Analyses of diffusional release of several typical radionuclides in spent fuel from waste packages emplaced in a repository in basalt were conducted to assess the effects of system characteristics and boundary conditions on computed release rates. Radionuclide releases, including spatial and temporal variations that may be present, represent the source term for transport in the geohydrologic setting and are therefore critical to the assessment of repository acceptability.
Two mathematical approaches were utilized to determine radionuclide release rate versus time characteristics; (1) an analytical solution for one-deimensional diffusion based upon a Dirichlet (constant-concentration) boundary at the waste form surface; and (2) a finite-element numerical solution based upon a Neumann (zero-flux boundary at the waste form surface. The latter method is suitable for radionuclides such as 129I, whose total inventory in spent fuel could be quickly depleted from the waste form and dissolved in the pore spaces of the packing material surrounding the waste form and which, therefore, cannot be adequately represented by a constant concentration at the waste form (i.e., container) surface.
The analysis revealed several system characteristics that are not intuitively obvious. For example, strong sorption in the near-field host rock behaves like a strong mass sink and can yield calculated transient release rates exceeding allowable limits. Similarly, a short half-life effectively removes the radionuclide from the host rock, which induces a steep concentration gradient at the host rock/packing interface and thereby increases the diffusional release rate at that boundary.
Typical results for 79Se and 129I are presented to illustrate these effects. The effects of perturbations to key assumptions are shown to indicate the importance of (1) formulating models that accurately represent the physical system and (2) interpreting analytical results carefully to ensure understanding of the capability of the system.