Investigation of critical non-linear flow behavior for fractures with different degrees of fractal roughness

Non-linear flow behavior in rough fractures with shear dislocations is numerically investigated in this study with the validated multi-relaxation time lattice Boltzmann method. Fracture flow tests with different degrees of fractal roughness are simulated and the results show that the surface roughness has an inhibiting effect on fracture flow. With increasing roughness parameter, the effective transmissivity decreases accordingly. Deviation of fracture flow from the linear regime appears earlier for fractures with rougher surfaces and the non-linearity of fracture flow is enhanced with the tortuous flow-path and corner eddies during the closure process. The non-linearity of fracture flow was found to be anisotropic when applying the pressure gradient parallel and perpendicular to the shear direction. Though the anisotropic feature shows a non-monotonic trend during the closure process, it is enhanced with the increasing roughness parameter. Evaluation of the Forchheimer law in quantifying the nonlinear fracture flow is also conducted. The relative difference between the Forchheimer linear transmissivity and intrinsic linear transmissivity is about 1?3%. Assuming that the Forchheimer linear transmissivity is equal to intrinsic linear transmissivity, the linear pressure drop can be underestimated. Relating the non-linear parameters with the dimensionless effective hydraulic aperture, a new model is proposed to predict the critical hydraulic behavior of rough fractures.