Homogenization of the degenerate two-phase flow equations
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Date
2012-04-02
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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.
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Keywords
degenerate permeability, homogenization, two-phase flow