An energy-stable and conservative numerical method for multicomponent Maxwell–Stefan model with rock compressibility

Numerical simulation of gas flow in porous media is becoming increasingly attractive due to its importance shale and natural production carbon dioxide sequestration. In this paper, taking molar densities as the primary unknowns rather than pressure fractions, we propose an alternative formulation multicomponent Maxwell–Stefan (MS) model with rock compressibility. Benefiting from definitions solid free energies, MS has a distinct feature that it follows energy dissipation law, namely, consistent second law thermodynamics. Additionally, obeys famous Onsager's reciprocal principle. An efficient energy-stable numerical scheme constructed using stabilized factorization approach for Helmholtz density certain carefully designed formulations involving explicit implicit mixed treatments coupling between densities, pressure, porosity. We rigorously prove inherits at discrete level. The fully ability ensure mass conservation each component well preserve tests are conducted verify our theories, particular, demonstrate good performance proposed stability expected theories.