Impact of scaling break and fracture orientation on effective permeability of fractal fracture network

Abstract

Fractures and fracture networks determine the permeability of many natural rocks. In this study, new solutions are developed to calculate the effective permeability of fractal fracture network with non-universal scaling of fracture aperture and trace length. One component of the permeability tensor is derived by assuming that the hydraulic gradient is perpendicular to the trace direction. A new solution is also derived to examine the reduction in the effective permeability of fracture network due to the influence of random fracture orientation. The fracture lengths in the network are assumed to follow the fractal scaling law. The orientation dispersion of factures in the fracture network varies according to the Fisher distribution. The effective permeability is derived by treating the fractal fracture network as a porous medium and using Darcy’s law. Results demonstrate that the effective permeability decreases with the scaling exponent before the break when the scaling break occurs early. However, the effective permeability increases with the scaling exponent before the break if the scaling break occurs late. The effective permeability increases with the scaling exponent after the break. The extent of increase varies with the location of the scaling break. If the scaling break occurs early, the increase in the effective permeability is more significant. The effective permeability of fractal fracture network increases with the location of scaling break. The reduction in the effective permeability due to fracture orientation dispersion varies from 2/3 to 0 depending on the degree of orientation dispersion as quantified by the precision parameter.