Effect of capillary number on the relative permeability function for two-phase flow in porous media

Abstract

Expressions for both drainage and imbibition relative permeabilities for wetting and nonwetting phases have been derived using the cut and random rejoin model approach. The pore structure is modeled by using information about the pore size distribution that determines the capillary pressure. The nonwetting phase is considered to be present as both connected and disconnected fluid. The appropriate permeability equations are obtained by considering laminar flow equations at the randomly formed pore throat constrictions. Based on the percolation theory, the relative permeability equations are presented for capillary numbers for which viscous forces are nonnegligible. These equations consider both the mobilization of disconnected nonwetting phase and the displacement of connected nonwetting phase. The theoretical results of relative permeability for natural and synthetic porous media agree with the available experimental data for drainage as well as imbibition. Moreover, the limited experimental data for high capillary numbers corroborate the assumptions of the model. The injection or in situ generation of surface active agents alters the fractional flow of oil in a reservoir due to an increase in the capillary number. This change in the fractional flow is also dependent upon the connected and disconnected nonwetting phase saturations at the onset of high N c imbibition. The present approach takes both of these factors into account and presents algebraic relations for relative permeabilities. The model, therefore, can be put to use in describing surfactant and caustic flooding processes.