Near-Field Diffusion Releases Through One and Two Finite Planar Zones from a Nuclear Waste Package

For a nuclear waste package emplacement in a potential repository in partially saturated rock, a rock rubble or backfill zone may act more as a barrier than as a pathway for diffusive release of radionuclides. We approximate the diffusive transport process using one-dimensional, one-and two-barrier geometries. The one-barrier model suffices when the effective diffusion coefficient in the first zone, the rubble, is substantially lower than that in the second zone, the host rock. For more generality, such as two zones of comparable diffusivities, or for an additional barrier zone, we model two barrier zones both of finite extent. We present solutions for three types of radionuclide mobilization at the source: a pulse transient input, a steady input rate, and a constant concentration. The algebraic series form of the solutions aids analysis of sensitivity of breakthrough times and peak release rates. For the one-zone case, dimensionless parameters allow plotting of the family of transient solutions on a single graph. Comparisons between results of one- and two-zone models and with published results for different geometries and solution methods support verification of the solutions in this study.