Hydraulic properties of two‐dimensional random fracture networks following a power law length distribution: 1. Effective connectivity

Abstract

Natural fracture networks involve a very broad range of fractures of variable lengths and apertures, modeled, in general, by a power law length distribution and a lognormal aperture distribution. The objective of this two‐part paper is to characterize the permeability variations as well as the relevant 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 we study the sole influence of the fracture length distribution on permeability 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 length fracture networks can be classified into three types of simplified model. If a power law length distributionn(l) ∼l−ais used in the network design, the classical percolation model based on a population of small fractures is applicable for a power law exponentahigher than 3. Foralower than 2, on the contrary, the applicable model is the one made up of the largest fractures of the network. Between these two limits, i.e., forain 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 percolation theory, above which networks can be homogenized and below which networks have a multipath, multisegment structure. Moreover, the determination of the effective fracture length range, within which fractures significantly contribute to flow, corroborates the relevance of the previous models and clarifies their geometrical characteristics. Finally, whatever the exponenta, the sole significant scale effect is a decrease of the equivalent permeability for networks below or at percolation threshold.