The relative permeabilities of an idealized model of two-phase flow in porous media

A simplified model is presented for two-phase flow in a porous medium consisting of circular capillary tubes. The equation of motion (Navier-Stokes equation) is solved for the system giving the velocity distributions for the wetting and nonwetting phases. The velocity distributions are used to derive expressions for the relative permeabilities to the wetting and nonwetting phases. It was found that the relative permeability to the nonwetting phase at a given saturation is a function of the viscosity ratio of the two phases while the relative permeability to the wetting phase is independent of the viscosity ratio. The validity of these findings for more complicated porous systems is discussed.