DOI QR코드

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A spent nuclear fuel source term calculation code BESNA with a new modified predictor-corrector scheme

  • Duy Long Ta (Department of Nuclear Engineering, Hanyang University) ;
  • Ser Gi Hong (Department of Nuclear Engineering, Hanyang University) ;
  • Dae Sik Yook (Korea Institute of Nuclear Safety (KINS))
  • 투고 : 2022.04.12
  • 심사 : 2022.07.18
  • 발행 : 2022.12.25

초록

This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation - Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.

키워드

과제정보

This work was supported by the NRF (National Research Foundation of Korea) through Project No. NRF-2019M2D2A1A02057890 and by the Korea Institute of Nuclear Safety (KINS).

참고문헌

  1. J.Ch. Sublet, J.W. Eastwood, J.G. Morgan, M.R. Gilbert, M. Fleming, W. Arter, FISPACT-II: an advanced simulation system for activation, transmutation and material modeling, Nuclear Data Sheets 139 (2017) 77-137.  https://doi.org/10.1016/j.nds.2017.01.002
  2. E. Hairer, M. Roche, C. Lubich, The Numerical Solution of Differential-Algebraic System by Runge-Kutta Methods, 2006. 
  3. J. Cetnar, General solution of bateman equations for nuclear transmutations, Annals of Nuclear Energy 33 (2006) 640-645.  https://doi.org/10.1016/j.anucene.2006.02.004
  4. E. Tavakkoli, M. Zangian, A. Minuchehr, A. Zolfaghari, Development and Validation of ISOBURN, a new depletion code, Annals of Nuclear Energy 159 (2021), 108319. 
  5. C. Moler, C.V. Loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, Society for Industrial and Applied Mathematics, 2003. 
  6. A.G. Croff, A User's Manual for the ORIGEN2 Computer Code, 1980. ORNL/TM-7175. 
  7. A. Yamamoto, M. Tatsumi, N. Sugimura, Numerical solution of stiff burnup equation with short half lived nuclides by the krylov subspace method, Journal of Nuclear Science and Technology 44 (2) (2007) 147-154.  https://doi.org/10.1080/18811248.2007.9711268
  8. X. Li, J. Cai, A new Krylov subspace method based on rational approximation to solve stiff burnup equation, Annals of Nuclear Energy 118 (2018) 99-106.  https://doi.org/10.1016/j.anucene.2018.04.005
  9. N. J. Higham, The scaling and squaring method for the matrix exponential revisited, Society for Industrial and Applied Mathematic 51 (4), 747-764. 
  10. M. Pusa, J. Leppanen, Computing the matrix exponential in burnup calculations, Nuclear Science and Engineering 164 (2010) 140-150.  https://doi.org/10.13182/NSE09-14
  11. M. Pusa, Rational approximations to the matrix exponential in burnup calculations, Nuclear Science and Engineering 169 (2011) 155-167.  https://doi.org/10.13182/NSE10-81
  12. J. Leppanen, Serpent - A Continuous-Energy Monte Carlo Reactor Physics Burnup Calculation Code, 2015. 
  13. B.T. Rearden, M.A. Jessee (Eds.), SCALE Code System, ORNL/TM-2005/39, Version 6.2.1, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 2016. 
  14. Los Alamos National Laboratory, MCNP6 User's Manual, LA-CP-13-00634, 2013. 
  15. A.E. Isotalo, G.G. Davidson, T.M. Pandya, W.A. Wieselquist, S.R. Johnson, Flux renormalization in constant burnup calculations, Annals of Nuclear Energy 96 (2016) 148-157.  https://doi.org/10.1016/j.anucene.2016.05.031
  16. B. Ebiwonjumi, S. Choi, M. Lemaire, D. Lee, H. Shin, Validation of lattice physics code STREAM for predicting pressurized water reactor spent nuclear fuel isotopic inventory, Annals of Nuclear Energy 120 (2018) 431-449.  https://doi.org/10.1016/j.anucene.2018.06.002
  17. B. Ebiwonjumi, S. Choi, M. Lemaire, D. Lee, H. Shin, H. Lee, Verification and validation of radiation source term capabilities in STREAM, Annals of Nuclear Energy 124 (2019) 80-87.  https://doi.org/10.1016/j.anucene.2018.09.034
  18. J. Jang, C. Kong, B. Ebiwonjumi, Y. Jo, D. Lee, Uncertainties of PWR spent nuclear fuel isotope inventory for back-end cycle analysis with STREAM/RAST-K, Annals of Nuclear Energy 158 (2021), 108267. 
  19. S. Jafarikia, S.A.H. Feghhi, H. Afarideh, Validation of IRBURN calculation code system through burnup benchmark analysis, Annals of Nuclear Energy 37 (2010) 325-331.  https://doi.org/10.1016/j.anucene.2009.12.008
  20. K. Okumura, Y. Nagaya, T. Mori, MVP-BURN, Burn-up Calculation Code Using A Continuous-Energy Monte Carlo Code MVP, Japan Atomic Energy Agency, 2005. 
  21. M. Pusa, Correction to Partial Fraction Decomposition Coefficients for Chebyshev Rational Approximation on the Negative Real Axis, 2012. 
  22. W.A. Wieselquist, The SCALE 6.2 ORIGEN API for High Performance Depletion, ANS MC2015, Nashville, TN, 2015. 
  23. W.B. Wilson, et al., SOURCES 4A: Code for Calculating, (α n) Spontaneous Fission, and Delayed Neutron Sources and Spectra, LA-13639-MS, 1999. 
  24. E.F. Shores, Data Updates for the SOURCES-4A Computer Code, LA-UR-00-5016, 2000. 
  25. W.L. Wilson, T.R. England, K.A. Van Riper, Status of CINDER'90 codes and data, proceedings of the fourth workshop on simulating accelerator radiation environments (SARE4), Knoxville (1998) 14-16. September. 
  26. F. Michel-Sendis, et al., SFCOMPO-2.0: an OECD NEA database of spent nuclear fuel isotopic assays, reactor design specifications, and operating data, Annals of Nuclear Energy 110 (2017) 779-788.  https://doi.org/10.1016/j.anucene.2017.07.022
  27. A.B. Svensk Karnbranslehantering, Measurements of Decay Heat in Spent Nuclear Fuel at the Swedish Interim Storage Facility, CLAB, December, 2006.