A fractal model for the starting pressure gradient for Bingham fluids in porous media

In this paper, we present a fractal model for the starting pressure gradient for Bingham fluids in porous media based on the fractal characteristics of pores in the media and on the capillary pressure effect. Every parameter in the proposed models has clear physical meaning, and the proposed model relates the starting pressure gradient of Bingham fluids to the structural parameters of porous media, the yield stress, the capillary pressure parameters and the fractal dimensions of porous media. The model predictions from the present model for the starting pressure gradient are in good agreement with the available expression Eq. (2). The results also show that at smaller radii (r¯<0.3mm) and low porosity (ϕ < 0.3), the capillary pressure has the significant influence on the starting pressure gradient in porous media and thus cannot be neglected. However, at high porosity, the starting pressure gradient is primarily produced by the shear stress and the contribution to the starting pressure gradient from the capillary pressure is negligible.