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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.

A novel analytical model is derived based on fractal geometry theory to characterize the permeability of power-law fluids through fractured porous media with fractal asperities on surfaces. The proposed model is expressed as a function of structure parameters of fractured porous media, fractal dimensions for porous matrix and for fracture as well as the index $n$ of power-law fluid behavior. The influences of these parameters on the permeability are analyzed in detail. It is found that the relationship between permeability and roughness exhibits nonlinear characteristics. A higher power-law fluid behavior index significantly affects the reduction rate of permeability with relative roughness. Moreover, permeability is sensitive to the perturbation due to the rate of aperture to length. The proposed fractal model can clearly reveal more physical mechanisms for power-law fluid in fractured porous media than the existing models. Compared with the experimental data available in the literature, the validity of model predictions is verified.