Non-Darcian flow in multiscale tortuous fractures: Insights from a fractal model

Water flow in subsurface fractures often deviates from Darcy's law, especially under varying scales and tortuous geometries. This study develops multiscale fracture models with tortuosity autocorrelation to investigate the scale-dependent transition between Darcy and non-Darcian flow. Fractures were constructed using Koch snowflake curves at scales of 10−1, 10−2, and 10−3 m to ensure geometric similarity. Numerical simulations based on the Navier–Stokes equations reveal that smaller-scale fractures (i.e., L = 10−2–10−3 m) exhibit stronger non-Darcian flow as greater tortuosity lengthens the fluid pathway and induces local velocity deviation and recirculation, thereby amplifying inertial losses and nonlinear flow effects. As the scale decreases, the flow field becomes increasingly asymmetric, with more recirculation zones and low-velocity regions forming. These features lead to greater flow path deviation and reduced hydraulic efficiency. An equivalent deviation aperture is proposed to quantify the effect of flow path deviation, providing a more accurate representation of non-Darcian flow mechanisms in multiscale fractures. The results provide theoretical guidance for predicting nonlinear seepage in fractured reservoirs, with potential applications in geothermal energy extraction, CO2 sequestration, and hydrocarbon recovery.