Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities.

The asymptotic behaviors of the permeability of isotropic fracture networks at small and large densities are characterized, and a general heuristic formula is obtained which complies with the limiting behaviors and accurately predicts the permeability of these networks over the whole density range. Theses developments are based on extensive numerical calculations and on theoretical arguments inspired by the examination of the flow distribution in the fractures at large densities. Then, the results are extended to anisotropic networks with a Fisher distribution of the fracture orientations, to polydisperse networks, and to fractured porous media. Finally, guidelines are provided for the practical evaluation of the required parameters from typical field data. A summary of the results is given in Table III.