Permeability and percolation of anisotropic three-dimensional fracture networks

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.