Transport in Porous Media

, Volume 95, Issue 3, pp 603–626 | Cite as

Time Analysis of the Three Characteristic Behaviours of Dual-Porosity Media. I: Fluid Flow and Solute Transport

  • P. Royer
  • C. BoutinEmail author


Homogenisation of consolidation and compressible fluid flow in dual-porosity media has highlighted the existence of three characteristic macroscopic behaviours. These three behaviours are, namely, a dual-porosity description which includes memory effects, a single-porosity description with which the microporosity is simply ignored and an intermediate behaviour which we refer as behaviour with reservoir effect. With this latter, the whole dual-porosity medium is represented by an equivalent single-porosity medium. In contrast with a single-porosity behaviour, the porosity of the entire dual-porosity medium is accounted for. During solute transport in dual-porosity media, while memory effects are most often experimentally observed, the homogenised model obtained for the most general values of the involved parameters leads to a model with reservoir effect. Therefore, the observed memory effects are not reproduced by this model and a clear interpretation of the origins of these effects remains an unresolved issue. The study is presented in two complementary articles. The objective of this article is, first, to determine a physical interpretation of the existence of the three characteristic behaviours of dual-porosity media. This is performed by exploring the homogenised models and their domains of validity for the analogy of heat conduction in a dual-conductivity composite. This leads to the original result that consists to relate each type of behaviour to a specific relationship between two characteristic times. This is then used for interpreting the results obtained for compressible flow in dual-porosity media. Finally, it allows to elucidate the conditions under which memory effects may occur during solute transport in dual-porosity media.


Dual-conductivity Dual-porosity Fluid flow Solute Transport Homogenisation of multiple scale asymptotic expansions 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Génie Civil (LMGC), UMR 5508 CNRSUniversité Montpellier IIMontpellier Cedex 5France
  2. 2.DGCB-CNRS 3237Université de Lyon – Ecole Nationale des Travaux Publics de l’EtatVaulx-en-VelinFrance

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