Homogenization of the degenerate two-phase flow equations

Abstract

We analyze two-phase flow in highly heterogeneous media. Problems related to the degeneracy of the permeability coefficient functions are treated with a new concept of weighted solutions. Instead of the pressure variables we formulate the problem with the weighted pressure function ψ, which is obtained as the product of permeability and pressure. We perform the homogenization limit and obtain effective equations in the form of a two-scale limit system. The nonlinear effective system is of the classical form in the non-degenerate case. In the degenerate case, the two-scale system uses again a weighted pressure variable. Our approach allows to work without the global pressure function. Even though internal interfaces are included, our approach provides the homogenization limit without any smallness assumptions on permeabilities or capillary pressures.