Prediction of relative permeability from capillary pressure based on the fractal capillary bundle model

The accurate prediction of relative permeability is one of the most important issues in the study of multiphase flow in porous media and is involved in many fields, such as geothermal energy development and petroleum engineering. Traditional models such as the Purcell model and Burdine model for predicting relative permeability from capillary pressure usually assume that the wetting phase (WP) flows in small pores and that the nonwetting phase (NWP) flows in large pores, which is a limiting assumption, such that these models cannot describe the process of WP being displaced by NWP. In this study, we propose a generalized theoretical model for calculating relative permeability based on the fluid distribution characteristics and the fractal capillary bundle model. The relative location alpha of the interface between NWP and WP is introduced to characterize the transport of the two-phase interface in porous media. The developed model was validated with relative permeability experimental data of gas-water/oil and compared with the Li model and the Brooks-Corey model. The comparison results show that the new model provides an improved match to experimental data than the Li model and the Brooks-Corey model. The sensitivity analysis results of the model show that tortuosity and pore size distribution play a key role in predicting relative permeability from the capillary pressure curve. The relative permeability of wetting phase decreases significantly with increasing fractal dimension of tortuosity and fractal dimension of pore size distribution. The effect of parameter alpha, which reflects fluid transport characteristics, on relative permeability of wetting phase is more pronounced in porous media with complex structures and low/ ultralow permeability.