Discontinous Galerkin and Mixed-Hybrid Finite Element Approach to Two-Phase Flow in Heterogeneous Porous Media with Different Capillary Pressures

A modern numerical scheme for simulation of flow of two immiscible and incompressible phases in inhomogeneous porous media is proposed. The method is based on a combination of the mixed-hybrid finite element (MHFE) and discontinuous Galerkin (DG) methods. The combined approach allows for accurate approximation of the flux at the boundary between neighboring finite elements, especially in heterogeneous media. In order to simulate the non-wetting phase pooling at material interfaces (i.e., the barrier effect), we extend the approach proposed in Hoteit and Firoozabadi (2008) by considering the extended capillary pressure condition. The applicability of the MHFEDG method is demonstrated on benchmark solutions and simulations of laboratory experiments of two-phase flow in highly heterogeneous porous media.