Summary
This paper presents a multiblock-discretization method—the enhanced-velocity mixed-finite-element method (EVMFEM) (Wheeler et al. 2002)—for coupled multiphase flow and reactive-species-transport modeling in porous-media applications. The method provides local mass balance and a continuous approximation of fluxes across interfaces of elements and subdomains. It can treat nonmatching grids, allowing for a flexible choice of grid refinements. Further, by distributing the blocks among processors such that each block has approximately the same number of elements, this method can be implemented efficiently in parallel, thereby offering further reductions in computational cost.
The paper also presents recent application of EVMFEM to challenging problems such as compositional flow simulations of CO2 sequestration. Tests with EVMFEM suggest that it is advantageous to apply grid refinements around wells and to areas in which dynamics of chemical-species concentration is highest. Allowing for variable grid refinements greatly reduces the simulation cost, while preserving overall accuracy of the solution. 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 discretization and application of EVMFEMs 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.
A comparison study of multi-component Lattice Boltzmann models for flow in porous media applications