DOI QR코드

DOI QR Code

An innovative method for determining the diffusion coefficient of product nuclide

  • Chen, Chih-Lung (Department of Nuclear Back-end Management, Taiwan Power Company) ;
  • Wang, Tsing-Hai (Department of Biomedical Engineering and Environment Sciences, National Tsing Hua University)
  • 투고 : 2016.12.01
  • 심사 : 2017.03.29
  • 발행 : 2017.08.25

초록

Diffusion is a crucial mechanism that regulates the migration of radioactive nuclides. In this study, an innovative numerical method was developed to simultaneously calculate the diffusion coefficient of both parent and, afterward, series daughter nuclides in a sequentially reactive through-diffusion model. Two constructed scenarios, a serial reaction (RN_1 ${\rightarrow}$ RN_2 ${\rightarrow}$ RN_3) and a parallel reaction (RN_1 ${\rightarrow}$ RN_2A + RN_2B), were proposed and calculated for verification. First, the accuracy of the proposed three-member reaction equations was validated using several default numerical experiments. Second, by applying the validated numerical experimental concentration variation data, the as-determined diffusion coefficient of the product nuclide was observed to be identical to the default data. The results demonstrate the validity of the proposed method. The significance of the proposed numerical method will be particularly powerful in determining the diffusion coefficients of systems with extremely thin specimens, long periods of diffusion time, and parent nuclides with fast decay constants.

키워드

참고문헌

  1. I. Neretnieks, Diffusion in the rock matrix: an important factor in radionuclide retardation, J. Geophys. Res. 85 (1980) 4379-4397. https://doi.org/10.1029/JB085iB08p04379
  2. M. Garcia-Gutierrez, J.L. Cormenzana, T. Missanal, M. Mingarro, J. Molinero, Overview of laboratory methods employed for obtaining diffusion coefficients in FEBEX compacted bentonite, J. Iberian Geol. 32 (2006) 37-53.
  3. C.D. Shackelford, Laboratory diffusion testing for waste disposal - a review, J. Contam. Hydrol. 7 (1991) 177-217. https://doi.org/10.1016/0169-7722(91)90028-Y
  4. M. Zhang, M. Takeda, H. Nakajima, Strategies for solving potential problems associated with laboratory diffusion and batch experiments-part 1. An overview of conventional test methods, in: WM'06 Conference, Tucson, AZ, 2006.
  5. M. Takeda, H. Nakajima, M. Zhang, T. Hiratsuka, Laboratory longitudinal diffusion tests: 1. Dimensionless formulations and validity of simplified solutions, J. Contam. Hydrol. 97 (2008) 117-134. https://doi.org/10.1016/j.jconhyd.2008.01.004
  6. M. Takeda, M. Zhang, H. Nakajima, Strategies for solving potential problems associated with laboratory diffusion and batch experiments-part 2. Future improvements, in: WM'06 Conference, Tucson, AZ, 2006.
  7. M. Zhang, M. Takeda, H. Nakajima, Determining the transport properties of rock specimens using an improved laboratory through-diffusion technique, MRS Proc. 932 (2006) 113.1. http://dx.doi.org/10.1557/PROC-932-113.1.
  8. H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, second ed., Oxford University Press, New York, 1959.
  9. J. Crank, The Mathematics of Diffusion, second ed., Clarendon, Oxford, UK, 1975.
  10. W.F. Brace, J.B. Walsh, W.T. Frangos, Permeability of granite under high pressure, J. Geophys. Res. 73 (1968) 2225-2236. https://doi.org/10.1029/JB073i006p02225
  11. X. Lu, J. Ahl, Studying of salt diffusion coefficient in brick: analytical and numerical methods, J. Mater. Sci. 40 (2005) 3795-3802. https://doi.org/10.1007/s10853-005-3321-9
  12. G.J. Moridis, Semianalytical solutions for parameter estimation in diffusion cell experiments, Water Resour. Res. 35 (1999) 1729-1740. https://doi.org/10.1029/1999WR900084
  13. T.V. Bharat, P.V. Suvapullaiah, M.M. Allam, Swarm intelligence-based solver for parameter estimation of laboratory through-diffusion transport of contaminants, Comput. Geotechnics 36 (2009) 984-992. https://doi.org/10.1016/j.compgeo.2009.03.006
  14. C.L. Chen, T.H. Wang, C.H. Lee, S.P. Teng, The development of a through-diffusion model with a parent-daughter decay chain, J. Contam. Hydrol. 138-139 (2012) 1-14. https://doi.org/10.1016/j.jconhyd.2012.06.002
  15. M. Garcia-Gutierrez, J.L. Cormenzana, T. Missanal, M. Mingarro, Diffusion coefficients and accessible porosity for HTO and $^{36}Cl$ in compacted FEBEX bentonite, Appl. Clay Sci. 26 (2004) 65-73. https://doi.org/10.1016/j.clay.2003.09.012