Characterization of Size-Dependent Inertial Permeability for Rough-Walled Fractures

Inertial permeability is a critical parameter that quantifies the pressure loss caused by inertia in fluid flow through rough-walled fractures, described by the Forchheimer equation. This study investigates the size effect on the inertial permeability of rough-walled fractures and establishes a characterization model for fractures of varying sizes. Numerical simulations are conducted on five large-scale fracture models (1 m × 1 m) by resolving the Navier–Stokes equations. Smaller models are extracted from these large-scale fracture models for detailed size-dependent analysis. The results show that the peak asperity height (ξ), asperity height variation coefficient (η), and the fitting coefficient of the aperture cumulative distribution curve (C) significantly affect inertial permeability. Specifically, as ξ increases, the fluid flow experiences greater resistance, resulting in a reduction of inertial permeability. Similarly, a larger η corresponds to more variable asperity heights, further decreasing permeability. In contrast, a higher C value, indicating a more uniform aperture distribution, increases inertial permeability by facilitating smoother fluid flow. Quantitatively, the relationship between inertial permeability and fracture size follows a power law, with the sensitivity to roughness parameters diminishing as fracture size increases. This characterization model provides a method for scaling from laboratory-scale to field-scale fractures, offering practical implications for hydraulic engineering and subsurface fluid flow management.