Continuum Modelling of Contaminant Transport in Fractured Porous Media
Résumé
This work is aimed towards deriving macroscopic models that describe pollutant migration through fractured porous media. A homogenisation method is used, that is, macroscopic models are deduced from the physical description over a representative elementary volume (REV), which consists of an open fracture surrounded by a porous matrix block. No specific geometry is at issue. The fractured porous medium is saturated by an incompressible fluid. At the REV's scale, the transport is assumed to be advective-diffusive in the porous matrix and due to convection and molecular diffusion in the fracture's domain. It is also assumed that there is no diffusion in the solid. We demonstrate that the macroscopic behaviour is described by a single-continuum model. Fluid flow is described by Darcy's law. Four macroscopic single-continuum models are obtained for the contaminant transport: a diffusive model, an advective-diffusive model and two advective-dispersive models. One of the two advective-dispersive models accounts for the advection process in the porous matrix. The domains of validity of these models are defined by means of the orders of magnitude of the local Péclet numbers in the porous matrix block and in the fracture's domain.
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