Two-Phase Flow in Porous Media with Slip Boundary Condition

2-phase flow in porous media is typically described by Darcy's law extended with the concept of relative permeability, $k_{r}$, for the water and the oil phase. Using a single phase permeability of a wetting fluid (water) as reference, $kr $naturally assumes a maximum value of 0 $\le kr \le $ 1. Several reports in literature and our own experimental data show in some cases endpoint relative permeabilities of the non-wetting phase with 2 $< kr <$ 4. That means that in 2-phase flow in the porous medium, the flux of the non-wetting phase is higher when a small amount of the wetting phase is present. We explain this behavior by drawing an analogy between $kr $>1 and a \textit{slip-boundary condition} for the pore scale flow using 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.