Contaminant transport in fractured porous media

International audienceThis work is aimed towards deriving mathematical models that describe pollutant migration through fractured porous media. A homogenisation method is used, i .e. macroscopic models are rigorously deduced from the physical description which is valid within a Representative Elementary Volume (REV). The fundamental addumption behind homogenisation is the separation of scales which is expressed by : l/L=E<<1. In the present work, l denotes the characteristic size of the REV, i.e. at the fracture’s scale and L is the characteristic macroscopic size. The approach introduced in (Auriault, 1991) is used. This methodology is on the basis of definition and estimation of dimensionless numbers arising from the description at the REV’s scale. It is shown that the macroscopic behaviour strongly depends upon the local transport regime characterised by the Péclet number in the fractures. Four distinct macroscopic models for solute transport in fractured porous media are derived.Le but de cette étude est de déterminer les modèles mathématiques qui décrivent la migration de polluants en milieux poreux fracturés. On utilise une méthode d’homogénéisation, c’est à dire que les modèles macroscopiques sont rigoureusement déduits de la description physique à l’échelle d’un Volume Elémentaire Représentatif (VER). Pour pouvoir appliquer l’homogénéisation, la condition fondamentale de séparation des échelles doit vérifiée : l/L=E<