Continuous models for solute transport in fractured porous media

This 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 assumption behind homogenisation is the separation of scales which is expressed by: l/L = epsilon much less than 1. In the present work, l is 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 Peclet number in the fractures. Four distinct macroscopic models for solute transport in fractured porous media are derived.