Validation of UNF-ST&DARDS As-loaded safety analysis methods for BWR decay heat calculations

The assessment in this paper is necessary to demonstrate that sufficient decay heat conservatism is retained in the UNF-ST&DARDS bounding as-loaded spent fuel analysis methodology. This paper also demonstrates the time dependent impact of various parameters such as last cycle power on decay heat values.

Progress in Nuclear Energy 143 (2022) 104042 Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene Research Paper Validation of UNF-ST&DARDS As-loaded safety analysis methods for BWR decay heat calculations☆,☆☆ Justin B Clarity a, *, Henrik Liljenfeldt b, Kaushik Banerjee c, L Paul Miller a a Oak Ridge National Laboratory, Nuclear Energy and Fuel Cycle Division, Oak Ridge, TN, USA Noemi Analytics, Uppsala, Sweden c Pacific Northwest National Laboratory, Richland, WA, USA b A R T I C L E I N F O Keywords: Spent nuclear fuel UNF-ST&DARDS Decay heat LWR A novel assessment of the conservatism in the UNF-ST&DARDS decay heat calculations has been performed UNF-ST&DARDS is used to quantify the uncredited margin in safety analysis calculations for spent nuclear fuel (SNF) storage, transportation, and disposal systems The goal of the assembly-specific as-loaded safety analysis approach in UNF-ST&DARDS is to determine the time-dependent realistic state of the SNF systems; however, it is desirable to conservatively estimate safety analysis parameters, such as decay heat, for a given set of fuel characteristics The primary source of conservatism in the generic UNF-ST&DARDS assembly-specific as-loaded analysis (also referred to as bounding within UNF-ST&DARDS) is the conservative assumptions of various reactor operational parameters that attempt to envelop wide spectrum of reactor operating scenarios The assessment in this paper is necessary to demonstrate that sufficient decay heat conservatism is retained in the UNF-ST&DARDS bounding as-loaded spent fuel analysis methodology This paper also demonstrates the time dependent impact of various parameters such as last cycle power on decay heat values A comparison between the UNF-ST&DARDS bounding decay heat calculations and calculations performed using a detailed description of the fuel assembly operating histories, referred to as detailed calculations, was performed using recently acquired data The data used to perform this evaluation are from one set of 3019 assemblies from a US boiling water reactor (BWR) site and one set of 2117 assemblies (952 × 8, and 1165 10 × 10) from a Swedish BWR reactor Analyses of the US data involved two sets of assumptions for the bounding calculations and produced two data sets The first analysis, in which the cycle-wise burnups were derived for the bounding calculations from the detailed data, generated the derived data set; the second, in which the assumptions associated with incorporating US nuclear fuel data survey (Form GC-859) data were included in the calculations for a subset of the same assemblies, generated the GC-859 data set When bounding assumptions were used, the average level of conservatism (overestimation of decay heat) ranges between 9.0% and 17.7% for the derived data set, between 11.4% and 32.3% for the GC-859 data set, between 10.1% and 62.6% for the Swedish × fuel and between 8.3% and 44.7% for the Swedish 10 × 10 fuel The level of conservatism and the scatter in the ratio between bounding and detailed data increase significantly for the 100- and 200-year cases for derived US and Swedish data sets The GC859 data set had large conservatisms in the early cooling times that initially shrank with time and then increased for the 100-year and 200-year cooling times These results show that, while UNF-ST&DARDS can be used to calculate assembly decay heat based on assembly characteristics and operating history to identify potential significant margins to the licensing basis decay heat calculations, the decay heats calculated by UNF-ST&DARDS ☆ Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE) The US gov­ ernment retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to so, for US government purposes DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-acce ss-plan).☆☆ Notice: This is a technical paper that does not take into account contractual limitations or obligations under the Standard Contract for Disposal of Spent Nuclear Fuel and/or High-Level Radioactive Waste (Standard Contract) (10 CFR Part 961) To the extent discussions or recommendations in this paper conflict with the provisions of the Standard Contract, the Standard Contract governs the obligations of the parties, and this paper in no manner supersedes, overrides, or amends the Standard Contract * Corresponding author E-mail address: clarityjb@ornl.gov (J.B Clarity) https://doi.org/10.1016/j.pnucene.2021.104042 Received June 2021; Received in revised form 27 October 2021; Accepted November 2021 Available online 25 November 2021 0149-1970/© 2021 The Authors Published by Elsevier Ltd This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 are still conservative compared to more detailed calculations for the range of assemblies and operating condi­ tions assumptions evaluated in this study Introduction analysis for subsequent use in thermal evaluation of SNF canisters in their as-loaded configurations The aim of this section is to provide context for the application of the bounding decay heat analysis process and a basis for comparison to the detailed decay heat analysis process (Section 2.2) The decay heat calculational process is initiated by providing the canister identifier and analysis date to UNF-ST&DARDS The canister identifier is used to look up all assembly identifiers asso­ ciated with the canister in the Unified Database (UDB) The assembly identifiers are then used to look up the necessary Oak Ridge Isotope Generation and Depletion Code (ORIGEN) reactor libraries (Gauld et al., 2011), assembly average enrichments, burnups, discharge dates, and assembly masses for each of the assemblies from the UDB The assembly type–specific ORIGEN libraries and irradiation information from the discharge concentrations are then used to perform ORIGEN Assembly Isotopics (ORIGAMI) depletion calculations to generate axial segmented, node-wise, assembly-specific discharge nuclide concentra­ tions (Skutnik et al., 2015; Williams et al., 2020) UNF-ST&DARDS then passes the discharge concentrations to the ORIGAMI decay calculation, along with analysis-specific decay data necessary to produce decay heat values for analysis The decay heat information would then typically be passed on to Coolant Boiling in Rod Arrays–Spent Fuel Storage (COBRA-SFS) to perform canister-level thermal analysis to evaluate quantities such as peak clad temperature The thermal analysis calcu­ lations with COBRA-SFS are beyond the scope of this work but are dis­ cussed extensively in (Robb et al., 2017) The ORIGAMI point depletion calculations that generate the discharge nuclide concentrations use one-group cross-section libraries generated with the Transport Rigor Implemented with the TRITON sequence ((DeHart and Bowman, 2011), Sect 3.1 (Rearden and Jessee, 2016)) using the NEWT lattice physics code and ENDF/B-VII.1 nuclear data Because the TRITON/NEWT calculations are relatively time intensive, it is advantageous to use a set of prescribed modeling condi­ tions for operating history during the library generation process, thus leaving only assembly type, enrichment, and burnup as the variables available for the ORIGAMI calculation The depletion assumptions used in the TRITON calculations for UNF-ST&DARDS are discussed exten­ sively in Section II.D.3 of (Clarity et al., 2017) for BWR fuel and are briefly reiterated in Section 2.4.2 to allow for comparison to the detailed data presented here Because they are required to accommodate all fuel assemblies of a specific type, the depletion assumptions must be con­ servative This work quantifies the conservatism of the bounding decay heat calculations for BWR fuel assemblies Fig provides a diagram of the UNF-ST&DARDS bounding decay heat calculation process The dual-purpose canisters (DPCs) that are currently used for storage and transportation of spent nuclear fuel (SNF) are designed and evalu­ ated for bounding (enveloping) characteristics such as fuel type, fuel dimensions, initial enrichment, discharge burnup, and cooling time The bounding fuel characteristics for a system are used to establish upper limits on safety analysis parameters such as decay heat, radiation source terms, and canister keff values Realistically, there are wide variations in SNF assembly burnups, initial enrichments, and cooling times There­ fore, dry storage systems are typically loaded with assemblies that satisfy the bounding fuel characteristics defined in the licensing analysis with some amount of unquantified and uncredited margin The Used Nuclear Fuel-Storage, Transportation & Disposal Analysis Resource and Data System (UNF-ST&DARDS) is being developed to gain a better un­ derstanding of the true safety margins that exist for SNF canisters (Banerjee et al., 2016; Lefebvre et al., 2017) The work done with UNF-ST&DARDS to date provides estimates of the margins associated with modeling accurate assembly enrichments, burnups, and cooling times for thermal (Robb et al., 2017), criticality (Clarity et al., 2017), shielding (Radulescu et al., 2017a), and contain­ ment (Radulescu et al., 2017b) analyses However, due to the limited detail associated with the available information, many assumptions with regard to initial fuel composition, geometry, and operating history remain in the UNF-ST&DARDS depletion and safety analysis method­ ology Detailed fuel and operating history information from 3019 fuel assemblies from two operating boiling water reactors (BWRs) at one US site were obtained by ORNL This paper also includes results for 2117 assemblies from one Swedish reactor Analyses using Swedish data were performed by a joint SKB, ORNL subcontractor (one of the authors of this paper) using UNF-ST&DARDS The Swedish data were not directly ob­ tained by ORNL Calculations were performed for each assembly using the typical UNF-ST&DARDS as-loaded margin assessment approach, referred to here as bounding calculations, and with a new process capable of modeling the fuel and operating history in full detail, referred to here as detailed calculations Comparisons between the detailed and bounding calculations are performed for decay heat in this work Decay heat is an important input to canister-level thermal analysis and is the primary driver of peak clad temperature calculations (DeVoe et al., 2017) at an assembly level, as well as a crucial parameter for repository design This paper provides an assessment of the amount of conservatism in the bounding calculations relative to the detailed calculations as well as the operating history parameters that are most highly correlated with the conservatism and the nuclides that are most responsible for the differences This paper is organized as follows: Section discusses the compu­ tational workflow of the bounding and detailed calculations Section contains analyses of the detailed data provided by the operating reactors and comparisons of the assumptions used for the bounding calculations Section documents the assembly decay heat calculations and compares the detailed and bounding results, seeks to understand the drivers of the differences, and looks at the nuclides that cause the differences Section presents the conclusions of this work and discusses future work needed to further establish the conservatism of as-loaded analysis 2.2 Detailed calculations The detailed modeling process within UNF-ST&DARDS uses the most accurate representation of the fuel and operational history possible given the data available to estimate safety margins inherent in the bounding calculation approach The high-fidelity fuel and operational history information is specified for each node of each assembly The combination of the unique fuel description and the unique operational history for each fuel node requires that the roles of the library generation and discharge calculation from the bounding UNF-ST&DARDS modeling process be combined Combining these roles significantly increases the number of lattice physics calculations, making it desirable to execute the lattice calculations more quickly To accomplish this, the SCALE lattice physics code Polaris is used for the discharge concentration portion of the detailed calculations Polaris is a relatively new module released in SCALE 6.2 that provides 2D lattice physics analysis capability specif­ ically streamlined for light water reactor (LWR) fuel designs A detailed Methods 2.1 Bounding decay heat calculations with UNF-ST&DARDS This section discusses the overall flow of information, codes, and methods used by UNF-ST&DARDS to perform bounding decay heat J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 description of Polaris methods and its calculational approach is provided by Jessee et al (Jessee and Wieselquistet al, 2014) As in TRI­ TON/NEWT, the Polaris lattice physics capability is based on multigroup neutron transport coupled with the ORIGEN depletion/decay module for time-dependent transmutation of depletion materials (Gauld et al., 2011) The major differences between Polaris and TRITON/NEWT lie in the resonance self-shielding and transport methods Polaris employs the embedded self-shielding method (ESSM) for resonance self-shielding (Williams and Kim, 2012) For the transport calculation, Polaris em­ ploys the method of characteristics (MOC), which is sometimes referred to as long characteristics MOC solves the characteristic transport equa­ tion over a set of equally spaced particle tracks across the lattice ge­ ometry at prescribed angular quadratures Polaris provides an easy-to-use input format, allowing users to set up lattice models with minimal input Polaris has been tested extensively and found to perform well for LWR fuel calculations (Mertyurek et al., 2018) The output of the Polaris calculation is an F71 discharge composition file containing pin-wise and node-wise data The discharge composition data is stored for future usage in the UDB The information used in the safety analysis models is prepared by performing decay calculations with the composition information ob­ tained from the discharge composition data from the UDB using ORI­ GEN The ENDF/B-VII.1 nuclear data library is used for both the Polaris depletion calculations and the ORIGEN decay heat calculations The discharge composition data are combined with desired analysis data in a manner similar to that used in the normal UNF-ST&DARDS analysis calculations to generate isotopic number densities to generate decay heats and other safety analysis inputs as desired A diagram of the detailed decay heat calculations is presented in Fig This method of calculation was used for the detailed decay heat calculations using the US data calculates isotopic concentrations, radiation source terms, and decay heats for spent pressurized water reactor (PWR) and BWR fuel Using the detailed 3D power history from SIMULATE and isotopic inventories from CASMO, the SNF code provides accurate answers for a variety of calculations SNF-calculated decay heats were compared with ORIGEN calculations, decay heat standards and measured decay heats from the Swedish interim spent fuel storage facility and were found to agree closely (Beker et al., 2009; Børresen, 2004) The calculations performed in 2004 (Børresen, 2004) that compared the SNF code with ORIGEN show decay heat agreement within 0.1% between the two codes For comparison to the bounding and detailed processes in Figs and 2, the detailed calculations using the direct method for importing SNF-generated discharge nuclides is show in Fig 2.4 Potential sources of difference between the detailed and bounding calculations The UNF-ST&DARDS bounding analysis process needs to be flexible enough to analyze a large portion of the SNF This is done using infor­ mation in the UDB The UDB is populated with widely available infor­ mation, such as information from the GC-859 fuel survey (Nuclear Fuel Data Survey, 2012) and the fuel information available from the open source literature The expansive nature of the bounding analysis capa­ bility necessitates compromises on the modeling fidelity Compromises that have the potential to affect decay heat calculations include the use of assembly type aliasing (using ORIGEN libraries from one assembly design to represent a group of assembly designs), depletion conditions such as moderator density and blade insertion, and in some cases GC-859 data approximations such as approximated burnups and algo­ rithmically determined power histories The following subsections discuss each of these data and modeling differences within the context of BWR fuel analysis 2.3 Direct discharge import method 2.4.1 Fuel type aliasing Many of the fuel designs are not explicitly modeled in the UNFST&DARDS bounding calculations because sufficient information is not publicly available to build models for all assembly types To model a large variety of fuel, representative fuel assemblies are used in place of detailed designs for the depletion models The fuel type used for the US fuel for which detailed information is available is the ATRIUM 10 fuel design Design information for the ATRIUM 10 fuel is not publicly available The fuel type aliased to ATRIUM 10 for the bounding calcu­ lations is the GE 14 fuel type Additionally, the dominant lattice of the GE 14 fuel assembly is used for depletion The ATRIUM 10 fuel assembly has a set of partial-length rods that only extend part of the length of the assembly, leaving empty or vanished locations in the upper portion of the assembly A comparison of the geometric representation of the ATRIUM 10 dominant lattice and the GE 14 lattice used for the bounding calculations is shown in Fig The Swedish fuel assemblies all contain either × or 10 × 10 lattices of unknown type (due to proprietary considerations, SKB did not disclose the types of lattices to the author) The assemblies that have × Because many modern core simulators can give detailed discharge nuclides, an import capability for discharge nuclides has been imple­ mented into UNF-ST&DARDS For situations in which discharge (postirradiation with no cooling time) nuclide inventories are available from core simulator results, core-monitoring software outputs, or previously performed node-level calculations with other lattice physics codes, it is possible to import results directly into the UDB The results can then be used for subsequent decay and safety analysis calculations This is a flexible method for gathering data to validate the UNF-ST&DARDS bounding calculation input assumptions Using this technique allows for the detailed decay data and other downstream processes to be leveraged without including all operating data This method was used to collab­ orate with the Swedish Nuclear Fuel and Waste Management Company (SKB) The SNF code developed by Studsvik (SNF) was used by SKB to determine the discharge nuclide concentrations that were subsequently imported into the UDB and decayed using the UNF-ST&DARDS ORIGEN calculations similar to those discussed in Section 2.2 The SNF code Fig Bounding decay heat calculation process within UNF-ST&DARDS Progress in Nuclear Energy 143 (2022) 104042 J.B Clarity et al Fig Analysis flow of UNF-ST&DARDS detailed decay heat calculations Fig Analysis flow of UNF-ST&DARDS detailed decay heat calculations using the direct discharge import method from the SNF code Fig Radial layout comparison between the ATRIUM 10 (left) and GE 14 (right) fuel assemblies lattices are aliased to an early-generation GE fuel design with a single water rod; the assemblies that have 10 × 10 lattices are aliased to the GE 14 fuel design, as was done with the US ATRIUM 10 fuel Table Summary of BWR depletion parameters 2.4.2 Depletion Conditions The BWR depletion parameters used for the BWR ORIGEN library generation in the bounding analysis sequence are discussed extensively in an article by Clarity et al (2017) and are presented in Table The depletion parameters of the highest importance with regard to actinide buildup, which affects long-term SNF decay heat, are moderator density and control blade insertion, which are shown to be holistically conser­ vative for criticality calculations in (Clarity et al., 2017) Parameter Value Fuel rod mixture Fuel density (g/cm3) Fuel temperature (K) Moderator temperature (K) Moderator density (g/ cm3) Absorber exposure UO2 10.74 1200.00 560.70 0.30 Gd2O3 admixed with fuel pellets in a small number of rods based on fuel type and full-length control blade exposure throughout irradiation history J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 2.4.3 GC-859 data approximations For the US fuel, the GC-859 fuel survey information contains only the final discharge burnup of the assembly and the cycles in which it was irradiated This information does not give any information with regard to the temporal distribution that resulted in the final burnup of the fuel To perform the point depletion calculations, UNF-ST&DARDS distrib­ utes the burnup of the assembly according to the time over which each cycle occurred, resulting in a constant power depletion Common fuel management strategies result in more burnup being accrued by fuel during its first and/or second cycle of operation and less during the final cycle in many cases For the particular fuel used in this analysis, the burnups are also rounded to the nearest gigawatt-day per metric ton of uranium The rounded values represent approximations in the data that should be considered sometimes at reduced power The integral values, VH, and nodal burnup are useful because they are cumulative The VH is the burnup averaged void fraction over the assembly’s operational history to that point in its life The second data format provided for the US plant is the control blade insertion data, which is provided for several statepoints within a cycle where the control blades are either inserted or removed This data was modeled as a histogram of bladed and unbladed portions of each cycle for each node of each assembly These histograms were then combined with the assembly-wise end-of-cycle data to provide a complete description of the depletion history of each node of each assembly 3.1.1 Derived and GC-859 data sets UNF-ST&DARDS typically runs bounding calculations using data available from the GC-859 fuel survey The aim of this work is to determine the level of conservatism inherent in the UNF-ST&DARDS methods These methods encompass both the operating history and fuel modeling assumptions that are used in the depletion and safety analysis modeling and the techniques used to process the assembly burnups into UNF-ST&DARDS safety analysis inputs The isolated impact of the operating history assumptions was investigated by deriving bounding data input from the detailed data available for the US fuel assemblies The bounding data for these calculations were derived by averaging the enrichments and discharge burnups of each of the 25 nodes to determine an assembly-averaged enrichment and burnup similar to what is pro­ vided in the GC-859 survey In doing this, differences in total assembly burnup and the burnup achieved in each cycle of operation, and hence the specific power at which the fuel assembly was operated during that cycle, are eliminated For the remainder of this work, bounding calcu­ lations that are performed with data prepared in this manner are referred to as the derived data set Derived calculations are performed for all 3019 fuel assemblies used in this work The combined impact of UNFST&DARDS data-processing techniques and the operational history ef­ fect was assessed by using the GC-859 data provided for the assemblies Not all of the fuel for which detailed information is available have in­ formation available from the GC-859 fuel survey because some of the fuel began operation after the latest available survey was completed (2013) The data set for which GC-859 data are available contains a 1472 assembly subset of the derived data set and is referred to as the GC859 data set The detailed calculations for both the derived data set and the GC-859 data set use the same fuel and operating history assump­ tions, making the GC-859 detailed calculations simply a subset of the derived data A summary of what is included in the derived and GC-859 data sets is provided in Table Data This section discusses structure of the data used in the comparative analysis between the bounding and detailed calculations for the US and Swedish fuel Statistical summaries of the important parameters are also provided 3.1 US data The calculations performed for US fuel were based on data for a single two-unit BWR site in the United States The reactors at the site are GE BWR Class reactors with C-lattice cores The C-lattice designation indicates that the water gap is the same size on both sides of the fuel assemblies Each core contains 764 channeled fuel assemblies with an active fuel length of 149.45 in (modeled as 150 in.) The data contained information for 3019 assemblies that were introduced in cycles of operation for each reactor (10 total cycles) Each fuel assembly was followed through its full irradiation history, which includes consider­ ation of depletion of the fuel in an additional one to two cycles of operation for each unit beyond the 10 cycles in which the fuel is intro­ duced Each fuel assembly is of the Framatome ATRIUM-10 design and contains 83 full-length rods, part-length fuel rods, and one central water channel occupying fuel rod positions Gadolinia (Gd2O3 blended with UO2) rods are designed to control assembly axial and radial power distribution and core reactivity The fuel rods have natural uranium blankets at the upper and lower ends Each core also contains 185 control blades The control blades have a cruciform cross section containing neutron absorber for reactivity con­ trol The original equipment control blades contain boron carbide powder in stainless steel tubes, and newer-generation control blades contain a combination of boron carbide–filled tubes and solid hafnium rods Each of the blades can be inserted from the bottom of the core between four adjacent fuel assemblies The fuel information for US fuel includes a complete specification of the axial and radial layout of each assembly The ATRIUM 10 fuel design used for all US BWR cycles is provided It is a modern BWR fuel assembly categorized as multi-lattice according to the description provided in Clarity et al (2017) The fuel assembly specification designates which lattices occupy each of the 25 nodes used in the Framatome core design calculations For each of the specified lattices, pin-wise fuel composi­ tions and radial orientations of the rods are provided Detailed operating history information is provided for the US BWR cycles of interest in two formats 3.1.2 Assembly burnup The burnups of the US fuel assemblies in the derived data set ranged Table Comparison of the number of assemblies and input data for the derived and GC859 data sets Data Set The first format is the assembly-wise end-of-cycle information, including the axial node number, the nodal burnup, the instanta­ neous moderator density, the void history (VH), and the fuel tem­ perature Because the end-of-cycle values are specified, the instantaneous information—including the moderator density and fuel temperature—is not representative of the assembly’s cumulative behavior, particularly because the end-of cycle-statepoints are Name Derived GC-859 Number of Assemblies Bounding Calculation Description 3019 1472 (subset of Derived set) Detailed Calculation Description Bounding operating history Bounding operating history assumptions with assembly assumptions with assembly enrichment, burnup and enrichment and burnup from cycle-wise burnup GC-859 fuel survey and cycledistribution derived from wise burnup distribution detailed data constant power assumption Full axial and radial description of fuel geometry and composition with time dependent operating conditions J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 from 33,312 to 51,628 MWd/MTU, with a mean and standard deviation of 43,802 ± 3045 MWd/MTU The GC-859 data set burnups range from 33,312 to 50,860 MWd/MTU with a mean and standard deviation of 43,922 ± 3209 MWd/MTU Histograms of the assembly burnups for the derived and GC-859 data sets are shown in Fig Based on examination of the summary statistics and the histograms in Fig 5, there are no gross deviations in the assembly average burnups between the derived and GC-859 data sets One source of potential deviations between the results of the detailed and bounding calculations for the GC-859 data set is the difference be­ tween the burnup data provided in the GC-859 fuel survey and the detailed fuel and operational information obtained for this work The declared burnups from the GC-859 data for the US BWR site evaluated in this study are reported in integer numbers of GWd/MTU, such as 37 or 38 GWd/MTU Fig provides a histogram of the differences between the GC-859 assembly average burnups and the assembly average burn­ ups derived from the nodal data provided with the detailed data The difference in burnup was calculated by subtracting the detailed burnup from the GC-859 burnup The differences in burnup range between − 142.0 and 1049.2 MWd/MTU, with a mean and standard deviation of 456.4 ± 304.9 MWd/MTU The histogram in Fig indicates that the burnup was rounded up for most of the assemblies in the GC-859 set for this particular site Fig Difference in burnup between the GC-859 data and detailed information using 1472 assemblies from GC-859 set burnup information, it is also important to understand the differences in the operating history of the detailed data compared to the bounding assumptions used in the UNF–ST&DARDS depletion method The two operating parameters with the largest impact on the neutron energy spectrum during depletion and therefore the buildup of actinides in the fuel are the moderator density and the presence of control blades during depletion As noted in Section 2.4.2, the control blades are modeled as being present for the entirety of the depletion, and the moderator den­ sity is modeled as being 0.3 g/cm3 for the bounding calculations For the detailed calculations, the moderator density information provided for the US fuel assemblies is the VH, which is calculated using Eq (1), ∑N ∑C k=1 j=1 BUjk VFjk VH = ∑N ∑C (1) k=1 j=1 BUjk 3.1.3 Moderator density and control blade insertion In addition to understanding the fuel’s initial composition and where BU is the cycle burnup of an axial node, VF is the instantaneous void fraction, N is the number of nodes, C is the number of cycles The VH values were then converted to burnup averaged moderator density using a liquid phase density of 0.743 g/cm3 and a vapor phase density of 0.0353 g/cm3, corresponding to the values used from the Polaris code Conversion to burnup-average moderator density allows for better comparison to the Swedish data The measure of control rod exposure used for this work is the bladed fraction (BF), which is calcu­ lated using Eq (2), ∑N k=1 BUk BF = ∑C ∑S if Bladed i=1 CFijk { if not Bladed ∑N ∑C k=1 j=1 BUjk j=1 (2) where CF is the fraction of cycle burnup in a statepoint, and S is the number of statepoints in a cycle The histograms of the moderator density and BF for the detailed data for the assemblies in the Derived and GC-859 data sets are shown in Fig and Fig Fig shows that the history-averaged moderator density ranges between 0.366 and 0.508 g/cm3, with an average of 0.414 g/cm3 for the derived data set, and ranges between 0.372 and 0.508 g/cm3 with an average of 0.419 g/cm3 for the GC-859 data set Even at the lowest observed moderator density, the densities are higher than the 0.3 g/cm3 value used in the bounding calculations Fig shows that the history-averaged BF ranges from (in many cases) to 0.366 for both the derived data and the GC-859 data The average BF is 0.074 for the derived data; the average BF for the GC-859 data is 0.075 These values are substantially lower than the value of 1.0 assumed in the bounding calculations A lower moderator density and a higher fraction Fig Distributions of assembly average burnups for the derived data set as­ semblies (top), and the GC-859 data set (bottom) J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig Distribution of moderator density for the derived data set (top), and the GC-859 data set (bottom) Fig Distribution of BF for the derived data set (top), and the GC-859 data set (bottom) of the assembly’s history being bladed will lead to a harder neutron energy spectrum and therefore more actinide buildup at a given burnup This should lead to conservatism in decay heat calculations, particularly at cooling times longer than five years It is notable that there is little difference in the appearance of the histograms for the derived and GC859 data set moderator density and BF values, indicating that the GC859 set it is likely to be an unbiased subset of the assemblies detailed and bounding analyses To aid further discussion, the last cycle specific power (LCP) for the Derived data set and the for the GC-859 data set detailed and bounding calculations are provided in Fig There is only one set of LCPs for bounding and detailed calculations for the derived data set because the bounding cycle burnups and therefore powers are calculated from the detailed data for the derived data set The LCPs in Fig range from 4.27 to 33.54 MW/MTU with an average of 20.55 MW/MTU for the derived data set They range from 4.27 to 32.90 MW/MTU with an average of 19.88 MW/MTU for the detailed calculations in the GC-859 data set, and from 19.81 to 33.09 MW/MTU with an average of 26.57 MW/MTU for the bounding calcu­ lations This shows that for the GC-859 data, there appears to be bias toward higher specific powers in the bounding data due to the way that data are processed upon import by UNF-ST&DARDS There is also a noticeable striping in GC-859 LCP values in the bottom of Fig due to the rounding to the GC-859 reported burnups Equation (3) is used to provide a single-parameter descriptor of how large the overprediction in the last cycle power is The last cycle power ratio (LCPR) is calculated by dividing the power in the last cycle of operation for the bounding calculation by the power in the last cycle of operation from the detailed data calculation The LCPR parameter is only applicable to the GC-859 data set because the derived data set 3.1.4 Last cycle power Most of the safety analysis calculations performed by UNFST&DARDS are relatively insensitive to the temporal distribution of burnup by the fuel assembly; however, a few short-lived nuclides (134Cs, 106 Rh, and 144Pr) that contribute to decay heat saturate with burnup and are largely dependent on the assembly power level during the last portion of the assemblies’ irradiation These nuclides contribute to decay heat over a relatively short time period following assembly discharge (less than 10 years) If the power towards the end of the irradiation is too low in the bounding calculations it could result in a nonconservative estimate of the decay heat relative to the detailed cal­ culations To investigate this the effect, the specific power level in the last cycle of operation was calculated by dividing the burnup accrued in the last cycle of operation by the length of the last cycle for both the J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 10 Distribution of LCPR values for the GC-859 data set 3.2 Swedish data Discharge nuclides from 2117 Swedish BWR assemblies were generated using their full operational histories The discharge nuclides were imported by SKB staff using Studsvik’s SNF Code and were im­ ported into UNF-ST&DARDS for subsequent decay calculations using the direct discharge import method described in Section 2.3 The calcula­ tions have undergone the quality assurance process that is performed as part of the nuclear plants’ operation and core monitoring The data are from a single BWR unit and include data for both × and 10 × 10 types from multiple vendors; the specific fuel designs are not known The discharge dates for the fuel assemblies studied here range from the 1989 to 2017 The assembly average burnups range between 27,544 and 47,608 MWd/MTU, with an average and standard deviation of 41,527 ± 2845 MWd/MTU When the fuel was broken down by the fuel type, burnups for the × fuel (952 assemblies) ranged from 27,544 to 44,644 MWd/MTU with a mean and standard deviation of 39,525 ± 2570 MWd/MTU, and burnups for the 10 × 10 fuel (1165 assemblies) ranged from 38,806 to 47,608 MWd/MTU with a mean and standard deviation of 43,202 ± 1946 MWd/MTU This in­ dicates that the 10 × 10 fuel generally achieved more burnup than the × fuel A histogram of the Swedish data set burnups is shown in Fig 11 Moderator densities were directly provided for the Swedish data The lifetime averaged moderator densities range from 0.404 to 0.594 g/cm3 with a mean and standard deviation of 0.490 ± 0.035 g/cm3 When broken down by fuel type the × fuel assemblies had moderator density ranging from 0.408 to 0.594 g/cm3 with a mean and standard deviation of 0.500 ± 0.040 g/cm3 and the 10 × 10 fuel assemblies had moderator densities ranging from 0.404 to 0.579 g/cm3 with a mean and standard deviation of 0.489 ± 0.029 g/cm3 A histogram of the moderator densities is provided in Fig 12 The values of BF were also directly taken from the core simulator calculations The values of BF ranged from 0.004 to 0.0.230 with a mean and standard deviation of 0.046 ± 0.047 for the Swedish data set When considering the different fuel types the BF values for the × fuel as­ semblies ranged from 0.004 to 0.179 with a mean and standard devia­ tion of 0.028 ± 0.031 and the BF values for the 10 × 10 fuel assemblies ranged 0.008 to 0.230 with a mean and standard deviation of 0.061 ± Fig Distribution of LCP used for the derived data detailed and bounding calculations (top), the GC-859 detailed calculations (middle), and the GC-859 bounding calculations (bottom) calculates the cycle-wise bounding burnups from the detailed data and would always result in an LCPR of 1.0 LCPR = LCPBounding LCPDetailed (3) The LCPR values were calculated for all of the 1472 fuel assemblies in the GC-859 data set The LCPR values for the GC-859 data set range from 0.860 to 5.022 with a mean and standard deviation of 1.704 ± 0.860 A histogram of the LCPR values is provided in Fig 10 Based on an examination of the results in Fig 10, it is apparent that there are a number of assemblies with LCPR values in the near vicinity of 1.0, indicating that the algorithm used in UNF-ST&DARDS provides results that are in good agreement with actual operation much of the time; however, there are an also a large number of assemblies for which the specific power is substantially overpredicted during the last cycle of operation J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 11 Distribution of assembly burnups for the Swedish data set Fig 13 Distribution of BF values for the Swedish data set Fig 14 Distribution of LCP values for the Swedish data set Fig 12 Distribution of burnup averaged moderator densities for the Swedish data set 4.1 Derived US data set 0.052 A histogram of the values of BF for the Swedish data set are provided in Fig 13 LCP values for the Swedish data set were derived from information taken from core simulator values The values of LCP range from 1.34 to 25.64 MW/MTU with a mean and standard deviation of 7.17 ± 4.57 MW/MTU When the different fuel types were considered, the × assemblies had LCPs ranging from 1.34 to 23.27 MW/MTU with a mean and standard deviation of 7.19 ± 5.30 MW/MTU and the 10 × 10 fuel assemblies range from 1.78 to 25.65 MW/MTU with a mean and stan­ dard deviation of 7.15 ± 3.86 MW/MTU This distribution of LCP values for the Swedish data set is shown in Fig 14 An important input to thermal safety analysis of SNF for storage, transportation, and disposal system design is decay heat This section presents an analysis of the impact of the operating histories on the decay heat of discharged fuel assemblies Calculations were performed for the 3019 fuel assemblies considered here using the bounding and detailed analysis sequences available in UNF-ST&DARDS Each assembly was decayed to 1, 5, 10, 20, 100, and 200 years following assembly discharge, and the decay heat was calculated The decay heat ratio (DHR) is used as a means of comparing the detailed and bounding decay heats and was calculated by dividing the bounding decay heat by the detailed decay heat as shown in Eq (4) The DHR is effectively the amount of conservatism in the bounding decay heat For example, a DHR of 1.35 would represent a 35% conservatism in the bounding decay heat The minimum, maximum, mean, and standard deviation of the detailed and bounding decay heats and DHRs for each cooling time are shown in Table for the derived data set Additionally, the detailed and bounding decay heats are plotted as a Results and discussion This section presents the results of the bounding and detailed decay heat calculations The results of the US derived data set are discussed in Section 4.1, the results of the US GC-859 data set are discussed in Section 4.2, and the results of the Swedish data set are discussed in Section 4.3 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Table Summary statistical comparison between the detailed decay heats and the derived bounding decay heats (watts) Decay Time (years) 10 20 100 200 Detailed Bounding Min Mean ± σ Max Min Mean ± σ Max Min Mean ± σ Max 829.7 287.3 196.9 155.6 50.2 27.2 1535.8 ± 336.5 386.8 ± 29.1 270.8 ± 20.2 212.9 ± 15.9 68.1 ± 4.6 36.3 ± 2.3 2033.9 488.0 332.8 257.7 79.5 42.2 934.2 323.4 215.4 167.7 57.2 32.7 1669.5 ± 343.3 439.7 ± 32.7 300.5 ± 24.2 232.1 ± 19 76.3 ± 5.5 42.7 ± 2.9 2189.3 560 374.4 285.5 91.1 50.1 1.053 1.099 1.070 1.052 1.060 1.082 1.091 ± 1.137 ± 1.109 ± 1.090 ± 1.121 ± 1.177 ± 1.133 1.180 1.151 1.131 1.200 1.297 function of discharge burnup for the derived data in Fig 15 The DHRs for all of the decay times are plotted against the detailed decay heat in Fig 16 DHR = DHBounding DHDetailed DHR 0.018 0.015 0.015 0.016 0.032 0.048 all of the decay heats with burnup It is also noticeable that there are two distinct bands of decay heats with burnup, and the bands are most distinct at low cooling time, merging to a single band at the later cooling times The presence of the two bands at low cooling time is likely due to the multimodal nature of the LCP distribution that is apparent in top portion of Fig 9, where the top band is likely correlated with the higher mode of Fig and the bottom band is likely due to the lower modes of Fig The merging of the bands of decay heats is more pronounced for the bounding data and occurs almost completely by 20 years of cooling time The detailed data merges over the first 20 years of decay time but then shows more pronounced scatter for the 100- and 200-year cases The increase in scatter at longer cooling times is due to the dominance of the actinides, which are more sensitive to variations in the neutron energy spectrum during depletion at longer cooling times (4) A few observations can be made when the detailed and derived bounding data calculated decay heats in Table and Figs 15 and 16 are examined The first observation is that, in all cases, the bounding decay heat is greater than the detailed decay heat in terms of the minimum, maximum, and average values and by inspection of the burnupdependent plots This confirms the conservatism associated with oper­ ating history assumptions made within the bounding sequence of UNFST&DARDS For the derived data set, the average level of conservatism ranges between 9.0% and 17.7%, with the conservatisms having an approximate range about a mean of 8% between minimum and maximum for decay times between and 20 years The level of conservatism and the scatter in the DHR data increase significantly for the 100- and 200-year cases The second observation is that there is a roughly linear behavior for 4.1.1 Irradiation parameter and nuclide contributions to variability of decay heat for the derived data set Correlations with operating history parameters and the individual nuclide contributions to decay heat were examined to further investigate Fig 15 Detailed and derived bounding decay heats vs burnup for 1, 5, 10, 20, 100, and 200 years of cooling time 10 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 16 Decay heat ratio vs detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the derived data set the causes of the conservatism in the bounding decay heats relative to the detailed decay heats The derived data set is examined first because the differences associated with processing the GC-859 data into cyclewise burnups are not included in this data set The operating parame­ ters considered for the decay heat evaluation are VH, BF, the sum of VH and BF (VH + BF), and LCP VH is used rather than moderator density because it is positively correlated with increases in decay heat, as is BF, so the sum of the two numbers results in a potentially meaningful metric for assessing the combined effect of operational parameters on the neutron energy spectrum The nuclides considered in the evaluation are listed in Table For simplicity, the decay heat from 137mBa is combined with the decay heat from 137Cs, and the decay heat from 90Y is combined with the decay heat from 90Sr because the latter nuclides are short lived and are in secular equilibrium with the former nuclides For all cooling times of the detailed and bounding calculations, this set of nuclides was sufficient to capture more than 95% of the total assembly decay heat For cooling times greater than year, these nuclides capture more than 99% of the total assembly decay heat A correlation analysis was performed on the detailed decay heats, the bounding decay heats, and the DHRs to investigate the operating pa­ rameters that most heavily influence the conservatism in decay heat calculations It is widely known that decay heat at a constant cooling time is strongly influenced by burnup Because burnup is explicitly accounted for in UNF-ST&DARDS calculations and the goal is to deter­ mine what factors lead to the conservatism discussed in Section 4.1, it is desirable to remove burnup as variable from the analysis To control for burnup, a linear fit of the detailed and bounding decay heats was per­ formed as a function of assembly average burnup, and the residual decay heat about the trend line was calculated by subtracting the fitted values from each of the explicitly calculated assembly decay heats The re­ siduals were not calculated for the DHR values because the detailed and bounding decay heats are calculated at the same burnup The Pearson correlation coefficient was then calculated for the detailed decay heat residuals, the bounding decay heat residuals, and the DHR values with the LCP, VH, BF, and VH + BF variables for each of the cooling times considered here The correlation coefficients are shown in Fig 17 Fig 18, and Fig 19 for the detailed decay heat residuals, the bounding decay heat residuals, and the DHRs, respectively The corre­ lation coefficient inherently ranges from − to and the color coding in Fig 17 through 19 shades values closer to one in red and values closer to negative one in blue, with values near zero being lighter shades of each color It is apparent from an examination of the correlations for the detailed decay heat residuals in Fig 17 that there is a strong correlation between the decay heat residuals and LCP and VH with the strength of the cor­ relations varying based on the cooling time considered The correlation between the decay heat residuals and LCP is 0.996 and 0.975 at year and years of cooling time, respectively, representing a nearly perfect linear relationship The correlation drops to 0.725 at 10 years of cooling time and to values that are approximately 0.6 for the higher cooling times This indicates that at short cooling times the variation in the Table Nuclides used for decay heat investigations Actinides 241 243 Fission Products 242 244 Am, Am, Cm, Cm, Pu, 240Pu and 241Pu 239 238 Pu, 144 144 Ce, 134Cs, 137Cs (137Cs + 137mBa), Pr, 106Rh, and 90Sr (90Sr + 90Y) 154 Eu, Fig 17 Correlation coefficient between detailed decay heat and LCP, VH, BF, and the sum of VH and BF by cooling time 11 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 residuals and BF It is apparent from an examination of the correlations for the bounding decay heat residuals in Fig 18 that again there is a strong correlation between the bounding decay heat residuals and LCP for the 1-year and 5-year cases Because the high correlation was present in the 1- and 5-year cases for the detailed calculations and the cycle-wise burnups for each assembly were calculated based on the average of the nodal information used for the detailed calculations, it is logical that the same correlations would be present in the bounding calculations Also, there are mild correlations between the bounding decay heat re­ siduals and VH and VH + BF The correlations are likely a result of the cross correlation between VH and LCP, like what was noted for the detailed decay heat residuals No other strong correlations were observed for the bounding decay heat residuals This is expected because the depletion conditions for the bounding calculations are fixed based on the assumptions discussed in Section 2.4.2, and little variability should be expected outside total burnup and the temporal burnup distribution The correlations for the DHR values with the operating parameters shown in Fig 19 indicate negative correlations to the same parameters as the detailed decay heat residuals, namely, LCP, and VH It is intuitive that the DHR would be negatively correlated with VH because VH causes the detailed decay heat to skew high for a given burnup, and the bounding decay heat is insensitive to it, so the ratio of bounding decay heat to detailed decay heat should trend negatively with increasing VH The negative correlation between LCP and DHR is less intuitive because both the bounding and detailed decay heat residuals had positive cor­ relations with LCP There is a correlation coefficient of 0.999 between the bounding and detailed decay heats at year of cooling time, indi­ cating that the negative correlation is possibly due to the bounding decay heats and detailed decay heats having different sensitivities to LCP The change in individual nuclide decay heat between the bounding and detailed calculations vs DHR is plotted in Fig 20 for all of the cooling times analyzed here The data in the upper left portion of Fig 20 indicate that the primary nuclides contributing positively to the conservatism in the bounding calculations in the 1-year cooling time case are 134Cs, 244Cm, 106Rh, and 238Pu, with 90Sr and 144Pr contributing negatively to the conservatism between the two sets of calculations The increased decay heat contributions of 244Cm, 134Cs, and 238Pu in the bounding calculations relative to the detailed calculations are due to the harder neutron energy spectrum The decreased decay heat contribu­ tions of 90Sr and 144Pr in the bounding calculations relative to the detailed calculations are due to the lower 239Pu/235U fission ratio associated with a softer energy spectrum during the detailed depletion calculations The fission yields of 90Sr and 144Pr are lower from 239Pu than from 235U The data in the upper right portion of Fig 20 show that a similar set of nuclides contribute to the conservatism in the bounding calculations in the 5-year case For the five-year case, the negative contribution of 144Pr and the positive contribution of 106Rh have virtually disappeared, and the positive contribution of 134Cs has decreased relative to 244Cm because of the short half-life of 134Cs By 10 years, the conservatism in the decay heat calculations is due almost entirely to 244Cm; the effect of 134Cs has dropped out completely The 20-year case begins to show relatively increased contributions of 241Am, which is the primary driver of the conservatism in the 100- and 200-year cases Fig 18 Correlation coefficient between bounding decay heat and LCP, VH, BF, and the sum of VH and BF for the derived data set Fig 19 Correlation coefficient between DHR and LCP, VH, BF, and the sum of VH and BF for the derived data set specific power of the fuel explains the variation in the detailed decay heat that is not due to burnup variation The correlation between VH and the detailed decay heat residuals is strongest for the 100 year (0.900) and 200 year (0.880) of cooling time cases and gradually drops off with decreasing cooling time to a value of 0.612 for the 1-year case The strong correlation between VH and the residual decay heat for the detailed calculations is expected due to the impact of increased VH on the actinide source term, which dominates decay heat at longer cooling times Correlations between input variables can sometimes affect the cor­ relations between the outputs The correlation between the inputs LCP and VH is 0.602 for the derived data set This correlation is logical because assemblies that experience higher specific powers during operation result in larger enthalpy rises in coolant and therefore higher void fractions; however, the correlation between LCP and VH is limited because LCP only considers the last cycle of operation, to which shortlived nuclides are sensitive The cross correlation between LCP and VH is responsible for the correlations between LCP and the decay heat residuals at high cooling times and VH and the decay heat residuals at short cooling times A moderate correlation between BF and residual decay heat was also observed for the 100-year case (0.553) and 200-year cases (0.559), although the correlation between the VH + BF and the detailed decay heat residuals is slightly smaller than the correlation on VH alone The correlation between BF and VH is 0.311 and likely does not explain the moderate correlation between the detailed decay heat 4.2 GC-859 US decay heat This section discusses the decay heat results for the 1472 assemblies for which GC-859 survey data were available Comparison of those data to the data found in Section 4.1 allows for insight into the effect that the GC-859 data processing has on conservatism of the UNF-ST&DARDS decay heat calculations in addition to the impact of the operating history effects Each assembly was decayed to 1, 5, 10, 20, 100, and 200 years following assembly discharge, and the decay heat was calculated Like 12 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 20 Nuclide decay heat changes vs DHR for the derived data set 13 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 the derived data set, the DHR values were also calculated for each as­ sembly using Eq (4) The minimum, maximum, mean, and standard deviation of the detailed and bounding decay heats and DHRs for each cooling time are shown in Table for the GC-859 data set Additionally, the detailed and bounding decay heats are plotted as a function of discharge burnup (as calculated from the detailed data) for the GC-859 data in Fig 21 The DHRs for all of the decay times are plotted against the detailed decay heat in Fig 22 Four observations were made based on an examination of the detailed and GC-859 bounding data calculated decay heats in Table 5, Figs 21, and Fig 22 The first observation is that, in all cases, the bounding decay heat is greater than the detailed decay heat in terms of the minimum, maximum, and average values and by inspection of the burnup-dependent plots This confirms the conservatism associated with operating-history assumptions made within the bounding sequence of UNF-ST&DARDS as well as with the algorithm used to process the GC859 burnup data into cycle-wise burnups for depletion calculations (discussed in Section 2.4.3 For the GC-859 data set, the average level of conservatism ranges between 11.4% and 32.3%, with the conservatisms having a widely varied range about mean for all decay times The level of conservatism and the scatter in the data are largest for the 1-year case (32.3% ± 24.4%), and they decrease progressively, reaching a minimum at the 20-year case (11.4% ± 2.4%), at which point they increase for the 100-year (14.6% ± 3.3%) and 200-year (20.5% ± 4.9%) cases The high level of conservatism and the scatter in the data at low cooling times, which are larger than were observed with the derived data set, are caused by variation in the power level of the last cycle introduced by the algorithm that assigns cycle-wise burnups based on the GC-859 discharge burnup declarations The higher degrees of conservatism and scatter in the data for the longer cooling times are likely due to the conservatism in the depletion parameter assumptions, like what was observed in the derived data set The second observation is that there is a roughly linear behavior for both the detailed and bounding the decay heats with burnup across all decay times It is also noticeable that both the detailed and bounding decay heats have two distinct bands, which are most distinct at low cooling time For the bounding decay heat, the bands merge to a single band by 10-year case and remain merged through the 200-year case The detailed data bands merge over the first 20 years of decay time but have increased scatter for the 100- and 200-year cases The increase in scatter at longer cooling times is due to the dominance of the actinides, which are more sensitive to variations in the neutron energy spectrum during depletion at longer cooling times The burnup-dependent behavior of the plots is similar to those of the detailed data set shown in Fig 15 The third observation is that there is a “stairstep” behavior to the bounding data when plotted against the burnups derived from the detailed data The stairstep behavior results from the GC-859 burnups having been rounded to the nearest 1000 MWd/MTU when reported by the plant staff responsible for completing the GC-859 survey This in­ troduces an additional source of uncertainty into the calculated decay heats, but it appears to be insignificant in comparison to the overall behavior of the data The fourth observation is that the approximations used to process the GC-859 data into the bounding calculations introduce additional conservatism relative to the derived data set at short cooling times This is evidenced by the DHR values being larger for the GC-859 data set than for the derived data set at each decay time considered This increase is shown by the much larger variation in the 1-yr cooled data in Fig 22 in comparison to Fig 16 The increase in the conservatism is most notable for the early cooling time, as is expected because short-lived nuclides are most sensitive to temporal burnup distribution 4.2.1 Irradiation parameter and nuclide contributions to variability of decay heat for GC-859 data set Correlations with operating history parameters and the individual nuclide contributions to decay heat differences were examined to further investigate the causes of the conservatism in the bounding decay heats relative to the detailed decay heats for the GC-859 data set The same operating parameters that were considered for the derived data set were used here, namely, VH, BF, VH + BF, and LCP In the same manner as was done for the derived data set, a linear fit of the detailed and bounding decay heats as a function of fuel burnup was performed, and the residual decay heats about the trend line were calculated by sub­ tracting the fitted values from each of the explicitly calculated assembly decay heats The residuals were not calculated for the DHR values because the detailed and bounding decay heats are calculated at the same burnup The Pearson correlation coefficient was then calculated between the detailed decay heat residuals, the bounding decay heat residuals, and the DHR values, with the LCP, VH, BF, and VH + BF for each of the cooling times considered here The LCP values used here are different for the detailed data (middle portion of Fig 9), the bounding data (bottom portion of Fig 9), and the DHR (LCPR values in Fig 10) The correlation coefficients are shown in Fig 23, Fig 24, and Fig 25 for the detailed decay heat residuals, the bounding decay heat residuals, and the DHRs The same color shading scheme as is discussed in Section 4.1.1 is applied here for the correlation shading The nuclide contribu­ tion analysis was performed in the same manner as was discussed in Section 4.1.1 It is apparent from an examination of the correlations for the detailed decay heats in Fig 23 that there is a strong correlation between the decay heat residuals and LCP and VH; the strength of the correlations varies based on the cooling time considered The correlation coefficients between the decay heat residuals and LCP is 0.996 and 0.975 at year and years of cooling time, respectively, representing a nearly perfect linear relationship The correlation drops to 0.727 at 10 years of cooling time and to values that are approximately 0.6 for the higher cooling times This indicates that at short cooling times the variation in the specific power of the fuel explains the variation in the detailed decay heat that is not due to burnup variation The correlation between VH and the detailed decay heat residuals is strongest for the 100-year (0.900) and 200-year (0.871) cooling time cases It gradually drops off with decreasing cooling time to a value of 0.576 for the 1-year case The strong correlation between VH and the residual decay heat for the detailed calculations is expected, due to the impact of increased VH on the actinide source term, which dominates decay heat at longer cooling times The correlation between LCP and VH is 0.574 for the detailed calculations The cross correlation is responsible for the higher-than- Table Summary statistical comparison between the detailed decay heats and the GC-859 bounding decay heats (watts) Decay Time (years) 10 20 100 200 Detailed Bounding DHR Min Mean ± σ Max Min Mean ± σ Max Min Mean ± σ Max 878.6 287.3 196.9 155.6 50.2 27.2 1513.2 ± 340.7 386.3 ± 28.9 271.2 ± 20.8 213.2 ± 16.5 68.0 ± 4.7 36.2 ± 2.3 2033.9 464.7 322.8 252.3 78.1 41.0 1470.6 337.2 221.7 172.0 58.5 33.5 1926.0 ± 163.5 466.7 ± 37.0 310.0 ± 27.6 237.7 ± 20.9 78.0 ± 6.1 43.7 ± 3.1 2249.5 543.0 377.0 284.9 90.6 50.1 1.037 1.108 1.080 1.063 1.085 1.125 1.323 ± 1.209 ± 1.142 ± 1.114 ± 1.146 ± 1.205 ± 1.892 1.343 1.207 1.167 1.231 1.328 14 0.244 0.063 0.026 0.021 0.033 0.049 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 21 Detailed and GC-859 bounding decay heats vs burnup for 1, 5, 10, 20, 100, and 200 years of cooling time Fig 22 Decay heat ratio vs detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the GC-859 data set expected correlations of LCP at long cooling times and VH at short cooling times A moderate correlation between BF and residual decay heat was also observed for the 100-year (0.525) and 200-year cases (0.538) although the correlation between the VH + BF and the residual decay heat produced a correlation slightly smaller than the correlation on VH alone The correlation between BF and VH is 0.328 and likely 15 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 does not explain this effect alone All of the correlation results are similar to what was seen for the Derived data set, which is expected since these assemblies are merely a subset for the detailed calculations It is apparent from an examination of the correlations for the bounding decay heat residuals in Fig 24 that again there is a strong correlation (0.971) between the bounding decay heat residuals and LCP for the 1-year case and significant but less strong correlation (0.791) for the 5-year case There is a mild correlation significant correlation be­ tween the VH and the bounding decay heat residuals for the 1-year and 5-year cases with values of 0.787 and 0.783 They are likely due to the cross correlation of VH and LCP of 0.838 for the bounding calculations There is a mild correlation between the decay heat residuals and the VH + BF in the 1-year and 5-year cases; however, that correlation is also likely a result of the same cross correlation, however, diluted by the addition of BF No other strong correlations were observed for the bounding decay heat residuals That finding is important because the depletion conditions are fixed based on the assumptions discussed in Section 2.4.2, and little variability should be expected outside of total burnup and the temporal burnup distribution The correlations for the DHR values with the operating parameters are shown Fig 25 The correlation between LCPR and DHR was stron­ gest for the 1-year case, incrementally dropping off for subsequent years This is similar to the observations for both the detailed and bounding decay heat residuals, although the decrease in the DHR correlation with increased cooling time is more subtle than was observed with the either the detailed or bounding decay heat residuals The correlation between the DHR values and the difference in burnup between the detailed values and the GC-859 reported values (ΔBU) is minimal with the exception of the 10-year and 20-year cases For those cases moderate correlations of 0.454 and 0.491 were observed The 10-year and 20-year cooling times are dominated by changes in 244Cm, which is known to be highly sen­ sitive to differences in burnup Strong negative correlations of DHR to VH with cooling time were observed to increase progressively as well; the strongest correlations occurred at the higher cooling times This is logical because detailed decay heat is preferentially increased with increased VH, and the bounding decay heats are insensitive to it, thus resulting in decreased margins at higher values of VH There is moderate negative correlation between DHR and BF for the 100-year and 200-year cases and a progressively increasing in magnitude negative correlation for the VH + BF across cooling times that is largely due to the VH component The change in individual nuclide decay heat between the bounding and detailed calculations is plotted vs DHR in Fig 26 for all of the cooling times analyzed here The data in the upper left portion of Fig 26 indicate that the primary nuclides contributing positively to the conservatism in the bounding calculations in the 1-year cooling time case are 106Rh, 144Pr, and 134Cs, with additional positive contributions from 244Cm and 242Cm and a negative contribution from 90Sr The increased decay heat contributions of 244Cm, 242Cm, and 238Pu in the bounding calculations relative to the detailed calculations are due to the harder neutron energy spectrum The decreased decay heat contribution of 90Sr in the bounding calculations relative to the detailed calculations is due to the lower 239Pu/235U fission ratio associated with a softer en­ ergy spectrum during the detailed depletion calculations The increases in 106Rh and 144Pr decay heats in the bounding vs detailed calculations are primarily due to the increase in LCP for the bounding cases The contribution for 144Pr to the derived data set was negative because of the shift in the 239Pu/235U fission ratio; however, the shift is smaller than the effect of the increased LCP values for the GC-859 data set Some dif­ ferences in 144Pr decay heat are negative for the GC-859 data set in cases where the LCPR values are near The increase in the 134Cs contribution is due to a combination of the harder spectrum and increased LCP for the bounding calculations The data in the upper right portion of Fig 26 show that the nuclides contributing to the conservatism in the bounding calculations in the 5-year case are primarily 244Cm and 134Cs For the 5year case, the contribution of 144Pr has virtually disappeared, and the Fig 23 Correlation coefficients between detailed decay heat and LCP, VH, BF, and the sum of VH and BF for the GC-859 data set Fig 24 Correlation coefficients between bounding decay heat and LCP, VH, BF, and the sum of VH and BF for the GC-859 data set Fig 25 Correlation coefficient between DHR and LCPR, ΔBU, VH, BF, and the sum of VH and BF for the GC-859 data set 16 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 26 Nuclide decay heat changes leading to total decay heat changes for 1, 5, 10, 20, 100 and 200 years of cooling time between GC-859 and detailed data 17 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 contribution of 106Rh is significantly lessened For the 10-year case, the conservatism in the decay heat calculations is largely due to 244Cm The effect of 134Cs lessened significantly, and there is a minor contribution from 238Pu The 20-year case begins to show relatively increased con­ tributions of 238Pu and 241Am, and the conservatism in the 100- and 200year cases is mostly driven by 241Am While there are remarkable differences in the data from the derived data set in the 1-year case and 5-year cases that increase the conserva­ tism, it is notable that most of these difference are minimized by the 10 years of cooling time This indicates that the impact of the GC-859 dataprocessing algorithm on decay heat is likely limited to the first 10 years of cooling time calculations, the × fuel has higher decay heat values at a given burnup than the 10 × 10 fuel The different lattice types have different geometric characteristics as well as time periods during which they were irradiated Although specific details of the designs are not available for either fuel type, the × fuel designs represent an earlier generation of BWR fuel design, which in general did not use part-length rods and made more limited use of water rods in the lattices than did 10 × 10 fuel, so it is reasonable to expect a harder neutron spectrum during irradiation for the × fuel The earlier operation of the × fuel is also possibly correlated with operation of the reactor at lower overall power levels, although the moderator densities in Fig 12 and the LCP values in Fig 14 are similar between the two lattice types 4.3.1 Irradiation parameter and nuclide contributions to variability of decay heat for the Swedish data set To further investigate the causes of the conservatism in the bounding decay heats relative to the detailed decay heats for the Swedish data set, correlations with operating history parameters and the individual nuclide contributions to decay heat differences are examined for both the × and 10 × 10 fuel assemblies The same operating parameters that were considered for both US data sets (i.e., VH, BF, the VH + BF, and LCP) were used In the same manner as was done for the both US data sets, a linear fit of the detailed and bounding decay heats as a function of fuel burnup was performed, and the residual decay heats about the trend line were calculated by subtracting the fitted values from each of the explicitly calculated assembly decay heats The Pearson correlation coefficient was then calculated between the detailed decay heat residuals, the bounding decay heat residuals, and the DHR values, with each of LCP, VH, BF, and VH + BF for each of the cooling times considered here It was reported that cycle-wise burnups for the bounding calculations were taken from the SNF code data, so the LCP values are the same for the detailed and bounding calculations as was the case for the derived US data set The correlation coefficients are shown in Fig 29, Fig 30, and Fig 31 for the detailed decay heat re­ siduals, the bounding decay heat residuals, and the DHRs, respectively The left half of each figure contains the data for the × fuel; the right half of the figure contains the data for the 10 × 10 fuel The same color scheme as is discussed in Section 4.1.1 is applied the figures for the correlation shading The nuclide contribution analysis was performed in the same manner as was discussed in Section 4.1.1 The results of the nuclide analysis are shown in Fig 32 for the × fuel and in Fig 33 for the 10 × 10 fuel It is apparent from an examination of the correlations for the detailed decay heat residuals in Fig 29 that there is a strong correlation between the decay heat residuals and LCP and VH for the × fuel and that the strength of the correlations vary based on the cooling time considered The correlation coefficients between the decay heat residuals and LCP are 0.903 and 0.790 at year and years of cooling time, indicating a very strong linear relationship The correlation drops to 0.615 at 10 years of cooling time and mildly declines over the remainder of the decay times to a value of 0.445 at 200 years The cross correlation be­ tween LCP and VH is 0.471 and is likely responsible for the correlation between the detailed decay heat residuals and LCP at longer cooling times for the × fuel There is a strong and relatively constant with 4.3 Swedish decay heat data Bounding and detailed assembly discharge calculations and subse­ quent decay calculations were performed for the 2117 Swedish BWR fuel assemblies, and the decay heat was calculated for post-irradiation cooling times of 1, 5, 10, 20, 100, and 200 years The DHR was calcu­ lated by dividing the bounding decay heat by the detailed decay heat, as shown in Eq (4) Investigation of the results showed that there were marked differences in the behavior of the × fuel (952 assemblies) and 10 × 10 fuel (1165 assemblies), so it was decided to treat those fuel types independently The minimum, maximum, mean, and standard deviation of the decay heats and DHRs for each cooling time are shown in Table for the × fuel and in Table for the 10 × 10 fuel Addi­ tionally, the detailed and bounding decay heats are plotted as a function of burnup for the Swedish BWR data in Fig 27, and the DHRs are plotted against the detailed decay heat in Fig 28 In each figure the × and 10 × 10 fuel assemblies are indicated by separate colors A couple of observations were made when the calculated decay heats in Tables and and Fig 27 were examined The first observation is that, in all cases, the bounding decay heat is greater than the detailed decay heat in terms of the minimum, maximum, and average values and by inspection of the burnup-dependent plots This confirms the conser­ vatism associated with operating history assumptions made within the bounding sequence of UNF-ST&DARDS for the Swedish data set regardless of fuel type The DHR data in Tables and and Fig 28, show that the average level of conservatism ranges between 10.1% and 62.6% for the × fuel and 8.3%–44.7% for the 10 × 10 fuel, depending on decay time, with the conservatisms varying relatively widely about the mean for each decay time The level of conservatism and the scatter in the DHR data within each lattice type increase significantly with increasing decay time and are markedly increased for the 100- and 200year cases compared with the shorter decay times This information is shown in Fig 28 The second observation is that the behavior is roughly linear for all of the decay heats with burnup within each of the fuel types for cooling times considered except year, which is heavily scattered due to vari­ ations in LCP It is also noticeable that there are two distinct bands of decay heats with burnup (Fig 27), and the bands become increasingly distinct with increasing cooling time (Figs 27 and 28) The bands are related to the Swedish BWR data set, which is composed of data for × and 10 × 10 fuel assemblies For both the detailed and bounding Table Summary statistical comparison between the Swedish × fuel assembly detailed and the bounding decay heats (watts) Decay Time (years) 10 20 100 200 Detailed Bounding DHR Min Mean ± σ Max Min Mean ± σ Max Min Mean ± σ Max 482.3 228.8 162.5 128.2 41.9 23.6 940.5 ± 267.2 316.3 ± 40.8 232.8 ± 23.3 183 ± 17.1 56.8 ± 4.8 30.4 ± 2.4 1668.2 427.4 290.3 223.1 68.2 36.4 550.6 266.6 181.6 143.6 54.5 33.5 1032.7 ± 282.9 374.4 ± 46.0 280.1 ± 28.1 222.3 ± 21.2 81.9 ± 7.0 49.5 ± 3.9 1815.4 492.8 343.2 266.7 94.8 56.3 1.005 1.123 1.117 1.120 1.300 1.419 1.101 ± 0.020 1.185 ± 0.013 1.203 ± 0.013 1.215 ± 0.016 1.441 ± 0.036 1.626 ± 0.052 1.212 1.214 1.234 1.253 1.529 1.761 18 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Table Summary statistical comparison between the Swedish 10 × 10 fuel assembly detailed and the bounding decay heats (watts) Decay Time (years) 10 20 100 200 Detailed Bounding DHR Min Mean ± σ Max Min Mean ± σ Max Min Mean ± σ Max 547.5 268.2 212.6 168.2 50.2 26.1 975.3 ± 189.9 332.1 ± 24.3 243 ± 13.3 189.9 ± 9.7 56.7 ± 2.6 29.5 ± 1.3 1770.3 415.1 282.0 216.4 63.6 32.8 600.1 312.7 246.9 196.5 66.7 38.3 1055.1 ± 200 383.4 ± 27.1 284.4 ± 15.7 222.8 ± 11.6 74.6 ± 3.4 42.7 ± 1.7 1867.3 470.3 325.1 252.2 82.5 46.5 1.011 1.114 1.129 1.128 1.242 1.328 1.083 ± 1.155 ± 1.170 ± 1.174 ± 1.316 ± 1.447 ± 1.133 1.201 1.211 1.213 1.384 1.551 0.021 0.012 0.011 0.012 0.024 0.037 Fig 27 Swedish detailed and bounding decay heats vs burnup for 1, 5, 10, 20, 100, and 200 years of cooling time respect to decay time correlation between VH and the detailed decay heat residuals of approximately 0.8 for the × fuel A strong corre­ lation between the residuals and VH is expected at longer cooling times, however, the correlation at short cooling times is unexpected and is too high to be explained by the cross correlation between VH and LCP It is not understood why the VH correlation is invariant with time The × detailed decay heat residuals show virtually no correlation with BF, and the correlation with the VH + BF is slightly lower in magnitude than the correlation between the residuals and VH as was observed in the US Data sets The correlations for the 10 × 10 fuel detailed decay heat residuals with LCP are somewhat reduced in comparison to the × fuel at one year (0.796) and five (0.656) years of cooling time but are still strong The 10 × 10 fuel detailed decay heat residuals correlation with LCP also drops off more steeply than with decay time after years than the × fuel correlation does because the cross correlation between LCP and VH is only 0.060, which is logical, given the lack of influence of LCP on decay heat after the first years The correlation between 10 × 10 fuel detailed decay heat residuals and VH was lower than the correlation observed with the maximum value of 0.537 occurring for the 10-year case Because VH primarily influences the actinide compositions, it was expected that the correlation would grow with time, but it did not It is not currently understood why the correlation of the 10 × 10 fuel detailed decay heat residuals with VH is lower for the Swedish data set than the correlations for the other data sets and why it does not grow with time, although it is possible it is a result of there being multiple fuel designs considered in the data set The detailed decay heat residuals show a moderate correlation with BF for 100-year and 200-year cases The correlation of the VH + BF is greater than that for either VH or BF individually for the 100-year and 200-year cases and indicates that there may be some synergy between these two variables for the 10 × 10 fuel The correlation between the residuals and the VH + BF increases consistently with decay time It is apparent from an examination of the correlations for the bounding decay heat residuals in Fig 30 that both the × and 10 × 10 fuel have 1-year and 5-year correlations with LCP that are similar to what was observed in the detailed decay heat residuals This correlation is expected because the LCP values for bounding calculations should be 19 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 28 Decay heat ratio vs detailed decay heat for 1, 5, 10, 20, 100, and 200 years of cooling time for the Swedish data set Fig 29 Correlation coefficients between detailed decay heat residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set Fig 30 Correlation coefficients between bounding decay heat residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set the same as those in detailed calculations such as the derived US data set The LCP correlations tail off significantly with increasing decay time, as is expected For the × fuel, this indicates that the detailed decay heat residual correlations for the longer cooled cases were likely a result of the cross correlation with VH The correlation of the × fuel bounding residuals with VH is higher than would be expected at early cooling times because the depletion conditions are invariant to opera­ tional history This is likely partially a result of the cross correlation with LCP The 10 × 10 fuel shows no strong correlations with VH, as is ex­ pected Neither fuel type shows any significant correlation with BF The 20 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 31 Correlation coefficients between DHR residuals and VH, BF and the sum of VH and BF, separated by fuel type for the Swedish data set correlation of the × fuel with the VH + BF appears to be a result of the VH component, which is partially explained by the cross correlation with LCP The 10 × 10 fuel shows no significant correlation with VH + BF It is apparent from an examination of the correlations of DHR with the operating history parameters in Fig 31 that DHR is most highly correlated with VH and the sum of VH + BF for both fuel categories The × fuel correlation VH is highest at for the 5-year case but otherwise ranges between − 0.46 and − 0.61 and increases gradually over the 20year to 200-year cases It is non-physical that the correlation would be so high in the 5-year case and decreased in later years There is currently no explanation for this The same behavior is observed for the VH + BF; however, the correlations are slightly more negative It is logical that VH and the VH + BF would be negatively correlated with DHR because they would cause an increase in the detailed decay heat and no change in the bounding decay heat The correlation of DHR with VH for the 10 × 10 fuel is larger in magnitude than it was for the 8× fuel, although the 5year case still seem higher than it should be The correlations of DHR with BF and the VH + BF increase in magnitude smoothly with decay time The change in individual nuclide decay heat between the bounding and detailed calculations is plotted vs DHR for the × fuel in Fig 32 The data in the upper left portion of Fig 32 indicates that the primary nuclides contributing positively to the conservatism in the bounding calculations in the 1-year cooling time case are 244Cm, 134Cs, 242Cm, and 238 Pu and negative contributions are from 90Sr and 144Pr The increased decay heat contributions of 244Cm, 134Cs, 242Cm, and 238Pu in the bounding calculations relative to the detailed calculations are due to the harder neutron energy spectrum The decreased decay heat contribu­ tions of 90Sr and 144Pr in the bounding calculations relative to the detailed calculations are due to the lower 239Pu/235U fission ratio The fission yields of 90Sr and 144Pr are lower from 239Pu than from 235U The 5-year nuclide contributions in the upper right corner of Fig 32 shows that the dominant positive contributions are from 244Cm and 238Pu with a negative contribution from 90Sr The same nuclides the 5-year case remain major contributors to the conservatism in the decay heat through the 20-year case with increasing contributions from 241Am over time 241 Am is the dominant driver of decay heat conservatism in the 100-year and 200-year cases, with 238Pu contributing in the 100-year case The change in individual nuclide decay heat between the bounding and detailed calculations is plotted vs DHR for the 10 × 10 fuel in Fig 33 The nuclide decay heat results for the 10 × 10 fuel look quali­ tatively similar to the results for the × fuel, showing that same nu­ clides primarily contribute to conservatism at the same time periods in a qualitative manner It appears that the differences between the detailed and bounding actinide decay heats are somewhat smaller in many in­ stances for the 10 × 10 fuel, driving the smaller DHR values in com­ parison to the × fuel The cycle-wise burnups and therefore power histories for the Swedish data are derived from the detailed information Therefore, comparison to the derived US data is most appropriate In comparison to the derived US data, the changes in actinide contributions between the detailed and bounding calculations are qualitatively similar to the Swedish data set but higher in magnitude for both fuel types It is likely that the magnitude differs because the overall moderator densities experienced by Swedish fuel (average of 0.489 g/cm3) were higher than those experienced by the US fuel (average of 0.414 g/cm3) There are also differences in the short-lived fission products in the 1-year and 5year decay time results because of the differences between the LCP values between the data sets; the US data have significantly higher LCP values (average of 20.55 MW/MTU) than the Swedish data (7.17 MW/ MTU) The higher LCP values experienced by the US fuel exacerbate any decay heat differences induced by changes in neutron energy spectrum or fission yield between the bounding and detailed calculations Conclusions and future work Licensing evaluations for SNF storage, transportation, and disposal systems are typically performed using bounding operating history as­ sumptions and canister contents The canister contents are assumed to be limiting in an attempt to envelop maximum possible loading varia­ tions in comparison to their actual loading The UNF-ST&DARDS tool has been designed to analyze SNF systems so that the margin to the licensing basis can be characterized and used to inform decision making Although the aim of as-loaded analysis is to take credit for the actual fuel type, burnup, enrichment, and cooling time associated with assemblies loaded in the SNF systems, it is desired that some level of conservatism associated with the depletion conditions be retained for safety analysis work This paper examines the level of conservatism in the UNFST&DARDS bounding assembly-specific decay heat calculations A comparison between the UNF-ST&DARDS bounding decay heat calcu­ lations and calculations using a detailed description of the operating histories of several fuel assemblies was performed using recently ac­ quired data The data used to perform the evaluation were one set of 3019 assemblies from a US twin-reactor site and one set of 2117 as­ semblies for a Swedish reactor The US data set was analyzed using two different sets of assumptions The first analysis derived the cycle-wise burnups for the bounding calculations from the detailed data, referred to as the “derived data set”; the second analysis was based on the as­ sumptions associated with incorporating GC-859 data in UNFST&DARDS, where the cycle-wise burnup is derived from the average discharge burnups and cycle lengths assuming constant power (referred to as the “GC-859 data set”) For each data set the decay heat values were calculated for all assemblies using the detailed and bounding analysis pipelines, and the results were compared For each data set, the bounding and detailed decay heats were compared with one another as a function of burnup, and DHRs were calculated by dividing the bounding decay heat by the detailed decay heat Additionally, correlations be­ tween the various operating history parameters and the bounding and 21 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 32 Nuclide decay heat changes vs DHR for the × Swedish fuel 22 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 Fig 33 Nuclide decay heat changes vs DHR for the 10 × 10 Swedish fuel 23 J.B Clarity et al Progress in Nuclear Energy 143 (2022) 104042 detailed decay heat residuals and DHR values were examined, as were the nuclide contributions to decay heat conservatism The derived US data set compared decay heats calculated using the detailed analysis pipeline to bounding decay heats using axially aver­ aged burnups developed from the detailed data An important conclu­ sion of this work is that for the derived data set, the average level of conservatism ranges between 9.0% and 17.7%; the conservatisms have an approximate range about the mean of 8% between minimum and maximum for decay times between and 20 years The level of conservatism and the scatter in the data increase significantly for the 100- and 200-year cases The conservatisms for the derived data set are most highly correlated with LCP in the 1-year and 5-year cases and most highly correlated with VH at longer cooling times Differences in shortlived fission products contribute significantly to the conservatism in the 1-year and 5-year cases; 244Cm contributed significantly to the conser­ vatism over the first 20 years of cooling time, and 241Am significantly contributed to the conservatism in the 100-year and 200-year cases The GC-859 US data set compared decay heat values calculated using the detailed analysis pipeline to bounding decay heat values calculated using assembly burnups from the GC-859 data collection process for the 1472 assembly subset of the derived data set for which the GC-859 in­ formation was available The primary difference in the bounding cal­ culations between the GC-859 data set and the derived data set is that the assembly average burnups were rounded up to the nearest 1000 MWd/MTU in most cases in the values report to GC-859 survey and that the cycle-wise burnup distribution was developed using the algorithm that UNF-ST&DARDS uses to process the GC-859 data For the GC-859 data set, the average level of conservatism ranges between 11.4% and 32.3% The level of conservatism and the scatter in the data are largest for the 1-year case and decrease progressively, reaching minimums at the 20-year case, at which point they increase for the 100-year and 200year cases An important conclusion arising from this data set is the processing of the GC-859 discharge burnups into cycle-wise burnups adds significant additional conservatism to the 1-year and 5-years cooled cases, however, the additional conservatism declines signifi­ cantly beginning with the 10-years cooled case Strong correlations are shown between the LCPR and DHR for the 1-year and 5-year cases, and strong correlations are found with VH for the 100-year and 200-year cases The same nuclides as were discussed for the derived data set contributed to the difference Additional contributions are expected to come from the short-lived fission products in the 1-year and 5-year cases The Swedish data set provided for a comparison of the detailed decay heats calculated using the inventory of nuclide compositions imported from core simulator models and decayed using the UNF-ST&DARDS detailed pipeline with bounding decay heats calculated using the cyclewise burnups from the SNF Code Little is known about the character­ istics of the fuel designs; however, the number of rods in the lattice of the fuel assemblies was disclosed, and the data set was divided into two subsets: × fuel and 10 × 10 fuel The average level of conservatism ranges between 10.1% and 62.6% for the × fuel and 8.3%–44.7% for the 10 × 10 fuel, depending on decay time Unlike that of the US data sets, the level of conservatism for the Swedish data sets increased monotonically across all decay times The nuclide results for both Swedish data subsets indicated that the substantially lower last cycle power likely limited the contribution of the short-lived nuclides to the conservatism in early cooling time cases There was also more conser­ vatism in the longer cooling time cases because the Swedish fuel was operated at a substantially higher moderator density, which results in a more pronounced difference between the detailed and bounding calcu­ lation actinide compositions Future work in this area should focus on expanding the amount of fuel and variety of fuel designs considered as well as the variety of an­ alyses This work represents an investigation of the conservatism of decay heat calculations for BWR fuel from two sites The conservatism of decay heat should be investigated for a broader range of fuel types and reactors to confirm that these results apply broadly Many other types of analyses such as criticality, dose rate and thermal analyses must be performed to demonstrate the safety of SNF Additional investigations of the conservatism of the operating history assumptions within UNFST&DARDS will be performed for criticality, dose rate and thermal an­ alyses will be performed A companion paper, which covers criticality safety of BWR SNF systems, is forthcoming These types of analyses should also be performed for PWR fuel assemblies as well to determine whether similar conclusions can be drawn Additionally, validations of the predictions of reactor physics codes such as Polaris and criticality codes such as KENO must be performed by comparison to measured data Analysis sequences within UNF–S&TDARDS are currently being developed to address these validation needs as well Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper Acknowledgment The work was sponsored the US Department of Energy, Office of Nuclear Energy, Integrated Waste 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disposal system design is decay heat This section presents an analysis of the impact of the operating histories on the decay heat of. .. their as-loaded configurations The aim of this section is to provide context for the application of the bounding decay heat analysis process and a basis for comparison to the detailed decay heat analysis