A theoretical model and experimental investigation of fluid flow in granite rough fracture

The fissure serves as the primary flow channel within a rock mass and plays a crucial role in the flow behavior of rock fractures. The geometric features of the fracture, combined with nonlinear flow phenomena, complicate the flow process significantly. To investigate the fluid flow characteristics in fractures of rough granite, this study presents an improved mathematical model that correlates the geometric features of the rock's true rough surfaces with the pressure variations during fluid flow. The model effectively describes the relationship between pressure drop and flow velocity. To investigate the flow characteristics of fluids in rough rock fractures, this study proposes an improved mathematical model based on Forchheimer's law to describe the relationship between pressure drop and flow rate. The model accounts for two flow conditions: linear flow in the low Reynolds number region and nonlinear flow in the higher Reynolds number region. Hydraulic tests were conducted on three granites with varying fracture geometries, validating the model's accuracy. Subsequently, the flow characteristics in rough granite fractures are quantitatively described, and the underlying mechanisms are illustrated through the analysis of the experimental data. Finally, an empirical formula was established to describe the critical Reynolds number based on the geometrical characterization parameters of the fracture, with clear physical significance. These results enhance the understanding of flow behavior in granite rough fractures and contribute to the numerical simulation of nonlinear flow processes.