Numerical study of factors influencing relative permeabilities of two immiscible fluids flowing through porous media using lattice Boltzmann method

Relative permeability curves have practical implications in petroleum reservoir simulations. Study of the effects of reservoir wettability, pore shape geometry, and viscosity ratio of flowing fluids on the relative permeabilities is of great importance in reservoir modeling. In this paper, lattice Boltzmann method (LBM) is employed for analyzing the two-fluid flow in rigid porous media. The developed LBM code proved to be a robust numerical tool for analyzing the factors that influence the relative permeabilities of two immiscible fluids flowing through porous media. The numerically derived relative permeability curves demonstrate that in neutrally wet reservoirs, the effect of viscosity ratio on the relative permeability curves of both fluids are almost the same, however, in strongly wet reservoirs, while the effects of the viscosity ratio on the relative permeability of wetting fluid is negligible, it has a remarkable effect on the relative permeability of non-wetting fluid. The LBM numerical study also reveals that the pore shape geometry has virtually no effect on relative permeability of wetting fluid. But increasing the specific surface area of the porous medium may reduce the relative permeability coefficient of non-wetting fluid to a high extent.