Hydraulic properties of two-dimensional random fracture networks followinga power law length distribution 1. Effective connectivity

Natural fracture networks involve a very broad range of fractures of variab le lengths and apertures, modeled, in general, by a power law length distri bution and a lognormal aperture distribution. The objective of this two-par t paper is to characterize the permeability variations as well as the relev ant flow structure of two-dimensional isotropic models of fracture networks as determined by the fracture length and aperture distributions and by the other parameters of the model (such as density and scale). In this paper w e study the sole influence of the fracture length distribution on permeabil ity by assigning the same aperture to all fractures. In the following paper [de Dreuzy et al., this issue] we study the more general case of networks in which fractures have both length and aperture distributions. Theoretical and numerical studies show that the hydraulic properties of power law leng th fracture networks can be classified into three types of simplified model . If a power law length distribution n(l) similar to l(-a) is used in the n etwork design, the classical percolation model based on a population of sma ll fractures is applicable for a power law exponent a higher than 3. For a lower than 2, on the contrary, the applicable model is the one made up of t he largest fractures of the network. Between these two limits, i.e., for a in the range 2-3, neither of the previous simplified models can be applied so that a simplified two-scale structure is proposed. For this latter model the crossover scale is the classical correlation length, defined in the pe rcolation theory, above which networks can be homogenized and below which n etworks have a multipath, multisegment structure. Moreover, the determinati on of the effective fracture length range, within which fractures significa ntly contribute to flow, corroborates the relevance of the previous models and clarifies their geometrical characteristics. Finally, whatever the expo nent a, the sole significant scale effect is a decrease of the equivalent p ermeability for networks below or at percolation threshold.