Finite‐Size Scaling for the Permeability of Discrete Fracture Networks

Abstract

Abstract We formulate a finite‐size scaling hypothesis to predict the global permeability of fracture networks. To validate the hypothesis, numerous discrete fracture networks are generated, and the permeability is numerically calculated. Results suggest that the dimensionless permeability, scaled by moments of local conductivity and fracture sizes and corrected by two stereological ratios, can capture variations in fracture attributes (orientations, sizes, and apertures). The universal form obtained in this study can also explain the contradictory observations where the permeability decreases or increases with the domain size of fracture networks. We show that how a clear transition point, where the permeability does not change with the domain size, is obtained from this universal form. This study provides a solid theoretical foundation to understand the connection between fracture attributes and field‐scale hydraulic properties.

Keywords

• discrete fracture networks
• permeability
• scaling
• percolation