A more generalized model for relative permeability prediction in unsaturated fractal porous media

Abstract

Although lots of models for relative permeability prediction have been developed in literature, the effect of pore geometric tortuosity on relative permeability has not been well discussed, as usually the tortuosity of pores with various sizes is assumed the same. However, there is a high possibility that tortuosity is unequal and increases with the decrease in pore size. A new and more generalized analytical model for relative permeability prediction has been developed based on the fractal characteristics of pore size distribution (PSD) and tortuosity in porous media. The analytical expressions of relative permeability for wetting phase and nonwetting phase have been derived, which are the function of normalized wetting phase saturation, PSD fractal dimension, tortuosity fractal dimension and the ratio of the entry capillary pressure to the maximum capillary pressure. The studies show that the increasing PSD fractal dimension and tortuosity fractal dimension can significantly reduce wetting phase relative permeability, but the increase in nonwetting phase relative permeability is insignificant. The developed model has been validated with relative permeability experimental data and compared with other classic relative permeability models. The comparison results demonstrate the reliability of the relative permeability model developed in this paper.