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Article Dans Une Revue Advances in Water Resources Année : 2018

Effective permeability of three-dimensional porous media containing anisotropic distributions of oriented elliptical disc-shaped fractures with uniform aperture

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Résumé

Solution for the fluid potential within a fractured porous medium is described. This solution is derived numerically for the particular case of a Pouseuille's elliptical fracture plane with uniform aperture. A closed-form solution of total flow integrated over a single fracture is obtained as a function of matrix permeability, fracture permeability and fracture geometry parameters. This solution allows firstly the comparison between two approaches: Poiseuille's fracture and Darcy's flattened ellipsoidal inclusion. This shows the difference of pressure and flow fields in the fractures and the equivalence of total flow transported by fractures. Then, a semi-analytical solution is used to establish an effective permeability model based on the self-consistent scheme for a porous medium containing an anisotropic distribution of oriented elliptical plane fractures. The proposed model is in good agreement with numerical solutions reported in the literature for a random distribution of oriented fractures. The present model exhibits a percolation threshold for a three-dimensional fractured network. The percolation threshold is a critical value of fracture density, beyond which the effective permeability is greater than zero for the case of an impermeable parent material.
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Dates et versions

hal-02860760 , version 1 (08-06-2020)

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Minh-Ngoc Vu, Amade Pouya, Darius Seyedi. Effective permeability of three-dimensional porous media containing anisotropic distributions of oriented elliptical disc-shaped fractures with uniform aperture. Advances in Water Resources, 2018, 118, pp.1-11. ⟨10.1016/j.advwatres.2018.05.014⟩. ⟨hal-02860760⟩
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