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

Abstract

This study presents a probabilistic analysis of 3D Navier‐Stokes (NS) fluid flow through 30 randomly generated sheared fractures with equal roughness properties (Hurst exponent = 0.8). The results of numerous 3D NS realizations are compared with the highly simplified local cubic law (LCL) solutions regarding flow orientations and regimes. The transition between linear and nonlinear flow conditions cannot be described with a generally valid critical Reynolds number (italicRecrit), but rather depends on the individual fracture's void geometry. Over 10% reduction in flow is observed for increased global Re (>100) due to the increasing impact of nonlinear conditions. Furthermore, the fracture geometry promotes flow anisotropy and the formation of channels. Flow perpendicular to the shearing leads to increased channeling and fluid flow (∼40% higher) compared to flow parallel to the shearing. In the latter case, dispersed flow and irregular flow paths cause a reduction of LCL validity.

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

“…By examining the distributions of D v in Figure 8 along with the velocity magnitude distributions in Figure 4, we found that a majority of the misprediction took place in regions of low velocity/flow especially near the wall and contact boundaries (Egert et al., 2021; Zou et al., 2017). As the low‐flow regions generally contribute less to the overall flow behaviors of the fracture, the large misprediction of local velocity in these regions may still represent weak impact on the overall fracture transmissivity.…”

“…One reason may be that these local-scale approximations have not been widely appreciated due to a lack of comprehensive evaluation of their performances in describing fluid flow in complex fracture voids under subsurface stresses. Although later works have also evaluated individual local-approximation such as in Egert et al (2021), the latest systematic evaluation of various local-scale approximations was perhaps done by Konzuk and Kueper (2004). In their work, transmissivity obtained from applying different local-scale approximations was compared with that from fracture flow experiments.…”

Spatial Characterization of Channeling in Sheared Rough‐Walled Fractures in the Transition to Nonlinear Fluid Flow

“…Egert et al. (2021) were able to demonstrate the need for solving the NSE to consider both the three‐dimensional fracture void space and growing nonlinear effects in the small‐scale fracture‐internal flow field by comparing NSE and LCL for Reynolds numbers up to 220. The natural small‐scale flow field in a fracture is not homogeneously distributed.…”

“…The solution of the nonlinear Navier-Stokes equations (NSE) on rough fracture surfaces allows to circumvent these limitations, but they are rarely used due to high computational complexity (Javadi et al, 2014;Liu, He et al, 2020) and are mostly limited to small Re (Aghajannezhad & Sellier, 2022;He et al, 2022). Egert et al (2021) were able to demonstrate the need for solving the NSE to consider both the three-dimensional fracture void space and growing nonlinear effects in the small-scale fracture-internal flow field by comparing NSE and LCL for Reynolds numbers up to 220. The natural small-scale flow field in a fracture is not homogeneously distributed.…”

Water‐Mineral Reactions in a Translated Single Realistic Fracture: Consequences for Contaminant Uptake by Matrix Diffusion

“…Open fractures are primary conduits for groundwater flow and thus constitute preferential transport pathways for dissolved contaminants. Fracture internal variability, caused, for example, by shearing, leads to significant variability in the in‐plane groundwater velocity field (Egert et al., 2021; Zou et al., 2017), which in turn affects mass exchange processes with the stagnant water in the bordering porous rock matrix (Trinchero, Poteri, et al., 2020). Fracture filling minerals, that might have precipitated during past hydrothermal events, add more pieces to this already complex puzzle.…”