The effect of fracture roughness on the onset of non-linear flow
Creators: name: Cunningham, David
Publisher: name: No Publisher Supplied
Year: 2021

description: It is generally understood that a large portion of subsurface flow occurs through underground fractures that have permeabilities that are orders of magnitude larger than their surrounding rock matrix. These fractures are typically connected in long-range, complex networks that can conduct flow and transport solutes over large distances. There is significant interest across many engineering disciplines, including those related to hydrocarbon recovery and nuclear waste repositories, to understand fluid flow and solute transport in fracture networks. Although fracture networks are often the big question in mind a major challenge in predicting network flow is understanding how the flow in a single fracture is affected by fracture characteristics such as roughness and aperture. In fractures where surface fluctuations are large compared to their aperture (narrow fractures) the flow is forced to move in tortuous paths that produce additional viscous friction and are subject to inertia effects. We consider the relation between the magnitude of surface roughness and the onset of inertial effects in pressure driven flow through a single open fracture. We perform experiments systematically varying the average aperture of the open fracture and cover a wide range of Reynolds numbers. For each aperture, we analyze the data in terms of the Forchheimer equation and show that the critical Reynolds number, defined as the Reynolds number at which the inertial effects contribute 10% of the total pressure losses, is highly correlated with the roughness of the surface. In particular, we show that significant inertial effects appear early as the relative importance of surface roughness increases. We present results showing that the magnitude of the deviations in the pressure field compared to a linear profile, taken at different points in the fracture along the flow direction, also increase with the relative surface roughness of the fracture. The roughness of realistic fractures takes place over a spectrum of many characteristic lengths. We justify our investigation to study the relationship between the length scale of roughness and flow by considering 2D sinusoidal channels in which the amplitude and wavelength can be controlled. We first show that the permeability at low Reynolds numbers for a sinusoidal channel with parallel and symmetric walls agree with analytical predictions from the literature and, in the parallel case, agrees with a simple approximation that accounts for the channel tortuosity. We also demonstrate that the sinusoidal channel exhibits nonlinear flow and develop a method to determine the critical Reynolds number directly from the simulations. We find that the critical Reynolds number does not trend monotonically with respect to amplitude or wavelength. We find that tube-like channels (long amplitude and wavelength) and long wavelength channels do not exhibit much inertial flow. The lowest critical Reynolds number we observe, correspond to amplitudes and wavenumbers between these limits. Furthermore, the streamlines for specific cases are presented for both Stokes flow and at the critical Reynolds. We find that eddying flow at Stokes flow occurs under certain conditions for the wavelength and amplitude which is supported by a predicting model from the literature.