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In this paper, we consider a parallel finite volume algorithm for modeling complex processes in porous media that include multiphase flow and geochemical interactions. Coupled flow and reactive transport phenomena often occur in a wide range of subsurface systems such as hydrocarbon reservoir production, groundwater management, carbon dioxide sequestration, nuclear waste repository or geothermal energy production. This work aims to develop and implement a parallel code coupling approach for non-isothermal multiphase multicomponent flow and reactive transport simulation in the framework of the parallel open-source platform DuMuX. Modeling such problems leads to a highly nonlinear coupled system of degenerate partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. We propose a sequential fully implicit scheme solving firstly a multiphase compositional flow problem and then a Direct Substitution Approach (DSA) is used to solve the reactive transport problem. Both subsystems are discretized by a fully implicit cell-centred finite volume scheme and then an efficient sequential coupling has been implemented in DuMuX. We focus on the stability and robustness of the coupling process and the numerical benefits of the DSA approach. Parallelization is carried out using the DUNE parallel library package based on MPI providing high parallel efficiency and allowing simulations with several tens of millions of degrees of freedom to be carried out, ideal for large-scale field applications involving multicomponent chemistry. As we deal with complex codes, we have tested and demonstrated the correctness of the implemented software by benchmarking, including the MoMaS reactive transport benchmark, and comparison to existing simulations in the literature. The accuracy and effectiveness of the approach is demonstrated through 2D and 3D numerical simulations. Parallel scalability is investigated for 3D simulations with different grid resolutions. Numerical results for long-term fate of injected CO2 for geological storage are presented. The numerical results have demonstrated that this approach yields physically realistic flow fields in highly heterogeneous media and showed that this approach performs significantly better than the Sequential Iterative Approach (SIA).

The goal of the paper is to describe the large time behavior of a Markov process associated with a symmetric diffusion in a high contrast random stationary environment and to characterize the limit process under the diffusive scaling.The advantage of the proposed approach is that we explicitly present the limit operator on the extended space. That gives us a possibility to use this operator for approximations of diffusion processes inporous media with random structure of inclusions. We also describe the spectrum of the limit operator.Our approach uses auxiliary Markov processes defined on extended state spaces, as well as tools from homogenization theory in random media. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and test numerically a fully coupled fully implicit finite volume (FV) method for solving the nonlinear coupling between two-phase flows and geochemical reactions in porous media on a reservoir scale. The problem is modeled by a highly nonlinear system of degenerate partial differential equations (PDEs governing a compositional two-phase flow model) coupled to ordinary and/or algebraic differential equations (modeling kinetic and equilibrium chemical reactions respectively). The spatial discretization uses a cell-centered FV scheme. After discretizing in time with an implicit Euler scheme, the resulting systems of nonlinear algebraic equations are solved with Newton's method and the systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. We discuss two strategies for selecting local time steps. We have developed and implemented this scheme in a new module in the context of the parallel open source platform DuMuX. Parallelization is carried out using the DUNE parallel library package. Two numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed solver for 3D problems modeling scenarios of CO2 geological storage into a deep saline aquifer. We also report the parallel scalability of the proposed algorithm on a supercomputer with up to 768 processor cores. The proposed method is accurate, numerically robust and exhibits the potential for tackling realistic problems. Lastly, a comparison with a sequential method consisting in decoupling the original problem into a two-phase flow and a reactive transport problem, is performed in term of accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we formulate and test numerically a fully coupled fully implicit finite volume (FV) method for solving the nonlinear coupling between two-phase flows and geochemical reactions in porous media on a reservoir scale. The problem is modeled by a highly nonlinear system of degenerate partial differential equations (PDEs governing a compositional two-phase flow model) coupled to ordinary and/or algebraic differential equations (modeling kinetic and equilibrium chemical reactions respectively). The spatial discretization uses a cell-centered FV scheme. After discretizing in time with an implicit Euler scheme, the resulting systems of nonlinear algebraic equations are solved with Newton's method and the systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. We discuss two strategies for selecting local time steps. We have developed and implemented this scheme in a new module in the context of the parallel open source platform DuMuX. Parallelization is carried out using the DUNE parallel library package. Two numerical experiments are presented to demonstrate the effectiveness and efficiency of the proposed solver for 3D problems modeling scenarios of CO2 geological storage into a deep saline aquifer. We also report the parallel scalability of the proposed algorithm on a supercomputer with up to 768 processor cores. The proposed method is accurate, numerically robust and exhibits the potential for tackling realistic problems. Lastly, a comparison with a sequential method consisting in decoupling the original problem into a two-phase flow and a reactive transport problem, is performed in term of accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a study of immiscible incompressible twophase ow through fractured porous media. The results obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli¯c (1996) and L. M. Yeh (2006) are revisited. The main goal is to incorporate some of the most recent improvements in the convergence of the solutions in the homogenization of such models. The microscopic model consists of the usual equations derived from the mass conservation of both uids along with the Darcy-Muskat law. The problem is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. We will consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. The fractured medium consists of periodically repeating homogeneous blocks and fractures, the permeability being highly discontinuous. Over the matrix domain, the permeability is scaled by εθ, where " is the size of a typical porous block and θ > 0 is a parameter. The model involves highly oscillatory characteristics and internal nonlinear interface conditions. Under some realistic assumptions on the data, the convergence of the solutions, and the macroscopic models corresponding to various range of contrast are constructed using the two-scale convergence method combined with the dilation technique. The results improve upon previously derived effective models to highly heterogeneous porous media with discontinuous capillary pressures. [ABSTRACT FROM AUTHOR]

The paper deals with a degenerate model of immiscible compressible two-phase flow in heterogeneous porous media. We consider liquid and gas phases (water and hydrogen) flow in a porous reservoir, modeling the hydrogen migration through engineered and geological barriers for a deep repository for radioactive waste. The gas phase is supposed compressible and obeying the ideal gas law. The flow is then described by the conservation of the mass for each phase. The model is written in terms of the phase formulation, i.e. the liquid saturation phase and the gas pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear degenerate parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the liquid saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. The aim of this paper is to extend our previous results to the case of an ideal gas. In this case a new degeneracy appears in the pressure equation. With the help of an appropriate regularization we show the existence of a weak solution to the studied system. We also consider the corresponding nonlinear homogenization problem and provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence. [ABSTRACT FROM AUTHOR]

A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. [ABSTRACT FROM AUTHOR]