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 ω, a ratio of global permeabilities ∈K, and a ratio of the order of capillary forces ∈c. The limit when ω tends to zero at different values of ∈K and ∈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.