The Pennsylvania State University The Graduate School UNCERTAINTY ANALYSIS OF SPENT NUCLEAR FUEL ISOTOPICS AND ROD INTERNAL PRESSURE

Transcription

1 The Pennsylvania State University The Graduate School UNCERTAINTY ANALYSIS OF SPENT NUCLEAR FUEL ISOTOPICS AND ROD INTERNAL PRESSURE A Dissertation in Nuclear Engineering by Ryan N. Bratton c 2015 Ryan N. Bratton Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2015

2 The dissertation of Ryan N. Bratton was reviewed and approved by the following: Kostadin N. Ivanov Professor of Nuclear Engineering Dissertation Co-Adviser Co-Chair of Committee Igor Jovanovic Professor of Nuclear Engineering Dissertation Co-Adviser Co-Chair of Committee Maria N. Avramova Associate Professor of Nuclear Engineering Dissertation Co-Adviser Co-Chair of Committee Monique Yaari Professor of French Studies Matthew A. Jessee Special Member Associate Researcher at Oak Ridge National Laboratory William A. Wieselquist Special Member Associate Researcher at Oak Ridge National Laboratory Arthur Motta Professor of Nuclear Engineering and Materials Science and Engineering Chair of Nuclear Engineering Signatures are on file in the Graduate School.

3 Abstract The bias and uncertainty in fuel isotopic calculations for a well-defined radiochemical assay benchmark are investigated with Sampler, the new sampling-based uncertainty quantification tool in the SCALE code system. Isotopic predictions are compared to measurements of fuel rod MKP109 of assembly D047 from the Calvert Cliffs Unit 1 core at three axial locations, representing a range of discharged fuel burnups. A methodology is developed which quantifies the significance of input parameter uncertainties and modeling decisions on isotopic prediction by comparing to isotopic measurement uncertainties. The SCALE Sampler model of the D047 assembly incorporates input parameter uncertainties for key input data such as multigroup cross sections, decay constants, fission product yields, the cladding thickness, and the power history for fuel rod MKP109. The effects of each set of input parameter uncertainty on the uncertainty of isotopic predictions have been quantified. In this work, isotopic prediction biases are identified and an investigation into their sources is proposed; namely, biases have been identified for certain plutonium, europium, and gadolinium isotopes for all three axial locations. Moreover, isotopic prediction uncertainty resulting from only nuclear data is found to be greatest for Eu-154, Gd-154, and Gd-160. The discharge rod internal pressure (RIP) and cladding hoop stress (CHS) distributions are quantified for Watts Bar Nuclear Unit 1 (WBN1) fuel rods by modeling core cycle design data, operation data (including modeling significant trips and downpowers), and as-built fuel enrichments and densities of each fuel rod in FRAPCON-3.5. A methodology is developed which tracks inter-cycle assembly movements and assembly batch fabrication information to build individual FRAPCON inputs for each considered WBN1 fuel rod. An alternate model for the amount of helium released from zirconium diboride (ZrB 2 ) integral fuel burnable absorber (IFBA) layers is derived and applied to FRAPCON output data to quantify the RIP and CHS for these fuel rods. SCALE/Polaris is used to quantify iii

4 fuel rod-specific spectral quantities and the amount of gaseous fission products produced in the fuel for use in FRAPCON inputs. Fuel rods with ZrB 2 IFBA layers (i.e., IFBA rods) are determined to have RIP predictions that are elevated when compared to fuel rod without IFBA layers (i.e., standard rods) despite the fact that IFBA rods often have reduced fill pressures and annular fuel blankets. The primary contributor to elevated RIP predictions at burnups less than and greater than 30 GWd/MTU is determined to be the total fuel rod void volume and the amount of released fission gas in the fuel rod, respectively. Cumulative distribution functions (CDFs) are prepared from the distribution of RIP and CHS predictions for all standard and IFBA rods. The provided CDFs allow for the determination of the portion of WBN1 fuel rods that exceed a specified RIP or CHS limit. Results are separated into IFBA and standard rods so that the two groups may be analyzed individually. FRAPCON results are provided in sufficient detail to enable the recalculation of the RIP while considering any desired plenum gas temperature, total void volume, or total amount of gas present in the void volume. A method to predict the CHS from a determined or assumed RIP is also proposed, which is based on the approximately linear relationship between the CHS and the RIP. Lastly, improvements to the computational methodology of FRAPCON are proposed. iv

5 Table of Contents List of Figures List of Tables Acronyms Acknowledgments viii xii xiii xvi Chapter 1 Introduction Importance of Spent Nuclear Fuel Modeling and Analysis Motivation and Purpose of Research Reactor Systems to be Analyzed Calvert Cliffs Unit Available Data Goals of Analysis Watts Bar Nuclear Unit Available Data Goals of Analysis Computational Tools SCALE Code System FRAPCON Nuclear Data Libraries Dissertation Overview Chapter 2 Relevant Background Fuel Performance Background v

6 2.1.1 Rod Internal Pressure Fission Gas Release Integral Fuel Burnable Absorbers Fuel Swelling Fuel Rod Void Volume Fuel Plenum Volume Fuel-Cladding Gap Volume Fuel Annulus Volume Fuel Cracking Volume Fuel Dishing and Chamfer Volumes Fuel Open Porosity Volume Fuel Roughness Volume Zirconium Hydrides Cladding Hoop Stress Fuel Isotopic Concentrations Uncertainty Quantification and Sensitivity Analysis Background Uncertainty Propagation Sensitivity Quantification Bias Quantification Chapter 3 Calvert Cliffs Unit 1 Analysis Experimental Data Methodology Bias Assessment Procedure Modeling-Based Bias Assessment Analysis Self-Shielding Treatment Fuel Temperature Distribution Nuclide Tracking Set Input-Based Bias Assessment Analysis Power History Other Uncertainties Final Sampler Model Results Analysis Conclusions vi

7 Chapter 4 Watts Bar Nuclear Unit 1 Multicycle Analysis Experimental Data Methodology Pre-processing FRAPCON Input Generation Inter-cycle Assembly Movements Fuel Pellet Composition and Geometry Fuel Rod Geometry and Fabrication Irradiation and Operational History Fission Production of Gaseous Isotopes Fast Flux Factor Post-processing Summary of Assumptions Results and Discussion Operating History FRAPCON Parameters Total Fuel Rod Void Volume Released Fission Gas IFBA Layer Helium Production Rod Internal Pressure Cladding Hoop Stress Analysis Conclusions Chapter 5 Conclusions and Future Work Project Achievements PhD Contributions Evaluation of Achievements and Future Work Bibliography 124 vii

8 List of Figures 1.1 Layout of assembly D047 and the location of fuel rod MKP Axial arrangement of assembly D047 fuel rods Radial orientation of Watts Bar Nuclear Unit 1 (WBN1) 17x17 assemblies Axial arrangement of a general WBN1 fuel rod A simplified flowchart of FRAPCON The Vitanza threshold temperature for fission gas release (FGR) behavior Thermal expansion of cylindrical fuel pellets leading to pellet hourglassing and pellet-cladding mechanical interaction (PCMI) A fuel pellet with top and bottom axial surface dishes A fuel pellet with a radial surface dish Cross-section of a fuel rod s cladding showing hydrides oriented primarily in a circumferential direction Cross-section of a fuel rod s cladding with significant amounts of radially oriented hydrides An example distribution of changes in Y due to variations in multiple input quantities X n plotted against a single input quantity X i. The slope of the linear fit represents an approximation of the sensitivity coefficient between Y and X i The location of assembly D047 for each cycle of Calvert Cliffs Unit 1 (CC-1) Isotopic uncertainty due to input parameter uncertainty Isotopic uncertainty due to nuclear data uncertainty Biases not exceeding 20% with 1-sigma error bars for each axial location Biases exceeding 20% with 1-sigma error bars for each axial location Biases for the gigawatt days per metric ton uranium (GWd/MTU) case with and without power history normalization viii

9 4.1 A visualization of the operational history of a fuel rod. Data point colors correspond to the average fuel rod temperature. An intercycle down time of 50 days is assumed The axial power profile progression of a typical fuel rod across three consecutive fuel cycles A simplified flowchart of the sequence of calculations of the FRAPCON Input Generator (FIG) The distribution of discharge burnups for cycle 1 through cycle 10 fuel rods The distribution of peak rod-averaged fuel temperatures throughout the lifetimes of cycle 1 through cycle 10 fuel rods The distribution of lifetime-averaged LHGR values of cycle 1 through cycle 10 fuel rods Predictions of Γ calculated from SCALE/Polaris output using equation The fuel specific power was kept constant at 40 W/g and the initial enrichment was 3 wt% U Predictions of Γ calculated from SCALE/Polaris output using equation 4.20 with a constant specific power of 40 W/g evaluated at a fuel burnup of 60 GWd/MTU Predictions of Γ calculated from SCALE/Polaris output using equation 4.20 with a initial enrichment of 3 wt% U-235 evaluated at a fuel burnup of 60 GWd/MTU A visualization of trilinear interpolation where the desired prediction p is bound between eight pre-calculated data points The distribution of Γ predictions for WBN1 cycle 1 through cycle 10 fuel rods calculated from SCALE/Polaris output data using equation Predictions of F F ast calculated from SCALE/Polaris output data using equation The fuel specific power was kept constant at 40 W/g and the initial enrichment was 3 wt% U Predictions of F F ast calculated from SCALE/Polaris output data using equation The fuel specific power and burnup correspond to 40 W/g and 60 GWd/MTU, respectively Predictions of F F ast calculated from SCALE/Polaris output data using equation The fuel specific power and initial enrichment correspond to to 40 W/g and 3 wt% U-235, respectively The distribution of predicted values for F F ast calculated from SCALE/Polaris output data using equation The distribution of predicted values for total flux over the fast flux calculated from SCALE/Polaris output data ix

10 4.17 Total rod void volume vs. discharge burnup under vacuum drying conditions (P Ext =133 Pa, T =400 C) for cycle 1 through cycle 10 fuel rods Total rod void volume vs. discharge burnup under vacuum drying conditions (P Ext =133 Pa, T =400 C) for cycle 1 through cycle 10 fuel rods. Colors correspond to the amount of data within each discharge burnup and total void volume bin The distribution of total void volumes for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T =400 C) Relative void volume predictions (V f /V i ) for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T f =400 C). Colors correspond to the amount of data within each discharge burnup and void volume bin The distribution of relative void volume predictions (V f /V i ) for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T f =400 C) Released fission gas for WBN1 cycle 1 through cycle 10 fuel rods Released fission gas for WBN1 cycle 1 through cycle 10 fuel rods. Colors correspond to the amount of data within each discharge burnup and released fission gas bin The distribution of released fission gas for cycle 1 through cycle 10 fuel rods The B-10 utilization factor of each ZrB 2 IFBA layer vs. discharge burnup for cycle 1 through cycle 10 fuel rods, calculated using equation The distribution of B-10 utilization factors of cycle 1 through cycle 10 fuel rods, calculated using equation Rod internal pressure vs. discharge burnup for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T =400 C) rod internal pressure (RIP) predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T =400 C). Colors correspond to the amount of data within each discharge burnup and RIP bin The distribution of rod internal pressures for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T =400 C) x

11 4.30 Cladding hoop stress factor predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T F =400 C). Colors correspond to the amount of data within each discharge burnup and cladding hoop stress factor bin The distribution of cladding hoop stress factor predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T F =400 C) Cladding hoop stress predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T F =400 C) Cladding hoop stress predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T F =400 C). Colors correspond to the amount of data within each discharge burnup and cladding hoop stress bin The distribution of cladding hoop stress predictions for cycle 1 through cycle 10 fuel rods under vacuum drying conditions (P Ext =133 Pa, T =400 C) The rod internal pressure cumulative distribution function for cycle 1 through cycle 10 standard rods under vacuum drying conditions at various rod-averaged plenum gas temperatures The rod internal pressure cumulative distribution function for cycle 1 through cycle 10 IFBA rods under vacuum drying conditions at various rod-averaged plenum gas temperatures The cladding hoop stress cumulative distribution function for cycle 1 through cycle 10 standard rods under vacuum drying conditions at various rod-averaged plenum gas temperatures The cladding hoop stress cumulative distribution function for cycle 1 through cycle 10 IFBA rods under vacuum drying conditions at various rod-averaged plenum gas temperatures xi

12 List of Tables 3.1 Relevant assembly design and operating data for CC Relevant fuel rod data for CC Relevant fuel rod data for CC Axially-dependent data for fuel rod MKP109 of CC Pacific Northwest National Laboratory (PNNL) isotopic composition measurement data for CC-1 samples Khlopin Radium Institute (KRI) isotopic composition measurement data for CC-1 samples Power histories and boron concentrations for rod MKP109 of assembly D end-of-cycle (EOC) and end-of-life (EOL) burnups in GWd/MTU for each axial location of fuel rod MKP Predicted fuel ring temperatures (in K) for fuel rod MKP109 axial location of cm calculated using equation 3.8 and equation Summary of modeling-based bias assessment studies performed Summary of input-uncertainty studies performed Isotopes with significant biases (shown as number of SDs) in isotopic predictions Statistical uncertainties in RIP predictions for standard and integral fuel burnable absorber (IFBA) rods within the specified rod-averaged discharged burnup bins Statistical uncertainties in burnup predictions for standard and IFBA rods within the specified rod-averaged discharged burnup bins. 116 xii

13 Acronyms ATM approved testing material BOC beginning-of-cycle BOL beginning-of-life CASL Consortium for Advanced Simulation of Light water reactors CC-1 Calvert Cliffs Unit 1 CDF cumulative distribution function CE Combustion Engineering CHS cladding hoop stress CT cooling time DBTT ductile-to-brittle transition temperature DSC dry storage cask EFPD effective full power days EOC end-of-cycle EOL end-of-life FGR fission gas release FIG FRAPCON Input Generator GE General Electric xiii

14 GT guide tube GWd/MTU gigawatt days per metric ton uranium HDF hierarchical data format IFBA integral fuel burnable absorber IT instrument tube KRI Khlopin Radium Institute LHGR linear heat generation rate MCNP Monte Carlo N-Particle MeV mega-electronvolt MPa megapascals MTU metric ton uranium NDLs nuclear data libraries NPP nuclear power plant NRC Nuclear Regulatory Commission PCMI pellet-cladding mechanical interaction PNNL Pacific Northwest National Laboratory ppm parts per million PWR pressurized water reactor RCA radiochemical assay RCCA rod cluster control assembly RIP rod internal pressure RMS root mean square RSD relative standard deviation SCALE Standardized Computer Analysis for Licensing Evaluation xiv

15 SD standard deviation SNF spent nuclear fuel TVA Tennessee Valley Authority UK United Kingdom UOX uranium oxide, UO 2 UQ uncertainty quantification US United States WBN1 Watts Bar Nuclear Unit 1 wt.% weight percent ZrB 2 zirconium diboride xv

16 Acknowledgments Sincere thanks are due two my two mentors at Oak Ridge National Laboratory (ORNL), Matt Jessee and Will Wieselquist, who selflessly provided me with invaluable guidance throughout my research. Further, I would like to thank the Reactor and Nuclear Systems Division (RNSD) at ORNL, who have been nothing but helpful and kind; they all serve as my professional role models and working with them has truly been a privilege and an honor. Thanks are also due to my advisor Dr. Kostadin Ivanov, who has been indispensable with regard to my professional and intellectual development. Lastly, I d like to thank my family for the support and prayers they have given me throughout this stage of my life. This work was supported by (1) the U.S. Nuclear Regulatory Commission (NRC) Nuclear Education Grant Program, (2) the Graduate Opportunities (GO!) Program at ORNL as a part of the Department of Energy (DOE) Office of Nuclear Energy (NE) Fuel Cycle Technologies Used Fuel Disposition Campaign (UFDC), and (3) the Nuclear Engineering Science Laboratory Synthesis (NESLS) program of ORNL. This work would not have been possible without the generous contributions of information from the Tennessee Valley Authority, the Westinghouse Electric Company, and the VERA benchmarking of Watts Bar Nuclear Unit 1 performed by CASL, which is funded to improve the methods and software capabilities of the nuclear industry. xvi

17 Dedication To my wife, Caitlin, whose companionship and love I wouldn t trade for anything. xvii

18 Chapter 1 Introduction 1.1 Importance of Spent Nuclear Fuel Modeling and Analysis The safe transportation and storage spent nuclear fuel (SNF) is a chief concern of the nuclear industry. In the case of the United States (US), the safe storage of SNF is important since no SNF is reprocessed for future fuel cycles. In other words, all nuclear fuel discharged from nuclear reactors in the US needs to be either kept on-site in a spent fuel pool or transferred to a SNF storage container and stored offsite for potentially several decades. The necessity of safe storage of SNF presents a constant challenge for the nuclear industry of the US as well as globally because of the tangible effect it has nuclear plant licensing and operation. The accurate modeling of SNF as it is discharged from a nuclear reactor and placed in dry storage is essential in order to determine the proper infrastructure that is required in order to facilitate the safe storage and transportation of SNF. Further, accurate modeling of SNF provides a cheaper means for fuel designers, manufacturers, and safety authorities of the nuclear industry to analyze a variety of nuclear systems without having to perform more costly physical experiments.

19 2 1.2 Motivation and Purpose of Research Dry storage of low burnup SNF [less than 45 gigawatt days per metric ton uranium (GWd/MTU)] has been commonplace since 1986 and its use as a nuclear system for SNF modeling and analysis has been performed extensively for the past several decades. However, the capability to store high-burnup SNF is of increasing importance in recent years since nearly all SNF currently being loaded into storage containers in the US contains high-burnup fuel [1]. For example, between December 2012 and March 2014 nearly 200 dry storage casks were loaded with high-burnup SNF. Transportation and storage of high-burnup SNF is challenging since high-burnup SNF has different mechanical properties than those of low-bu SNF. In addition to the fuel burnup, the irradiation history of SNF (i.e., how much power the fuel produced as a function of time while it was in a nuclear reactor core) may also need to be considered when preparing SNF for storage because fuel temperatures during irradiation have an effect on the amount of fission gas and internal pressure of the fuel rod [2, 3], which is an important parameter to consider when preparing SNF for storage. This imposes an added challenge on modeling high-burnup SNF due to the significance of detailed time-dependent data, which are often not available. Assuming that all of the necessary data were present for a given reactor system, the SNF of that system could be modeled on a rod-by-rod basis to yield distributions of critical fuel performance parameters for SNF discharged from the reactor. Modeling SNF as individual fuel rods with unique operational history data as opposed to a fuel assembly model composed of fuel rods with identical operational data is valuable because fuel assemblies are considered damaged if a single fuel rod experiences a failure. Performing analyses on the assembly-level with identical fuel rod irradiation histories would not capture the behavior of the fuel pins with atypical behavior, such as fuel rods in high-flux regions or those near assembly boundaries or guide tubes. Results that model SNF rods with unique irradiation histories could be helpful by illuminating any subtle or unobserved differences between high- and low-burnup SNF. Further, analyzing distributions of fuel performance parameters could give valuable insight on how the SNF should be stored on an assembly-by-assembly basis by identifying assemblies that could

20 3 experience a fuel rod failure during preparation for dry storage. The results of this type of analysis could have further use as a means to estimate the uncertainty in SNF observables if certain information were unavailable. For instance, if the irradiation history of SNF assembly to be loaded into a dry storage cask were unknown then a comprehensive distribution of SNF observables for the assemblies of a related reactor system could provide an estimate or guidance for the appropriate storage for the fuel assembly. The goals of this work are i) to identify a reactor system which has fuel rodspecific operational history and fuel fabrication data, ii) to develop the necessary tools and methodology to model each fuel pin in the highest possible fidelity given the available data, iii) produce and analyze distributions of SNF observables or compare their predicted values to measurements, iv) to quantify the uncertainty propagated to these chosen parameters when realistic or assumed uncertainties are utilized in the SNF model and v) to quantify the sensitivities of the chosen fuel performance parameters to perturbations in any input quantity of the SNF model. 1.3 Reactor Systems to be Analyzed In order to quantify SNF observables with sufficient fidelity, a nuclear system must be chosen which has detailed operational and geometric data on the fuel rod-level. SNF observables cover a wide range of physical quantities, however, and it is unlikely that the data set of a single reactor system would allow for the quantification of all SNF parameters. For example, the initial fill pressure for a fuel rod is required in order to quantify the discharge rod internal pressure (RIP) of a fuel rod but this value has no effect on SNF isotopic concentrations so it is unlikely to be provided in a data set that was created with the purpose of quantifying discharge fuel isotopics. Consequently, choosing a single reactor system for SNF analysis is challenging when multiple SNF parameters are to be calculated. In order to predict SNF isotopic concentrations and rod internal pressures, two reactor systems are chosen that each contain all (or most) of the necessary data that are required to quantify the SNF parameter of interest with high fidelity.

21 Calvert Cliffs Unit 1 Calvert Cliffs Unit 1 (CC-1) is a pressurized water reactor (PWR) designed by Combustion Engineering (CE) located in Calvert County Maryland and operated by General Electric (GE). The CC-1 core is loaded with 217 fuel assemblies [4] in a 14x14 lattice configuration with 176 fuel rods and five large guide tubes, which are characteristic of CE designs. Assembly D047 was present in the CC-1 core throughout four consecutive cycles (cycles 2 through 5) and has been analyzed and utilized as a validation benchmark for isotopic predictions extensively in the literature [4, 5, 6, 7, 8, 9]. Fuel rod MKP109 is one of the fuel rods of assembly D047 that were destructively analyzed at various axial locations to allow for the measurement of fuel isotopic concentrations. The location of fuel rod MKP109 and the radial configuration of assembly D047 are shown in Figure 1.1. Each fuel pin of assembly D047 is composed of radially-dished fuel pellets (see Figure 2.4 in section ). The axial arrangement of D047 fuel rods is shown in Figure 1.2 and is reproduced from [4]. Figure 1.1. Layout of assembly D047 and the location of fuel rod MKP109.

22 5 Figure 1.2. Axial arrangement of assembly D047 fuel rods Available Data Fuel rod MKP109 of assembly D047 was destructively analyzed at three axial locations: 13.20, 27.70, and cm from the bottom of the active fuel region [7] corresponding to discharge fuel burnups of 27.35, 37.12, and GWd/MTU, respectively [5]. A detailed operating history is available for each considered axial location of fuel rod MKP109, containing data such as the soluble boron concentration and local linear heat generation rate (LHGR) as a function of effective full power days (EFPD) over four consecutive cycles (cycles 2-5). The operating history of fuel rod MKP109 will not be reproduced herein but is available in [7]. Isotopic measurements of fuel rod MKP109 were conducted by two separate institutions: Pacific Northwest National Laboratory (PNNL) [8] and Khlopin Radium Institute (KRI) [10]. The fuel isotopic measurements and their respective measurement uncertainties are summarized in [9] for both institutions Goals of Analysis The principle objective of the CC-1 analysis is to develop a methodology by which sensitivity information of PWR output observables to input parameters may be obtained from the output of SCALE/Sampler, the new sampling-based uncertainty quantification tool in the Standardized Computer Analysis for Licensing Evaluation (SCALE) code system [11]. This improvement would widen the applicability of the Sampler module by allowing it to automatically determine sensitivity infor-

23 6 mation from its stochastically-determined LWR model predictions. In addition, a rigorous investigation into whether a significant bias in isotopic calculations may be found for a well-defined radiochemical assay (RCA) benchmark will be conducted. Identifying unintended biases in isotopic predictions from SCALE may identify errors in the nuclear data which may be partially corrected in order to improve SCALE isotopic predictions. Isotopic predictions will be compared to measurement data from fuel rod MKP109 of CC-1 for each axial layer and any apparent biases resulting from modeling decisions will be analyzed. Uncertainty in geometric parameters, the operating history, and nuclear data will be propagated into SCALE isotopic predictions and their uncertainty contributions will be compared Watts Bar Nuclear Unit 1 Watts Bar Nuclear Unit 1 (WBN1) is a Westinghouse-designed PWR located in Rhea County, Tennessee operated by the Tennessee Valley Authority (TVA). The reactor core is composed of 193 fuel assemblies containing fuel rods organized in a 17x17 lattice. Each fuel assembly has 24 guide tubes allowing the insertion of either discrete burnable poisons or a rod cluster control assembly (RCCA). Each assembly also has a central instrument tube (IT) to enable the insertion of a neutron flux detector. WBN1 is currently being modeled on the pin, assembly, and core levels in the VERA Core Physics Benchmark [12], which conveniently organizes all non-proprietary data for WBN1. The guide tube (GT) and IT radial orientation is fixed for all assemblies and is displayed in Figure 1.3, which is reproduced from [12]. The fuel rods (shown as gray boxes in Figure 1.3) utilize uranium oxide, UO 2 (UOX) fuel in a 12 ft fuel stack with Zircaloy-4 cladding [13]. Each fuel rod contains an upper gas plenum with a plenum spring and upper and lower end plugs. The WBN1 fuel rod arrangement is displayed in Figure 1.4 and is reproduced from [13]. In addition to what is shown in Figure 1.4, there are fuel blanket regions on the top and bottom of the fuel pellet stack. These blanket regions often have unique initial fuel enrichments and densities and can be several inches long. The fuel blankets may also be annular in order to accommodate a higher RIP, which is characteristic for high-burnup fuel rods with zirconium diboride (ZrB 2 ) integral

24 7 fuel burnable absorber (IFBA) layers. Figure 1.3. Radial orientation of WBN1 17x17 assemblies. Figure 1.4. Axial arrangement of a general WBN1 fuel rod.

25 Available Data There is a large amount of data available for WBN1, however, in general, only data from WBN1 cycle 1, which is summarized in [12], is not proprietary. The WBN1 cycle 1 data set contains time-dependent core powers, inlet coolant temperatures, and detailed geometric and composition information for the three assembly batches that make up the WBN1 core of cycle 1. Further, from the analysis of the VERA multi-cycle benchmarking of the WBN1 core [14], predicted time- and axially-dependent powers are available for each pin in the first cycle of WBN1. Measurements for several important parameters are not provided in this WBN1 cycle 1 data set, however, such as the rod fill pressure, which is critical for discharge RIP quantification. Further, irradiation histories corresponding to only one cycle have limited applicability since all end-of-cycle (EOC) burnups will be considered low burnup. As discussed previously in section 1.2, the majority of SNF being produced currently is high burnup so any analyses to be performed in this work should be applicable and valuable to the storage of high burnup SNF. In June 2015 this work was partially incorporated into the Consortium for Advanced Simulation of Light water reactors (CASL) project for modeling WBN1 which expanded the WBN1 data set to include all of the data mentioned above except twelve cycle s worth of data are now available as opposed to just a single cycle. Additionally, detailed geometric information for all fuel batches present in WBN1 throughout all cycles were provided as well as the initial fill pressure for all fuel pins. The WBN1 data were also expanded further to include the operational history and all inter-cycle assembly movements of the WBN1 core. Lastly, the predicted pin-level operational histories and time-dependent axial power profiles, as calculated by a core simulator utilizing all of the previously-mentioned WBN1 data, were made available from the VERA Core Physics Benchmark [12]. These data augmented the applicability of this work because few assumptions need to be made regarding WBN1 fuel rod models and allow for the quantification of highfidelity SNF observables such as the RIP and cladding hoop stress (CHS). However, these data can not be reproduced in this dissertation and the use of proprietary data restricts how and what results can be published freely. Measured values for the discharge RIP and discharge isotopic concentrations are not available for any fuel rods of WBN1.

26 Goals of Analysis The WBN1 data sets are being utilized in this work in order to determine the physical distributions of RIP and CHS predictions for all fuel rods of WBN1. Statistical extrema will be identified and potential causes will be proposed and discussed. Further, the uncertainty in RIP predictions will be quantified for all considered fuel rods of WBN1 within considered burnup bins. WBN1 is an acceptable choice for this type of analysis because of the breathe of data that are available including fuel rod irradiation histories. Although measurement data for the discharge RIP are not available for any fuel rods, comparing RIP predictions from fuel rods with very different operational histories will be valuable in order to observe patterns and behavior of the RIP with respect to variations in discharge fuel burnup and cycle-average LHGR. 1.4 Computational Tools The proposed goals of this work require a variety of high-fidelity computational tools that can provide best-estimate predictions for the parameters of interest, namely the discharge RIP and isotopic concentrations of SNF. Uncertainties from all pertinent input quantities should also be propagated into the predictions for these values, which places an additional restriction on any utilized computation tools. Further, the two desired parameters demand detailed methodologies that are unlikely to be contained within one computation tool. Due to these restrictions, predictions for SNF isotopic predictions will be obtained through the use of the SCALE code system (see section 1.4.1) and predictions for discharge RIP will be obtained from the fuel performance code, FRAPCON (see section 1.4.2) SCALE Code System SNF isotopic predictions will be carried out by the utilizing Sampler in conjunction with the 2-D depletion sequence TRITON/NEWT in the SCALE code system [15]. TRITON/NEWT can model the entire D047 assembly and output time-dependent isotopic predictions for fuel rod MKP109 throughout its lifetime in the CC-1 core and at the any specified time after discharge (cooling time). SCALE/Sampler

27 10 will facilitate perturbations to input quantities of D047 assembly model and will incorporate uncertainty into the nuclear data utilized in the TRITON/NEWT depletion calculations FRAPCON-3.5 Discharge RIP predictions will be obtained through the use of FRAPCON 3.5 [16], the steady-state fuel performance code developed by PNNL. FRAPCON will be utilized to model WBN1 fuel rods with batch-specific geometries and compositions as well as the specific irradiation history for that fuel rod. FRAPCON does not consider uncertainties in any provided input parameters but perturbed FRAPCON input files may be generated by computational tools developed for this work by the researcher. FRAPCON considers several interrelated effects in its calculation of the RIP, such as fuel and cladding temperatures, fuel and cladding deformation, release of fission product gases, fuel swelling and densification, cladding thermal expansion and irradiation-induced growth, cladding corrosion and hydriding, and crud deposition for a given buildup rate as functions of time and fuel rod specific power [16]. A simplified overview of the calculation procedure of FRAPCON is shown in Figure 1.5 and is reproduced from [16].

28 11 Input data are specified Iteration on gas pressure convergence criterion <1% P Iteration on gap temperature difference criterion <1% T Initial conditions are computed Fuel rod temperatures are computed Fuel and cladding deformation are computed Gas release, void volumes, and internal gas pressure are computed New time step Figure 1.5. A simplified flowchart of FRAPCON Nuclear Data Libraries Often used in conjunction with lattice physics and depletion codes are nuclear data libraries (NDLs), which can provide the computation tool with reaction crosssections, decay constant, and fission product yield percents for a variety of isotopes. NDLs may also contain uncertainties for each of these parameters, allowing their propagation to any desired prediction in the computation tool. Less often, NDLs are accompanied by covariance libraries, which contain any covariances or correla-

29 12 tions between isotopes, such as the 44-group SCALE-6.0 covariance library [15]. 1.5 Dissertation Overview This dissertation documents the efforts undertaken and accomplishments achieved throughout the pursuance of the goals of this work. Initially, this project focused on quantifying bias and uncertainty fuel isotopic predictions but eventually began to focus on uncertainty quantification and sensitivity analysis of RIP predictions. Even though the two parameters of interest are quite different, both phases of this work share a focus on SNF analysis, which is why they are presented together. Due to the breadth of this work, Chapter 2 will summarize the background information that is required in order to follow and understand the progress of this project. Chapter 3 will focus on the portion of this work that took place during the summer of 2013, namely, the CC-1 analysis with the intent of analyzing bias and uncertainty in SCALE isotopic predictions for SNF. This chapter can effectively be referred to as the first phase of this work since it deals primarily with the quantification and analysis of isotopic predictions. The next phase of this work focuses on discharge RIP of SNF and begins in Chapter 4 with the multicycle analysis of WBN1. The implications and significance of each analysis are outlined in their respective chapters but the final chapter, Chapter 5, summarizes the overall conclusions of this project and suggestions as to what efforts should be made by future researchers when performing related studies.

30 Chapter 2 Relevant Background 2.1 Fuel Performance Background In order to adequately understand how nuclear fuel should be modeled for SNF storage analysis, a general understanding of the physics driving changes in a nuclear system during irradiation is necessary. First and foremost the metric by which nuclear fuel are compared to determine how much energy it has produced throughout its usage in a nuclear reactor is the fuel s burnup. Since a system with more nuclear fuel is expected to produce more energy, the fuel burnup is typically expressed in terms of how much nuclear fuel is present in the reactor system during power production (energy per unit mass, typically GWd/MTU). Consequently, the fuel burnup is a convenient means of comparing how spent nuclear fuel is from various nuclear systems. As nuclear fuel produces energy in a nuclear reactor, the burnup of the fuel increases but a plethora of other system observables change as well. Fuel system parameters that change as the fuel produces energy are therefore called burnup-dependent parameters. Akin to the fuel burnup, fuel performance parameters all attempt to measure changes within the nuclear fuel throughout its lifetime. The concept of fuel performance is an attempt to describe and predict the state of the fuel over the course of its lifetime. The complete description of the nuclear fuel, however, requires knowledge and concepts from several different scientific and engineering disciplines such as chemistry, nuclear and solid-state physics, metallurgy, ceramics, and applied thermal mechanics [2]. In order to accurately capture the complex

31 14 behavior of nuclear fuel during irradiation, computer codes are developed that consider the detailed interrelationships between these disciplines in order to calculate predictions for the observables of a given nuclear system. An event of chief concern to SNF analysis and modeling is a cladding wall failure where radioactive isotopes accumulated in the fuel void volume are allowed to escape into the storage container. When a cladding wall failure has occurred, the SNF of the whole assembly is considered damaged, even if just a single fuel pin s cladding has failed. Storage criteria for damaged SNF is much more expensive and rigorous than undamaged SNF so obviously it is advantageous to predict under what conditions these failures are likely to occur so that they may be avoided. In general, the probability for a cladding failure increases with cladding stress so understanding the sources of cladding stress is crucial for SNF analysis. Potential sources of cladding stress are the fuel RIP, hydride reorientation and relocation inside the cladding material, and fuel swelling during irradiation leading to pelletcladding mechanical interaction (PCMI). A scenario of SNF handling where the cladding stresses have been observed to be significant is during the vacuum drying process of a dry storage cask (DSC) [17]. Vacuum drying of SNF occurs after the fuel has been moved from a spent fuel pool to a dry storage cask. The dry storage cask evacuated of the its internal water and fuel temperature increases to a maximum temperature of 400 C [18]. The evacuation process is considered complete when the internal pressure of the dry storage cask is reduced to 1-3 torr (1 torr is equivalent to about 133 Pa or atm). The dry storage cask is at this point backfilled with helium gas. Since undamaged SNF rods are sealed (airtight) systems, the low external pressure of the dry storage cask interior during vacuum drying imposes a stress gradient across the fuel cladding. This stress gradient, coupled with the high fuel temperatures (relative to storage conditions) of vacuum drying, represents conditions under which cladding failures are more likely to occur. In order to better understand this process, the contributors of the cladding stress should be discussed in detail, starting with the RIP.

32 Rod Internal Pressure The RIP of SNF is one of the driving forces of microstructural changes in the fuel cladding. At the time of fuel discharge, the RIP sets the initial conditions for crucial time-dependent transients that occur before and during spent fuel storage. When a nuclear fuel rod is manufactured for use in a nuclear power plant, the void space of the fuel rod is filled with an inert gas (typically helium) up to a certain fill pressure and then sealed. For PWR fuel rods, this fill pressure is typically on the order of a few megapascals (MPa). During the fuel rod s time in the reactor core, the RIP changes significantly due to changes in the void volume and the amount and temperature of the void gas. Void gas refers to the amount of gaseous particles present inside the void volume of the fuel rod. At beginning-oflife (BOL), the void gas corresponds to just the fill gas of the fuel rod. During irradiation, however, the void gas increases (unless there is a cladding leak) due to fission gas release (FGR) and helium production from any materials in the fuel rod. Before the details of FGR and helium production are discussed, the principle that is assumed to determine the behavior of the RIP should first be discussed: the ideal gas law. The ideal gas law is a simple (but effective for most inert gases) approximation for the interrelationship between the pressure, volume, temperature, and the amount of gaseous atoms in a sealed system. The most common form of the ideal gas law is the following P V = nrt, (2.1) where P is the pressure of the ideal gas, V is the volume of the closed system, n is the amount of the ideal gas (commonly referred to as the number of moles, where 1 mol = 6.022x10 23 ), T is the temperature of the ideal gas, and R is the ideal gas constant (8.314 cm 3 MPa / mol K). Several assumptions must be made in order to apply the ideal gas law to a system, most importantly that the gas atoms only experience elastic collisions between themselves and the walls of the system and that the gas atoms have a negligible volume (i.e., the gas atoms are point masses). The ideal gas law can be applied to a sealed system filled with helium with negligible error since helium is a noble gas and behaves as a near-ideal gas under standard conditions.

33 16 The ideal gas law is assumed to determine the behavior of the internal gas of a fuel rod before, during, and after irradiation for several highly regarded fuel performance codes [16]. This assumption is used despite the fact that the composition of the internal void gas changes from completely fill gas at BOL to a mixture of fill gas and gaseous fission products at end-of-life (EOL). The RIP safety limit (i.e., the highest internal pressure that doesn t damage the fuel rod) has been previously set at the pressure where the fuel-cladding gap begins to reopen due to outward cladding creep during normal operation. The nuclear industry of the United Kingdom (UK) has applied this guideline to limit the RIP at exactly the PWR system pressure (15.5 MPa) [19]. This limit has been suggested to be somewhat conservative however and for Westinghouse 17x17 fuel rods, the RIP limit is considered to be 19.3 MPa for the same system pressure of 15.5 MPa [20]. Since this technique for setting the RIP limit depends on the system pressure, the RIP limit could technically vary for different reactor systems. It is important to note that this RIP limit should be obeyed throughout the entire fuel rod s lifetime, which obviously includes periods of extremely elevated temperatures during reactor operation Fission Gas Release FGR is the primary contributor to changes in the amount of void gas of a fuel rod during irradiation (with the exception of fuel rods containing ZrB 2 IFBA, which is discussed in the next section). Throughout the lifetime of a fuel rod in a reactor core, fission products are continuously produced in the nuclear fuel. The fission products themselves undergo a cascade of transformations as they are present in the fuel due to radioactive decay or neutron absorption. Considering these mechanisms, about 0.3 Xe and Kr atoms are produced cumulatively per fission [2, 16]. Xe and Kr are particularly important fission products when the RIP is being considered since these isotopes are gaseous and only minimally soluble in the nuclear fuel (only 0.3% by mass of the Xe produced can be dissolved in the nuclear fuel) [2]. Helium is another element that is gaseous and minimally soluble in nuclear fuel and is produced either by alpha emission of a fission product (either as a decay mechanism or a neutron absorption reaction, termed n-alpha) or by ternary fission events. Ternary fissions are quite rare occurrences [21] where a

34 17 fission event results in three fission products instead of two (i.e., binary fission). Of the three fission products, one is typically much smaller than the other two. Most commonly, this third fission product is a helium-4 nucleus (referred to as an alpha particle). Given that helium is produced from alpha emission of fission products or as a rare ternary fission product, helium release is mostly overshadowed by Xe and Kr production. Helium is also produced by ZrB 2, which is an IFBA, however, since helium produced in this manner is not a fission gas it is discussed in a subsequent section. As these gaseous fission products are produced in the fuel, there are two possible phenomena that can occur: either the gaseous fission products are absorbed or trapped within the fuel (trapping) or they are released into the void space of the fuel rod (FGR). Both of these scenarios are detrimental to the overall resilience of the fuel rod. The first scenario, where fission gas is trapped in the fuel rod, contributes to fuel swelling which may lead to PCMI, which in turn may cause a cladding failure due to the increased stress on the cladding wall. An important exception is when gaseous fission products are trapped in the pores of the fuel material, which are present due to the fuel having a non-zero open porosity. In this case, the resulting fuel swelling is decreased [22]. FGR also has a detrimental effect of the lifetime of nuclear fuel due to increased RIP and possibly higher fuel temperatures [2]. The higher fuel temperatures from FGR results in an increasing rate of FGR (i.e., a positive feedback loop), which could potentially increase the RIP until cladding failure. Due to the significance of these two phenomena, the underlying physics of fission gas release and fuel swelling should be discussed. Simply put, FGR has two regimes of behavior: the first being a slower rate of release that mostly independent of the fuel temperature (athermal release) and a second behavior regime that begins when the fission gas bubbles at the fuel grain boundaries interconnect to form a tunnel through the fuel to the fuel boundary, resulting in an instantaneous release of the trapped fission gas (burst release). The transition from the first regime to the second is dependent on both the fuel s burnup and temperature. Explicitly, fission gas bubble interconnection is expected to occur for fuel of a specified burnup once the fuel temperature exceeds the Vitanza

35 18 threshold temperature [2], which can be written as T C = 9800, (2.2) ln BU where T C is the threshold fuel temperature (in C) and BU is the fuel burnup (in GWd/MTU). The burnup required for the fuel to transition out of the athermal region of fission gas release is often called the incubation period and it s relationship with the fuel temperature is shown in Figure 2.1 which is reproduced from [2]. Figure 2.1. The Vitanza threshold temperature for FGR behavior. There are three mechanisms for athermal release, the first of which occurs when fission products are produced near enough to the cladding wall (<6-7 µm) with a high enough kinetic energy [ mega-electronvolt (MeV)] to escape from the fuel [2], which is referred to as recoil release. The second mechanism entails when a particle moving within the fuel (i.e., a fission product or any particle that is moving as a result of a fission reaction) collides with a stationary fission gas atom near the boundary of the fuel. If the gas atom is given enough energy to escape the fuel, then it is deemed a release by knockout. The third and final mechanism occurs when a fission product becomes stationary near the surface of the fuel, which causes the surrounding area to increase in temperature and evaporate or sputter, causing a release of any trapped fission gas in the zone. Athermal release is completely overshadowed by burst release in typical (moderately burnt) SNF, making up about 3% of the released fission gas of spent fuel with a burnup of 60

36 19 GWd/MTU. Bubbles containing gaseous fission products accumulate at fuel grain boundaries (known as intragranular movement or bubble migration) after a certain fuel burnup and temperature. When enough bubbles interconnect, they form a tunnel network where fission gases can travel much more easily. If the bubble interconnections reach the periphery of the fuel, then all of the fission gas enclosed in the tunnel will escape into the fuel void volume. This process is enabled by the interconnection of the fission gas bubbles as well as fuel cracking, which instantly connects any neighboring fuel grains and allows the connection of previously separated fission gas tunnels Integral Fuel Burnable Absorbers Several measures are taken in modern reactor core design to make nuclear energy as economic as possible. One general guideline to maximizing the efficiency of a nuclear power plant (NPP) is to minimize reactor downtime in between cycles and to maximize the cycle length. In order to extend the cycle length of a reactor core, the core must be loaded with an increased amount of excess reactivity, which will help mitigate the negative reactivity feedback effects that are intrinsic in reactor core operation. With an increased amount of excess reactivity present in the core, the NPP may operate at its rated power for an extended period of time. By varying the amount of reactivity present in the core (i.e., core loading), cycle lengths can vary significantly: typically between 12 and 18 months. Of course, increasing the core loading during of a core design presents many challenges, the most critical being the safe and accurate control of a core s power during operation. In order to compensate for the increased core loading throughout the cycle, control absorbers (or negative reactivity) are introduced to the reactor system (either during fuel manufacturing or reactor operation) to help the reactor power remain constant over the course of the cycle. One category of control absorbers are burnable poisons, whose effectiveness at absorbing neutrons decreases as the cycle progresses. Burnable poisons are common in modern core design as IFBA, which are either blended into the fuel itself (which is the case for fuel containing gadolinium-oxide) or placed on the fuel periphery as a thin layer (typically

37 20 ranging between 5 and 15 microns in thickness). An example of an IFBA layer is ZrB 2, whose use may have significant implications regarding the RIP at the time of discharge. Essentially, the only neutron absorbing-nuclide of ZrB 2 is the B-10 isotope. Natural boron only has an isotopic abundance of about 20%, however ZrB 2 IFBA layers have the amount of B-10 (termed B-10 enrichment) increased significantly in order to increase neutron absorption. Throughout irradiation, a ZrB 2 IFBA layer produces helium gas since the dominant neutron-absorbing reaction of B-10 is its n-alpha reaction: 10 5 B + 1 0n 7 3Li + 4 2He, (2.3) where 4 2He is also referred to as an alpha-particle. The helium production of an ZrB 2 IFBA layer can significantly increase the RIP of a fuel rod. Due to this, IFBA rods may be manufactured with annular fuel blanket regions (to increase the internal volume of the fuel rod) and a decreased fill pressure Fuel Swelling As uranium oxide nuclear fuel is irradiated in the reactor core, the composition of the fuel changes considerably. These changes alter the density of the fuel material, consequently causing a measurable change in the fuel rod s geometry. This behavior is called fuel swelling. Fuel swelling should be considered in fuel performance codes where parameters that depend on the fuel void volume are calculated, such as the RIP. Four physical mechanisms contribute to changes in density of the nuclear fuel during irradiation; namely, the accumulation of solid fission products, the trapping of gaseous fission products, densification, and hot pressing [2]. The first two contributors, involving the accumulation of fission products in the fuel, contribute to a decrease in the fuel density. This is understandable since any combination of fission products are not more dense than the fissioning nuclide. Fuel densification occurs at relatively low burnups (<10 GWd/MTU) and is due to the disappearance of some fabrication porosity due to fission fragments colliding with pores within the fuel [2, 4, 22]. This leads to an initial increase in the fuel density (i.e., fuel shrinkage). The last contributor, hot swelling, also leads to fuel shrinkage and is similar to densification since it also leads to the disappearance

38 21 of fabrication porosity. Hot swelling occurs when the fuel is experiencing large temperatures, stress levels, and defect production rates [2, 22] Fuel Rod Void Volume As discussed previously in section 2.1.1, the RIP fluctuates throughout the lifetime of the fuel due to changes in the amount and temperature of the void gas, and the void volume. Contributors to changes in the amount of void gas of a fuel rod during irradiation have already been discussed; namely, FGR in section and helium production from IFBA layers in section This section will focus on how the behavior of the fuel rod void volume during irradiation and under vacuum drying conditions. The total void volume of a fuel rod is not simply composed of the fuel-cladding gap and the plenum volume. In modern fuel performance codes [16], there are generally eight different contributors to the fuel rod void volume: 1. The plenum volume, V P l 2. The fuel-cladding gap volume, V Gap 3. The fuel central or annular hole volume, V An 4. The fuel cracking volume, V Cr 5. The fuel dishing and chamfer volume, V Di,Ch 6. The fuel open porosity volume, V P o 7. The fuel roughness volume, V Ro Therefore, the total fuel void volume V T used in fuel performance codes to calculate the RIP (see equation 2.1) can be written as V T = V P l + V Gap + V An + V Cr + V P l + V Di,Ch + V P o + V Ro. (2.4) In order to understand how each of the aforementioned volume terms is expected to change during irradiation and dry storage conditions, each term should be briefly discussed.

39 Fuel Plenum Volume The fuel plenum is the space between the top of the pellet stack and the welded end-plugs. There is typically a spring in the plenum to apply a compressive force onto the fuel stack to prevent its movement although it is not always modeled in fuel performance codes. The purpose of the plenum is to accommodate the axial thermal expansion of the fuel and to provide additional void volume to mitigate the effect of FGR and other gas production during irradiation. This is due to the fact that, with an increased void volume, it takes more fill gas to bring the fuel rod to its designated fill pressure so the amount of gas released during irradiation (which does not depend on the fuel volume) will have a smaller contribution to the total void gas and consequently the RIP. In fact, the fuel plenum often makes up a substantial portion of the fuel rod void volume. During irradiation, the plenum volume varies due to the thermal expansion of the fuel stack and cladding as well as fuel densification and swelling. Since the plenum is defined as the void space above the fuel stack, a decrease in the fuel stack height will change the lower boundary of the plenum, increasing its volume. Typically, the thermal expansion of the cladding (radially and axially) overshadows the negative volume contributions so the plenum volume increases with fuel burnup Fuel-Cladding Gap Volume The fuel-cladding gap is determined, generally, as the volume between two concentric cylinders: the inner surface of the fuel rod cladding and the outer surface of the fuel. Although several physical characteristics of the fuel could be considered to invalidate the assumption that the outer surface of the fuel is a perfect cylinder (e.g., surface roughness, pellet dishings, non-concentric pellets, etc.), the fuel-cladding gap is still calculated with this assumption and the other volume terms are considered later. With the exception of the initial increase in fuel density at low burnups due to densification (see section 2.1.4), the fuel density typically decreases as a function of burnup. This increases the fuel volume and contributes to a smaller fuel-gap volume or gap closure. The main contributor to gap closure however, especially

40 23 near BOL, is the larger thermal expansion coefficient of UOX fuel compared to the fuel cladding [2]. Due to these two mechanisms, the volume growth (or outward creep) of the fuel will outpace the outward creep of the cladding. Recall the discussion in section that the RIP of a fuel rod is limited by the pressure that would cause the cladding outward creep to outpace the fuel, which would lead to reopening of the gap Fuel Annulus Volume Fuel pins are sometimes designed with annular fuel regions in order to account for increased amounts of void gas and fuel swelling. Annular regions can also be formed inside irradiated nuclear fuel due to the migration of pores to the fuel center [22]. The volume of the inner void space of an annular fuel pellet is easily determined from the height of the pellet and the diameter of the central hole. Annular holes behave the same way as the fuel-cladding gap volume since its behavior is determined by the swelling or densification of the fuel. Explicitly, the inner hole will increase in volume due to densification near BOL and then decrease in volume due to fuel swelling and thermal expansion Fuel Cracking Volume As soon as the fuel goes from room temperature to producing power at beginningof-cycle (BOC) fuel cracking occurs. The driving force of the cracking is a large temperature gradient between the hot center of the fuel rod and its periphery when the fuel begins to produce power. The center of the fuel rod expands outward and imposes a thermoelastic stress on the periphery that exceeds the fracture strength of the colder fuel causing it to crack. Since the periphery of the fuel is still below its ductile-to-brittle transition temperature (DBTT) (< 1400 C), it is much more prone to cracking than the hotter center [22]. The fuel cracks further after each power change, most notably when at BOC. The fuel cladding is far less prone to cracking since it is ductile. Cracks on the inner and outer walls of the cladding are common in spent fuel but these are due to either, manufacturing defects, oxide or hydride layers on the outer wall, or corrosion of the inner wall [23]. Fuel fragments thermally expand to a much greater extent relative to their

41 24 size than an intact fuel cylinder. Fuel with even a minimal amount of cracking can consequently experience some degree of fuel relocation, where fuel pellets are driven outward towards the cladding. Fuel relocation is an important phenomenon to consider in fuel performance calculations because it contributes significantly to fuel-cladding gap closure at low burnups [2]. Further, the increased void volume from the fuel cracks need to be considered in fuel performance codes Fuel Dishing and Chamfer Volumes Physical fuel pellets used in NPP cores are not manufactured as perfect cylinders due to the behavior of nuclear fuel under hot conditions. Thermal expansion of cylindrical fuel pellets results in an hourglass or bamboo ridge formation of the fuel, which places significant stress on the cladding due to the resulting PCMI. The progression of fuel hourglassing to PCMI is shown in Figure 2.2 and is reproduced from [2]. Fuel dishes and chamfers are alterations made to nuclear fuel pellets that are meant to counteract fuel pellet hourglassing by providing more space in between and at the periphery of fuel pellets to facilitate the thermal expansion of the fuel. Chamfers also help facilitate the addition of the fuel into the cladding [24] and reduce the likelihood of fuel pellet chipping during manufacturing [25]. Figure 2.2. and PCMI. Thermal expansion of cylindrical fuel pellets leading to pellet hourglassing Fuel dishes are concave indentations in cylindrical fuel and can be located on

42 25 the fuel pellet s axial or (less commonly) radial surface. The configuration of a fuel pellet with top and bottom axial dishes is shown in Figure 2.3 and is reproduced from [25]. A similar example of a fuel pellet with a radial dish is shown in Figure 2.4 and is reproduced from [4]. Figures 2.3 and 2.4 also demonstrate fuel pellet chamfers, where the corner of the fuel pellet has been reduced by a certain angle. Figure 2.3. A fuel pellet with top and bottom axial surface dishes. Figure 2.4. A fuel pellet with a radial surface dish. Fuel pellet dishes and chamfers increase the void volume of the fuel rod when compared to perfectly cylindrical fuel pellets. The contribution of the fuel pellet dishes and chamfers to the rod void volume are considered in some fuel performance codes when calculated the RIP [16].

43 Fuel Open Porosity Volume Porosity is a measure of how much empty space is present in a material and is typically written as the volume percent the empty space occupies when compared to the total volume of the material. In nuclear fuel, the empty space is referred to as pores and is an important design variable in nuclear fuel design since pores in nuclear fuel help reduce fuel swelling by trapping fission gas (see section 2.1.2) [22]. Most nuclear fuel currently being manufactured has initial fuel porosities ranging from 4.5-7% [24]. Open fuel porosity is the small percentage of pores in the nuclear fuel that are open to free gas flow. These pores contribute slightly to the total void volume of a fuel rod and are sometimes considered in fuel performance codes when calculating the RIP [16] Fuel Roughness Volume Although nuclear fuel materials are often represented as smooth surfaces, in reality they are covered with nonuniformities can have an effect on fuel performance calculations. The arithmetic mean height of these nonuniformities is referred to as the roughness of the material. The roughness of nuclear fuel is an important factor to consider in fuel performance codes since it helps prevent FGR by allowing for more collisions with the nuclear fuel before a gaseous fission product escapes [22] and reduces the heat transfer through conduction between the fuel and the cladding during PCMI [2]. Fuel roughness also adds a small amount of void volume when compared to a perfectly smooth fuel surface, which can be calculated in fuel performance codes for consideration in RIP quantification [16] Zirconium Hydrides An important structural distinction between high- and low-bu is the presence of zirconium hydrides (commonly referred to as hydrides) in fuel rod cladding, the amount of which is proportional to the irradiation time. Explicitly, fuel rods with higher burnups will have a greater concentration of hydrides present in the cladding than those of low-bu fuel. Zirconium hydrides are produced in the cladding due to the absorption of hydrogen nuclei (protons) into the cladding material. The primary source of hydrogen in a fuel rod is from the oxidation reaction of the Zir-

44 27 conium cladding with the surrounding water (Zr + 2H 2 O ZrO 2 + 4H). About 15% of hydrogen produced through this reaction is absorbed into the cladding material, resulting in the formation of hydrides [26]. Further, the rate of oxide formation (i.e., corrosion rate) is directly related to the fuel temperature, so the rate of hydride formation is increased for fuel rods with higher temperatures [27]. Hydrides that are absorbed into the cladding material precipitate out of the cladding in a direction normal to the tensile stresses [23]. Under normal conditions, the fuel cladding will experience these stresses in a radially outward direction due to the RIP and the hydrides will consequently form in a circumferential orientation as is shown below in Figure 2.5, which is reproduced from [1]. Figure 2.5. Cross-section of a fuel rod s cladding showing hydrides oriented primarily in a circumferential direction. Under normal reactor operation, the majority of hydrides present in the fuel will be circumferentially oriented with few or small amounts of radial hydrides. Radial hydrides are able to form where the cladding stresses are circumferential; however, such as at the tip of a crack present in the inner or outer cladding surface. Figure 2.6 displays hydrides in a radial orientation and is reproduced from [1]. During the vacuum drying process of SNF in a DSC, the fuel cladding is exposed to a stress

45 28 gradient (from the pressure difference between the RIP and the external pressure during vacuum drying, 1-3 Torr) and experiences high fuel temperatures (limited to 400 C [18]) and the hydrides can dissolve back into the cladding material and diffuse to other highly-stressed regions where they will later precipitate when the DSC cools. Hydride reorientation is expected to occur in significant amounts if the CHS exceeds 90 MPa during the cooling process if the fuel has experienced an elevated temperature (greater than 400 C) [28]. The cladding does not have to be cooled down to room temperature to experience significant hydride relocation and radial reorientation. In fact, when the cladding as been cooled to about 200 C, most of the dissolved hydrogen re-precipitates as hydrides [29]. Figure 2.6. Cross-section of a fuel rod s cladding with significant amounts of radially oriented hydrides. Radial hydrides are much more likely to be present in significant amounts in highly-burnt SNF due to the presence of cracks along the inner and outer cladding