the parallel performance in the solution of the linear systems, we employ the static condensation method for solving the intermediate velocity at vertex and centroid nodes separately. We compare performance results of the static condensation method with the approach of solving the complete system. In our tests the static condensation method shows better performance for large problems, at the cost of an increased memory usage. Performance results for other intensive parts of the code in a computer cluster are also presented.
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.
Universal formula for the energy–momentum tensor via a flow equation in the Gross–Neveu model
International Nuclear Information System (INIS)
Suzuki, Hiroshi
2015-01-01
For the fermion field in the two-dimensional Gross–Neveu model, we introduce a flow equation that allows a simple 1/N expansion. By employing the 1/N expansion, we examine the validity of a universal formula for the energy–momentum tensor which is based on the small flow-time expansion. We confirm that the formula reproduces a correct normalization and the conservation law of the energy–momentum tensor by computing the translation Ward–Takahashi relation in the leading non-trivial order in the 1/N expansion. Also, we confirm that the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy–momentum tensor via the gradient/Wilson flow in lattice gauge theory
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.
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)
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)
Modeling and Control of a Manufacturing Flow Line using Partial Differential Equations
Berg, van den R.A.; Lefeber, A.A.J.; Rooda, J.E.
2008-01-01
This brief deals with a control framework for manufacturing flow lines. For this framework, a continuous approximation model of the manufacturing system is required, which is computationally feasible and able to accurately describe the dynamics of the system (both throughput and flow time). Often
Directory of Open Access Journals (Sweden)
Gang Chen
2015-11-01
Full Text Available A calibrated three-dimensional Environmental Fluid Dynamics Code model was applied to simulate unsteady flow patterns and temperature distributions in the Bankhead river-reservoir system in Alabama, USA. A series of sensitivity model runs were performed under daily repeated large releases (DRLRs with different durations (2, 4 and 6 h from Smith Dam Tailrace (SDT when other model input variables were kept unchanged. The density currents in the river-reservoir system form at different reaches, are destroyed at upstream locations due to the flow momentum of the releases, and form again due to solar heating. DRLRs (140 m3/s with longer durations push the bottom cold water further downstream and maintain a cooler bottom water temperature. For the 6-h DRLR, the momentum effect definitely reaches Cordova (~43.7 km from SDT. Positive bottom velocity (density currents moving downstream is achieved 48.4%, 69.0% and 91.1% of the time with an average velocity of 0.017, 0.042 and 0.053 m/s at Cordova for the 2-h, 4-h and 6-h DRLR, respectively. Results show that DRLRs lasting for at least 4 h maintain lower water temperatures at Cordova. When the 4-h and 6-h DRLRs repeat for more than 6 and 10 days, respectively, bottom temperatures at Cordova become lower than those for the constant small release (2.83 m3/s. These large releases overwhelm the mixing effects due to inflow momentum and maintain temperature stratification at Cordova.
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
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
Existence and Uniqueness of Solutions to the Stochastic Porous Media Equations of Saturated Flows
International Nuclear Information System (INIS)
Ciotir, Ioana
2010-01-01
This paper proves the existence and uniqueness of nonnegative solutions for the stochastic porous media equations with multiplicative noise, infinite jump and discontinuous diffusivity function relevant in description of saturation processes in underground water infiltration in a bounded domain of R 3 .
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 ... Blood plasma; Zakharov equations; viscosity; modulation instability. PACS Nos 52.27. .... For fluid, the proton thermal velocity vT p is much less than the phase ..... The heavy ion can transfer greater momentum, then in general ...
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
Energy Technology Data Exchange (ETDEWEB)
Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)
2011-02-15
This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)
Scott, James R.; Atassi, Hafiz M.
1990-01-01
A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
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
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)
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.
Fujii, K.
1983-01-01
A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
Cholet, Cybèle; Charlier, Jean-Baptiste; Moussa, Roger; Steinmann, Marc; Denimal, Sophie
2017-07-01
The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection-diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection-diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space - between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) - as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit-matrix exchanges, inducing a complex water mixing effect in the saturated zone
Directory of Open Access Journals (Sweden)
C. Cholet
2017-07-01
Full Text Available The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection–diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection–diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space – between the two reaches located in the unsaturated zone (R1, and in the zone that is both unsaturated and saturated (R2 – as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions and localized infiltration in the secondary conduit network (tributaries in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit–matrix exchanges, inducing a complex water mixing effect
Directory of Open Access Journals (Sweden)
Itissam ABUIZIAH
2014-03-01
Full Text Available When transient conditions (water hammer exist, the life expectancy of the system can be adversely impacted, resulting in pump and valve failures and catastrophic pipe rupture. Hence, transient control has become an essential requirement for ensuring safe operation of water pipeline systems. To protect the pipeline systems from transient effects, an accurate analysis and suitable protection devices should be used. This paper presents the problem of modeling and simulation of transient phenomena in hydraulic systems based on the characteristics method. Also, it provides the influence of using the protection devices to control the adverse effects due to excessive and low pressure occuring in the transient. We applied this model for two main pipeline systems: Valve and pump combined with a simple surge tank connected to reservoir. The results obtained by using this model indicate that the model is an efficient tool for water hammer analysis. Moreover, using a simple surge tank reduces the unfavorable effects of transients by reducing pressure fluctuations.
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)
Direct Computation of Sound Radiation by Jet Flow Using Large-scale Equations
Mankbadi, R. R.; Shih, S. H.; Hixon, D. R.; Povinelli, L. A.
1995-01-01
Jet noise is directly predicted using large-scale equations. The computational domain is extended in order to directly capture the radiated field. As in conventional large-eddy-simulations, the effect of the unresolved scales on the resolved ones is accounted for. Special attention is given to boundary treatment to avoid spurious modes that can render the computed fluctuations totally unacceptable. Results are presented for a supersonic jet at Mach number 2.1.
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
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.
Hill, Mary C.
1990-01-01
This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.
DEFF Research Database (Denmark)
Yang, Tian; Cao, Yingchang; Friis, Henrik
2018-01-01
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...
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
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.
Hall, Philip; Bennett, James
1986-01-01
The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.
Amplitude various angles (AVA) phenomena in thin layer reservoir: Case study of various reservoirs
Energy Technology Data Exchange (ETDEWEB)
Nurhandoko, Bagus Endar B., E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com [Wave Inversion and Subsurface Fluid Imaging Research Laboratory (WISFIR), Basic Science Center A 4" t" hfloor, Physics Dept., FMIPA, Institut Teknologi Bandung (Indonesia); Rock Fluid Imaging Lab., Bandung (Indonesia); Susilowati, E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com [Rock Fluid Imaging Lab., Bandung (Indonesia)
2015-04-16
Amplitude various offset is widely used in petroleum exploration as well as in petroleum development field. Generally, phenomenon of amplitude in various angles assumes reservoir’s layer is quite thick. It also means that the wave is assumed as a very high frequency. But, in natural condition, the seismic wave is band limited and has quite low frequency. Therefore, topic about amplitude various angles in thin layer reservoir as well as low frequency assumption is important to be considered. Thin layer reservoir means the thickness of reservoir is about or less than quarter of wavelength. In this paper, I studied about the reflection phenomena in elastic wave which considering interference from thin layer reservoir and transmission wave. I applied Zoeppritz equation for modeling reflected wave of top reservoir, reflected wave of bottom reservoir, and also transmission elastic wave of reservoir. Results show that the phenomena of AVA in thin layer reservoir are frequency dependent. Thin layer reservoir causes interference between reflected wave of top reservoir and reflected wave of bottom reservoir. These phenomena are frequently neglected, however, in real practices. Even though, the impact of inattention in interference phenomena caused by thin layer in AVA may cause inaccurate reservoir characterization. The relation between classes of AVA reservoir and reservoir’s character are different when effect of ones in thin reservoir and ones in thick reservoir are compared. In this paper, I present some AVA phenomena including its cross plot in various thin reservoir types based on some rock physics data of Indonesia.
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
Dewi, Dina Silvia; Osaigbovo Enomayo, Augustine; Mohsin, Rizwan; Karmakar, Shyamal; Ghergut, Julia; Sauter, Martin
2016-04-01
Flow-storage repartition (FSR) analysis (Shook 2003) is a versatile tool for characterizing subsurface flow and transport systems. FSR can be derived from measured signals of inter-well tracer tests, if certain requirements are met - basically, the same as required for equivalence between fluid residence time distribution (RTD) and a measured inter-well tracer signal (pre-processed and de-convolved if necessary). Nominally, a FSR is derived from a RTD as a trajectory in normalized {1st, 0th}-order statistical moment space; more intuitively, as a parametric plot of 0th-order against 1st-order statistical moments of RTD truncated at time t, with t as a parameter running from the first tracer input to the latest available tracer sampling; 0th-order moments being normalized by the total tracer recovery, and 1st-order moments by the mean RT. Fracture-dominated systems plot in the upper left (high F , low S) region of FSR diagrams; a homogeneous single-continuum with no dispersion (infinite Peclet number) displays a straight line from {F ,S}={0,0} to {F ,S}={1,1}. This analysis tool appears particularly attractive for characterizing markedly-heterogeneous, porous-fissured-fractured (partly karstified) formations like those targeted by geothermal exploration in the Malm-Molasse basin in Southern Germany, and especially for quantifying flow and transport contributions from contrasting facies types ('reef' versus 'bedded'). However, tracer tests conducted in such systems with inter-well distances of some hundreds of metres (as required by economic considerations on geothermal reservoir sizing) face the problem of very long residence times - and thus the need to deal with incomplete (truncated) signals. For the geothermal well triplet at the Sauerlach site near Munich, tracer peak arrival times exceeding 2 years have been predicted, and signal tails decreasing by less than 50% over >10 years, which puts great uncertainty on the (extrapolation-based) normalizing factors
Lee, James D.; Mobbs, Stephen D.; Wellpott, Axel; Allen, Grant; Bauguitte, Stephane J.-B.; Burton, Ralph R.; Camilli, Richard; Coe, Hugh; Fisher, Rebecca E.; France, James L.; Gallagher, Martin; Hopkins, James R.; Lanoiselle, Mathias; Lewis, Alastair C.; Lowry, David; Nisbet, Euan G.; Purvis, Ruth M.; O'Shea, Sebastian; Pyle, John A.; Ryerson, Thomas B.
2018-03-01
An uncontrolled gas leak from 25 March to 16 May 2012 led to evacuation of the Total Elgin wellhead and neighbouring drilling and production platforms in the UK North Sea. Initially the atmospheric flow rate of leaking gas and condensate was very poorly known, hampering environmental assessment and well control efforts. Six flights by the UK FAAM chemically instrumented BAe-146 research aircraft were used to quantify the flow rate. The flow rate was calculated by assuming the plume may be modelled by a Gaussian distribution with two different solution methods: Gaussian fitting in the vertical and fitting with a fully mixed layer. When both solution methods were used they compared within 6 % of each other, which was within combined errors. Data from the first flight on 30 March 2012 showed the flow rate to be 1.3 ± 0.2 kg CH4 s-1, decreasing to less than half that by the second flight on 17 April 2012. δ13CCH4 in the gas was found to be -43 ‰, implying that the gas source was unlikely to be from the main high pressure, high temperature Elgin gas field at 5.5 km depth, but more probably from the overlying Hod Formation at 4.2 km depth. This was deemed to be smaller and more manageable than the high pressure Elgin field and hence the response strategy was considerably simpler. The first flight was conducted within 5 days of the blowout and allowed a flow rate estimate within 48 h of sampling, with δ13CCH4 characterization soon thereafter, demonstrating the potential for a rapid-response capability that is widely applicable to future atmospheric emissions of environmental concern. Knowledge of the Elgin flow rate helped inform subsequent decision making. This study shows that leak assessment using appropriately designed airborne plume sampling strategies is well suited for circumstances where direct access is difficult or potentially dangerous. Measurements such as this also permit unbiased regulatory assessment of potential impact, independent of the emitting
Icardi, Matteo; Ronco, Gianni; Marchisio, Daniele Luca; Labois, Mathieu
2014-01-01
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.
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.
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.
Kou, Jisheng; Sun, Shuyu
2017-01-01
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.
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.
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
Numerical-solution package for transient two-phase-flow equations
International Nuclear Information System (INIS)
Mahaffy, J.H.; Liles, D.
1982-01-01
The methods presented have proven to be extremely reliable tools for reactor safety analysis. They can handle a wide range of fluid conditions and time scales with minimal failures, while maintaining time step sizes well above those possible with most other techniques. This robustness is due not only to the finite-difference equations themselves, but also to the choice of solution technique, because poorly chosen iterative solution procedures often require a limit on the time-step size for proper convergence of the iteration
Augmented Lagrangian methods to solve Navier-Stokes equations for a Bingham fluid flow
International Nuclear Information System (INIS)
Boscardin, Laetitia
1999-01-01
The objective of this research thesis is to develop one or more methods for the numerical resolution of equations of movement obtained for a Bingham fluid. The resolution of Navier-Stokes equations is processed by splitting elliptic and hyperbolic operators (Galerkin transport). In this purpose, the author first studied the Stokes problem, and then addressed issues of stability and consistency of the global scheme. The variational formulation of the Stokes problem can be expressed under the form of a minimisation problem under the constraint of non linear and non differentiable functions. Then, the author proposes a discretization of the Stokes problem based on a hybrid finite element method. Then he extends the demonstrations of stability and consistency of the Galerkin-transport scheme which have been established for a Newtonian fluid, to the case of a Bingham fluid. A relaxation algorithm and a Newton-GMRES algorithm are developed to solve the problem, and their convergence is studied. To ensure this convergence, some constraints must be verified. In order to do so, a specific speed element has been developed [fr
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)
Feedback control for unsteady flow and its application to the stochastic Burgers equation
Choi, Haecheon; Temam, Roger; Moin, Parviz; Kim, John
1993-01-01
The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.
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
Directory of Open Access Journals (Sweden)
Akgül Ali
2016-01-01
Full Text Available In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.
International Nuclear Information System (INIS)
Kushner, Harold J.
2012-01-01
This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.
Anomalous dynamics triggered by a non-convex equation of state in relativistic flows
Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.
2018-05-01
The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.
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
Pore size determination using normalized J-function for different hydraulic flow units
Directory of Open Access Journals (Sweden)
Ali Abedini
2015-06-01
Full Text Available Pore size determination of hydrocarbon reservoirs is one of the main challenging areas in reservoir studies. Precise estimation of this parameter leads to enhance the reservoir simulation, process evaluation, and further forecasting of reservoir behavior. Hence, it is of great importance to estimate the pore size of reservoir rocks with an appropriate accuracy. In the present study, a modified J-function was developed and applied to determine the pore radius in one of the hydrocarbon reservoir rocks located in the Middle East. The capillary pressure data vs. water saturation (Pc–Sw as well as routine reservoir core analysis include porosity (φ and permeability (k were used to develop the J-function. First, the normalized porosity (φz, the rock quality index (RQI, and the flow zone indicator (FZI concepts were used to categorize all data into discrete hydraulic flow units (HFU containing unique pore geometry and bedding characteristics. Thereafter, the modified J-function was used to normalize all capillary pressure curves corresponding to each of predetermined HFU. The results showed that the reservoir rock was classified into five separate rock types with the definite HFU and reservoir pore geometry. Eventually, the pore radius for each of these HFUs was determined using a developed equation obtained by normalized J-function corresponding to each HFU. The proposed equation is a function of reservoir rock characteristics including φz, FZI, lithology index (J*, and pore size distribution index (ɛ. This methodology used, the reservoir under study was classified into five discrete HFU with unique equations for permeability, normalized J-function and pore size. The proposed technique is able to apply on any reservoir to determine the pore size of the reservoir rock, specially the one with high range of heterogeneity in the reservoir rock properties.
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
Directory of Open Access Journals (Sweden)
Costanza Aricò
2018-01-01
Full Text Available The shallow water equations are a mathematical tool widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. The interest of many researchers has been focused on the study of simplified forms of the original set of equations. One of the most commonly applied simplifications consists of neglecting the inertial terms. The effects of such a choice on the outputs of the simulations of flooding events are controversial and are an important topic of debate. In the present paper, two numerical models recently proposed for the solution of the complete and zero-inertia forms of the shallow water equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory scenarios of unsteady flow routing, starting from very simple geometries and gradually moving towards complex topographies. Unlike the studies of the range of validity of the zero-inertia model, based on a small perturbation of the linearized flow model, in unsteady flow propagation over irregular topographies, it is more difficult to specify criteria for the applicability of the simplified set of equations. In analyzing the role of the terms in the momentum equations, we try to understand the effect of neglecting the inertial terms in the zero-inertia formulation. We also analyze the computational costs.
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.
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.
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
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.
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...
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.
Cesium reservoir and interconnective components
International Nuclear Information System (INIS)
1994-03-01
The program objective is to demonstrate the technology readiness of a TFE (thermionic fuel element) suitable for use as the basic element in a thermionic reactor with electric power output in the 0.5 to 5.0 MW range. A thermionic converter must be supplied with cesium vapor for two reasons. Cesium atoms adsorbed on the surface of the emitter cause a reduction of the emitter work function to permit high current densities without excessive heating of the emitter. The second purpose of the cesium vapor is to provide space-charge neutralization in the emitter-collector gap so that the high current densities may flow across the gap unattenuated. The function of the cesium reservoir is to provide a source of cesium atoms, and to provide a reserve in the event that cesium is lost from the plasma by any mechanism. This can be done with a liquid cesium metal reservoir in which case it is heated to the desired temperature with auxiliary heaters. In a TFE, however, it is desirable to have the reservoir passively heated by the nuclear fuel. In this case, the reservoir must operate at a temperature intermediate between the emitter and the collector, ruling out the use of liquid reservoirs. Integral reservoirs contained within the TFE will produce cesium vapor pressures in the desired range at typical electrode temperatures. The reservoir material that appears to be the best able to meet requirements is graphite. Cesium intercalates easily into graphite, and the cesium pressure is insensitive to loading for a given intercalation stage. The goals of the cesium reservoir test program were to verify the performance of Cs-graphite reservoirs in the temperature-pressure range of interest to TFE operation, and to test the operation of these reservoirs after exposure to a fast neutron fluence corresponding to seven year mission lifetime. In addition, other materials were evaluated for possible use in the integral reservoir
Optimization of fracture length in gas/condensate reservoirs
Energy Technology Data Exchange (ETDEWEB)
Mohan, J.; Sharma, M.M.; Pope, G.A. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)
2006-07-01
A common practice that improves the productivity of gas-condensate reservoirs is hydraulic fracturing. Two important variables that determine the effectiveness of hydraulic fractures are fracture length and fracture conductivity. Although there are no simple guidelines for the optimization of fracture length and the factors that affect it, it is preferable to have an optimum fracture length for a given proppant volume in order to maximize productivity. An optimization study was presented in which fracture length was estimated at wells where productivity was maximized. An analytical expression that takes into account non-Darcy flow and condensate banking was derived. This paper also reviewed the hydraulic fracturing process and discussed previous simulation studies that investigated the effects of well spacing and fracture length on well productivity in low permeability gas reservoirs. The compositional simulation study and results and discussion were also presented. The analytical expression for optimum fracture length, analytical expression with condensate dropout, and equations for the optimum fracture length with non-Darcy flow in the fracture were included in an appendix. The Computer Modeling Group's GEM simulator, an equation-of-state compositional simulator, was used in this study. It was concluded that for cases with non-Darcy flow, the optimum fracture lengths are lower than those obtained with Darcy flow. 18 refs., 5 tabs., 22 figs., 1 appendix.
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.
Stochastic Differential Equations and Kondratiev Spaces
Energy Technology Data Exchange (ETDEWEB)
Vaage, G.
1995-05-01
The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.
Non-darcy flow behavior mean high-flux injection wells in porous and fractured formations
Energy Technology Data Exchange (ETDEWEB)
Wu, Yu-Shu
2003-04-25
This paper presents a study of non-Darcy fluid flow through porous and fractured rock, which may occur near wells during high-flux injection of waste fluids into underground formations. Both numerical and analytical models are used in this study. General non-Darcy flow is described using the Forchheimer equation, implemented in a three-dimensional, multiphase flow reservoir simulator. The non-Darcy flow through a fractured reservoir is handled using a general dual continuum approach, covering commonly used conceptual models, such as double porosity, dual permeability, explicit fracture, etc. Under single-phase flow conditions, an approximate analytical solution, as an extension of the Warren-Root solution, is discussed. The objectives of this study are (1) to obtain insights into the effect of non-Darcy flow on transient pressure behavior through porous and fractured reservoirs and (2) to provide type curves for well test analyses of non-Darcy flow wells. The type curves generated include various types of drawdown, injection, and buildup tests with non-Darcy flow occurring in porous and fractured reservoirs. In addition, non-Darcy flow into partially penetrating wells is also considered. The transient-pressure type curves for flow in fractured reservoirs are based on the double-porosity model. Type curves provided in this work for non-Darcy flow in porous and fractured reservoirs will find their applications in well test interpretation using a type-curve matching technique.
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.
M. L. Kavvas; A. Ercan; J. Polsinelli
2017-01-01
In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical di...
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.
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
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
Analysis and application of classification methods of complex carbonate reservoirs
Li, Xiongyan; Qin, Ruibao; Ping, Haitao; Wei, Dan; Liu, Xiaomei
2018-06-01
There are abundant carbonate reservoirs from the Cenozoic to Mesozoic era in the Middle East. Due to variation in sedimentary environment and diagenetic process of carbonate reservoirs, several porosity types coexist in carbonate reservoirs. As a result, because of the complex lithologies and pore types as well as the impact of microfractures, the pore structure is very complicated. Therefore, it is difficult to accurately calculate the reservoir parameters. In order to accurately evaluate carbonate reservoirs, based on the pore structure evaluation of carbonate reservoirs, the classification methods of carbonate reservoirs are analyzed based on capillary pressure curves and flow units. Based on the capillary pressure curves, although the carbonate reservoirs can be classified, the relationship between porosity and permeability after classification is not ideal. On the basis of the flow units, the high-precision functional relationship between porosity and permeability after classification can be established. Therefore, the carbonate reservoirs can be quantitatively evaluated based on the classification of flow units. In the dolomite reservoirs, the average absolute error of calculated permeability decreases from 15.13 to 7.44 mD. Similarly, the average absolute error of calculated permeability of limestone reservoirs is reduced from 20.33 to 7.37 mD. Only by accurately characterizing pore structures and classifying reservoir types, reservoir parameters could be calculated accurately. Therefore, characterizing pore structures and classifying reservoir types are very important to accurate evaluation of complex carbonate reservoirs in the Middle East.
Heisig, Paul M.
2004-01-01
Estimates of the quantity and quality of ground-water discharge from valley-fill deposits were calculated for nine valley reaches within the Pepacton watershed in southeastern New York in July and August of 2001. Streamflow and water quality at the upstream and downstream end of each reach and at intervening tributaries were measured under base-flow conditions and used in mass-balance equations to determine quantity and quality of ground-water discharge. These measurements and estimates define the relative magnitudes of upland (tributary inflow) and valley-fill (ground-water discharge) contributions to the main-valley streams and provide a basis for understanding the effects of hydrogeologic setting on these contributions. Estimates of the water-quality of ground-water discharge also provide an indication of the effects of road salt, manure, and human wastewater from villages on the water quality of streams that feed the Pepacton Reservoir. The most common contaminant in ground-water discharge was chloride from road salt; concentrations were less than 15 mg/L.Investigation of ground-water quality within a large watershed by measurement of stream base-flow quantity and quality followed by mass-balance calculations has benefits and drawbacks in comparison to direct ground-water sampling from wells. First, sampling streams is far less expensive than siting, installing, and sampling a watershed-wide network of wells. Second, base-flow samples represent composite samples of ground-water discharge from the most active part of the ground-water flow system across a drainage area, whereas a well network would only be representative of discrete points within local ground-water flow systems. Drawbacks to this method include limited reach selection because of unfavorable or unrepresentative hydrologic conditions, potential errors associated with a large number of streamflow and water-quality measurements, and limited ability to estimate concentrations of nonconservative
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.
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.
Li, Rui; Palm, Brett B; Ortega, Amber M; Hlywiak, James; Hu, Weiwei; Peng, Zhe; Day, Douglas A; Knote, Christoph; Brune, William H; de Gouw, Joost A; Jimenez, Jose L
2015-05-14
Oxidation flow reactors (OFRs) containing low-pressure mercury (Hg) lamps that emit UV light at both 185 and 254 nm ("OFR185") to generate OH radicals and O3 are used in many areas of atmospheric science and in pollution control devices. The widely used potential aerosol mass (PAM) OFR was designed for studies on the formation and oxidation of secondary organic aerosols (SOA), allowing for a wide range of oxidant exposures and short experiment duration with reduced wall loss effects. Although fundamental photochemical and kinetic data applicable to these reactors are available, the radical chemistry and its sensitivities have not been modeled in detail before; thus, experimental verification of our understanding of this chemistry has been very limited. To better understand the chemistry in the OFR185, a model has been developed to simulate the formation, recycling, and destruction of radicals and to allow the quantification of OH exposure (OHexp) in the reactor and its sensitivities. The model outputs of OHexp were evaluated against laboratory calibration experiments by estimating OHexp from trace gas removal and were shown to agree within a factor of 2. A sensitivity study was performed to characterize the dependence of the OHexp, HO2/OH ratio, and O3 and H2O2 output concentrations on reactor parameters. OHexp is strongly affected by the UV photon flux, absolute humidity, reactor residence time, and the OH reactivity (OHR) of the sampled air, and more weakly by pressure and temperature. OHexp can be strongly suppressed by high OHR, especially under low UV light conditions. A OHexp estimation equation as a function of easily measurable quantities was shown to reproduce model results within 10% (average absolute value of the relative errors) over the whole operating range of the reactor. OHexp from the estimation equation was compared with measurements in several field campaigns and shows agreement within a factor of 3. The improved understanding of the OFR185 and
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.
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.
A Simple Approach to Dynamic Material Balance in Gas-Condensate Reservoirs
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Heidari Sureshjani M.
2013-02-01
Full Text Available In traditional material balance calculations, shut-in well pressure data are used to determine average reservoir pressure while recent techniques do not require the well to be shut-in and use instead flowing well pressure-rate data. These methods, which are known as “dynamic” material balance, are developed for single-phase flow (oil or gas in reservoirs. However, utilization of such methods for gas-condensate reservoirs may create significant errors in prediction of average reservoir pressure due to violation of the single-phase assumption in such reservoirs. In a previous work, a method for production data analysis in gas-condensate reservoirs was developed. The method required standard gas production rate, producing gas-oil ratio, flowing well pressure, CVD data and relative permeability curves. This paper presents a new technique which does not need relative permeability curves and flowing well pressure. In this method, the producing oil-gas ratio is interpolated in the vaporized oil in gas phase (Rv versus pressure (p data in the CVD table and the corresponding pressure is located. The parameter pressure/two-phase deviation factor (p/ztp is then evaluated at the determined pressure points and is plotted versus produced moles (np which forms a straight line. The nature of this plot is such that its extrapolation to point where p/ztp = 0 will give initial moles in place. Putting initial pressure/initial two-phase deviation factor (pi/ztp,i (known parameter and estimated initial moles (ni into the material balance equation, average reservoir pressure can be determined. A main assumption behind the method is that the region where both gas and condensate phases are mobile is of negligible size compared to the reservoir. The approach is quite simple and calculations are much easier than the previous work. It provides a practical engineering tool for industry studies as it requires data which are generally available in normal production
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.
Haisch, B. M.
1976-01-01
A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
International Nuclear Information System (INIS)
Gastaldo, L.
2007-11-01
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
International Nuclear Information System (INIS)
Fakhar, K.; Kara, A. H.
2012-01-01
We study the symmetries, conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena. These could be the ordinary differential equations (ODEs) that are reductions of partial differential equations (PDEs) or, alternatively, PDEs related to given ODEs. In this class, the analysis includes the well-known Blasius, Chazy, and other associated third-order ODEs. (general)
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
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)
International Nuclear Information System (INIS)
Rocha, Jussiê S.; Maciel, Edisson Sávio de Góes; Lira, Carlos A.B.O.; Sousa, Pedro A.S.; Neto, Raimundo N.C.
2017-01-01
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 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)
International Nuclear Information System (INIS)
Reuter, W.G.; Place, T.A.
1981-01-01
An accurate assessment of the influence of defects on structural component integrity is needed. Generally accepted analytical techniques are not available for the very ductile materials used in many nuclear reactor components. Some results are presented from a test programme to obtain data by which to evaluate proposed models. Plate and pipe specimens containing surface flaws were fabricated from annealed Type 304 stainless steel and tested at room temperature. An evaluation of an empirical equation based on flow stress is presented. In essentially all instances the flow stress is not a constant but varies as a function of the size of the surface flaw. (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.
International Nuclear Information System (INIS)
Tomiyama, Akio; Matsuoka, Toshiyuki.
1995-01-01
A simple numerical method for solving a transient incompressible two-fluid model was proposed in the present study. A general curvilinear coordinate system was adopted in this method for predicting transient flows in practical engineering devices. The simplicity of the present method is due to the fact that the field equations and constitutive equations were expressed in a tensor form in the general curvilinear coordinate system. When a conventional rectangular mesh is adopted in a calculation, the method reduces to a numerical method for a Cartesian coordinate system. As an example, the present method was applied to transient air-water bubbly flow in a vertical U-tube. It was confirmed that the effects of centrifugal and gravitational forces on the phase distribution in the U-tube were reasonably predicted. (author)
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
International Nuclear Information System (INIS)
Le Coq, G.; Boudsocq, G.; Raymond, P.
1983-03-01
The Control Variable Method is extended to multidimensional fluid flow transient computations. In this paper basic principles of the method are given. The method uses a fully implicit space discretization and is based on the decomposition of the momentum flux tensor into scalar, vectorial, and tensorial, terms. Finally some computations about viscous-driven flow and buoyancy-driven flow in cavity are presented
Local Refinement of the Super Element Model of Oil Reservoir
Directory of Open Access Journals (Sweden)
A.B. Mazo
2017-12-01
Full Text Available In this paper, we propose a two-stage method for petroleum reservoir simulation. The method uses two models with different degrees of detailing to describe hydrodynamic processes of different space-time scales. At the first stage, the global dynamics of the energy state of the deposit and reserves is modeled (characteristic scale of such changes is km / year. The two-phase flow equations in the model of global dynamics operate with smooth averaged pressure and saturation fields, and they are solved numerically on a large computational grid of super-elements with a characteristic cell size of 200-500 m. The tensor coefficients of the super-element model are calculated using special procedures of upscaling of absolute and relative phase permeabilities. At the second stage, a local refinement of the super-element model is constructed for calculating small-scale processes (with a scale of m / day, which take place, for example, during various geological and technical measures aimed at increasing the oil recovery of a reservoir. Then we solve the two-phase flow problem in the selected area of the measure exposure on a detailed three-dimensional grid, which resolves the geological structure of the reservoir, and with a time step sufficient for describing fast-flowing processes. The initial and boundary conditions of the local problem are formulated on the basis of the super-element solution. This approach allows us to reduce the computational costs in order to solve the problems of designing and monitoring the oil reservoir. To demonstrate the proposed approach, we give an example of the two-stage modeling of the development of a layered reservoir with a local refinement of the model during the isolation of a water-saturated high-permeability interlayer. We show a good compliance between the locally refined solution of the super-element model in the area of measure exposure and the results of numerical modeling of the whole history of reservoir
Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.
1986-01-01
A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.
Xu, Xianmin; Wang, Xiaoping
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.
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.
Multilevel techniques for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour
The subject of this thesis is the development, application and study of novel multilevel methods for the acceleration and improvement of reservoir simulation techniques. The motivation for addressing this topic is a need for more accurate predictions of porous media flow and the ability to carry...... Full Approximation Scheme) • Variational (Galerkin) upscaling • Linear solvers and preconditioners First, a nonlinear multigrid scheme in the form of the Full Approximation Scheme (FAS) is implemented and studied for a 3D three-phase compressible rock/fluids immiscible reservoir simulator...... is extended to include a hybrid strategy, where FAS is combined with Newton’s method to construct a multilevel nonlinear preconditioner. This method demonstrates high efficiency and robustness. Second, an improved IMPES formulated reservoir simulator is implemented using a novel variational upscaling approach...
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe; Sarmiento, Adel; Cortes, Adriano Mauricio; Dalcin, Lisandro; Calo, Victor M.
2015-01-01
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
International Nuclear Information System (INIS)
Rocha, Jussie Soares da; Maciel, Edisson Savio de G.; Lira, Carlos A.B. de O.
2015-01-01
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)
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
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.
Energy Technology Data Exchange (ETDEWEB)
Lee, Keumsook [Department of Geography, Sungshin University, Seoul 136-742 (Korea, Republic of); Goh, Segun; Choi, M Y [Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul 151-747 (Korea, Republic of); Park, Jong Soo [School of Information Technology, Sungshin University, Seoul 136-742 (Korea, Republic of); Jung, Woo-Sung, E-mail: kslee@sungshin.ac.kr, E-mail: mychoi@snu.ac.kr [Department of Physics and Basic Science Research Institute, Pohang University of Science and Technology, Pohang 790-784 (Korea, Republic of)
2011-03-18
The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.
International Nuclear Information System (INIS)
Lee, Keumsook; Goh, Segun; Choi, M Y; Park, Jong Soo; Jung, Woo-Sung
2011-01-01
The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is found to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.
1981-01-01
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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.
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)
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.
Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.
2013-01-01
The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784
International Nuclear Information System (INIS)
Girish Shastry, C.; Mathew, M.D.; Bhanu Sankara Rao, K.; Mannan, S.L.
2004-01-01
The Voce equation was used to model the tensile flow and work-hardening behaviour of a service-exposed 2.25Cr-1Mo steel. The applicability of Voce parameters obtained from the fit to experimental true stress-true strain datasets for estimating the validity of the fit was examined. The Voce equation was found to model the stress-strain curve closely. The Voce parameter n v was correlated to the underlying dislocation activities. It was found that the values of Voce parameters at various temperatures and strain rates can be used to infer the operating recovery mechanism during stage III hardening. A low absolute value of n v is indicative of recovery by cross-slip, whereas the high temperature transition to climb or sub-boundary migration driven recovery is accompanied by an increase in the value of n v
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)
Production Optimization of Oil Reservoirs
DEFF Research Database (Denmark)
Völcker, Carsten
with emphasis on optimal control of water ooding with the use of smartwell technology. We have implemented immiscible ow of water and oil in isothermal reservoirs with isotropic heterogenous permeability elds. We use the method of lines for solution of the partial differential equation (PDE) system that governs...... the uid ow. We discretize the the two-phase ow model spatially using the nite volume method (FVM), and we use the two point ux approximation (TPFA) and the single-point upstream (SPU) scheme for computing the uxes. We propose a new formulation of the differential equation system that arise...... as a consequence of the spatial discretization of the two-phase ow model. Upon discretization in time, the proposed equation system ensures the mass conserving property of the two-phase ow model. For the solution of the spatially discretized two-phase ow model, we develop mass conserving explicit singly diagonally...
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
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
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.
African Journals Online (AJOL)
Keywords: reservoir model, siltation, sediment, catchment, sediment transport. 1. Introduction. Sediment ... rendered water storage structures useless in less than 25 years. ... reservoir, thus reducing the space available for water storage and ...
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
Petrofsky, Jerrold; Paluso, Dominic; Anderson, Devyn; Swan, Kristin; Yim, Jong Eun; Murugesan, Vengatesh; Chindam, Tirupathi; Goraksh, Neha; Alshammari, Faris; Lee, Haneul; Trivedi, Moxi; Hudlikar, Akshay N; Katrak, Vahishta
2011-04-01
As predicted by the Pennes equation, skin blood flow is a major contributor to the removal of heat from an external heat source. This protects the skin from erythema and burns. But, for a person in a thermally neutral room, the skin is normally much cooler than arterial blood. Therefore, if skin blood flow (BF) increases, it should initially warm the skin paradoxically. To examine this phenomenon, 10 young male and female subjects participated in a series of experiments to examine the contribution of skin blood flow in the initial warming the skin after the application of local heat. Heat flow was measured by the use of a thermode above the brachioradialis muscle. The thermode was warmed by constant temperature water at 44°C entering the thermode at a water flow rate of 100 cm(3)/min. Skin temperature was measured by a thermistor and blood flow in the underlying skin was measured by a laser Doppler imager in single point mode. The results of the experiments showed that, when skin temperature is cool (31-32°C), the number of calories being transferred to the skin from the thermode cannot account for the rise in skin temperature alone. A significant portion of the rise in skin temperature is due to the warm arterialized blood traversing the skin from the core areas of the body. However, as skin temperature approaches central core temperature, it becomes less of a heat source and more of a heat sync such that when skin temperature is at or above core temperature, the blood flow to the skin, as predicted by Pennes, becomes a heat sync pulling heat from the thermode. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George
2017-04-01
We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.
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.
International Nuclear Information System (INIS)
Botelho, D.A.; Moreira, M.L.
1991-06-01
The Reynolds turbulent transport equations for an incompressible fluid are integrated on a bi-dimensional staggered grid, for velocity and pressure, using the SIMPLER method. With the resulting algebraic relations it was developed the TURBO program, which final objectives are the thermal stratification and natural convection analysis of nuclear reactor pools. This program was tested in problems applications with analytic or experimental solutions previously known. (author)
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.
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.
Directory of Open Access Journals (Sweden)
Tomislav Špaldon
2005-11-01
Full Text Available This article presents results of the research concentrated on the content of selected elements, mostly heavy metals, in samples of stream waters and stream deposits from selected profiles of streams in the drainage basins of the Hnilec and Hornád river, which flow in the water-work Reservoir “Ružín I”. The sampling was carried out from the winter to the summer months, 2004. The major part of the drainage basins of these two rivers is located in the territory of the central Spiš, which is well-known from the historic times until these days by its intensive mining, mineral processing and metallurgical activities. The wastes generated by such activities are sources of metals, which penetrate into the surface waters and consequently into the stream deposits. From the point of view of the transfer and the transformation of these metal elements, their monitoring deserves a continuous attention
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.
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
International Nuclear Information System (INIS)
Tzanos, C.P.
1992-01-01
A higher-order differencing method was recently proposed for the convection-diffusion equation, which even with a coarse mesh gives oscillation-free solutions that are far more accurate than those of the upwind scheme. In this paper, the performance of this method is investigated in conjunction with the performance of different iterative solvers for the solution of the Navier-Stokes equations in the vorticity-streamfunction formulation for incompressible flow at high Reynolds numbers. Flow in a square cavity with a moving lid was chosen as a model problem. Solvers that performed well at low Re numbers either failed to converge or had a computationally prohibitive convergence rate at high Re numbers. The additive correction method of Settari and Aziz and an iterative incomplete lower and upper (ILU) solver were used in a multigrid approach that performed well in the whole range of Re numbers considered (from 1000 to 10,000) and for uniform as well as nonuniform grids. At high Re numbers, point or line Gauss-Seidel solvers converged with uniform grids, but failed to converge with nonuniform grids
International Nuclear Information System (INIS)
Bojtsov, V.V.; Tsepin, M.A.; Karpilyanskij, N.N.; Ershov, A.N.
1982-01-01
Results of statistical analysis of the description accuracy of superplasticity S-form curve by different analytic expressions, suggested on the basis of phenomenological and metallophysical concepts about the nature of superplastic deformation, are given. Experimental investigations into the dependence of flow stresses on the deformation rate were conducted on VT3-1 two-phase titanium alloy. Test samples were cut out of a rod, 30 mm in diameter, produced by lengthwise rolling in α+#betta#-region. Optimal temperature of superplasticity manifestation was determined by the method of stress relaxation from a relaxation time value to a given stress. It was established that the Smirnov phemonemological equation describes in the best way the rate dependence of flow stress of superplastic material. This equation can be used for solution of problems of studying mechanism, physical nature of superplastic deformation, analysing strain-stress state and the structure of deformation zone during the processes of pressure shaping of superplastic materials, when considerably wide range (in the limits of 7-8 orders) of deformation rate variation takes place
Directory of Open Access Journals (Sweden)
Yang Li
2018-04-01
Full Text Available Extreme weather has recently become frequent. Heavy rainfall forms storm runoff, which is usually very turbid and contains a high concentration of organic matter, therefore affecting water quality when it enters reservoirs. The large canyon-shaped Heihe Reservoir is the most important raw water source for the city of Xi’an. During the flood season, storm runoff flows into the reservoir as a density current. We determined the relationship among inflow peak discharge (Q, suspended sediment concentration, inflow water temperature, and undercurrent water density. The relationships between (Q and inflow suspended sediment concentration (CS0 could be described by the equation CS0 = 0.3899 × e0.0025Q, that between CS0 and suspended sediment concentration at the entrance of the main reservoir area S1 (CS1 was determined using CS1 = 0.0346 × e0.2335CS0, and air temperature (Ta and inflow water temperature (Tw based on the meteorological data were related as follows: Tw = 0.7718 × Ta + 1.0979. Then, we calculated the density of the undercurrent layer. Compared to the vertical water density distribution at S1 before rainfall, the undercurrent elevation was determined based on the principle of equivalent density inflow. Based on our results, we proposed schemes for optimizing water intake selection and flood discharge during the flood season.
Kou, Jisheng; Sun, Shuyu
2018-01-01
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.
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.
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.
CSIR Research Space (South Africa)
Combrinck, ML
2015-07-01
Full Text Available be either inertial or non-inertial depending on the cases analyzed. This frame shares an origin with the rotational frame Ô. Frame Ô is the non-inertial, rotational frame and is therefore not orientation preserving. Now consider a point P which can... Descriptions This point is described in frame O from where a modified Galilean transformation, GM, will be used to describe it in frame O’. The rotational transform, RΩt, will then be used to transform the resulting equations (as described in frame O...
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
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
International Nuclear Information System (INIS)
Mihalas, D.; Kunasz, P.B.; Hummer, D.G.
1976-01-01
We investigate the importance of the advection and aberration terms, which are of order V/c, in the comoving-frame transfer equation in spherical geometry. Characteristic trajectories are found which reduce the spatial derivatives to a perfect differential, and a generalization of the numerical procedure developed in the earlier papers of this series that permits the integration of the transfer equation on these characteristics is presented. For cases in which V/cvery-much-less-than1, a perturbation solution is developed which reduces the problem to that solved in the first paper in this series. For velocities of the form V (r) approx.r/subn/(n=0,1,2), it is shown that the magnitude of the effects arising from the advection and aberration terms is about 5V/c relative to the solution with these terms omitted. In stellar winds V/capproximately-less-than0.01; hence we conclude that aberration and advection terms may safely be ignored, and that consideration of the Doppler-shift term alone is adequate in the computation of spectra from such expanding atmospheres
Ecological operation for Three Gorges Reservoir
Directory of Open Access Journals (Sweden)
Wen-xian Guo
2011-06-01
Full Text Available The traditional operation of the Three Gorges Reservoir has mainly focused on water for flood control, power generation, navigation, water supply, and recreation, and given less attention to the negative impacts of reservoir operation on the river ecosystem. In order to reduce the negative influence of reservoir operation, ecological operation of the reservoir should be studied with a focus on maintaining a healthy river ecosystem. This study considered ecological operation targets, including maintaining the river environmental flow and protecting the spawning and reproduction of the Chinese sturgeon and four major Chinese carps. Using flow data from 1900 to 2006 at the Yichang gauging station as the control station data for the Yangtze River, the minimal and optimal river environmental flows were analyzed, and eco-hydrological targets for the Chinese sturgeon and four major Chinese carps in the Yangtze River were calculated. This paper proposes a reservoir ecological operation model, which comprehensively considers flood control, power generation, navigation, and the ecological environment. Three typical periods, wet, normal, and dry years, were selected, and the particle swarm optimization algorithm was used to analyze the model. The results show that ecological operation modes have different effects on the economic benefit of the hydropower station, and the reservoir ecological operation model can simulate the flood pulse for the requirements of spawning of the Chinese sturgeon and four major Chinese carps. According to the results, by adopting a suitable re-operation scheme, the hydropower benefit of the reservoir will not decrease dramatically while the ecological demand is met. The results provide a reference for designing reasonable operation schemes for the Three Gorges Reservoir.
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.
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)
Reservoir Models for Gas Hydrate Numerical Simulation
Boswell, R.
2016-12-01
/linear way. Significant progress has also occurred in recent years with regard to the geologic characterization of reservoir boundaries. Vertical boundaries with overlying clay-rich "seals" are now widely-appreciated to have non-zero permeability, and lateral boundaries are sources of potential lateral fluid flow.
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.
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