Quantitative characterization of single-phase flow through rough-walled fractures with variable apertures

Fluid flow through rock media is highly significant in underground water management, the geothermal recovery process, and various underground engineering applications. Fractures have a critical effect on the fluid flow through low-permeability rocks since they serve as the major flow channels in the rock formation. Consequently, the evaluation of fracture permeability is crucial to many engineering applications, such as the geothermal recovery process, exploitation of hydrocarbon resources, and various underground engineering applications. However, fluid flow through rough fractures is complex under the effects of rough profiles and variable apertures. The variation of fracture apertures causes the nonlinear distribution of the pressure along the fracture and thus intensifies the difficulties of studying the flow in fractures. In this study, variable-aperture fractures were simplified as axisymmetric fractures using the Weierstrass-Mandelbrot function. To address the nonlinear distribution of pressure caused by aperture variations, a method is proposed to segment fractures with variable lengths by considering the weights of fracture apertures. With the segmented results, we evaluated the permeability of rough fractures using a modified local law. The evaluation results aligned with the lattice Boltzmann simulation results. Finally, combining the analytical solution of flow through asymmetric fractures with sinusoidal profiles, the proposed methods were thereby validated.