Percolation mechanism of seepage in rough rock fractures

In studies of fluid flow through single-fractured rock media, the classical geometric percolation threshold loses its validity, and the threshold pressure gradient (TPG), as an empirical parameter describing the onset condition of actual flow, cannot directly provide a basis for the theoretical determination of the percolation threshold. This is because TPG relies on fluid mechanics mechanisms, whereas the percolation threshold is based on network topology statistics. Therefore, it is essential to define a “transport percolation threshold” that characterizes hydraulic critical behavior. Consequently, this study addresses the determination of the inflection point in Darcy-non-Darcy flow through rough fractures and investigates the transport percolation threshold in seepage flow, focusing on the discontinuous relationship between pressure gradient and flow velocity during transitions from low to high velocities. A comprehensive Bingham fluid seepage model, incorporating fractal dimensions of fracture tortuosity and aperture, is developed. By integrating unit percolation models with diffusion equations, a global percolation model is established, allowing for numerical solutions for full-field percolation in rough fractures. The results indicate that, compared to the assumptions of Darcy flow, the unit percolation model under the Forchheimer flow assumption—characterized by its unique inertial term—more accurately captures the influence of geometric percolation parameters (such as roughness angles and hydraulic aperture) on fluid flow paths during the percolation stage. During phase transitions in percolation, the outlet flow velocity conforms more closely to the nonlinear characteristics described by Forchheimer′s equation rather than Darcy′s linear assumption. This understanding offers a novel perspective for investigating the mechanisms of low-velocity non-Darcian flow.