核廢料能否安全處置為核電能源永續發展的關鍵。核廢料處置通常是利用緩衝材料如膨潤土進行隔離，以防止核廢料從處置罐中洩漏。因此，正確量測緩衝材料的水文地質參數特性是核廢料處置重要之技術。MX-80膨潤土常用於核廢料處置中的緩衝材料，而李等人 (2013) MX-80膨潤土進行實驗推估之擴散係數，研究發現擴散係數見有尺度效應，其結果與序率理論相衝突，因為尺度效應通常只出現於延散係數，而非出現於擴散係數。我們重新檢視李等人 (2013) 之實驗結果，並重新估算MX-80 膨潤土之水文地質參數。本研究使用擴散方程式與平流延散方程式進行參數評估，考慮膨潤土的微觀異質性，使用序率參數反推之馬可夫鍊蒙地卡羅方法 (MCMC)，由不同管柱長度的土壤穿透濃度數據，分析速度、延散係數與擴散係數。結果顯示此實驗應有滲流速度之影響。利用擴散模式進行土壤穿透數據之擬合發現會產生明顯的誤差，而使用平流延散模式則擬合效果較佳。延散係數呈現尺度效應，隨著試驗管柱增長而增加，而平流延散模式較能解釋MX-80 膨潤土傳輸試驗之結果。

Nuclear waste deposit is commonly isolated by buffer material, such as bentonite, to prevent its leak from deposit cane. Therefore, the hydrogeological property of buffer material is the key issue for the success of nuclear waste deposition. Lee et al. (2013) performed an experimental work to explore the diffusion coefficient of Bentonite (MX-80) which is used as the buffer material of nuclear waste deposits. Scale effect was found in the diffusion coefficient. The result contradicts to the stochastic theory which states that the scale effect appears for the dispersion coefficient but not the diffusion coefficient. We reexamine the experimental data to explore the issue. Both analytical solutions of diffusion and advection-dispersion equations (ADE) were applied to estimate the parameters. Considering the micro-heterogeneity of bentonite, Markov chain Monte Carlo (MCMC) method is used to analyze the velocity, dispersion and diffusion coefficients of the breakthrough data from column tests. The results show that the experiment is influenced by the velocity. Diffusion model generates significant error in matching the breakthrough data. ADE model which considers velocity and dispersion performs better than the diffusion model. Scale effect is found in dispersion coefficient. Dispersion coefficient increases linearly with experimental lengths. We conclude that ADE model is better representative for the solute transport experiment of bentonite material.

1.Atkinson, A., A. K. Nickerson, The diffusion of ions through water-saturated, cement. J. Mater. Sci. 19, 3068–3078, 1984.
2.Bear, J., Hydraulic of Groindwater, McGraw-Hill, New York, 1979.
3.Brooks, S. P., Markov chain Monte Carlo method and its application, The Statisticain, 47, part1, pp. 69-100, 1998.
4.Bucur, C., M. Olteanu, C. Cristache and M. Pavelescu, Radionuclide transport through cement matrices, 2010.
5.Cattle, B. A., A model problem for restricted-data gamma ray emission tomography, Annals of Nuclear Energy, 34, 591–599, 2007
6.Crank, J., The mathematic of diffusion, Great Baitain ,Oxford university, 1975.
7.De Hoog, F. R., J. H. Knight and A. N. Stokes, An improved method for numerical inversion of Laplace transforms, SIAM J. SCI. STAT. COMPUT, 1982
8.Eriksen, T., A. Jacobsson, Diffusion in clay-experimental techniques and theoretical models. SKB TR 84-05, 1984.
9.Genuchten, V., Analytical solutions of the one-dimensional convective-dispersive solution transport equation, Technical Bulletin Number, 1982.
10.Gelhar, L. W, A critical review of data on field-scale dispersion in aquifers, WATER RESOUCES RESEARCH, VOL. 28, NO. 7, PAGES 1955-1974, 1992.
11.Gelhar, L. W, Stochastic sunsurface hydrology, Prentic Hall, New Hersey, 1993
12.García-Gutiérrez, M., J. L. Cormenzana, T. Missana1, M. Mingarro, J. Molinero, Overview of laboratory methods employed for obtaining diffusion coefficients in FEBEX compacted bentonite, Journal of Iberian Geology 32: 37-53, 2006
13.Kim, H. T., T, W Suk and S, H Park, Diffusivities for ions through compacted Na-Bentonite with varying dry, WASTE MANAGEMENT, Vol. 13. pp. 303-308, 1993
14.Klotz, D., K. P. Seiler, H. Moser and F. Neumaier, Dispersivity and velocity relationships from laboratory and field experiments, J. Hydrol., 45, 169-87, 1980.
15.Lee, C. P., M. C. Wu, C. Y. Liu, C. H. Pan, T. L. Tsai, H. J. Wei and L. C. Men, Diffusion of cesium in compacted bentonite with different column lengths, Nation Cheng Kung University, 2013.
16.Metropolis, M. and S. Ulam., The Monte Carlo Method, Journal of the American Statistical Association, 44, 335-341, 1949.
17.PNC, Research and development on geological disposal of high-level radioactive waste-First progress report, PNCTN1410 93-059, Power Reactor and Nuclear Fuel Development Corporation, 1992.
18.Metropolis, N., W. A. Rosenbluth, M. N. Rosenbluth and A. H. Teller, Equation of State Calculations by Fast Computing Machies, 1953.
19.Muurinen, P. Penttila-Hiltunen, K. Uusheimo, Diffusion of chloride and uranium in compacted sodium bentonite, at. Res. Soc. Symp. Proc., 127, 743–748, 1989.
20.Molera, M., T. Eriksen and M. Jansson, Anion diffusion pathways in bentonite clay compacted to different dry densities, Applied Clay Science 23, 69– 76, 2003.
21.Molera, M. and T. Eriksen, Anion diffusion pathways in bentonite clay compacted
to different dry densities, Appl. ClaySci.23, 69–76, 2003.
22.Martin, J., L. C. Wlkcox, C. Burstedde and O. Ghattas, A stochastic Newton MCMC method for large-scale statistical inverse problems with application to seismic inversion, 2012.
23.NAGRA, Technical Report 93-22 Kristallin-I Safety Assessment Report, NAGRA NTB 93-22, 1994.
24.SKB, Final storage of spent nuclear fuel, KBS-3, Swedish Nuclear Fuel and Waste Management Co, 1983.
25.Ogata, A., and R.B. Banks, A Solution of the differential equation of longitudinal dispersion in Porous Media, US Geol. Surv. Prof., pp 411-A 1–9, 1961.
26.Petra, N., J. Martin, G. Stadler and O. Ghattas, A computational framework for infinite- dimensional Bayesian inverse problems, part II: stochastic Newton MCMC with application ice sheet flow inverse problems, 2014.
27.Suzuki, S., H. Sato and Y. Tachi, A Technical Problem in the Through-Diffusion Experiments for Compacted Bentonite, Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 40, No. 9, p. 698–701, 2003
28.Suzuki, S., M. Haginuma and K. Suzuki, Study of sorption and diffusion of 137Cs in compacted Bentonite saturated with saline water at 60 C^0, 2007.
29.Tsia, S. C., S. Ouyang and C. N. Hsu, Sorption and diffusion behavior of Cs and Sr on Jih-Hsing bentonite, Applied Radiation and Isotopes,54 ,209-215, 2003.
30.Wieland, E., H. Wanner., Y. Albinsson, P. Wersin, O. Karnland, A surface chemical model of the bentonite/water interface and its implications for modelling the near field chemistry in a repository for spent fuel, SKB TR 94-26, 1994.