A Flow Resistance Model for Self-Affine Fractures with Variable Apertures Based on Optimized Aperture-Weighted Segmentation

Predicting fluid flow through rough fractures is critical for subsurface engineering, yet conventional models relying on equivalent hydraulic aperture often fail to capture the complex effects of aperture heterogeneity and spatial correlation. This study proposes a novel flow resistance framework that directly characterizes fracture permeability without assuming uniform apertures. We introduce an aperture-weighted segmentation method to identify flow bottlenecks and derive an effective hydraulic aperture formula incorporating the Hurst exponent to quantify surface roughness and spatial variability. The model is validated against high-fidelity lattice Boltzmann simulations across diverse synthetic fracture geometries, demonstrating superior accuracy compared to classical cubic law and existing empirical corrections. Results show that flow resistance, rather than permeability, serves as a more fundamental descriptor for irregular fractures, as it inherently accounts for localized constrictions and tortuosity. The proposed approach bridges the gap between micro-scale aperture statistics and macro-scale flow behavior, offering a physically consistent and computationally efficient tool for modeling fractured media. This work advances the understanding of structure–flow relationships in rough fractures and provides a robust alternative to traditional aperture-based parameterizations in reservoir simulation, geothermal energy extraction, and groundwater remediation applications.