Viscous coupling effects for two-phase flow in porous media

Abstract

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].