The Effect of Fracture Surface Roughness and Mechanical Aperture on the Onset of Nonlinear Flow Behaviors in 3D Self-Affine Rough Fractures

Equivalent hydraulic aperture and fracture surface roughness are two significant factors affecting the fluid flow behaviors in rock fractures. To understand the role of fracture surface roughness and aperture in the fluid flow through 3D self-affine rough fractures, roughness fracture surfaces with joint roughness coefficients equal to 2.5, 7.5, 12.5, and 17.5 were established, and the Navier–Stokes equation was used to compute the fluid flow in these 3D self-affine rough fractures with a mechanical aperture increase from 0.2 mm to 0.8 mm with a gradient of 0.2 mm. The results show that when the fracture mechanical aperture is 0.2 mm, the impact of fracture surface roughness on fluid flow is considerable, while this effect decreases obviously with the increase of fracture mechanical aperture. Comparing the permeability obtained by the Navier–Stokes equation with the cube law under different hydraulic gradients, we found that their deviation increased with the increase of hydraulic gradients. This allows for the definition of a critical hydraulic gradient (Jc), below which the permeability can be properly predicted using the cubic law for its simplicity, and above which Forchheimer’s equation should be applied, and Forchheimer’s coefficients A, B, and Jc can be calculated by the prediction equations established in this study.