A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

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 similar to K-DT/(1+DT), where D-T 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.