A permeability model for power-law fluids in fractal porous media composed of arbitrary cross-section capillaries

• A permeability model for power-law fluids in porous media is developed.
• The permeability is a function of fluid property and structure parameters of media.
• The effects of structure parameters on permeability and velocity are discussed.
• The average flow velocity is compared with existing macroscopic model.
• Our permeability model can be considered as an extension of Yu and Cheng’s model.

The fractal theory and technology has been applied to determine the flow rate, the average flow velocity, and the effective permeability for the power-law fluid in porous media composed of a number of tortuous capillaries/pores with arbitrary shapes, incorporating the tortuosity characteristic of flow paths. The fractal permeability and average flow velocity expressions are found to be a function of geometrical shape factors of capillaries, material constants, the fractal dimensions, microstructural parameters. The effects of the porosity, the tortuosity fractal dimension, material constants, and geometrical shape factors on the effective permeability are also analyzed in detail. To verify the validity of the present model, our proposed model is compared with the available macroscopic model and experimental data and there is good agreement between them.