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Overview of Nuclear Data Uncertainty in Scale and Application to Light Water Reactor Uncertainty Analysis

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Overview of Nuclear Data Uncertainty in Scale and Application to Light Water Reactor Uncertainty Analysis NUREG/CR-7249 ORNL/TM-2017/706 Overview of Nuclear Data Uncertainty in Scale and Application to Light Water Reactor Uncertainty Analysis Office of Nuclear Regulatory Research AVAILABILITY OF REFERENCE MATERIALS IN NRC PUBLICATIONS NRC Reference Material Non-NRC Reference Material As of November 1999, you may electronically access Documents available from public and special technical NUREG-series publications and other NRC records at libraries include all open literature items, such as books, NRC’s Library at www.nrc.gov/reading-rm.html. Publicly journal articles, transactions, Federal Register notices, released records include, to name a few, NUREG-series Federal and State legislation, and congressional reports. publications; Federal Register notices; applicant, Such documents as theses, dissertations, foreign reports licensee, and vendor documents and correspondence; and translations, and non-NRC conference proceedings NRC correspondence and internal memoranda; bulletins may be purchased from their sponsoring organization. and information notices; inspection and investigative reports; licensee event reports; and Commission papers Copies of industry codes and standards used in a and their attachments. substantive manner in the NRC regulatory process are maintained at— NRC publications in the NUREG series, NRC regulations, The NRC Technical Library and Title 10, “Energy,” in the Code of Federal Regulations Two White Flint North may also be purchased from one of these two sources. 11545 Rockville Pike Rockville, MD 20852-2738 1. The Superintendent of Documents U.S. Government Publishing Office These standards are available in the library for reference Washington, DC 20402-0001 use by the public. Codes and standards are usually Internet: bookstore.gpo.gov copyrighted and may be purchased from the originating Telephone: (202) 512-1800 organization or, if they are American National Standards, Fax: (202) 512-2104 from— American National Standards Institute 2. The National Technical Information Service 11 West 42nd Street oa 5301 Shawnee R d New York, NY 10036-8002 Alexandria, VA 22312-0002 www.ansi.org www.ntis.gov (212) 642-4900 1-800-553-6847 or, locally, (703) 605-6000 Legally binding regulatory requirements are stated only in A single copy of each NRC draft report for comment is laws; NRC regulations; licenses, including technical available free, to the extent of supply, upon written specifications; or orders, not in NUREG-series publications. request as follows: The views expressed in contractor prepared publications in this series are not necessarily those of the NRC. Address: U.S. Nuclear Regulatory Commission The NUREG series comprises (1) technical and Office of Administration administrative reports and books prepared by the staff Multimedia, Graphics, and Storage & (NUREG–XXXX) or agency contractors (NUREG/CR–XXXX), (2) proceedings of conferences (NUREG/CP–XXXX), Distribution Branch (3) reports resulting from international agreements Washington, DC 20555-0001 (NUREG/IA–XXXX),(4) brochures (NUREG/BR–XXXX), and E-mail: [email protected] (5) compilations of legal decisions and orders of the Facsimile: (301) 415-2289 Commission and Atomic and Safety Licensing Boards and of Directors’ decisions under Section 2.206 of NRC’s regulations (NUREG–0750). Some publications in the NUREG series that are posted at NRC’s Web site address www.nrc.gov/reading-rm/ DISCLAIMER: This report was prepared as an account doc-collections/nuregs are updated periodically and may of work sponsored by an agency of the U.S. Government. differ from the last printed version. Although references to Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or implied, material found on a Web site bear the date the material or assumes any legal liability or responsibility for any third was accessed, the material available on the date cited party’s use, or the results of such use, of any information, may subsequently be removed from the site. apparatus, product, or process disclosed in this publication, or represents that its use by such third party would not infringe privately owned rights. NUREG/CR-7249 ORNL/TM-2017/706 Overview of Nuclear Data Uncertainty in Scale and Application to Light Water Reactor Uncertainty Analysis Manuscript Completed: December 2017 Date Published: December 2018 Prepared by: W. Wieselquist M. Williams D. Wiarda M. Pigni U. Mertyurek Oak Ridge National Laboratory Bethel Valley Road Oak Ridge, TN 37831 Mourad Aissa, NRC Project Manager Office of Nuclear Regulatory Research ABSTRACT This report presents the current state of the art in SCALE for nuclear data uncertainty analysis capability, and it provides an overview of the uncertainty in multigroup cross sections, fission product yields, and decay data. The effect of nuclear data uncertainty is demonstrated for a typical light water reactor (LWR) depletion analysis problem involving a Combustion Engineering 14 × 14 assembly irradiated in Calvert Cliffs Unit 1. A single fuel rod from assembly D047, designated as MKP109, has been subjected to destructive radiochemical assay to measure the isotopic contents. The 95% range width (difference between the 97.5th and 2.5th percentiles) is used in this study to assess the calculation uncertainty. This approach uses the actual distribution of the data and does not make any assumptions about the normality of the distributions. If the distribution were normal, then the 95% range width would correspond to 4-sigma range, or +/- 2 sigma. The calculation uncertainty determined in nuclide concentrations for the MKP109 rod ranges from a few percent to 50%. The power factor for this fuel rod shows a very low uncertainty of less than 0.5%. Uncertainties in the macroscopic cross sections, reactivity, and power distributions are generally low, in the few percent range. The effective delayed neutron fraction, 훽푒푓푓, shows higher uncertainty of 20–100%. iii FOREWORD Consideration of nuclear data uncertainty in calculations is an active area of research in data and software development. On the nuclear data side, uncertainty adds another dimension to an already complex database, and although the topic of uncertainty data is receiving attention— each subsequent ENDF/B release has additional data uncertainty—there is still not widespread usage of the uncertainty data due in part to lack of software tools, but also due to disagreements within the nuclear engineering analysis community on how exactly it can be used. This report demonstrates usage of the uncertainty data in one of the areas where many code developers and analysts spend a lot of time: code and model validation. This report recommends error metrics that use uncertainty, additional avenues for interpreting validation results when calculation uncertainty is included, and avenues for additional usage of the uncertainty data. Ideally, data uncertainty should become standard in validation, leading to new pathways for data improvement. v TABLE OF CONTENTS ABSTRACT ................................................................................................................... iii FOREWORD ................................................................................................................... v LIST OF FIGURES......................................................................................................... ix LIST OF TABLES .......................................................................................................... xi EXECUTIVE SUMMARY ............................................................................................. xiii ABBREVIATIONS AND ACRONYMS .......................................................................... xv 1 INTRODUCTION ..................................................................................................... 1-1 1.1 Model Equations ...........................................................................................................1-1 1.1.1 Transport Equation .........................................................................................1-2 1.1.2 Transmutation Equation ..................................................................................1-3 1.1.3 Multigroup Representation ..............................................................................1-4 1.2 Additional Models .........................................................................................................1-5 1.2.1 Few-Group Macroscopic Cross Sections ........................................................1-5 1.2.2 Activity and Decay Heat ..................................................................................1-5 1.2.3 Reactivity Coefficients ....................................................................................1-5 1.2.4 Kinetics Parameters........................................................................................1-6 1.2.5 Power Peaking Factors ...................................................................................1-6 1.3 Uncertainty Quantification Methods ..............................................................................1-7 1.3.1 Perturbation Theory ........................................................................................1-7 1.3.2 Sampling ........................................................................................................1-7 2 DATA UNCERTAINTY ............................................................................................ 2-1 2.1 Cross Section Uncertainty ............................................................................................2-1
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