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

Water

Linchong Huang¹  Jianjun Ma²  Peijie Yin³  Can Zhao³ 

[1] School of Aeronautics and Astronautics, Sun Yat-Sen University, Guangzhou 510006, China;School of Civil Engineering, Sun Yat-Sen University, Zhuhai 519082, China;School of Highway, Chang’an University, Xi’an 710064, China;

关键词: fluid flow;    fracture;    lattice Boltzmann method;    permeability;    Z₂;   

DOI  :  10.3390/w11051081

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown