Numerical study of transitional flow in fractures: the role of roughness on the road to turbulence

In aquifers and petroleum reservoirs, fractures are ubiquitous, and the majority of the fluid transport in such systems often occurs through fracture networks. Knowledge of the flow properties in the single fractures that together form the networks is hence necessary for safe operation downhole. Non-linear, high-velocity flow in such systems is of particular importance for geothermics, since turbulent mixing is known to increase heat conduction by several orders of magnitude. This is of importance both in terms of storing and recovering heat from aquifers. On the other hand, flow in rough fractures is interesting from a turbulence perspective. The onset of turbulence in pipes and channels is a phenomenon that historically has received broad attention since the early experiments by Reynolds, and only during the last decades, the phenomenon is beginning to be fully understood. However, in the presence of roughness, much less is known. In this work, we present comprehensive numerical simulations of flow in synthetic rough channels, representing single fracture joints. Using the finite element method, we solve the full-fledged, time-dependent Navier-Stokes equations for flow in the channels, from laminar flow, through transitional, to turbulent flow. We link the descriptions of microscopic to macroscopic properties, using geometric properties such as effective aperture, paying particular attention to the role of inertia and roughness for the transport properties of the channels. Finally, we discuss implications of our study for the transition to turbulence in the presence of roughness.