Influence of spatial correlation of fracture centers on the permeability of two-dimensional fracture networks following a power law length distribution

Observations of outcrops of fractured media show that fractures are correlated at all scales of the medium and that there are also fractures of sizes ranging from the microscale to the macroscale. Recent studies have shown that the correlation pattern is often a fractal characterized by its dimension D-c and that the fracture length distribution is a power law of characteristic exponent -a. We study the influence of these long-range heterogeneities on the equivalent medium permeability. Fracture correlation and fracture length are present at all scales of the medium and may thus influence the hydraulic properties and their scaling at all scales. We have numerically investigated the effect of the fractal correlation pattern and of the power law length distribution on the equivalent permeability of fracture networks. The correlation and the length distribution have opposite effects on connectivity and permeability. Increasing correlation lets connectivity and permeability decrease and conversely for the length distribution. In most cases, one of the characteristics (i.e., length or correlation) supersedes the other. There is only a small area defined by a > 2 and a less than or equal to D-c + 1 where both characteristics have a simultaneous influence on permeability. In this area the influence of the correlation remains low, more precisely a scale increase of at least 5 orders of magnitude is required to produce a permeability increase of 1 order of magnitude. Although the correlation pattern does not have much influence on the equivalent permeability, its influence on the flow pattern increases from negligible for networks at threshold to important for dense networks.