Analytical model for gravity segregation of horizontal multiphase flow in porous media

Abstract

Simultaneous horizontal injection of two immiscible fluids into a porous medium gives rise to three regions of constant saturation. Due to gravity impact, the region with fluid saturation reflecting the volume fraction and viscosity ratio of the injected fluids morphs into two horizontal layers fully saturated with one fluid or the other. The location of the discontinuity separating constant saturation regions is often estimated with the Stone-Jenkins (SJ) formula. Our numerical simulations of multiphase flow in porous media demonstrate that, for a wide range of hydraulic parameters of practical significance, the SJ formula has substantial error. We derive an approximate analytical solution, which neglects the vertical component of flow velocity and introduces a correction factor to enforce mass conservation. Comparison with numerical simulations reveals that our solution is accurate in the parameter regimes for which the SJ formula is not and vice versa. The two solutions are complementary, covering the entire range of physically realizable parameters.