Dynamics of fluid flow in natural fracture networks

Abstract

In complex fracture networks, dynamic fluid-flow patterns arise already at flow velocities in the centimetre-per-second (cm/s) range. Yet, these phenomena get ignored or underestimated when such flows are modelled using Stokes’ equation or the steady-state Darcy’s law approximations of the Navier–Stokes equation (NSE).

Here we apply Detached-Eddy Simulation to solve the NSE in interconnected rock fractures, carrying out an investigation of transient flow phenomena. Our field-data-based numerical simulation-derived results reveal that fracture flow becomes unsteady at cm/s velocities. Dynamic eddies emerge across several length scales, increasing the tortuosity of the flow and altering the fluid distribution in fracture branches. Pressure fluctuations are detectable at the network scale, reaching magnitudes of $\sim 10\text{\%}$ of the total pressure drop. The contribution of inertial losses to the hydraulic head gradient across the network increases substantially with the onset of non-stationary eddies, confirming that they are the primary source of flow nonlinearity.