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Stochastic 3D Navier‐Stokes Flow in Self‐Affine Fracture Geometries Controlled by Anisotropy and Channeling
Author(s) -
Egert Robert,
Nitschke Fabian,
Gholami Korzani Maziar,
Kohl Thomas
Publication year - 2021
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2020gl092138
Subject(s) - mechanics , hele shaw flow , reynolds number , anisotropy , flow (mathematics) , shearing (physics) , turbulence , nonlinear system , geometry , open channel flow , stokes flow , shear flow , materials science , fluid dynamics , physics , mathematics , thermodynamics , optics , quantum mechanics
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 ( Re crit ) , 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.