Effective model of two-phase flow in a porous medium made of different rock types

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Abstract
We consider the behavior of immiscible and incompressible two-phase flows in a porous medium made of several rock types. Each rock type, is defined by one porosity, one absolute rock permeability tensor, two relative permeability curves and one capillary pressure curve. Using two-scale convergence, we get an homogenized model which governs the global behavior of the flow. In this model, macroscopic equations are generally coupled with local equations; but under some assumptions, these two problems can be decoupled.