A fractal model for the starting pressure gradient for Bingham fluids in porous media embedded with randomly distributed fractal-like tree networks |
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Authors: | Shifang Wang Boming Yu Qian ZhengYonggang Duan Quantang Fang |
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Institution: | a School of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074 Hubei, PR China b School of Physics and Electronic Information, Hubei University of Education, 29 Optical Valley No. 2 Road, Wuhan East Hi-Tech Zone, Wuhan, 430205 Hubei, PR China c State Key of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, 8 Xindu Road, Chendu, 610500 Sichuan, PR China |
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Abstract: | 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. |
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Keywords: | Porous media Fractal-like tree network Bingham fluids Permeability Starting pressure gradient |
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