Empirical Relation for Capillary Pressure in Shale

Brooks and Corey (1964) and van Genuchten (1980) proposed the two most widely used relations for approximating capillary pressure. Petroleum engineers apply both, but they were originally proposed to understand the moisture content in soil whose void space differs from that of shale. This paper presents an empirical relation that can capture the nonplateau-like trend and the approximate capillary pressure in shale. It also implements the nonzero entry pressure, which the van Genuchten model cannot capture. This study compares the performance of the proposed model with those of Brooks and Corey and van Genuchten by determining the nonlinear regression coefficient (R2) and the mean square error (MSE). It uses mercury capillary pressure data of US shales available in the literature. The data set comprises 30 samples collected from the Bakken, Eagle Ford, and Greenhorn Formations with average permeability of less than 1 md and average porosity of 5%. The proposed model has applications in characterizing two-phase displacement in shales.