On the capillary pressure function in porous media based on relative permeabilities of two immiscible fluids

The authors propose a new analytical approach and derive an explicit formula to determine a capillary pressure (Pc) curve in porous media, by combining the first principles of surface science with the classical concept of the phase relative permeability. The developed formulae for Pc and a modified Leverett Jm-function are based on the relative permeability functions for the wetting and nonwetting phases, an apparent specific surface area, and an apparent (calculated) contact angle Θ. The application of the proposed approach was tested using several sets of data from existing publications. The developed Jm-function can be described using the Weibull distribution model for drainage and imbibition conditions. The new approach can generally be used for any type of relative permeability functions and different types of wetting and nonwetting phases.