Safety implications of a sensitivity analysis of the reactor kinetics parameters for fast breeder reactors

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Polytechnic Institute and State University


The delayed neutron spectra for LMFBRs are not as well known as those for LWRs. These spectra are necessary for kinetics calculations which play an important role in safety and accident analyses. In this study, a sensitivity analysis was performed to study the sensitivity of the reactor power and power density to uncertainties in the delayed neutron spectra during a rod ejection accident.

The generalised methodology, developed by Cacuci et. al., was used to derive a set of sensitivity derivatives. This method is based on the use of adjoints so that it is not necessary to repeatedly solve the governing (kinetics) equations to obtain the sensitivity derivatives. This is of particular importance when large systems of equations are used.

A two-energy multigroup and two precursor group model was formulated for the INFCE reference design MOX-fuelled LMFBR. The accidents studied were central control rod ejections with ejection times of 2, 10, and 30 seconds.

The power and power density responses were found to be most sensitive to uncertainties in the spectrum of the second delayed neutron precursor group, resulting from the fission of U-238, producing neutrons in the first energy group. It was found, for example, that for a rod ejection time of 30 seconds, an uncertainty of 7.2% in the fast components of the spectra resulted in a 24% uncertainty in the predicted power and power density. These responses were recalculated by repeatedly solving the kinetics equations. The maximum discrepancy was only 1.6%.

The versatility and accuracy of Cacuci’s methodology has been demonstrated. The results of the sensitivity analysis indicates the need for improved delayed neutron spectral data in order to reduce the uncertainties in the accident analyses.

The model can be extended by using more energy groups, more precursor groups, and more spatial dimensions. Other important responses that may be studied are the linear power density, linear heat rate, and reactivity worths.