A Buckley-Leverett Theory Based Lattice Boltzmann Method for Immiscible Two-Phase Flow with Viscous Coupling in Porous Media (Advances in Applied Mathematics and Mechanics, 2024)
In this paper, a lattice Boltzmann method is developed to simulate the waterdisplacement of oil in porous media at the macroscopic-scale, which is built upon thegeneralized Darcy’s law while incorporating cross terms to consider the viscous coupling between two phases. The Buckley-Leverett equation is applied to describe thesaturation front advance, thus allowing the determination of water saturation at shockfront by using the Welge’s graphic method. We explore the effect of viscous couplingon the displacement by comparing the positions of the shock front under the conditions with different degrees of coupling and without viscous coupling. Results showthat the advancing speed of shock front increases with the degree of coupling when theviscosity 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 degreeof coupling equals the reciprocal of viscosity ratio. In addition, the effect of viscouscoupling on the displacement is very sensitive to the change of viscosity ratio, whichdecreases monotonously with the decrease of viscosity ratio under the same couplingdegree.