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

• Main Authors: Peijie Yin, Can Zhao, Jianjun Ma, Linchong Huang
• Format: Article
• Language: English
• Published: MDPI AG 2019-05-01
• Series: Water
• Subjects: fluid flow; fracture; lattice Boltzmann method; permeability; <i>Z</i>₂
• Online Access: https://www.mdpi.com/2073-4441/11/5/1081

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 (&#963;). 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 (<i>Z</i>₂), and an equation has been proposed to estimate the permeability based on the aperture and <i>Z</i>₂ of the fracture. The numerical simulations were further conducted on fluid flow though synthetic fractures with a wide range of D and &#963;. In order to unify the parameter that characterizes the roughness, <i>Z</i>₂ was obtained for each synthetic fracture, and the corresponding relationship between permeability, aperture and <i>Z</i>₂ was analyzed. Meanwhile, it was found that the fluid flow behaves differently with different ranges of <i>Z</i>₂ and the critical point was found to be <i>Z</i>₂ = 0.5. Based on extensive study, it was concluded that <i>Z</i>₂ is a generic parameter characterizing the roughness, and the proposed equation could be used to predict the permeability for fluid flow in fracture.