Abstract
A valid performance assessment of radioactive waste repository strongly depends on the reliability of nuclide transport parameters. These parameters (e.g. distribution coefficient or diffusion coefficient etc.) can be determined from laboratory experiemnts with suitable theoretical model. A through-diffusion model with nuclide decay chain was developed in this study. The developed model was validated with the Moridis model (Moridis, 1999) and Bharat model (Bharat et al., 2009). The results show the developed model in this study is appropriate. A simplified formula for estimating the apparent diffusion coefficient of parent nuclides based on the analytical solutions of compartmental model was proposed. The feasibility of the formula was verified by some numerical experiments.Depending on various designs of the two-reservoir through diffusion experiment, the concentrations in the source term (i.e., Injective Reservoir, IR) or the sink term (i.e., Diffusive Reservoir, DR) can be fixed or varied. The combinations involve four different models (i.e., the CC-CC model, CC-VC model, VC-CC model, and the VC-VC model). Studies on the VC-CC model are rare. An analytical method considering the decay effect is required to interpret the radioactive nuclide diffusion experiment results more accurately. To reach this end, we developed a CC-CC model and a CC-VC model considering decay effect. Also, the simplified formulas of these two models to determine the diffusion coefficient (i.e., the CC-CC method and CC-VC method) are noted. Applying our CC-VC method to those data reported from Lu et al., 2008; and Yamaguchi and Nakayama, 1998, derived comparable diffusion coefficient lying in the identical order of magnitude.We also proposed two simplified methods using VC-VC model to determine the diffusion coefficient straightforwardly based upon the concentration variations observed in IR and DR. More importantly, the best merit of proposed method over others is that one can derive three diffusion coefficients based on data obtained from one run of experiment. Furthermore, a formula is provided to determine the conceptual critical time (Tc), which is particularly beneficial to the selection of either CC-VC or VC-VC method. Based on this proposed method, it becomes possible to calculate diffusion coefficient from a through-diffusion experiment in a less time consuming manner.Finally, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and its chain series daughter nuclides in sequentially reactive through diffusion model. Two constructed scenarios including a serial reaction (RN_1 → RN_2→ RN_3) and a parallel reaction (RN_1→ RN_2A + RN_2B) were proposed and calculated for verification. The results show the validity of proposed method and could be particularly powerful when a diffusion experiment is conducted under a condition with a very thin specimen and parent nuclides having a large diffusive capacity.