Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov–Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure–saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov–Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure–saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov–Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks–Corey. The widely used dpc/dSw grad Sw formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of grad pc in combination with a chord-slope technique must be utilized. q 1998 Elsevier Science Limited. All rights reserved