Theoretical Development of the Brooks-Corey Capillary Pressure Model from Fractal Modeling of Porous Media

Abstract The capillary pressure model proposed empirically by Brooks and Corey has been used widely for several decades. However it is not clear why the Brooks-Corey capillary pressure model works so well. In this study, it has been found that the empirical Brooks-Corey capillary pressure model can be derived theoretically from fractal modeling of porous media. Also found was the correlation between the pore size distribution index in the Brooks-Corey capillary pressure model and the fractal dimension. The pore size distribution index increases with the decrease in fractal dimension of the porous media. Capillary pressure curves of different types of rock samples were measured using a mercury intrusion technique. The values of pore size distribution index and fractal dimension were calculated. The relationship between the two parameters obtained from the experimental data was consistent with the relationship derived theoretically. This implies that the fractal dimension of porous media may be inferred directly using the Brooks-Corey capillary pressure model instead of the fractal model. The theoretical development in this study demonstrates that the Brooks-Corey capillary pressure model, once considered as empirical, has a solid theoretical base. This may be why the Brooks-Corey capillary pressure model works satisfactorily in many cases.