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Open AccessArticle

A Unified Equation to Predict the Permeability of Rough Fractures via Lattice Boltzmann Simulation

by Peijie Yin 1, Can Zhao 1, Jianjun Ma 2,4 and Linchong Huang 3,4,*
School of Highway, Chang’an University, Xi’an 710064, China
School of Civil Engineering, Sun Yat-Sen University, Zhuhai 519082, China
School of Aeronautics and Astronautics, Sun Yat-Sen University, Guangzhou 510006, China
Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519082, China
Author to whom correspondence should be addressed.
Water 2019, 11(5), 1081;
Received: 28 April 2019 / Revised: 19 May 2019 / Accepted: 21 May 2019 / Published: 24 May 2019
In this paper, the fluid flow through rough fractures was investigated via numerical simulation based on the lattice Boltzmann method (LBM). The accuracy of LBM was validated through the numerical simulation of the parallel plate model and the verification of the mass conservation of fluid flow through rough fracture. After that, the effect of roughness on fluid flow was numerically conducted, in which, the geometry of fractures was characterized by the joint roughness coefficient (JRC), fractal dimension (D) and standard deviation (σ). It was found that the JRC cannot reflect the realistic influence of roughness on the permeability of single fracture, in which, an increase in permeability with increasing JRC has been observed at the range of 8~12 and 14~16. The reason behind this was revealed through the calculation of the root mean square of the first derivative of profile (Z2), and an equation has been proposed to estimate the permeability based on the aperture and Z2 of the fracture. The numerical simulations were further conducted on fluid flow though synthetic fractures with a wide range of D and σ. In order to unify the parameter that characterizes the roughness, Z2 was obtained for each synthetic fracture, and the corresponding relationship between permeability, aperture and Z2 was analyzed. Meanwhile, it was found that the fluid flow behaves differently with different ranges of Z2 and the critical point was found to be Z2 = 0.5. Based on extensive study, it was concluded that Z2 is a generic parameter characterizing the roughness, and the proposed equation could be used to predict the permeability for fluid flow in fracture. View Full-Text
Keywords: fluid flow; fracture; lattice Boltzmann method; permeability; Z2 fluid flow; fracture; lattice Boltzmann method; permeability; Z2
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Yin, P.; Zhao, C.; Ma, J.; Huang, L. A Unified Equation to Predict the Permeability of Rough Fractures via Lattice Boltzmann Simulation. Water 2019, 11, 1081.

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