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

Abstract

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.

A Systematic Investigation Into the Control of Roughness on the Flow Properties of 3D‐Printed Fractures

“…Near linear relationships (R 2 = 0.79-0.98) between JRC and k f are seen in FR#1-FR#5, with this trend becoming exponential when JRC > 6 (FR#6-FR#7; Figure 4). Considering laminar flow, as investigated here, numerical approaches suggest a variety of JRC-k f correlations, from near-linear decreases (e.g., Crandall, Bromhal, & Karpyn, 2010;Yin et al, 2019) to near-linear increases (e.g., Rasouli & Hosseinian, 2011), depending on aperture size and asperity arrangement. We find linear JRC-k f relations to be valid only in smoother fractures (JRC < 5.5), suggesting that flow properties not captured in these models may exist.…”

Hygrothermal simulation and risk evaluation - A literature review and assessment of the applicability of the Lattice Boltzmann Method to derive the influence of convection on moisture behaviour in building components

“…HAM-simulations), which are generally used in building physics, hasn't been found. When investigating LBM for porous media simulation, it was seen that a possibility to form such a coupling would be the deduction of parameters on the meso-scale which later can be applied to the simulations on the macro-scale, where Sousa and Nabovati (2008) [3] and Yin et al (2019) [56] show very promising applications which could be investigated in future research.…”

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

“…Yin et al [32] investigated numerically the fluid flow through rough fractures using the lattice Boltzmann method. The latter was shown to be an effective tool to solve the fluid flow problem with a complex boundary condition at desirable accuracy.…”