Errors in the upstream mobility scheme for countercurrent two-phase flow in heterogeneous porous media

In reservoir simulation, the upstream mobility scheme is widely used for calculating fluid flow in porous media and has been shown feasible for flow when the porous medium is homogeneous. In the case of flow in heterogeneous porous media, the scheme has earlier been shown to give erroneous solutions in approximating pure gravity segregation. Here, we show that the scheme may exhibit larger errors when approximating flow in heterogeneous media for flux functions involving both advection and gravity segregation components. Errors have only been found in the case of countercurrent flow. The physically correct solution is approximated by an extension of the Godunov and Engquist–Osher flux. We also present a new finite volume scheme based on the local Lax–Friedrichs flux and test the performance of this scheme in the numerical experiments.