Mixed Finite Elements for Multiphase Flow in Porous Media Consisting of Different Rock Types

Modelling of heterogeneous reservoirs has received increased attention during the last years. In high permeable zones, the flow could be dominated by advection, while processes such as imbibition or drainage might dominate in other parts. To illustrate the ideas presented in this paper, we consider two phase incompressible, immiscible flow in two spatial dimensions. The ideas could be generalized to more than two phases. The relative permeabilities kr l = w, nw (w: wetting phase, nw: nonwetting phase) and capillary pressure data Pc are highly dependent upon the rock type. Indeed, we shall define a rock type as a porous medium for which such data are dependent upon the saturations only. Let the reservoir domain Ω concist of Nr rock types.