Fractal analysis of Casson fluid flow in porous media

Fractal models for flow rate, velocity, starting pressure gradient and effective permeability for Casson fluid in porous media are proposed based on the fractal properties of porous media and capillary model. The proposed models are expressed as functions of fractal dimension, porosity, maximum pore size and representative length of porous media. All parameters in the proposed expressions have clear physical meaning, and the proposed models relate the properties of Casson fluid to the structural parameters of porous media. The velocity, starting pressure gradient and effective permeability versus different parameters are discussed, and the analytical expressions reveal the physical principles for flow velocity, starting pressure gradient and effective permeability in porous media.