Transport in Porous Media

, Volume 93, Issue 3, pp 475–493 | Cite as

Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method

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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 84:511–532, 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.

Keywords

Porous media Cracks Steady-state flow Singular integral equations Effective permeability 
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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Université Paris-Est, Laboratoire Navier (UMR CNRS-IFSTTAR-ENPC), IFSTTARParisFrance
  2. 2.BRGM/RNSCCedex 2France
  3. 3.Le Quy Don Technical UniversityHanoiVietnam

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