Fickian diffusion of radionuclides for engineered containment barriers: Diffusion coefficients, porosities, and complicating issues

A review of the literature was undertaken primarily with the goal of discerning the types of diffusion coefficients that have been reported with respect to diffusion of radionuclides through engineered containment barriers. Although the nomenclature and form for diffusion coefficients in porous media vary widely, the review identified four definitions of diffusion coefficients, viz., D⁎, De, Dp, and Da, which differ on the basis of the forms of Fick's first and second laws for governing macroscopic diffusion through porous media. All forms of Fick's first law for diffusive mass flux include an effective porosity, εeff, whether this term is shown explicitly in Fick's first law or is buried within the definition of the diffusion coefficient. The relative magnitudes of the different diffusion coefficients are shown to vary depending on whether the diffusing radionuclide is nonadsorbing (tracer) or adsorbing, and for adsorbing radionuclides, vary as a function of the relative magnitude between the total porosity, ε, and the inverse of the retardation factor, Rd− 1. In addition to εeff and ε, a diffusion accessible porosity, εdiff, that takes into account the possibility of diffusion into dead-end pores also has been identified. The three porosity terms vary as εeff ≤ εdiff ≤ ε, although there can be more than one value of εdiff depending on the species of radionuclide. The value of εdiff for a non-charged tracer, such as tritium (HTO), generally is found to be the same as ε, whereas the values of εdiff for anionic radionuclides (e.g., 36Cl−) generally are lower than ε due to anionic repulsion and/or steric hindrance. The common assumption that εdiff for a given chemical species is the same as εeff is shown conceptually to not necessarily always be valid. Finally, three potentially significant complicating issues were identified, viz., the geochemistry of the barrier system, the influence of surface and/or interlayer diffusion, and the existence of semipermeable membrane behavior as a result of anion exclusion. Each of these issues is described in detail. Overall, the review provides a basis for identifying the factors that need to be addressed in terms of studies that focus on the diffusion of radionuclides through engineered barriers used for radioactive waste containment.

► Four definitions of the diffusion coefficient were identified based on Fick's laws.
► The relative magnitudes of the diffusion coefficients vary.
► Diffusion accessible porosity for anions may not be the same as effective porosity.
► Complicating issues include geochemistry, surface diffusion, and membrane behavior.