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In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Sûreté Nucléaire). The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow.

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]