Fractal analysis of permeabilities for porous media

A fractal analysis of permeabilities for porous media, both saturated and unsaturated, is presented based on the fractal nature of pores in the media. Both the fractal-phase permeability and the fractal relative permeability are derived and found to be a function of the tortuosity fractal dimension, pore-area fractal dimension, phase fractal dimension, saturation, and microstructural parameters. The proposed models for permeabilities-both the phase permeability and the relative permeability-do not contain any empirical constant. The validity of the present analysis is verified by a comparison with the existing measurements, and excellent agreement between the model predictions and experimental data is found. In addition, the present work reveals that the relative permeability depends not only on saturation but also on the two fractal dimensions, pore fractal dimension (at porosity greater than 0.90), and tortuosity fractal dimension, which characterize the fractal characters of capillaries in porous media. The two fractal dimensions may be the two of the important mechanisms affecting the relative permeability in porous media, and this is a supplement to the available conclusion on relative permeability. (C) 2004 American Institute of Chemical Engineers