A novel equation to calculate primary drainage capillary pressure based on a porous plate model: Theory and application

Abstract

This study aims to develop an equation for primary drainage capillary pressure as a function of water saturation based on the porous plate model. Several empirical and semiempirical equations are available to calculate Pc-Sw. The results of the previous equations are not ideal, so this is an attempt to present an accurate equation to calculate Pc-Sw based on governing theoretical physical analysis to describe two-phase immiscible displacement flow in porous media. Volumetric flow rates through the core plug and porous plate are applied to calculate the transport phenomena in porous media. The equation is derived from mass and momentum transfer through a core plug, and Darcy’s law is applied to water flow through a porous plate. Finally, the modified Bessel function is obtained to calculate Pc as a function of Sw. The findings of this study help provide a better understanding of two-phase immiscible displacement flow in porous media. The novelty of this work lies in the ability of the new Pc-Sw equation to accurately fit the primary drainage capillary pressure experimental data obtained from a porous plate, centrifugal, and mercury injection apparatus without restriction. The new equation can be used to calculate the relative permeability and initial fluid distribution in the reservoir. The accuracy of the new equation is a significant advantage compared to Brooks-Corey's Pc-Sw equation; therefore, the research results lead to an incremental advance in the field. This study fills the gap between analytical and empirical models to find the Pc-Sw equation.