The Effect of Fracture Roughness on the Onset of Nonlinear Flow

Abstract

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 the pressure driving the flow through a single open fracture. We performed experiments systematically varying the average aperture of the open fracture and covering 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 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 earlier as the relative importance of surface roughness increases. Finally, 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, is directly related to the relative surface roughness of the fracture.

Characterizing the Relationship Between Non‐Darcy Effect and Hydraulic Aperture in Rough Single Fractures

“…While the size of low velocity regions increased with the roughness, and the increase of low velocity region led to the stronger heterogeneity of hydraulic characteristics between the area of roughness element and whole flow field in a single fracture. Thus, when RSD > R c , the non-Darcy effect was more likely to occur in fractures with higher roughness, that is, the E d decreased with the increase of roughness which is consistent with other researchers (Cunningham et al, 2020;Qian et al, 2015).…”

“…Moreover, in previous studies, the critical non‐Darcy effect factor E = 0.1 was used to quantify the onset of non‐Darcy flows, and this criterion has been widely used (Rong et al., 2020; Yu et al., 2017; Zeng & Grigg, 2006; Zhou et al., 2015). However, recent studies showed that geometric properties of single fractures imposed a great influence on the critical value of non‐Darcy effect (Cunningham et al., 2020). Researchers considered that the non‐Darcy effect of fluid flow became non‐negligible when the pressure drop caused by inertial effect accounted for 10% of the total pressure drop ( E = 0.1).…”

“…Yu et al (2017) used the ratio of apparent transmissivity and intrinsic transmissivity (T/T 0 ) to identify the critical Reynolds number at the onset of non-Darcy flow. Inspired by the method of identifying the onset of non-Darcy flow in previous studies (Cunningham et al, 2020;Yu et al, 2017), it was conducted the following preliminary theoretical analysis of hydraulic aperture. As mentioned in Section 1, most researchers believed the hydraulic aperture was defaulted as a constant which only related to the geometric properties of a single fracture and independent of inertial effect of fluid flow.…”

Stochastic 3D Navier‐Stokes Flow in Self‐Affine Fracture Geometries Controlled by Anisotropy and Channeling

“…Cunningham et al. (2020) showed experimentally on a mated fracture that the to consider nonlinear effects decreases with increasing local complexity of the fracture void geometry. Thus, both decreasing apertures and an increase in relative aperture fluctuations cause enhanced inertial effects.…”

The Effect of Fracture Surface Roughness and Mechanical Aperture on the Onset of Nonlinear Flow Behaviors in 3D Self-Affine Rough Fractures

“…Natural fracture surfaces are typically rough with 3D self-affine distribution and display complex hydraulic behavior coming from fracture surface roughness [9]. Fluid flow through individual fractures is affected by multiple factors, such as fracture aperture, surface roughness, and inertial effects, among which aperture and surface roughness may be the two most critical parameters that significantly affect fluid flow behavior [10,11].…”