Permeability and percolation of anisotropic three-dimensional fracture networks

Abstract

The percolation properties and permeability of a group of anisotropic three-dimensional fracture networks are studied numerically. Finite-size scaling is used to extrapolate the percolation thresholds of infinite networks in three spatial directions, i.e., X , Y , and Z directions. The influence of the angular dispersion parameter of fracture orientations on percolation thresholds is analyzed. In this analysis, we considered a family of fractures in a three-dimensional space that are oriented around the Z axis based on the Fisher distribution. We revealed that increased anisotropy leads to decreased percolation thresholds in both X and Y directions, and in these two directions percolation thresholds in anisotropic networks demonstrate a declining trend as anisotropy goes up. However, in the Z direction the trend is the opposite. The fracture networks are triangulated via an advancing front technique and the macroscopic permeability of the networks is determined by solving the two-dimensional Darcy equation in each fracture. We found that the macroscopic permeability in the X and Y directions is higher than the associated permeability of isotropic fracture networks, and this property for anisotropic networks in the Z direction is lower compared with that of the isotropic case. Furthermore, as the anisotropy of networks increases the differences become more remarkable.

Fractal analysis of permeability of dual-porosity media embedded with random fractures

“…The orientations of fractures in the medium are not uniform, but usually with a preferred orientation. It has been shown that the averaged/mean angle, the fracture azimuth and fracture dip of all fractures are constant [50,51], for instance, Massart et al [52] showed a mean dip of 70°and mean N-S orientation from the total number of 1878 fractures. Based on practical situation, in this work, the mean dip of fractures between fracture orientations and fluid flow direction, and the mean azimuth of fractures perpendicular to fluid flow direction are assumed to be h and a, respectively, as shown in Fig.…”

Three‐dimensional resistor network modeling of the resistivity and permeability of fractured rocks

“…The observation that fracture networks demonstrate a percolation threshold, below which the network is disconnected, has been noted in previous studies, most of which relate to fluid flow. A commonly applied method is Discrete Fracture Network (DFN) modeling, in which all the fluid flow is assumed to occur through the fractures [e.g., Mourzenko et al , ; Khamforoush et al , ; Ahmed Elfeel et al , ]. These studies have demonstrated that increasing the density of fractures in a network, which are controlled by the parameters α and a (section 2.3), increases both the probability of percolation in a fault network and its permeability.…”

“…This work also builds on many previous studies by considering the permeability and resistivity of the rock matrix in the modeling. In many previous DFN and resistor network models [e.g., Long and Witherspoon , ; Berkowitz , ; Bahr , ; Mourzenko et al , ; Khamforoush et al , ], it has been assumed that the rock matrix is impermeable and infinitely resistive, so when the fracture network is not fully connected the permeability (and resistivity) is zero. However, several authors [e.g., Paluszny and Matthai , ; Ahmed Elfeel et al , ; Kirkby et al , ] have noted that significant fluid and current can pass through the rock matrix.…”

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

“…Understanding the hydraulic properties of 3-D DFNs would help to gain an insight into the real flow mechanism of fluid, because the 2-D DFNs, which are cut planes of the 3-D models, tend to underestimate the equivalent permeability (Min et al 2004;Lang et al 2014). The permeability of 3-D fracture networks with complex topology is commonly determined using a boundary element method (BEM; Andersson and Dverstorp 1987), and a finite volume method (FVM; Koudina et al 1998;Khamforoush et al 2008;Mourzenko et al 2011). Hsieh and Neuman (1985) proposed a method to calculate the 3-D hydraulic conductivity tensor of an anisotropic medium, and analyzed the effect of planar no-flow and constant-head boundaries on the response.…”