A spatial fractional seepage model for the flow of non-Newtonian fluid in fractal porous medium

In the present study, a fractional seepage model (FSM) is proposed for non-Newtonian fluid via spatial fractional derivative to characterize the non-local characteristics of the non-Newtonian fluid in space and the fractal attributes of the porous medium. The analytical expressions of the permeability and the resistance are derived, in which each parameter contains clear physical meaning. The comparison between the empirical equations and our model with respect to available experimental data verifies the predictive capability of the proposed model. In addition, this study makes the first attempt to bridge the relation between the fractional derivative order and the fractal dimension of tortuosity, and may reveal the correlation between the memory of the complex fluid and characteristic pattern of the microstructure.