Relative permeability of two-phase flow in three-dimensional porous media using the lattice Boltzmann method

The three-dimensional (3D) multi-relaxation-time (MRT) pseudopotential lattice Boltzmann model (LBM) which is able to handle high density ratio is employed to simulate two-phase flow in sphere-packed porous media. The effects of driving force, wettability, phase saturation, porosity and solid sphere distribution on the two-phase flow pattern as well as the relative permeability are investigated. The results show that the relative permeabilities of nonwetting phase and wetting phase increase with the driving force. As the wettability of porous media changes from strongly wet to neutrally wet, the relative permeability of the nonwetting phase reduces while the relative permeability of the wetting phase increases. With the increase of nonwetting saturation, the relative permeability of nonwetting phase increases but the relative permeability of wetting phase decreases. In addition, the heterogeneity of porous media can affect the steady state two-phase distribution pattern and the relative permeability significantly. The relative permeabilities of nonwetting phase and wetting phase in porous media of higher porosity are larger than the relative permeabilities with lower porosity. The present work demonstrates that the 3D MRT pseudopotential lattice Boltzmann model is an effective tool for understanding the transport mechanism of two-phase flow in porous media.