Phase diagram for preferential flow in dual permeable media

We study the preference of two-phase displacements systematically by theoretical derivations and numerical simulations via a non-uniform pore doublet model. All the most important impact factors, including viscosity ratio, capillary number, wetting conditions and boundary conditions, have been considered, and finally a complete phase diagram for preferential flow has been obtained. The simple treatment for the dual-permeability media has been validated, and further, with a few necessary corrections the phase diagram is applicable for disordered permeable media in general. These results help us to understand the occurrence and manipulation of preferential flow in heterogeneous permeable media.