Numerical Simulation of Flow in 2D Heterogeneous Porous Media Including CapillaryEffects

摘要

In this paper we study the effect of capillarity on immiscible two-phase flow ina porous medium of which the permeability is discontinuous. In Section 2 we present the standard model for immiscible two-phase flow in a porous medium. In Section 3 we derive jump conditions at the interfaces that separate areas of different permeability. As a starting point we take Yortsos and Chang's analysis of the steady-state flow in a simple one-dimensional heterogeneous structure. We extend their analysis to cases in which trapping due to capillary forces occurs. After defining interface conditions for two-dimensional problems, we develop in Section 4 a discretization scheme that incorporates these interface conditions. In Section 5 we show the results of numerical simulations for the flooding of a reservoir with lens shaped heterogeneities. It appears that capillary pressure strongly affects the efficiency of the displacement process only if the injected fluid is non-wetting and the initially resident fluid is wetting. In the final Section we summarize our conclusions. (Copyright (c) 1993 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)