A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media

In the present paper we study the immiscible two-phase flow in porous media using the lattice Boltzmann model proposed by He et al. [X. He, R. Zhang, S. Chen, G.D. Doolen, Phys. Fluids 11 (1999) 1143–1152]. By considering a set of appropriate boundary conditions for the density distribution function defined in that model, we account for the effect of wettability at solid–fluid interfaces and capillarity in the pores where the fluid–fluid interfaces reside. Different contact angles of the fluid–fluid interface at solid walls can be realized by taking appropriate values for the density distribution function at the solid sites of the porous domain. It is shown that the steady state contact angle is a linear function of the density value assigned to the solid sites.The model is then applied to the study of viscous coupling effects in immiscible two-phase flow in irregular pore networks, with respect to the overall wetting saturation, the viscosity ratio and the wetting angle. Our results show that when the wetting fluid is less viscous than the non-wetting fluid then the apparent relative permeability of the non-wetting phase may take values greater than unity due to the “lubricating” effect of the wetting films that cover the solid walls. The proposed model is an ideal tool for modeling immiscible two-phase flow in porous media, due both to its ability to incorporate complicated boundary conditions at the pore walls and also capture the physical aspects of the flow in the bulk and the interfaces. Furthermore, the width of the fluid–fluid interfaces is kept less than 3–4 lattice units allowing for simulations in relatively low resolution porous lattices.