Permeabilities of unsaturated fractal porous media

A fractal analysis of permeabilities for unsaturated fractal porous media is presented based on the fractal natures of pores in the media. Both the fractal phase permeabilities and the fractal relative permeabilities are derived and found to be a function of fractal dimension for tortuosity, pore area fractal dimension, fractal dimensions for wetting and non-wetting phases, saturation and microstructural parameters. The proposed fractal models for permeabilities, both the phase permeabilities and the relative permeabilities, do not contain any empirical constant. To verify the validity of the present analysis, the predicted relative permeability data are compared with those of the existing measurements, and excellent agreement between the model predictions and existing experimental data is found.