Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture

[1] Field observations have revealed that the diffusion properties of fractured materials are strongly influenced by the presence of fractures. Using power law fracture length and fracture permeability distributions currently observed on natural fractured networks, we model the equivalent permeability of two- dimensional (2D) discrete fracture networks by using numerical simulations and theoretical arguments. We first give the dependence of the network equivalent permeability, obtained at the scale of the network, on the characteristic power law exponents of the fracture length and fracture permeability distributions. We especially show that the equivalent permeability depends simply on the geometrical mean of the local fracture permeability distribution. Such networks are characterized by an increase of permeability with scale without limitations, provided that the fracture length and fracture permeability distributions are broad enough. Although a correlation length cannot be systematically defined, the flow structure is still characterized by simple properties. The flow is either extremely channeled in one dominant path or distributed in several separated structures. We show finally that the observed scale effects and flow structure are very different from the one obtained in the lognormal fracture permeability distribution case.