A Buckley-Leverett Theory Based Lattice Boltzmann Method for Immiscible Two-Phase Flow with Viscous Coupling in Porous Media

Abstract

In this paper, a lattice Boltzmann method is developed to simulate the water displacement of oil in porous media at the macroscopic-scale, which is built upon the generalized Darcy's law while incorporating cross terms to consider the viscous coupling between two phases. The Buckley-Leverett equation is applied to describe the saturation front advance, thus allowing the determination of water saturation at shock front by using the Welge's graphic method. We explore the effect of viscous coupling on the displacement by comparing the positions of the shock front under the conditions with different degrees of coupling and without viscous coupling. Results show that the advancing speed of shock front increases with the degree of coupling when the viscosity ratio of oil to water remains at 5. We also find that the effect of viscous coupling on the displacement can be neglected when the tolerance quantifying the degree of coupling equals the reciprocal of viscosity ratio. In addition, the effect of viscous coupling on the displacement is very sensitive to the change of viscosity ratio, which decreases monotonously with the decrease of viscosity ratio under the same coupling degree.