A fractal analysis of permeability for power-law fluids in porous media

A fractal analysis of permeability for power-law fluids in porous media is presented based on the fractal characters of pore size distributions and tortuous flow paths/streamlines in the media. The proposed permeability model for power-law fluids in porous media is expressed as a function of the fractal dimensions of pore size distributions and tortuous flow paths/streamlines, porosity and microstructural parameters, as well as power exponent, and there is no empirical constant in the proposed model and every parameter in the model has clear physical meaning. The results predicted by the present fractal permeability model show that the model predictions (as the power exponent is 1) are in agreement with the available experimental data, and the predicted permeabilities (as the power exponent is not equal to 1) increase with the power exponent, which is also consistent with the physical situation.