A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks

An analytical expression is derived for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks based on fractal theory and technique. The proposed model relates the flow rate and the starting pressure gradient to the structural parameters of porous media and microstructural parameters of fractal-like tree networks, the yield stress and fractal dimensions of porous media and maximum mother diameter of randomly distributed fractal-like tree networks. The results show that the starting pressure gradient decreases with the increase of porosity of matrix material, fractal dimension for mother diameters, diameter ratio and permeability, and the starting pressure gradient increases with the increase of the length ratio and the yield stress. The model predictions from the present model for the starting pressure gradient are in good agreement with the available expression.

► We obtain the analytical expression for the starting pressure gradient in the dual-porosity medium. ► It is found that the starting pressure gradient depends on the structural parameters of dual-porosity media. ► Our model can reveal more physical mechanisms of the starting pressure gradient than the conventional model Eq. (1). ► The model predictions from our model are in good agreement with those from the available expression.