SIMPLE-MODEL FOR MIGRATION OF COLLOID TRANSPORTED RADIONUCLIDES ALONG A FRACTURE

The long-term safety of nuclear waste disposal in a deep geological repository depends essentially on the capacity of artificial and natural barriers to slow down the possible return of long-lived radionuclides to the biosphere. Mathematical models applied to various geological formations have been developed for describing the time and space evolution of the radioactivity released by the waste packages. Such a study was carried out in Sweden in the case of a spent-fuel disposal in granitic bedrock. The basic problem is that of the transport of dissolved radioactive substances by the ground water flowing slowly along fractures in the rock. Retention of the radionuclides by sorption on the fracture walls and matrix diffusion is found to reduce drastically the nuclide migration; the conclusion is that the radiological impact of the repository should be negligible at any time in the future. One of the essential points in these calculations is that the nuclides are transported for the major part in an aqueous solution. We consider here the hypothetical case where a significant part of the nuclides would be transported by stable aggregates or colloids, small enough to follow the groundwater flow. It is clear that the nuclide transport might be much faster in such conditions than in the case of a simple aqueous solution. The model represents jointly the transport of the two phases, the solute phase and the colloidal one, in a fissure with constant aperture; the colloids are supposed to dissolve immediately when the concentration of the solute drops below the solubility limit through sorption of the fracture walls and diffusion into the matrix. In two typical cases (linear sorption of the colloids or strong sorption with maximum exchange capacity), analytical solutions may be obtained for the transport of the nuclides along the fissure, at the cost of approximations whose validity is briefly discussed.