Homogenization of a convection-diffusion model with reaction in a porous medium

We study the homogenization of a convection-diffusion equation with reaction in a porous medium when both the Péclet and Damkohler numbers are large. We prove that, up to a large drift, the homogenized equation is a diffusion equation. Our method is based on a factorization principle and two-scale convergence. The main consequence is that we obtain rigorous definitions of homogenized coefficients which justify heuristic arguments in the method of volume averaging. We perform 2-d numerical computations of the diffusion-dispersion homogenized coefficient which are in very good agreement with previous results obtained by the method of volume averaging. To cite this article: G. Allaire, A.-L. Raphael, C. R. Acad. Sci. Paris, Ser. I 344 (2007).