A brief history of Accident Chernobyl: Simulation of the influence of Neutron Absorbing Poisons and temperature feedback effects by Point Kinetics Equations

Natália Barros Barros Schaun; Fernanda Tumelero; Claudio Zen Petersen

doi:10.15392/bjrs.v10i3.2082

Authors

Natália Barros Barros Schaun Universidade Federal de Pelotas
Fernanda Tumelero
Claudio Zen Petersen

DOI:

https://doi.org/10.15392/bjrs.v10i3.2082

Keywords:

Neutron Point Kinetics Equations, Temperature feedback, Absorbers poisons, Chernobyl accident simulation, Rosenbrock method

Abstract

In this paper, the solution of the Neutron Point Kinetics model is presented, adding the effects of temperature and absorbers poisons within a historical and technical context to simulate the preliminary characteristics of the Chernobyl accident. The Point Kinetics model was able to extract physical information consistent with what was expected to predict the reactor situation until the accident. It was also possible to verify, given the results, that the Rosenbrock method was able to overcome the degree of stiffness of the ODE system, besides solving a non-linear problem. Thus, this study has contributed to highlighting the importance of temperature effects and especially absorbers poisons in the final power behavior, extremely relevant for decision making in the operation and safety of a nuclear power plant.

Views: 364
XML Downloads: 106
PDF Downloads: 231

Downloads

Download data is not yet available.

References

CASTILHO, M. A.; SUGUIMOTO, D. Y. L. Chernobyl - A catástrofe. Rev. da UninCor, v. 12, p. 316-322, 2014. DOI: https://doi.org/10.5892/ruvrd.v12i2.1506

CHAN, P. S. W.; DASTUR, A. R.; GRANT, S. D.; HOPWOOD, J. M.; CHEXAL, B. Multidimensional Analysis of the Chernobyl accident. Atomic Energy of Canada Limited and Electric Power Research Institute AECL-9604. Canada, 1988.

PLOKHY, S. Chernobyl: History of a Tragedy. London: Penguin Press, 2018.

MEDVEDEV, G. The Truth about Chernobyl. New York: Tauris, 1991.

FLETCHER, C.D.; CHAMBERS, R.; BOLANDER, M. A.; DALLMAN, R. J. Simulation of the Chernobyl accident. Nucl. Eng. Des., v. 105, p. 157-172, 1988. DOI: https://doi.org/10.1016/0029-5493(88)90337-8

YOSHIDA, K.; TANABE, F.; HIRANO, M.; KOHSAKA A. Analyses of Power Excursion Event in Chernobyl Accident with RETRAN Code. Taylor & Francis. J. Nucl. Sci. Technol. v. 23, p. 1107-1109, 1986. DOI: https://doi.org/10.1080/18811248.1986.9735104

GEER, L.; PERSSON, C.; RODHE, H. A Nuclear Jet at Chernobyl Around 21:23:45 UTC on April 25, 1986. Nucl. Technol., v. 201, p. 11-22, 2017. DOI: https://doi.org/10.1080/00295450.2017.1384269

PARISI, C. Nuclear Safety of RBMK Reactors. Tese de doutorado em Engenharia Leonardo da Vinci, Universidade de Pisa, 2008.

NAHLA, A. A. An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects. Ann. Nucl. Energy., v. 38, p. 2810-2817, 2011. DOI: https://doi.org/10.1016/j.anucene.2011.08.021

ABOANBER, A. E.; NAHLA, A. A.; AL-MALKI, F. A.. Stability of the analytical perturbation for nonlinear coupled kinetics equations. In: Intl. Conf. On Mathematics, Trends and Development ICMTD12, Egyptian Mathematical Society, Cairo, Egypt, 2012.

MOHIDEEN ABDUL RAZAK, M.; RATHINASAMY, N.. Haar wavelet for solving the inverse point kinetics equations and estimation of feedback reactivity coefficient under background noise. Nucl. Eng. Des., v. 335, p. 202-209, 2018. DOI: https://doi.org/10.1016/j.nucengdes.2018.04.022

ABOANBER, A.; HAMADA, D. Power series solution (PWS) of nuclear reactor dynamics with newtonian temperature feedback. Ann. Nucl. Energy., v. 30, p. 1111-1122, 2003. DOI: https://doi.org/10.1016/S0306-4549(03)00033-1

SATHIYASHEELA, T. Power series solution method for solving point kinetics equations with lumped model temperature and feedback. Ann. Nucl. Energy. v. 36, p. 246-250, 2009. DOI: https://doi.org/10.1016/j.anucene.2008.11.005

PAGANIN, T. M.; BODMANN, B. E. J.; VILHENA, M. T. On a point kinetic model for nuclear reactors considering the variation in fuel composition. J. Prog. Nucl. Energy., v. 118, p. 103-134, 2020. DOI: https://doi.org/10.1016/j.pnucene.2019.103134

YANG, X.; JEVREMOVIC, T. Revisiting the Rosenbrock numerical solutions of the reactor point kinetics equation with numerous examples. J. Nucl. Technol. Radiat. Prot., v. 24, p. 3-12, 2009. DOI: https://doi.org/10.2298/NTRP0901003Y

SCHAUN, N. B.; TUMELERO, F.; PETERSEN, C. Z. Solution of the Neutron Point Kinetics equations by applying the Rosenbrock method. In: 18th Brazilian Congress of Thermal Sciences and Engineering, Online, 2020. DOI: https://doi.org/10.26678/ABCM.ENCIT2020.CIT20-0765

SCHAUN, N. B.; TUMELERO, F.; PETERSEN, C. Z. Solução das equações da cinética pontual de nêutrons com feedback de temperatura via método de Rosenbrock. In: XXIII Encontro Nacional de Modelagem Computacional, Palmas, TO, 2020.

SCHAUN, N. B.; TUMELERO, F.; PETERSEN, C. Z. Influence of the main neutron absorbers poisons coupled to the Point Kinetics model by the Rosenbrock’s method. BRAZILIAN JOURNAL OF RADIATION SCIENCES, v. 10, p. 1-20, 2022. DOI: https://doi.org/10.15392/bjrs.v10i1.1705

DUDERSTADT, J., HAMILTON, L. Nuclear Reactor Analysis. New York: John Wiley & Sons, 1976.

CURTISS, C.; HIRSCHFELDER, J. Integration of Stiff Equations. Proceedings of the National Academy of Sciences of the United States of America, v. 38, p. 235-243, 1952. DOI: https://doi.org/10.1073/pnas.38.3.235

VOSS, D. A. Fourth-order parallel Rosenbrock formulae for stiff systems. J. Math. Comput. Model. Dyn. Syst., v. 40, p. 1193-1198, 2004. DOI: https://doi.org/10.1016/j.mcm.2005.01.013

ABOANBER, A. E; HAMADA, Y. Generalized Runge–Kutta method for two and three-dimensional space–time diffusion equations with a variable time step. Ann. Nucl. Energy., v. 35, p. 1024-1040, 2008. DOI: https://doi.org/10.1016/j.anucene.2007.10.008

KAPS, P.; RENTROP, P. Generalized Runge-Kutta methods of order four with step size control for stiff ordinary differential equations. Numer Math., v. 33, p. 55-68, 1979. DOI: https://doi.org/10.1007/BF01396495

ABOANBER, A. E. Stability of generalized Runge–Kutta methods for stiff kinetics coupled differential equations. J. Phys. A Math. Theor., v. 39, p. 1859-1876, 2006. DOI: https://doi.org/10.1088/0305-4470/39/8/006

SILVA, D. E. Acidente de Chernobyl (causas e consequências). Rio de Janeiro: Comissão Nacional de Energia Nuclear (CNEN), 1986.