Validation of a Modified Carman-Kozeny Equation To Model Two-Phase Relative Permeabilities

This paper presents a validation of an internally consistent, physically based model for relative permeability based on an extension of the Carman-Kozeny (CK) equation. The modified CK (MCK) expression is a function of surface areas of fluid-fluid and fluid-rock interfaces, as well as fluid saturations and tortuosity. The model uses interfacial and surface areas determined from capillary pressure measurements and, by this means, can incorporate variable wettability and hysteresis as well as assuring consistency of petrophysical properties. To validate the MCK approach, the model is fit to experiments where both capillary pressure and relative permeability are measured simultaneously during flow. The MCK model is further fit to literature-reported water-oil experimental data. Besides the MCK model, each data set is fit with a modification of the commonly used Brooks-Corey (MBC) model to compare the performances of the two. The surface areas derived from capillary pressure relationship used in the MCK model provide a good description of the experimental relative permeabilities measured under the same conditions. The investigated MCK model fits experimental data almost as well as the MBC model. Furthermore, the MCK model is physically based and appears to agree with the wetting characteristics of the investigated porous media when these are known.