Macro-scale models for Cesium transport in ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Macro-scale models for Cesium transport in sandy-clayed porous media
Paper
Author:Sébastien Cadalen <sebastien.cadalen@cea.fr> (CEA (DEN / DM2S / SFME / MTMS))
Michel Quintard <michel.quintard@imft.fr> (IMFT)
Presenter:Sébastien Cadalen <sebastien.cadalen@cea.fr> (CEA (DEN / DM2S / SFME / MTMS))
Date: 2006-06-18     Track: Special Sessions     Session: Pore-Scale Modelling: New Developments And Applications
DOI:10.4122/1.1000000629
DOI:10.4122/1.1000000630

This paper discusses the type of macro-scale or Darcy-scale model suitable for modelling Cesium transport in sandy-clayed soil. While the motivation for the study comes from the context of nuclear risk control, this study may be viewed in the more general framework of surface contaminations with reactive solute transport. The adopted strategy consists in looking at an idealized soil composed of Fontainebleau sand with a few percents of fine particules of Illite du Puy. This leads to a more simple system in terms of geochemical reactions compared to natural systems which present much more chemical components in the solid phases and in water. In many geochemical studies, the first approximation made in Darcy-scale models consists in assuming that all macro-scale concentrations correspond to equilibrium conditions. Comparing chemical and diffusion characteristic times in the clay grain to the advection in the intragranular porosity, it is plausible to find situations where the pore-scale solute concentration is not homogeneous. This suggests that two-medium effects are important, and this may be taken into account at the Darcy-scale by two-equation models. The remaining issue being the connection between Darcy-scale and micro-scale properties. The first idea, is to perform pore-scale direct simulation simulations. The system to be solved involves Stokes equation and a convection-diffusion equation in the water within the intragranular porosity, and a retardated-diffusive equation in the clay grain. The results are used later as a reference for testing the Darcy-scale models. Two averaged models have been tested. The first model corresponds to a two-equation model involving mainly dispersion in the macro-porosity, and an exchange term with the balance equation for the clay macro-scale domain, which is estimated from the use of a volume averaging upscaling technique. The second model corresponds to a mixed-model coupling a macro-scale equation for the intra-granular fluid phase with a direct simulation of diffusion in the clay particle with special boundary conditions involving the macro-scale concentration. Indications are given on the implementation of both models, and their ability to reproduce the direct simulations results.