Viscous coupling effects for two-phase flow in porous media

Recent studies have revealed that viscous coupling effects in immiscible two-phase flow, caused by momentum transfer between the two fluid phases, are important for a range of cases of porous medium flow. Generalized governing equations for coupled immiscible two-phase flow in porous media have been suggested through a formulation that includes two viscous coupling coefficients, in addition to the two conventional relative permeabilities. However, a quantitative understanding of the coupling effects and their dependence on factors including capillary number, viscosity ratio; and wettability still remains as an open issue. In this work, we use a three-dimensional parallel processing version of a two-fluid-phase lattice Boltzmann (LB) model to investigate this phenomenon. A multiple-relaxation-time (MRT) approximation of the LB equations is used in the simulator, which leads to stable results. We validate our model by verifying the velocity profile for flow through a channel with a square cross-section. We then simulate co-current flow through a sphere-pack porous medium and determine the relative permeabilities. Correlations of the relative permeabilities as a. function of the fluid viscosities and wettability are investigated. The results are qualitatively consistent with experimental observations by Avraam and Payatakes [1] and the numerical simulations of Langaas and Papatzacos [12].