Determination of the transmissivity of a heterogeneous anisotropic fracture in slip flow conditions

Tony Zaouter, Didier Lasseux, and Marc Prat
Phys. Rev. E 100, 033115 – Published 23 September 2019

Abstract

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are expected to play a significant role on the transport properties at the megascale. Focusing on the pressure-driven slightly compressible gas slip flow, a two-scale method is presented allowing the determination of the global transmissivity of a fracture on the basis of an upscaled Reynolds model. This model is applied on a tessellation of the fracture, each tile being affected by a macroscopic transmissivity tensor which encompasses the microscale transport information as a result of the first upscaling process. Then, the megascale flow problem in this structure, made of a set of tiles characterized by a heterogeneous and anisotropic transmissivity tensor field, is solved using a boundary element method. Numerical results obtained with this two-scale method are compared to the transmissivity computed with direct simulations carried out at the microscale on the whole fracture. This is performed on two model rough fractures, namely, a spiral groove and a fractal fracture, while varying their mean apertures to investigate a wide range of the average Knudsen number characteristic of the flow at the megascale. A good agreement is obtained between the two approaches showing the robustness of the two-scale method to determine the global transmissivity of the fracture while significantly reducing the overall computational time.

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  • Received 18 March 2019

DOI:https://doi.org/10.1103/PhysRevE.100.033115

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear Dynamics

Authors & Affiliations

Tony Zaouter1,2, Didier Lasseux3,*, and Marc Prat2

  • 1CEA, DEN, SEAD, Laboratoire d'Étanchéité, 30207 Bagnols-sur-Cèze, France
  • 2Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, 31400 Toulouse, France
  • 3CNRS, Institut de Mécanique et d'Ingénierie, I2M, UMR 5295-Esplanade des Arts et Métiers, 33405 Talence, Cedex, France

  • *didier.lasseux@u-bordeaux.fr

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Issue

Vol. 100, Iss. 3 — September 2019

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