A homogenization result for three-phase flow though periodic heterogeneus porous media

We give homogenization results for an immiscible and incompressible three-phase ow model in a heterogeneous petroleum reservoir with periodic structure, including capillary ffects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection-diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the ow. The determination of effective properties require the numerical resolution of local problems in a standard cell