Technischer Bericht NTB 80-06

Repositories in geological formations are planned for the final disposal of radioactive wastes produced by nuclear power. Generally, water entry leading to leaching of the waste matrix is considered as the critical process which can result in release of radionuclides from a waste repository /1/. Consequently, radionuclide transport through the geosphere is of crucial importance, because the geological medium acts as the last barrier to the biosphere.

In risk analyses for waste repositories the migration of radionuclides through the geosphere is usually described mathematically by a one-dimensional transport model (e. g. KBS study). On the other hand the hydrological calculational models used for determining the critical migration paths are invariably two­ or three-dimensional.

A one-dimensional transport calculation always gives conservative results for a specific migration path because the influence of the transverse dispersion/diffusion effect is neglected. This effect results in an additional decrease of the nuclide concentration along the migration path. On the other hand radionuclides can spread to adjacent geological formations which are not taken into account in a one-dimensional model. If the water velocities in these formations are higher than along the original (one-dimensional) migration path or if the distance to the biosphere (e.g. lake, river or well) is shorter, then the process of transverse diffusion/dispersion can represent an additional risk. In such cases the results from one-dimensional transport calculations may lead to false conclusions.

The present work deals with the influence of the transverse diffusion/dispersion effect on the migration of radionuclides through the geosphere. We restrict ourselves to migration in porous media which is the standard approach of most existing transport models. For modelling the transport of radionuclides in fissured systems there exist only a few preliminary calculational approaches to date. We are mainly interested in analytically soluble problems which take into account the transverse diffusion/dispersion effect. This procedure permits investigation of the most important effects in a simple and direct manner.

The present study shows that it is only for homogeneous-isotropic media that the three-dimensional time-dependent transport equation can be solved analytically – provided that only simple source geometries and leach processes are taken into account. For heterogeneous layered media only the two-dimensional quasi-stationary transport equation can be solved; the only time dependent process which can be handled is simple radioactive decay excluding extended decay chains. The study shows moreover that only for an idealized three-layer geology analytical solutions can be found. In particular the solutions for multi-layered media cannot be derived from single-layer solutions; each problem with special source and boundary conditions has to be solved directly.

The numerical results from the present study show a relatively strong influence of the transverse dispersion effect in the case of homogeneous-isotropic media. For example, for a longitudinal dispersivity which is three times as high as the transverse dispersivity, the expansion of the "nuclide cloud" one kilometer away from the repository can be of the order of several hundreds of meters. In layered media the spread of the "nuclide cloud" can be limited by highly impermeable layers or by layers with very small dispersivities. The diffusion into such layers is limited to a few meters. Our results show clearly that long­lived radionuclides will reach neighbouring layers because of the transverse dispersion effect. In the selection of a repository site, not only must the layer which contains the radioactive waste be examined in detail, but also the neighbouring layers must be characterised with respect to their geological structure and geochemical composition. In all cases, before starting a one-dimensional transport calculation for the migration of radionuclides in the geosphere, the influence of transverse dispersion effects must be estimated carefully.

A solution for the general three-dimensional time-dependent transport equation for heterogeneous-layered media can be found only by numerical methods.