Viscous coupling in two-phase flow in porous media and its effect on relative permeabilities

An idealized model of a porous rock consisting of a bundle of capillary tubes whose cross-sections are regular polygons is used to assess the importance of viscous coupling or lubrication during simultaneous oil-water flow. Fluids are nonuniformly distributed over tubes of different characteristic dimension because of the requirements of capillary equilibrium and the effect of interfacial viscosity at oil-water interfaces is considered. With these assumptions, we find that the importance of viscous coupling depends on the rheology of the oil-water interface. Where the interfacial shear viscosity is zero, viscous coupling leading to a dependence of oil relative permeability on oil-water viscosity ratio for viscosity ratios greater than one is important for a range of pore cross-section shapes and pore size distributions. For nonzero interfacial shear viscosity, viscous coupling is reduced. Using values reported in the literature for crude oil-brine systems, we find no viscous coupling.