Permeability of three-dimensional fracture networks

Abstract

The permeability of a three-dimensional network of polygonal fractures is determined by triangulating the network and solving the two-dimensional Darcy equation in each fracture. The general triangulation methodology and the numerical solution are presented. Networks of regular hexagonal fractures are detailed; finite-size scaling is used to analyze the data relative to the percolation threshold, but the conduction exponent $t$ is found close to its classical value in three dimensions; for large fracture densities, permeability is shown to tend towards the mean-field model of Snow [Water Resour. Res. 5, 1273 (1969)]. Finally, the influence of the shape of the fracture is studied and can be rationalized by means of the excluded volume.