Fractal Analysis of Robertson-Stiff Fluid Flow in Porous Media

The Robertson–Stiff (RS) fluid is the representative fluid which may be reduced to Bingham, power-law and Newtonian fluids under appropriate conditions. We present fractal models for the flow rate, velocity, starting pressure gradient and effective permeability for RS fluids in porous media based on the fractal characteristics of porous media and capillary models. The proposed models are expressed as functions of the fractal dimensions, porosity, maximum pore size and the representative length of the porous media. Every parameter in the proposed expressions has clear physical meaning, and the proposed models relate the flow characteristics of the RS fluids to the structural parameters of the porous media. The analytical expressions reveal the physical principles of RS fluid flow in porous media.