Two-Phase Flow in Porous Media with Slip Boundary Condition

Flow in porous media described by Darcy’s law extended to two-phase flow using the concept of relative permeabilities kr naturally assumes a maximum value of 0 ≤ kr ≤ 1. Reports in literature and our own experimental data show endpoint relative permeabilities kr > 1. In the porous medium, the flux of the non-wetting phase is in many cases about 2-4 times higher when a small amount of the wetting phase is present. Here, we draw an analogy between kr > 1 and a slip-boundary condition for the pore scale flow. We use a model description assuming flow in capillary tubes with a slip boundary condition. This model predicts that the flux increase due to slip depends on the equivalent capillary radius of the flow channels. Our kr data specifically follows this dependence indicating that slip is a plausible explanation for the observation of kr > 1.