Lattice Boltzmann Study of the Steady-State Relative Permeabilities in Porous Media

A multiple-relaxation-time (MRT) lattice Boltzmann model (LBM) is used to study the relative permeabilities in porous media. In many simulations in the literature, usually the periodic boundary condition at inlet and outlet and a uniform pressure gradient were applied to measure the relative permeabilities. However, it is not consistent with the pressure or velocity boundary conditions in the real experiments and may lead to unphysical results. Here using the convective outflow and constant velocity boundary conditions at outlet and inlet, respectively, we can simulate the real experimental setup. Meanwhile, the distribution of the two phases at the outlet can be resolved. The effects of wettability, initial saturation, viscosity ratio (M is an element of (1,50)), capillary number (Ca is an element of (10(-4), 10(-2))) and micro two-phase distribution at the inlet on permeabilities are investigated comprehensively. It is found that generally speaking, the strong wetting, drainage, larger Ca, and larger M may result in a larger relative permeability of the non-wetting phase. Different flow pattern, the lubrication effect of the wetting phase that attaches to the wall, and influence of stagnant pores may contribute to the feature. The study is helpful to further develop the LBM to simulate the real experimental process.