We consider the one-dimensional degenerate two-phase flow equations as a model for water drive in oil recovery. The effect of oil trapping is observed in strongly heterogeneous materials with large variations in the permeabilities and in the capillary pressure curves. In such materials, a vanishing oil saturation may appear at interior interfaces and inhibit the oil recovery. We introduce a free boundary problem that separates a critical region with locally vanishing permeabilities from a strictly parabolic region and we give a rigorous derivation of the effective conservation law.
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