Self-similar Profiles for Capillary Diffusion Driven Flow in Heterogeneous Porous Media Self-similar Prooles for Capillary Diiusion Driven Flow in Heterogeneous Porous Media

In this paper we consider the process of one-dimensional redistribution of two immiscible and incompressible uids in a heterogeneous porous medium. We treat in detail the special case in which the initial saturation as well as the properties of the porous medium have a single coinciding discontinuity. Then the time-dependent saturation proole is of self-similar form, i.e. depends only on x= p t. This self-similar pro-le can be used to validate numerical algorithms describing two-phase ow in porous media with discontinuous heterogeneities. We discuss the construction of the similarity solution, in which we give special attention to the matching conditions at the interface where the medium properties are discontinuous. We also outline a numerical procedure to obtain the similarity solution and we provide applications in terms of the Brooks-Corey and the Van Genuchten model.