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.
In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.
