- 學位論文
發展具核種衰變鏈之雙槽擴散模型
The Development of Two Reservoir Through-Diffusion Model with Nuclide Decay Chain
摘要
可靠的放射性廢棄物最終處置場安全評估主要取決於核種遷移參數的正確性，這些參數(如分配係數或擴散係數等)可由實驗室試驗並根據適合的理論模型推估。本研究發展考量衰變作用的雙槽擴散模型，並以Moridis模型(Moridis，1999)和Bhara模型(Bharat et al.，2009)來驗證本模型的正確性。此外，本研究亦提出推導母核種擴散係數(D1)的簡式，驗證結果顯示是可用的。 雙槽擴散實驗依注入槽或擴散槽維持為固定濃度(Constant Concentration，CC)或可變濃度(Variable Concentration，VC)，區分成四種不同擴散模型(即CC-CC模型、CC-VC模型、VC-CC模型和VC-VC模型)，其中VC-CC模型甚少被使用或討論。為能解釋放射性核種擴散試驗的結果，有必要考量衰變作用的解析方法，故本研究發展考量衰變作用的CC-CC模型和CC-VC模型，以及這二個模型推求擴散係數的方法(稱之為CC-CC法和CC-VC法)。CC-VC法經與兩組(取自Lu et al. (2008)和Yamaguchi and Nakayama (1998))實際擴散實驗結果比較，顯示CC-VC法推求的擴散係數與各實驗結果相當接近。 針對VC-VC模型提出運用注入槽(Injective Reservoir，IR)或擴散槽(Diffusive Reservoir，DR)內的濃度變化來推求擴散係數的方法，可額外取得VC-VC擴散試驗中的二組擴散係數以進行分析參數的交叉驗證。本研究提出關鍵時間(Critical Time，Tc)概念以探討CC-VC和VC-VC的實驗差異，若VC-VC實驗的操作時間小於Tc，則結果可以CC-VC法進行分析，否則當以VC-VC法進行之，這可幫助實驗人員節省實驗耗時。 最後，本研究發展雙槽核種衰變鏈反應擴散模型，包括連續衰變反應模型(即RN_1 → RN_2→ RN_3)和平行衰變反應模型(即RN_1→ RN_2A + RN_2B)，以及擴散模型中母核種和子核種的擴散係數推求方法，並以數值實驗案例進行驗證，結果顯示當岩樣甚薄或母核種擴散能力甚高時，本研究提出推求各核種擴散係數的方法極為可行。
並列摘要
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.
參考文獻
延伸閱讀
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