Effective two-phase flow through highly heterogeneous porous media: Capillary nonequilibrium effects

We consider the two-phase flow through a dual-porosity medium, characterized by a period of heterogeneity epsilon, a ratio of global permeabilities omega(K), and a ratio of the order of capillary forces omega(c). The limit when epsilon tends to zero at different values of omega(K) and omega(c) gives four classes of global behavior, differing by the type of elementary flows at the one-cell level. We propose a diagram of their predominance. A macro-scale model is constructed by formal homogenization techniques for one of these classes; it shows a nonlinear kinetic relationship for the averaged capillary pressure functions, and leads to a decomposition for the effective phase permeability tensors. A capillary relaxation time is explicitly determined.