Fractal Analysis of Shear-thinning Fluid Flow through Porous Media

Year 2017, Volume: 12 Issue: 2, 1 - 21, 01.10.2017

Fethi Kamışlı

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.

Keywords

Shear-thinning fluid, Porous media, Packed bed, Permeability, Fractal modeling

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