Numerical study of scale effect on fluid flow through a rough fracture

Abstract

Scale effect on fluid flow and rock joint roughness remains uncertain. Using photogrammetry, the topography of a fracture surface was replicated. A 3D model was reconstructed for a 2 m × 1 m granite sample, extracting a 1 m × 1 m subsample. This model was duplicated and shifted a 350-micrometer along the Z-axis. To study scale effect, different samplesizes ranging from 5 cm × 5 cm to 100 cm × 100 cm were used for roughness analysis and fluid flow simulations in COMSOL Multiphysics. The pressure gradients ranged from 20 to 100 kPa/m, with intervals of 20 kPa/m. As the sample sizes increased, the roughness approached a Joint Roughness Coefficient (JRC) of 10, with no significant change observed beyond approximately30 cm in sample size. Fluid flow simulations showed a nonlinear relationship between pressure gradients and flow rates, following For chheimer equation. Notably, beyond 30 cm sample size, the hydraulic aperture and non-Darcy coefficient reached a relatively stable state.