Finite Element Methods for Two-Phase Flow in Heterogeneous Porous Media

A mathematical model for the simultaneous flow of oil and water in porous rock formations is considered. The elliptic pressure equation and the hyperbolic saturation equation are discretized by various finite element methods of streamline diffusion type in space, and by finite differences in time. The main purpose of the chapter is to examine different solution strategies in four flow cases involving porous formations with different type of heterogeneities in absolute and relative permeability as well as in porosity. Fully implicit methods represent the most robust and reliable solution approach in challenging flow cases. Simpler solution strategies may, however, be satisfactorily robust and more efficient in problems with less severe heterogeneities.