Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow

In this paper, we justify by periodic homogenization the double-porosity model for immiscible incompressible two-phase flow. The volume fraction of the fissured part and the nonfissured part are kept positive constants and of the same order. The scaling is such that, in the final homogenized equations, the less permeable part of the matrix contributes as a nonlinear memory term. To prove the convergence of the total velocity and of the ''reduced'' pressure, we use the two-scale convergence since it seems to be appropriate For the problem, even though it would be possible 60 work with periodic modulation. However, in the final step, the degenerate ellipticity prevents the use of the two-scale convergence method and leads us to use periodic modulation.