Effect of fractal surface roughness and pressure gradient on the hydraulic behavior of fluid flow through a 3D single rough fracture

This study mainly aimed to numerically investigate the influence of fractal roughness and pressure gradient on the fluid flow through a three-dimensional (3D) single rough fracture with a constant mechanical aperture. To avoid confusion created by the Reynolds number caused by different definitions of characteristic length, the critical pressure gradient was utilized to characterize the onset of non-linear flow in rough fractures. Further, the effect of fractal dimension on the critical pressure gradient was also investigated. The rough fracture surfaces with different fractal dimensions are generated by an open source code SynFrac, and the COMSOL Multiphysics software package based on the finite element method was used to simulate the fluid flow through the generated 3D rough fracture model by solving the Navier-Stokes equations. For each case, Forchheimer's law was used to describe nonlinear flow and the numerical results show that the critical pressure gradient, ranging from 15.68 kPa/m to 1.50 kPa/m, decreases exponentially with the increase in fractal dimension. The results also show that the relationship between relative effective fracture aperture and pressure gradient can be fitted well by a power function. These results suggest that the non-linear flow appears earlier as the fractal dimension and pressure gradient increase.