Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method |
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Authors: | Ahmad Pouya Minh-Ngoc Vu |
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Affiliation: | 1. Universit?? Paris-Est, Laboratoire Navier (UMR CNRS-IFSTTAR-ENPC), IFSTTAR, 58 bd Lefebvre, 75732, Paris, France 2. BRGM/RNSC, Cedex 2, 45060, Orl??ans, France 3. Le Quy Don Technical University, 100 Hoang Quoc Viet, Hanoi, Vietnam
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Abstract: | The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo in Transp Porous Media 84:511?C532, 2010) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady-state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given. |
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