Generic differential equation for fractional flow of steady two-phase flow in porous media

We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two underlying observations of steady-flow simulations in two and three dimensions using biperiodic boundary conditions. The resulting equation is solved generally, and the result is tested against simulations and experimental relative permeability results found in the literature.