Lattice Boltzmann simulation of pressure-driven two-phase flows in capillary tube and porous medium

In this study, we present lattice Boltzmann simulations of two-phase immiscible displacements driven by constant pressure differentials. The method to implement the pressure boundary condition is based on bounce-back of the total non-equilibrium distribution. Simulations show that phase and pressure distributions are consistent with the imposed pressure boundaries. The accuracy was verified by simulating flows in a capillary tube, a problem with a moving interface for which an analytical solution is available. Following the verification, we simulated two-phase immiscible displacements in a random sphere packing and characterized the effects of capillary number, viscosity ratio, and wettability on the dynamics of displacement and the relative permeability.