SENSITIVITY AND UNCERTAINTY ANALYSIS OF MULTIPHYSICS NUCLEAR REACTOR CORE DEPLETION by Andrew Scott Bielen A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Nuclear Engineering and Radiological Sciences) in the University of Michigan 2015 Doctoral Committee: Professor Thomas J. Downar , Co-Chair Associate Professor Annalisa Manera, Co-Chair Associate Professor Krzysztof J. Fidkowski Professor John C. Lee Joseph L. Staudenmeier, US Nuclear Regulatory Commission For my wife, Lisa ii AKNOWLEDGEMENTS I would like to acknowledge the contributions of the many that helped and guided me through this Ph.D. process. First and foremost are my co-advisors Prof. Tom Downar and Prof. Annalisa Manera, whose guidance and support were instrumental in the completion of this dissertation. I would also like to thank my committee members, Prof. John Lee and Prof. Krzysztof Fidkowski, and Dr. Joe Staudenmeier of the US Nuclear Regulatory Commission, whose feedback on this dissertation was invaluable. Additionally, I thank my branch chief at the NRC, Dr. Chris Hoxie, for his patience, understanding, and support during the completion of this work. In addition to these members, I must also thank the following: Dr. Patrick Raynaud of the US NRC and Ken Geelhood of Pacific Northwest National Laboratory, for conversations and guidance on working with and developing the FRAPCON fuel performance code for coupled neutronics and uncertainty analysis was crucial; Dr. Andrew Ward of the University of Michigan, for assisting me with the necessary PARCS/PATHS development and cross section generation using HELIOS; Dr. Tim Drzewiecki of the US NRC for assistance in providing the computer resources required to complete the sensitivity and uncertainty portion of this thesis; and Michael Rose and Thomas Saller at the University of Michigan for supporting me on my visits back to Ann Arbor. Lastly, but most importantly, I thank my wife Lisa for supporting my desire to earn my doctorate, and her willingness to engage in considerable personal sacrifice to ensure that it happened. Without her emotional support, this work would not have been accomplished. This dissertation was completed with the support of the US NRC Graduate Fellowship Program from 2011-2015. iii TABLE OF CONTENTS Dedication ............................................................................................................................................ii Acknowledgements ........................................................................................................................... iii List of Figures ....................................................................................................................................vii List of Tables ...................................................................................................................................... ix List of Appendices .............................................................................................................................. x Abstract ............................................................................................................................................... xi Chapter 1 Introduction ..................................................................................................................................... 1 1.1 Motivation .................................................................................................................................. 1 1.2 Reactor Analysis Methods ........................................................................................................ 2 1.2.1 Simulation Needs and Approaches .................................................................................... 2 1.2.2 Uncertainty Analysis and Multiphysics Simulation ......................................................... 5 1.3 Demonstration Case: PWR Depletion ...................................................................................... 6 1.3.1 PARCS Model Description ................................................................................................ 6 1.3.2 Gap Conductance Calculation with FRAPCON ............................................................... 7 1.3.3 Neutronic Behavior as a Function of Gap Conductance .................................................. 9 1.3.4 Sensitivity Study Conclusions ......................................................................................... 12 1.4 Outline of Thesis ...................................................................................................................... 13 2 Review of Literature .................................................................................................................... 14 2.1 Introduction .............................................................................................................................. 14 2.2 Fuel Performance Analysis Codes .......................................................................................... 14 2.2.1 FRAPCON ........................................................................................................................ 16 2.2.2 FRAPTRAN ...................................................................................................................... 17 2.2.3 FALCON ........................................................................................................................... 18 2.2.4 INTERPIN ......................................................................................................................... 19 2.2.5 Advanced Fuel Codes ....................................................................................................... 19 2.3 Neutronics Analysis Codes and Methods............................................................................... 20 2.3.1 Generation of Cross Section Libraries for Lattice Calculations .................................... 21 2.3.2 Lattice Codes ..................................................................................................................... 21 2.3.3 Core Neutronics Simulators ............................................................................................. 23 2.3.4 Advanced Neutronics Codes ............................................................................................ 25 iv 2.4 Multiphysics Calculations ....................................................................................................... 26 2.4.1 General Approaches.......................................................................................................... 27 2.4.2 Neutronics/Thermal-Hydraulics ...................................................................................... 29 2.4.3 Neutronics/Fuel Thermal-Mechanics .............................................................................. 31 2.5 Sensitivity and Uncertainty Methods ..................................................................................... 32 2.5.1 S/UA Frameworks ............................................................................................................ 34 2.5.2 Applications ...................................................................................................................... 38 2.6 Conclusions .............................................................................................................................. 42 3 FRAPCON/PARCS/PATHS Coupling Methodology ............................................................. 43 3.1 Introduction .............................................................................................................................. 43 3.2 Fuel Performance Modeling with FRAPCON ....................................................................... 43 3.2.1 FRAPCON Computational Scheme ................................................................................ 44 3.2.2 Uncertainty Calculations with FRAPCON ..................................................................... 49 3.3 Reactor Core Simulation with PARCS/PATHS .................................................................... 53 3.3.1 PARCS Methods ............................................................................................................... 54 3.3.2 PATHS Methods ............................................................................................................... 56 3.3.3 PARCS/PATHS Coupling................................................................................................ 58 3.4 Algorithm Modifications for Coupling FRAPCON and PARCS/PATHS .......................... 58 3.4.1 Overview of Coupling Scheme ........................................................................................ 59 3.4.2 FRAPCON Modifications ................................................................................................ 62 3.4.3 PARCS/PATHS Modifications ........................................................................................ 63 3.4.4 FRAPARCS Driver Script ............................................................................................... 66 3.5 Sensitivity and Uncertainty Evaluation with DAKOTA ....................................................... 69 3.6 Conclusions .............................................................................................................................. 71 4 Application of FRAPARCS to Depletion .................................................................................. 72 4.1