On fluid flow regime transition in crossed rough rock fractures

Understanding the fluid flow behavior in crossed fractures is of great significance to fluid flow through the natural rock fracture system. To investigate the linear and nonlinear regime transitions of the fluid flow in crossed rock fractures, theoretical analyses and numerical simulations were first performed to identify the factors that cause hydraulic pressure head loss. Then, their influence on the onset of nonlinear fluid flow is further evaluated by performing fluid dynamic computation on crossed rock fractures of different configurations. The parameter identification shows that the fracture surface roughness, aperture, scale, and intersection angle are key factors influencing the fluid flow regime transition. Further single factor analyses indicate that the linear term coefficient A, nonlinear term coefficient B of the Forchheimer equation, and the critical hydraulic gradient Jc can be correlated with these parameters via different polynomial formulas. Compared with the other three parameters, further parameter sensitivity analyses reveal that the fracture aperture plays the most important role in the evolution of A, B, and Jc. Finally, a prediction model, where the critical hydraulic gradient Jc, the linear term coefficient A, and the nonlinear term coefficient B of the Forchheimer equation are determined via the fracture aperture, roughness, surface roughness, aperture, scale, and intersection angle, was proposed by a multivariate regression algorithm. The proposed model was verified by comparing the predicted A, B, and Jc with the results of numerical simulation and experiment on transparent crossed rock fracture replicas with 3 D printing technology. The proposed prediction model can be used to determine the critical hydraulic gradient to demark the fluid regime in crossed rock fractures and helps govern equation determination for the description of either linear or nonlinear fluid flow.