Two-phase flow equations with a dynamic capillary pressure

Abstract

We investigate the motion of two immiscible fluids in a porous medium described by the two-phase flow system. In the capillary pressure relation, we include static and dynamic hysteresis. The model is wellestablished in the context of the Richards equation, which is obtained by assuming a constant pressure for one of the two phases. We derive an existence result for this hysteresis-two-phase model for non-degenerate permeability and capillary pressure curves. A discretization scheme is introduced and numerical results for fingering experiments are obtained. The main analytical tool is a compactness result for two variables that are couled by an hysteresis relation.