Analytical derivation of Brooks–Corey type capillary pressure models using fractal geometry and evaluation of rock heterogeneity

The Brooks–Corey type capillary pressure models (three models on the relationship between capillary pressure and saturation) were derived theoretically from fractal modeling of porous media. The pore size distribution index is coupled with fractal dimension. The pore size distribution index increases with the decrease in fractal dimension. Capillary pressure curves of different rock samples were measured using a mercury intrusion technique. The values of fractal dimension were calculated using three fractal models and the results were compared. The heterogeneity of rock was evaluated using fractal dimension. The consistency between fractal dimension and the frequency graph of pore size distribution was examined. The theoretical derivation demonstrated that the three fractal models are correlated. Sensitivity analysis data showed that the accuracy in estimating irreducible wetting-phase saturation is essential to obtain the power-law relationship between the capillary pressure and the normalized wetting-phase saturation.