No‐Flow Fraction (NFF) Permeability Model for Rough Fractures Under Normal Stress

Abstract

Accurate estimation of rock permeability is a major challenge in industrial projects such as oil and gas extraction, geothermal energy production, radioactive waste containment, and CO 2 geosequestration. For many of these projects, the targeted formation exhibits low matrix permeability and the main fluid conduit is the fracture network (Berkowitz, 2002; Neuman, 2005; Sahimi, 2011). To accurately evaluate the hydraulic properties of such geoformations, understanding the behavior of a single rock fracture under in situ conditions is necessary. The permeability of fluids through a single rock fracture is often estimated using the Cubic law-a simplification of the Navier-Stokes (NS) equations based on several key assumptions. These include assuming that the fracture consists of two smooth and parallel plates (Witherspoon et al., 1980). Therefore, the geometry of the flow path can be represented by a single value, the uniform spacing between the two walls. However, no rock fracture is perfectly smooth and, as a result, its aperture field is heterogeneous. A natural way to reduce the heterogeneous aperture field to a single value is to average the fracture aperture distribution. Various averaging methods have been proposed in the literature (

A Systematic Investigation Into the Control of Roughness on the Flow Properties of 3D‐Printed Fractures

“…It is also the case that despite a certain correlation between R c and tortuosity, this relationship alone cannot adequately capture aperture heterogeneity (in relation to tortuosity), as R c only accounts for a portion of the fracture surface (Rong et al., 2020). Tortuosity is therefore also dependent on the evolution of overall surface and resulting aperture structure roughness, which is observed to increase (/ e m = 0.37 to 0.66) with σ ′, with e m decreasing more rapidly than , consistent with previous studies (Javanmard et al., 2021). Although it is evident that tortuosity plays a significant role in FR#7_2 's k f decrease, and, by proxy, the k f response of FR#1 – FR#6 , identifying which tortuosity‐contributing parameter primarily influences k f is key.…”

“…e m distributions narrow with increasing σ ′, illustrated by positive skewness (Figure 6a), consistent with previously measured rough fracture aperture distributions (Gentier et al., 1997; Pruess & Tsang, 1990; Sharifzadeh et al., 2008; Tatone & Grasselli, 2012; Y. W. Tsang & Tsang, 1990). −Δ e m with σ ′ has also been shown to be heterogeneous, with skewness increasing in prevalence (i.e., longer tail) (Javanmard et al., 2021; Kang et al., 2016; Muralidharan et al., 2004; Unger & Mase, 1993; R. Walsh et al., 2008), aligning with distributions seen here, albeit subtly. The lower cut‐offs observed for each σ ′ are likely controlled by voxel size.…”

“…Other studies have incorporated /e m coupled with the concept of a no‐flow fraction, as it has been shown that flow is not only diminished at specific contacting asperities (i.e., R c alone), but also in the surrounding void area (B. Li et al., 2008; Yeo, 2001). k f estimation from this method (Javanmard et al., 2021) (Figure 8, dashed yellow line): yields reasonable k f estimation at the highest σ ′ (within 39%). Nevertheless, insufficient k f predictions given by these relations imply surface roughness should be considered to better predict experimental k f , particularly at lower σ ′.…”

Implications of Local‐Scale Approximations on Describing Fluid Flow in Rock Fractures With Stress‐Induced Void Heterogeneity

“…As our focus was on subsurface stressed rock fractures in this study, we adopted the contact model described in Kling et al (2018) to account for the stress-dependent normal closure. The adopted contact model can realistically reproduce the detailed changes of fracture void structure at different stress levels (Javanmard et al, 2021). Mechanical parameters of the tested rocks including the uniaxial compressive strength, elastic modulus, and Poisson's ratio were experimentally obtained respectively as 165 MPa, 25 GPa, and 0.21 for granite, and 82 MPa, 13 GPa, and 0.25 for red sandstone from a previous study (Li et al, 2019).…”

Experimental Study on Grouting and Flow Characteristics of Rough Vertical Fractures

“…Zhou et al [17] studied the nonlinear flow characteristics of rough fractures at low Reynolds number under different stress states. Some studies show that aperture roughness increases three times when the normal stress increases to 50 MPa [18]. Chen et al [19] adopted 3D rough rock fracture model to conduct seepage tests under different confining pressures, which showed the streamline becomes more tortuous and the critical Reynolds number increases under high stress.…”