Effects of inertia on fluid flow in fractured rock masses: A comprehensive review

Fluid flow in fractured rock masses is important for many engineering applications. As fluid moves through the fractures, non-negligible pressure losses occur even at a moderate flow rate where the flow velocity changes. Centrifugal forces arise where fluid flows around bends such as at fracture intersections. These velocity changes consume energy, compromising the linear relationship between flow rate and pressure drop. For the flow in individual fractures, the Forchheimer number, Reynolds number, and critical hydraulic gradients have been used to distinguish between creeping flow, weak inertia, and turbulent flow regimes, but not fracture networks because of their intricate geometry and the erratic flow inside them. This paper reviews models and approaches applied to quantify pressure losses and predicts the flow rates in fracture networks during single-phase fluid flow, trying to establish the current level of understanding of these processes. We find that while Navier Stokes simulations have been applied to analyse flows for idealized fracture geometries, studies on fluid flow in complex fracture networks are rare. This review attempts to collect available quantitative constraints on the effect of inertia on pressure and velocity distributions in fracture sets, flow partitioning between them, and energy losses along the flow path, highlighting that there is a pressing need to develop a better understanding of flow in fracture networks at realistic flow rates, considering inertia effects and resulting nonlinearities.