Fractal Analysis of Shear-thinning Fluid Flow through Porous Media

Abstract

The fractal capillary models for calculating the volumetric flow rates and permeabilities for Newtonian, power-law, Ellis and Bingham fluids in packed beds are developed by considering fractal nature of the tortuous capillary. The fractal permeability models for Newtonian and non-Newtonian fluids are found to be a function of the tortuosity fractal dimension, the pore-area fractal dimension, sizes of particles and clusters, the effective porosity and the flow behavior of a non-Newtonian fluid. The volumetric flow rate of each fluid as a function of pressure drop are calculated from both the converging-diverging duct approach and the derived expressions in order to compare two models with one another. In addition, hydraulic conductivity is also obtained in terms of the fractal scaling parameters. The volumetric flow rates of shear-thinning fluids, including power-law and Ellis fluids decrease with increasing the tortuosity fractal dimension. It is found that the fractal capillary model for the Newtonian and the Ellis fluids is in good agreement with the converging-diverging duct approach for the considered values of the tortuosity fractal dimension.