Computational Methods for Burnup Calculations with Monte Carlo Neutronics

Aarno Isotalo

Research output: ThesisDoctoral ThesisCollection of Articles


The work described in this thesis deals with the computational methods and algorithms used in burnup calculations, which model changes in the composition of nuclear fuel under irradiation. While only cases where the neutron transport part of the calculation is handled by the Monte Carlo method are considered, most of the results should also be applicable with deterministic neutronics. During each step of a Monte Carlo burnup calculation, changes in material compositions are solved by evaluating an explicit solution to the Bateman equations with constant coefficients. Five depletion algorithms capable of doing this while explicitly modeling all of the thousands of nuclides and reactions encountered in burnup calculations were compared. The results are quite conclusive and, together with other studies, show rational approximation based matrix exponential methods to be the best choice for Monte Carlo burnup calculations. The constant coefficients of the Bateman equations are selected by a coupling scheme that uses one or more steady state neutronics solutions to predict their time development. Because the coefficients must be constant, these predictions are further approximated with their averages. New coupling schemes that use data from the previous step to make higher order predictions are presented. Since the old values are readily available, no additional calculations are required, and the stepwise running time is not affected. The coupling is further improved by dividing the steps to substeps, which are then solved sequentially. Since each substep can use different coefficients for the Bateman equations, this allows piecewise constant, rather than constant, approximation of the predicted behavior. These new methods greatly improve the accuracy obtainable with given step lengths, thus allowing longer steps to be used. Prior studies have shown that the existing coupling schemes used in Monte Carlo burnup calculations suffer from instabilities caused by spatial xenon oscillations. The new methods are also affected, but it is shown that the simulation models used in these tests actually describe physical xenon oscillations, not a stable state. Thus it is the models, not the methods used to solve them, that are unstable. Regardless, all xenon driven oscillations can be prevented by forcing a mutual equilibrium between the neutron flux and saturated xenon distribution. The equilibrium calculation can be integrated to Monte Carlo neutronics, which provides a simple and lightweight solution that can be used with any of the existing burnup calculation algorithms. However, oscillations driven by nuclides other than xenon may still arise if step lengths are too long.
Translated title of the contributionComputational Methods for Burnup Calculations with Monte Carlo Neutronics
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Salomaa, Ralf, Supervising Professor
  • Aarnio, Pertti, Thesis Advisor
Print ISBNs978-952-60-5397-4
Electronic ISBNs978-952-60-5398-1
Publication statusPublished - 2013
MoE publication typeG5 Doctoral dissertation (article)


  • nuclear reactor
  • burnup calculation
  • computational methods


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