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 analyzed. For flow in homogeneous media the Petrov-Galerkin method gives excellent results. But this method fails to caputre 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 dp_c/dS_w grad S_w formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of grad p_c in combination with a chord-slope technique must be utilized. (orig.)SIGLEAvailable from TIB Hannover: RR 6943(96/11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Multiphase flow in heterogeneous porous media: a classical finite element method versus an IMPES-based mixed FE/FV approach

Various discretization methods exist for the numerical simulation of multiphase flow in porous media. In this paper, two methods are introduced and analysed - a Full-Upwind Galerkin method which belongs to the classical finite element methods, and a mixed-hybrid finite element method based on an IMPES approach. Both methods are derived from the governing equations of two-phase flow. Their discretization concepts are compared in detail. Their efficiency is discussed using several examples. (orig.)Available from TIB Hannover: RR 6943(96/19) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman