DNS simulations of inertial flow phenomena in 3D intersecting rough fractures: Impact of roughness and intersection angle on non-linear flow regimes

Understanding fluid flow within fractured rock masses is critical for a wide range of applications, including groundwater modeling, geothermal energy extraction, mine water management, and resource recovery from fractured reservoirs. While flow in single fractures has been extensively studied, the complex interactions introduced by intersecting fractures with varying roughness and aperture significantly influence inertial flow behavior and transport dynamics.

This study applies three-dimensional Direct Numerical Simulations (DNS) using scanned rock fracture surfaces to quantify how roughness, aperture, and intersection angle affect non-Darcy flow regimes. Fluid flow through X-shaped, rough-walled fracture intersections was simulated over a range of flow rates (0–200 mL/s) revealing that the transition to inertial flow occurred at Reynolds numbers between 10 and 100, depending on geometry. The results show that fracture roughness is the primary driver of non-linear flow behavior, lowering the critical hydraulic gradient by up to 60 % and increasing the Forchheimer coefficient $\beta$ by up to an order of magnitude.

Non-linear flow behavior was characterized using the Forchheimer and Izbash equations, with the Izbash exponent $n$ ranging from 1.2 to 1.8, depending on roughness and angle. The inertial coefficients ($\beta$ and $n$) increase with roughness and intersection angle, reflecting enhanced inertial resistance. Empirical power-law relationships were derived to predict these coefficients such as $\beta \propto K^{-5/3}$.

These findings provide new insights into fluid dynamics in complex fracture networks and offer predictive tools for permeability modeling in subsurface systems. The results are relevant to geothermal reservoir engineering, mine dewatering, carbon storage, and other fluid-driven subsurface technologies.