The Relative Permeability Function for Two-Phase Flow in Porous Media: Effect of Capillary Number

Abstract

Abstract Expressions for both drainage and imbibition relative permeabilities for wetting and nonwetting phases have been derived using the cut and random rejoin approach. The pore structure is modeled by using information about the pore size distribution that determines capillary pressure. The nonwetting phase is considered to be present as both connected and disconnected fluid. The appropriate permeability equations are then obtained by considering laminar flow equations for the randomly formed pore throat constrictions. Based on the classical percolation theory for mobilization of disconnected nonwetting phase and data on entrapment of connected nonwetting phase, the relative permeability equations are presented for varying capillary numbers. The theoretical results of relative permeability for both natural and synthetic porous media agree with the available experimental data for drainage as well as imbitition. Moreover, the limited experimental data for high capillary numbers corroborate the basic considerations 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 (local) capillary number. This change in the fractional flow is also dependent upon the initial connected and disconnected nonwetting phase saturations. The present approach takes both of these factors into account and therefore can be put to direct use in modeling surfactant and caustic flooding processes.