This paper presents multiblock methods for coupled multiphase flow and species transport modeling in porous media applications. These methods provide local mass conservation and a continuous approximation of fluxes across inter-element faces and sub-domain (inter-block) interfaces and can treat non-matching grids, allowing for a flexible choice of grid refinements. Furthermore, they lend themselves naturally to parallel implementations of multiphysics, multinumerics, multiscale applications of porous media flow and transport.

The paper briefly introduces mortar mixed finite element methods (MMFEM) [1] for coupled porous media flow and transport applications, followed by the main emphasis of the paper which is a novel extension of an enhanced velocity mixed finite element method (EVMFEM) [2] to similar problems flow and reactive transport. The paper also presents the formulation of a recent application of EVMFEM to such challenging problems as compositional flow simulations of CO2 sequestration, that is now widely accepted as the most feasible solution to address the growing environmental concerns due to global warming, as well as a very effective means for enhanced oil and gas recovery.

Computational experiments with EVMFEM suggest that it is advantageous to apply grid refinements around wells and where plumes of chemical species are expected to be transported. Allowing for variable grid refinements greatly reduces the simulation cost (wall clock times), compared with single block fine-grid everywhere strategies, while preserving overall accuracy of the solution. Furthermore, initial studies indicate that the implementation is scalable in parallel simulations. For completeness, a few significant analytic results on convergence of the method are stated and referenced, omitting proof.

This work is significant in advancing the understanding and application of multiblock methods in reservoir simulation development. Problems such as transport of chemical species in multiphase flow and CO2 sequestration have begun to assume significant importance in decisions regarding the preservation of our environment and in the safe and reliable means of delivering energy. This paper offers useful methods and some innovative future directions to address the huge computational costs involved in solving such complex problems.

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