Numerical Analysis of Two Immiscible Fluids in Porous Media by the Multiscale and Homogenization Methods

Abstract

This paper proposes a numerical model for simulating an immiscible compressible two-phase flow in a periodic heterogeneous porous media with application to a coal-bed methane extraction system. Methane flow in a coal sample submerged in water is simulated using the multiscale homogenization method and the averaged macroscopic approach. A weak formulation is used to discretize the governing equations coupled with the boundary conditions using the finite element method and solved using the open-source code Freefem++. It was observed that the general behavior of both methods was in good agreement with actual gas saturation evolution. However, the multiscale approach provided more information regarding the global pressure evolution behavior of the mitigating gas.