A new capillary pressure model for fractal porous media using percolation theory

The capillary pressure-saturation relation in traditional models is obtained by representing porous medium as a bundle of capillary tubes. The effect of pore connectivity is ignored, which leads to the evident deviation frequently observed between the measured data and model prediction near the breakthrough pressure region. In the present work, a new fractal-percolation-based capillary pressure model is developed. The proposed model accounts for the characteristics of pore size distribution in fractal media, and is based on the percentage of pore volume rather than that of pore number in conventional percolation theory. In the new model, a simple and yet sufficiently accurate relation between the allowed and accessible saturations is applied near the threshold saturation. It results in a high-accuracy prediction of capillary pressure, especially near the breakthrough pressure region. The new model is validated by experimental data. Parameter sensitivity analysis and comparison with the results from conventional fractal theory are presented. This new model is an extension to the conventional fractal theory, as it is consistent when the threshold saturation is equal to zero.