PERMEABILITY OF 3-DIMENSIONAL FRACTURE NETWORKS

The permeability of a three-dimensional network of polygonal fractures is determined by triangulating the network and solving the two-dimens ional Darcy equation in each fracture. The general triangulation metho dology and the numerical solution are presented. Networks of regular h exagonal fractures an detailed; finite-size scaling is used to analyze the data relative to the percolation threshold, but the conduction ex ponent t is found close to its classical value in three dimensions; fo r 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 rati onalized by means of the excluded volume.