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Most classical predictive models of relative permeability conceptualize the pores in porous media as assemblies of uniform capillary tubes with different sizes. However, this simplification may overestimate the transport capacity of porous media due to overlooking the effects of the pore nonuniformity. This study presents a simple way to quantify the effect of the nonuniformity of pore cross section on the transport characteristic of unsaturated porous media. The way is based on the index relationship between the porosity of a newly defined reference cross section and that of porous media, which satisfies the intrinsic constraints for the nonuniform porosity of cross sections in porous media. Moreover, the index factor can be captured by a newly defined parameter, called the nonuniformity factor, which is used to establish an extended Darcy’s law. Based on these, a fractal-based continuous analytical model and a fractal-based Monte Carlo model of relative permeability as well as a permeability-porosity model are established. Experimental data of five wetting-nonwetting phase systems, including the water-air, water-steam, water-nitrogen, water-oil, and oil-gas systems, are selected to assess the performance of the proposed model. The results confirm the proposed model’s capacity in capturing the transport properties of various porous media. It is found that the nonuniformity of pores can significantly increase the resistance of fluid flow and thus reduce the transport capacity of porous media.

Relative Permeability of Porous Media with Nonuniform Pores