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

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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Contributor : Tony Zaouter <>
Submitted on : Wednesday, September 25, 2019 - 11:55:30 AM
Last modification on : Monday, August 31, 2020 - 9:36:05 AM
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Tony Zaouter, Didier Lasseux, Marc Prat. Determination of the transmissivity of a heterogeneous anisotropic fracture in slip flow conditions. Physical Review E , American Physical Society (APS), 2019, 100, pp.033115. ⟨10.1103/PhysRevE.100.033115⟩. ⟨cea-02296537⟩

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