Monte Carlo uncertainty quantification of the effective delayed neutron fraction

ABSTRACT

The applicability of Monte Carlo techniques, namely the Monte Carlo sensitivity method and the random-sampling method, for uncertainty quantification of the effective delayed neutron fraction β_eff is investigated using the continuous-energy Monte Carlo transport code, MCNP, from the perspective of statistical convergence issues. This study focuses on the nuclear data as one of the major sources of β_eff uncertainty. For validation of the calculated β_eff, a critical configuration of the VENUS-F zero-power reactor was used. It is demonstrated that Chiba's modified k-ratio method is superior to Bretscher's prompt k-ratio method in terms of reducing the statistical uncertainty in calculating not only β_eff but also its sensitivities and the uncertainty due to nuclear data. From this result and a comparison of uncertainties obtained by the Monte Carlo sensitivity method and the random-sampling method, it is shown that the Monte Carlo sensitivity method using Chiba's modified k-ratio method is the most practical for uncertainty quantification of β_eff. Finally, total β_eff uncertainty due to nuclear data for the VENUS-F critical configuration is determined to be approximately 2.7% with JENDL-4.0u, which is dominated by the delayed neutron yield of ²³⁵U.

KEYWORDS:

• Effective delayed neutron fraction
• uncertainty quantification
• sensitivity
• Bretscher's prompt k-ratio method
• Chiba's modified k-ratio method
• random-sampling method
• MCNP
• VENUS-F

Acknowledgments

The authors are grateful to Drs K. Nishihara and T. Sugawara of the Japan Atomic Energy Agency (JAEA) and Prof. G. Chiba of Hokkaido University for providing useful comments and suggestions. One of the authors (H. Iwamoto) would like to thank Dr S. Meigo of JAEA for encouraging his work at SCK•CEN.

Disclosure statement

No potential conflict of interest was reported by the authors.