C. Darcel

Flow in multiscale fractal fracture networks

Abstract The paper aims at defining the flow models, including equivalent permeability, that are appropriate for multiscale fracture networks. As a prerequisite of the flow analysis, we define the scaling nature of fracture networks that is likely quantified by power-law length distributions whose exponent fixes the contribution of large fractures versus small ones. Despite the absence of any characteristic length scale of the power-law model, the flow structure appears to contain three length scales at the very maximum: the connecting scale, the channelling scale, and the homogenization scale, above which the equivalent permeability tends to a constant value. These scales, including their existence, depend on the fracture length distribution and on the transmissivity distribution per fracture. They are basic in defining the flow properties of fracture networks.

A note on the angular correction applied to fracture intensity profiles along drill core

We derive the angular correction that has to be applied to borehole fracture intensities to recover the actual three-dimensional distribution when the fracture networks have a length distribution. We assume that the fracture intensity is calculated from the fractures that fully transect the core. Because of the length distribution, the classical Terzaghi correction, which involves the cosine of fracture dip, is no longer valid. Solutions have been calculated in the specific case of fractal fracture networks with power law length distribution. We show that the Terzaghi correction may significantly overestimate the frequency of fractures subparallel to the borehole. The correction procedure proposed here was tested on a fracture database recorded at a study site for a repository of spent nuclear fuel located in SE Sweden, with three outcrop maps and three boreholes. A consistency between the dip distributions of outcrops and boreholes was achieved when applying the angular correcting term calculated with the power law length distribution deduced from outcrop maps.