Scale and size effects on fluid flow through self-affine rough fractures

A permeability estimation of a single rough fracture remains challenging and has attracted broad attention because of its fundamental importance. This study examines the effects of surface roughness on fracture flow and proposes a new, triple-effect permeability estimation model that takes surface and hydraulic tortuosity other than surface roughness factor (SRF) into account according to the functioning patterns. Due to the scale effect on hydraulic and surface tortuosities, it can also be reformulated into a scaling aperture-permeability equation for a self-affine fracture. Results indicate that tortuosity effects are scaled by 4(H-1) (H is the Hurst exponent) with the mean aperture and that the local SRF, as expected, is stationary at the measurement scale of the mean aperture. In addition, based on the scaling equation and the size effect of self-affine objects, flow regimes are examined and three flow regimes are then identified. Consequently, different permeability models for these regimes are established by fabricating fundamental and well-defined physical properties. The estimation results from these models are in excellent agreement with results from lattice Boltzmann simulations.