Izvestiya vuzov. Yadernaya Energetika

The peer-reviewed scientific and technology journal. ISSN: 0204-3327

A study into the propagation of the uncertainties in nuclear data to the nuclear concentrations of nuclides in burn-up calculations

7/09/2020 2020 - #02 Modelling processes at nuclear facilities

Kolesov V.V.

DOI: https://doi.org/10.26583/npe.2020.2.10

UDC: 621.039.51

The key papers on estimating the uncertainties in nuclear data deal with the influence of these uncertainties on the effective multiplication factor by introducing the so-called sensitivity factors and only some of these are concerned with the influence of such uncertainties on the life calculation results.

On the other hand, the uncertainties in reaction rates, the neutron flux, and other quantities may lead to major distortions in findings, this making it important to be able to determine the influence of uncertainties on the nuclear concentrations of nuclides in their burn-up process.

The possibility for the neutron flux and reaction rate uncertainties to propagate to the nuclear concentrations of nuclides obtained as part of burn-up calculations are considered using an example of a MOX-fuel PWR reactor cell. To this end, three burn-up calculation cycles were performed, and the propagation of uncertainties was analyzed. The advantages of the uncertainty estimation method implemented in the VisualBurnOut code consists in that all of the root-mean-square deviations are obtained in one calculation as a statistical method, e.g. GRS (Generation Random Sampled), requires multiple calculations.

The VisualBurnOut calculation results for the root-mean-square deviations in nuclear concentrations were verified using a simple model problem. It is shown that there is a complex dependence of the propagation of the root-mean-square deviations in the nuclear concentrations of nuclides in the process of fuel burn-up, and, therefore, further studies need to aim at investigating the influence of uncertainties in nuclear data on the nuclear concentrations of nuclides.


  1. Aliberti G., Palmiotti G., Salvatores M., Kim T.K., Taiwo T.A., Anitescu M., Kodeli I., Sartori E., Bosq J.C., Tommasi J. Nuclear Data Sensitivity, Uncertainty And Target Accuracy Assessment for Future Nuclear Systems. Ann. Nucl. Energy. 2006, v. 33, no. 8, pp. 700-733; DOI: https://doi.org/10.1016/j.anucene.2006.02.003 .
  2. OECD/NEA. Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations. NEA/WPEC-26. ISBN 978-92-64-99053-1. 2008, v. 26, p. 465.
  3. Rochman D., Koning A.J., Da Cruz D.F. Propagation of 235,236,238U and 239Pu nuclear data uncertainties for a typical PWR fuel element. Nuclear Technology. 2012, v. 179, no. 3, pp. 323- 338; DOI: https://doi.org/10.13182/NT11-61 .
    1. Wieselquist W., Zhu T., Vasiliev A., Ferroukhi H. PSI Methodologies for Nuclear Data Uncertainty Propagation with CASMO-5M and MCNPX: Results for OECD/NEA UAM Benchmark Phase I. Science and Technology of Nuclear Installations. Article ID 549793. 2013, p. 15; DOI: https://doi.org/10.1155/2013/549793 .
  4. Stover Jr.T.E. Quantification of Back-End Nuclear Fuel Cycle Metrics Uncertainties Due to Cross sections. Master’s Thesis, Idaho National Laboratory. INL/EXT-07-13592. 2007, p. 170.
  5. Rochman D., Koning A.J., Da Cruz D.F., van der Marck S.C. Nuclear Data Uncertainty Propagation for a Sodium Fast Reactor. Journal of the Korean Physical Society. 2011, v. 59, no. 4, pp. 1191-1194; DOI: https://doi.org/10.3938/jkps.59.1191 .
  6. Aliberti G., Palmiotti G., Salvatores M., Stenberg C.G. Impact of Nuclear Data Uncertainties on Transmutation of Actinides in Accelerator-Driven Assemblies. Nuclear Science and Engineering. 2004, v. 146, no. 1, pp. 13-50; DOI: https://doi.org/10.13182/NSE02-94 .
  7. Gandini A., Salvatores M., Tondinelli L. New Developments in Generalized Perturbation Methods in the Nuclide Fields. Nuclear Science and Engineering. 1977, v. 62, no. 2, pp. 339- 344; DOI: https://doi.org/10.13182/NSE77-A26970 .
  8. Usachev L.N., Bobkov Yu.G., Krivtsov A.S. Perturbation Theory and Analysis in Fission Products Kinetics. Proc. of the Int. Conf. Nuclear CrossSection for Technology. Krokswill. USA. 1979, p. 4.
  9. Kolesov V.V., Novichkov A.V., Voznyakevich E.E., Terekhova A.M. Statistical Approach to Estimated Uncertainty of Nuclear Concentration in Problems of Isotope Kinetics. Proc. of the XIIIth International Youth Scientific and Practical Conference «FUTURE OF ATOMIC ENERGY AtomFuture 2017». KnE Engineering. 2017, pp. 261-267; DOI: https://doi.org/10.18502/ keg.v3i3.1625 .
  10. Garcia-Herranz N., Cabellos O., Sanz J., Juan J., Kuijper J.C. Propagation of statistical and nuclear data uncertainties in Monte Carlo burn-up calculations. Annals of Nuclear Energy. 2008, v. 35, no. 4, pp. 714-730; DOI: https://doi.org/10.1016/j.anucene.2007.07.022 .
  11. Takeda T., Hirokawa N., Noda T. Estimation of Error Propagation in Monte-Carlo Burnup Calculations. Nuclear Science and Technology. 1999, v. 36, no. 9, pp. 738-745; DOI: https:// doi.org/10.108018811248.1999.9726262 .
  12. Tohjoh M., Endo T., Watanabe M., Yamamoto A. Effect of error propagation of nuclide number densities on Monte Carlo burn-up calculations. Annals of Nuclear Energy. 2006, v. 33, no. 17-18, pp. 1424-1436; DOI: https://doi.org/10.1016/j.anucene.2006.09.010 .
  13. Park H.J., Shim H.J., Kim C.H. Uncertainty Propagation in Monte Carlo Depletion Analysis. Nuclear Science and Engineering. 2011, v. 167, no. 3, pp. 196-208; DOI: https://doi.org/ 10.13182/NSE09-106 .
  14. Quentin Newell, Charlotta Sanders. Stochastic Uncertainty Propagation in Monte Carlo Depletion Calculations. Nuclear Science and Engineering. 2015, v. 179, no. 3, pp. 253-263; DOI: https://doi.org/10.13182/NSE13-44 .
  15. Rochman D., Zwermann W., van der Marck S.C., Koning A.J., Sjostrand H., Helgesson P., Krzykacz-Hausmann B. Efficient Use of Monte Carlo: Uncertainty Propagation. Nuclear Science and Engineering. 2014, v. 177, no. 3, pp. 337-349; DOI: https://doi.org/10.13182/ NSE13-32 .
  16. Rochman D., Koning A.J., Da Cruz D.F. Propagation of 235,236,238U and 239Pu Nuclear Data Uncertainties for a Typical PWR Fuel Element. Nuclear Technology. 2012, v. 179, no. 3, pp. 323-338; DOI: https://doi.org/10.13182/NT11-61 .
  17. Andrew Conant, Anna Erickson, Martin Robel, Brett Isselhardt. Sensitivity and Uncertainty Analysis of Plutonium and Cesium Isotopes in Modeling of BR3 Reactor Spent Fuel. Nuclear Technology. 2017, v. 197, no. 1, pp. 12-19; DOI: https://doi.org/10.13182/NT16-88 .
  18. Da Cruz D.F., Rochman D., Koning A.J. Uncertainty Analysis on Reactivity and Discharged Inventory due to 235,238U, 239,240,241Pu, and Fission Products: Application to a Pressurized Water Reactor Fuel Assembly. Nuclear Technology. 2014, v. 185, no. 2, pp. 174-191; DOI: https:// doi.org/10.13182/NT12-154 .
  19. Sjostrand H., Alhassan E., Duan J., Gustavsson C., Koning A.J., Pomp S., Rochman D., Osterlund M. Propagation of nuclear data uncertainties for ELECTRA burn-up calculations. Proc. of the 2013 International Conference on Nuclear Data for Science and Technology. March 4- 8. 2013. New York. USA.
  20. Kolesov V.V., Khitrik D.V., Kamaev D.A. VisualBurnOut Program. Registration No. 2009617021 dated 23.12.2009 in Computer Program Register.

reactor facility burn-up calculations uncertainties in nuclear data uncertainties in nuclear concentrations of nuclides Monte Carlo method