Evaluation of Uncertainties in βeff by Means of Deterministic and Monte Carlo Methods

Due to the influence of delayed neutrons on the reactor dynamics an accurate estimation of the effective delayed neutron fraction (βeff), as well as good understanding of the corresponding uncertainty, is essential for reactor safety analysis. This paper presents the βeff sensitivity and uncertainty analysis based on the derivation of Bretscher's prompt k-ratio equation. Performance of both deterministic (SUSD3D generalized perturbation code) and Monte Carlo (XSUSA random sampling code) methods applied with the multi-group neutron transport codes XSDRN and DANTSYS were compared on a series of ICSBEP critical benchmarks. Using the JENDL-4.0m and SCALE-6.0 covariance matrices the typical βeff uncertainty was found to be around 3–4% and is generally dominated by the uncertainty of delayed nu-bar; depending on the considered assembly, the nu-prompt, inelastic, elastic and fission cross-section uncertainties may also significantly contribute to the overall uncertainty. The βeff measurements in combination with the sensitivity and uncertainty analysis can therefore be exploited for validation of nuclear cross sections, such as delayed fission yields, 238U elastic and inelastic cross section, complementing thus the information obtained from the keff measurements.