共查询到20条相似文献，搜索用时 500 毫秒
1.
Konstantin Brenner Mayya Groza Laurent Jeannin Roland Masson Jeanne Pellerin 《Computational Geosciences》2017,21(5-6):1075-1094
Fully implicit time-space discretizations applied to the two-phase Darcy flow problem leads to the systems of nonlinear equations, which are traditionally solved by some variant of Newton’s method. The efficiency of the resulting algorithms heavily depends on the choice of the primary unknowns since Newton’s method is not invariant with respect to a nonlinear change of variable. In this regard, the role of capillary pressure/saturation relation is paramount because the choice of primary unknowns is restricted by its shape. We propose an elegant mathematical framework for two-phase flow in heterogeneous porous media resulting in a family of formulations, which apply to general monotone capillary pressure/saturation relations and handle the saturation jumps at rocktype interfaces. The presented approach is applied to the hybrid dimensional model of two-phase water-gas Darcy flow in fractured porous media for which the fractures are modelled as interfaces of co-dimension one. The problem is discretized using an extension of vertex approximate gradient scheme. As for the phase pressure formulation, the discrete model requires only two unknowns by degree of freedom. 相似文献
2.
A FIC‐based stabilized mixed finite element method with equal order interpolation for solid–pore fluid interaction problems 
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下载免费PDF全文 A new mixed displacement‐pressure element for solving solid–pore fluid interaction problems is presented. In the resulting coupled system of equations, the balance of momentum equation remains unaltered, while the mass balance equation for the pore fluid is stabilized with the inclusion of higher‐order terms multiplied by arbitrary dimensions in space, following the finite calculus (FIC) procedure. The stabilized FIC‐FEM formulation can be applied to any kind of interpolation for the displacements and the pressure, but in this work, we have used linear elements of equal order interpolation for both set of unknowns. Examples in 2D and 3D are presented to illustrate the accuracy of the stabilized formulation for solid–pore fluid interaction problems. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
We consider two-component (typically, water and hydrogen) compressible liquid–gas porous media flows including mass exchange between phases possibly leading to gas-phase (dis)appearance, as motivated by hydrogen production in underground repositories of radioactive waste. Following recent work by Bourgeat, Jurak, and Smaï, we formulate the governing equations in terms of liquid pressure and dissolved hydrogen density as main unknowns, leading mathematically to a nonlinear elliptic–parabolic system of partial differential equations, in which the equations degenerate when the gas phase disappears. We develop a discontinuous Galerkin method for space discretization, combined with a backward Euler scheme for time discretization and an incomplete Newton method for linearization. Numerical examples deal with gas-phase (dis)appearance, ill-prepared initial conditions, and heterogeneous problem with different rock types. 相似文献
4.
In this paper, we present a numerical model for simulating two-phase (oil–water and air–water) incompressible and immiscible flow in porous media. The mathematical model which is based on a fractional flow formulation is formed of two nonlinear partial differential equations: a mean pressure equation and a water saturation equation. These two equations can be solved in a sequential manner. Two numerical methods are used to discretize the equations of the two-phase flow model: mixed hybrid finite elements are used to treat the pressure equation, h-based Richards' equation and the diffusion term in the saturation equation, the advection term in the saturation equation is treated with the discontinuous finite elements. We propose a better way to calculate the nonlinear coefficients contained in our equations on each element of the discretized domain. In heterogeneous porous media, the saturation becomes discontinuous at the interface between two porous media. We show in this paper how to use the capillary pressure–saturation relationship in order to handle the saturation jump in the mixed hybrid finite element method. The two-phase flow simulator is verified against analytical solutions for some flow problems treated by other authors. 相似文献
5.
Numerical simulation of gas migration driven by compressible two-phase partially miscible flow in porous media is of major importance for safety assessment of deep geological repositories for long-lived high-level nuclear waste. We present modeling of compositional liquid and gas flow for numerical simulations of hydrogen migration in deep geological radioactive waste repository based on persistent primary variables. Two-phase flow is considered, with incompressible liquid and compressible gas, which includes capillary effects, gas dissolution, and diffusivity. After discussing briefly the existing approaches to deal with phase appearance and disappearance problem, including a persistent set of variables already considered in a previous paper (Bourgeat et al., Comput Geosci 13(1):29–42, 2009), we focus on a new variant of the primary variables: dissolved hydrogen mass concentration and liquid pressure. This choice leads to a unique and consistent formulation in liquid saturated and unsaturated regions, which is well adapted to heterogeneous media. We use this new set of variable for numerical simulations and show computational evidences of its adequacy to simulate gas phase appearance and disappearance in different but typical situations for gas migration in an underground radioactive waste repository. 相似文献
6.
Astrid Holstad 《Computational Geosciences》1999,3(3-4):229-257
Speciation calculations involve the computation of the concentration of each individual chemical species in a multicomponent–multiphase chemical system. The numerical problem is to solve a system of coupled linear and nonlinear equations subject to the constraint that all unknowns are positive. The performance and accuracy of a series of nonlinear equation solvers are evaluated: A quasi-Newton method with the global step determined by different line search and trust region algorithms, the conjugate gradient method with the global step determined by line search, and the solvers in the codes TENSOLVE, CONMIN and LBFGS. 相似文献
7.
The energy balance of a solid subject to fracture has been explored using heat and mass transfer equations with regard to the volumetric and superficial components. In the suggested model, brittle fracture of a cracked solid considered as a heterogeneous two-phase medium is described by an equation analogous to the Griffith’s criterion for propagation of a single crack. The derived equation is used, together with estimates of relative change in specific interface area, to study the respective change of free strain energy and pressure in rocks associated with failure. 相似文献
8.
Based on the theory of double-porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non-linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd. 相似文献
9.
A numerical simulation is presented for three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation systen which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous medium. An elastoplastic soil model, based on a Mohr–Coulomb yield surface, is used. The finite element method is applied to obtain simultaneous solutions to the governing equations where displacement and fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. The developed model is used to investigate the problems of three-phase fluid flow in a deforming saturated oil reservoir. 相似文献
10.
T. Kuppusamy 《国际地质力学数值与分析法杂志》1993,17(7):457-469
Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed. 相似文献
11.
We consider the modeling and simulation of compositional two-phase flow in a porous medium, where one phase is allowed to
vanish or appear. The modeling of Marchand et al. (in review) leads to a nonlinear system of two conservation equations. Each
conservation equation contains several nonlinear diffusion terms, which in general cannot be written as a function of the
gradients of the two principal unknowns. Also the diffusion coefficients are not necessarily explicit local functions of them.
For the generalised mixed finite elements approximation, Lagrange multipliers associated to each principal unknown are introduced,
the sum of the diffusive fluxes of each component is explicitly eliminated and the static condensation leads to a “global”
nonlinear system of equations only in the Lagrange multipliers also including complementarity conditions to cope with vanishing
or appearing phases. After time discretisation, this system can be solved at each time step using a semi-smooth Newton method.
The static condensation involves “local” nonlinear systems of equations associated to each element, solved also by a semismooth
Newton method. The algorithm is successfully applied to 1D and 2D examples of water–hydrogen flow involving gas phase appearance
and disappearance. 相似文献
12.
Todd Arbogast Mika Juntunen Jamie Pool Mary F. Wheeler 《Computational Geosciences》2013,17(6):1055-1078
We consider the slightly compressible two-phase flow problem in a porous medium with capillary pressure. The problem is solved using the implicit pressure, explicit saturation (IMPES) method, and the convergence is accelerated with iterative coupling of the equations. We use discontinuous Galerkin to discretize both the pressure and saturation equations. We apply two improvements, which are projecting the flux to the mass conservative H(div)-space and penalizing the jump in capillary pressure in the saturation equation. We also discuss the need and use of slope limiters and the choice of primary variables in discretization. The methods are verified with two- and three-dimensional numerical examples. The results show that the modifications stabilize the method and improve the solution. 相似文献
13.
The separation features of the floatex density separator (FDS) are investigated through experimental and computational approaches. It has been shown that the performance of the FDS can be predicted reasonably well using a slip velocity model and steady-state mass balance equations. The approach for the formulation of the slip velocity model makes a difference in the prediction of FDS performance. The computed data from four different slip velocity models have been compared and contrasted with the experimental observations. It has been shown that a slip velocity model based on the modified Richardson and Zaki equation, in which the dissipative pressure gradient is considered to be the primary driving force for separation, predicts the performance more accurately than the other three. A deslimed feed is recommended for better performance of the FDS. 相似文献
14.
Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository 总被引：1，自引：0，他引：1
We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration
in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover,
it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance
or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate
gas generation in a water-saturated repository. 相似文献
15.
The surface subsidence above a compacting saturated oil reservoir is the main topic of this paper. From a literature review, it is obvious that extensive efforts have been conducted for investigating this phenomenon in various situations. Herein, a numerical model, based on the finite element method, was used for simulating three-dimensional three-phase fluid flow in a deforming saturated oil reservoir. The mathematical formulation describes a fully coupled governing equation system which consists of the equilibrium and continuity equations for three immiscible fluids flowing in a porous media. An elastoplastic soil model, based on a Mohr Coulomb yield surface, was utilized. The finite element method was applied to obtain simultaneous solutions to the governing equations where the displacements and the fluid pressures are the primary unknowns. The final discretized equations are solved by a direct solver using fully implicit procedures. A linear analysis was used to study the stability conditions of the present model. Finally, a series of simulations were conducted to indicate the validity and the utility of the developed model. 相似文献
16.
Savithru Jayasinghe David L. Darmofal Marshall C. Galbraith Nicholas K. Burgess Steven R. Allmaras 《Computational Geosciences》2018,22(2):527-542
This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers’ equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship. 相似文献
17.
Lara Loughrey Dan Marshall Peter Jones Paul Millsteed Arthur Main 《Central European Journal of Geosciences》2012,4(2):287-299
The Emmaville-Torrington emeralds were first discovered in 1890 in quartz veins hosted within a Permian metasedimentary sequence, consisting of meta-siltstones, slates and quartzites intruded by pegmatite and aplite veins from the Moule Granite. The emerald deposit genesis is consistent with a typical granite-related emerald vein system. Emeralds from these veins display colour zonation alternating between emerald and clear beryl. Two fluid inclusion types are identified: three-phase (brine+vapour+halite) and two-phase (vapour+liquid) fluid inclusions. Fluid inclusion studies indicate the emeralds were precipitated from saline fluids ranging from approximately 33 mass percent NaCl equivalent. Formational pressures and temperatures of 350 to 400 °C and approximately 150 to 250 bars were derived from fluid inclusion and petrographic studies that also indicate emerald and beryl precipitation respectively from the liquid and vapour portions of a two-phase (boiling) system. The distinct colour zonations observed in the emerald from these deposits is the first recorded emerald locality which shows evidence of colour variation as a function of boiling. The primary three-phase and primary two-phase FITs are consistent with alternating chromium-rich ??striped?? colour banding. Alternating emerald zones with colourless beryl are due to chromium and vanadium partitioning in the liquid portion of the boiling system. The chemical variations observed at Emmaville-Torrington are similar to other colour zoned emeralds from other localities worldwide likely precipitated from a boiling system as well. 相似文献
18.
19.
考虑方位漂移因素的设计约束方程组是一个具有3个独立未知数、多个隐含未知数的非线性方程组,需要使用数值迭代法才能求出其数值解。给出了解析形式的垂深增量公式,利用约束方程组中的垂深方程,将3个独立未知数中的一个未知数表示成其他2个未知数的函数,并用之对设计约束方程组进行降维处理。剖析了隐含未知数的计算细节,给出了隐含未知数的递推算法。提出了降维后的约束方程组的数值求解算法——缩半网格法,该算法可以快速、可靠地求出设计问题的数值解,适用于在开发计算机软件时编程实现。 相似文献
20.
Ettore Vidotto Rainer Helmig Martin Schneider Barbara Wohlmuth 《Computational Geosciences》2018,22(6):1487-1502
In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully implicit finite-volume methods are provided. 相似文献