Diffusion releases through one and two finite planar zones from a nuclear waste package

For a radioactive waste package emplacement in a potential repository, a partially saturated rock rubble zone may act more as a diffusive barrier than as a pathway to release. We approximate the diffusive transport from the waste packaging using one-dimensional one- and two-barrier geometries. When the effective diffusion coefficient in the first zone is several orders of magnitude lower than that in the host rock, then the two-zone geometry can be approximately by a one-zone problem, keeping only the narrow rubble zone. When the effective diffusion coefficients in the two zones are comparable, or there is an additional barrier, then a two-zone (both of finite extent) approach is adopted. We present solutions for the diffusion response in the two planar geometries for three input cases: a pulse transient input, a steady input rate, and a constant concentration at the source. The solutions have algebraic key elements allowing identification of sensitive factors. For the one-zone case, dimensionless parameters allow plotting of the family of transient response solutions on a single graph. Comparisons with several problems analyzed by others, and on problems where the one-zone and two-zone analyses should give comparable results, support verification of the method