Finite‐Size Scaling for the Permeability of Discrete Fracture Networks

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. Plain Language Summary Knowledge of the permeability of fractured rocks is critical for many geo‐engineering applications (such as deep geological disposal of radioactive wastes, mining and dam engineering) and environmental problems (such as ground water and pollutant transport). The influence of fracture attributes (e.g., orientations, sizes, and apertures) on hydraulic properties of rock masses is significant, but the task of correlating the permeability to individual fracture data is still a challenging one with remarkable knowledge gaps. In this letter, instead of using analytical solutions, we develop a finite‐size scaling (FSS) function, inspired by the percolation theory in statistic physics, to describe the permeability of fracture networks. The universality of the scaling function is validated by massive simulation data which cover a wide range of fracture attributes. Results demonstrate that, regardless of how domain sizes and fracture attributes change, the scaling for the permeability is of an invariant form, after considering the finite‐size effect. Our findings motivate further studies of applying the FSS function at the field scale and improve on the information that earth scientists can obtain from fracture statistics. Key Points A finite‐size scaling hypothesis for the permeability of discrete fracture networks (DFNs) is formulated with several dimensionless quantities Numerous DFN representations and flow simulations are implemented to validate the scaling hypothesis The scaling is found universal for different DFNs wit