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In this paper we give a new proof of the homogenization result for animmiscible incompressible two-phase flow in double porosity media obtainedearlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli\'c (1996)and in the paper of L. M. Yeh (2006) under some restrictive assumptions. Themicroscopic model consists of the usual equations derived from the massconservation laws for both fluids along with the standard Darcy-Muskat lawrelating the velocities to the pressure gradients and gravitational effects.The problem is written in terms of the phase formulation, i.e. where the phasepressures and the phase saturations are primary unknowns. The fractured mediumconsists of periodically repeating homogeneous blocks and fractures, where theabsolute permeability of the medium is discontinuous. The important differencewith respect to the results of the cited papers is that the global pressurefunction as well as the saturation are also discontinuous. This makes theinitial mesoscopic problem more general and, physically, more realistic. Theconvergence of the solutions, and the macroscopic models corresponding tovarious range of contrast are constructed using the two-scale convergencemethod combined with the dilation technique.

Homogenized model of immiscible incompressible two-phase flow in double porosity media : A new proof