Numerical simulations of water-gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure

We present an approach and numerical results for a new formulation modeling immiscible, compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion-convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunovtype method is used to treat the convection terms and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water-gas equations efficiently and accurately in nuclear underground waste disposal situations.