Total velocity-based finite volume discretization of two-phase Darcy flow in highly heterogeneous media with discontinuous capillary pressure

Abstract

Abstract This work proposes a finite volume scheme for two-phase Darcy flow in heterogeneous porous media with different rock types. The fully implicit discretization is based on cell-centered, as well as face-centered degrees of freedom in order to capture accurately the nonlinear transmission conditions at different rock type interfaces. These conditions play a major role in the flow dynamics. The scheme is formulated with natural physical unknowns, and the notion of global pressure is only introduced to analyze its stability and convergence. It combines a two-point flux approximation of the gradient normal fluxes with a Hybrid Upwinding approximation of the transport terms. The convergence of the scheme to a weak solution is established taking into account the discontinuous capillary pressure at different rock type interfaces and the degeneracy of the phase mobilities. Numerical experiments show the additional robustness of the proposed discretization compared with the classical Phase Potential Upwinding approach.