NUREG/CR-7252, Validation of Keff Calculations for Extended BWR Burnup Credit

NUREG/CR-7252 Validation of Keff Calculations for Extended BWR Burnup Credit

ML19009A008
Person / Time
Issue date:	12/31/2018
From:	Aissa M, Bowman S, Clarity J, Marshall W Office of Nuclear Regulatory Research, Oak Ridge
To:
Meyd, Donald
References
ORNL/TM-2018/797 NUREG/CR-7252
Download: ML19009A008 (117)

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NUREG/CR-7252 ORNL/TM-2018/797 Validation of keff Calculations for Extended BWR Burnup Credit Office of Nuclear Regulatory Research

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NUREG/CR-7252 ORNL/TM-2018/797 Validation of keff Calculations for Extended BWR Burnup Credit Office of Nuclear Regulatory Research Manuscript Completed: July 2018 Date Published: December 2018 Prepared by:

W. J. Marshall J. B. Clarity S. M. Bowman Oak Ridge National Laboratory Managed by UT-Battelle, LLC Oak Ridge, Tennessee 37831-6170 Mourad Aissa, NRC Project Manager

iii ABSTRACT The US Nuclear Regulatory Commission and consensus standards recommend validation of the numerical methods used in criticality safety analyses. This validation requires the comparison of computational results with measurements of physical systems which are neutronically similar to those used in the safety analysis being performed. To this end, this document examines the methods available to generate sensitivity data to help identify systems similar to spent boiling-water reactor (BWR) fuel in a flooded spent nuclear fuel transportation or storage cask. A large number of critical benchmark experiments are surveyed using sensitivity/uncertainty (S/U) techniques to assess their applicability to BWR burnup credit (BUC) beyond the burnup of peak reactivity. Multiple burnups of BWR assemblies are considered herein, as well as the actinide-only (AO) and actinide-and-major-fission-product (AFP) isotope sets. Sample validations are completed for representative application models to demonstrate that appropriate validation is possible and to indicate the bias and bias uncertainty values expected for related applications.

v TABLE OF CONTENTS ABSTRACT.......................................................................................................................................... iii TABLE OF CONTENTS........................................................................................................................ v LIST OF FIGURES.............................................................................................................................. vii LIST OF TABLES................................................................................................................................. ix EXECUTIVE

SUMMARY

..................................................................................................................... xi ABBREVIATIONS AND ACRONYMS.............................................................................................. xiii 1 INTRODUCTION............................................................................................................................. 1-1 2 CODES, METHODS, MODELS, AND DATA................................................................................ 2-1 2.1 Codes and Methods................................................................................................................ 2-1 2.1.1 TSUNAMI-3D................................................................................................................ 2-1 2.1.2 TSUNAMI-IP.................................................................................................................. 2-1 2.1.3 Validation Methods........................................................................................................ 2-2 2.1.4 Critical Experiment Correlations................................................................................... 2-3 2.2 Models...................................................................................................................................... 2-4 2.3 Data.......................................................................................................................................... 2-6 2.3.1 Nuclear Data................................................................................................................. 2-6 2.3.2 Sensitivity Data.............................................................................................................. 2-6 2.3.3 Covariance Data........................................................................................................... 2-6 3 IMPACT OF NEW COVARIANCE DATA ON PEAK REACTIVITY VALIDATION..................... 3-1 3.1 Potentially Applicable Experiments......................................................................................... 3-1 3.2 Bias and Bias Uncertainty Determination................................................................................ 3-3 3.2.1 Nontrending Analysis.................................................................................................... 3-3 3.2.2 Traditional Trending Analysis........................................................................................ 3-4 3.2.3 ck Trending.................................................................................................................... 3-5 3.3 Reactivity Margins for Unvalidated Isotopes........................................................................... 3-7 3.4 Summary.................................................................................................................................. 3-9 4 SENSITIVITY DATA GENERATION.............................................................................................. 4-1 4.1 MG TSUNAMI-3D Models....................................................................................................... 4-1 4.2 CE TSUNAMI-3D Models........................................................................................................ 4-3 4.3 Comparison of MG and CE Sensitivities................................................................................. 4-5 4.4 Comparison to GBC-32........................................................................................................... 4-8 5 POTENTIALLY APPLICABLE EXPERIMENTS........................................................................... 5-1 5.1 Application 1: 25 GWd/MTU and AO Isotope Set................................................................... 5-1 5.2 Application 2: 25 GWd/MTU and AFP Isotope Set................................................................. 5-2 5.3 Application 3: 50 GWd/MTU and AO Isotope Set................................................................... 5-4 5.4 Application 4: 50 GWd/MTU and AFP Isotope Set................................................................. 5-5 6 BIAS AND BIAS UNCERTAINTY DETERMINATION.................................................................. 6-1 6.1 Application 1: 25 GWd/MTU and AO Isotope Set................................................................... 6-1 6.2 Application 2: 25 GWd/MTU and AFP Isotope Set................................................................. 6-3 6.3 Application 3: 50 GWd/MTU and AO Isotope Set................................................................... 6-4 6.4 Application 4: 50 GWd/MTU and AFP Isotope Set................................................................. 6-6

vi 7 REACTIVITY MARGINS FOR UNVALIDATED ISOTOPES........................................................ 7-1 8

SUMMARY

AND CONCLUSIONS................................................................................................. 8-1 8.1 Assessment Summary............................................................................................................ 8-1 8.2 Conclusions............................................................................................................................. 8-2 9 REFERENCES................................................................................................................................ 9-1 APPENDIX A ASSESSMENT OF INTEGRAL PARAMETER E.................................................... A-1 APPENDIX B LIST OF CRITICAL BENCHMARK EXPERIMENTS CONSIDERED................... B-1 APPENDIX C EXPERIMENTS WITH CK VALUES OF AT LEAST 0.8........................................ C-1 APPENDIX D VALIDATION DATA FOR LCT EXPERIMENTS................................................... D-1

vii LIST OF FIGURES Figure 2-1 Radial View of the GBC-68 Cask Model in KENO in the VAN Lattice.................. 2-4 Figure 2-2 Axial View of the GBC-68 Cask KENO Model...................................................... 2-5 Figure 3-1 ck Values for Critical Experiments Compared to GBC-68 with Vanished Lattice and AFP Isotope Set............................................................................................ 3-2 Figure 3-2 ck Values Greater than 0.8 with Vanished Lattice and AFP Isotope Set.............. 3-3 Figure 3-3 C/E Trend as a Function of Enrichment............................................................... 3-5 Figure 3-4 C/E Trend as a Function of EALF......................................................................... 3-5 Figure 3-5 C/E Trend for the 103 experiment Set as a Function of ck Value......................... 3-6 Figure 3-6 C/E Trend for the 62 experiment Set as a Function of 56-group Covariance ck Value..................................................................................................................3-7 Figure 4-1 1H Total Sensitivity Profiles from MG and CE TSUNAMI-3D................................ 4-6 Figure 4-2 10B (n,) Sensitivity Profiles from MG and CE TSUNAMI-3D............................... 4-6 Figure 4-3 235U Total Sensitivity Profiles from MG and CE TSUNAMI-3D............................. 4-6 Figure 4-4 239Pu Total Sensitivity Profiles from MG and CE TSUNAMI-3D........................... 4-7 Figure 4-5 56Fe Elastic Scattering Sensitivity Profiles from MG and CE TSUNAMI-3D......... 4-8 Figure 5-1 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AO Isotope Set............................................................. 5-2 Figure 5-2 ck Values Greater than 0.8 at 25 GWd/MTU Burnup with the AO Isotope Set..... 5-2 Figure 5-3 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AFP Isotope Set............................................................ 5-3 Figure 5-4 Figure 5-5 ck Values Not Less than 0.8 at 25 GWd/MTU Burnup with the AFP Isotope Set...5-4 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AO Isotope Set.............................................................. 5-5 Figure 5-6 Figure 5-7 ck Values Not Less than 0.8 at 50 GWd/MTU Burnup with the AO Isotope Set.... 5-5 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set............................................................ 5-6 Figure 5-8 Figure 6-1 ck Values Not Less than 0.8 at 50 GWd/MTU Burnup with the AFP Isotope Set..5-7 C/E vs EALF Trend for Experiments Applicable to the 25 GWd/MTU AO Case.. 6-2 Figure 6-2 C/E vs Ck Trend for Experiments Applicable to the 25 GWd/MTU AO Case....... 6-2 Figure 6-3 C/E vs EALF Trend for Experiments Applicable to the 25 GWd/MTU AFP Case..6-3 Figure 6-4 C/E vs Ck Trend for Experiments Applicable to the 25 GWd/MTU AFP Case...... 6-4 Figure 6-5 C/E vs EALF Trend for Experiments Applicable to the 50 GWd/MTU AO Case.. 6-5 Figure 6-6 C/E vs Ck Trend for Experiments Applicable to the 50 GWd/MTU AO Case....... 6-5 Figure 6-7 C/E vs EALF Trend for Experiments Applicable to the 50 GWd/MTU AFP Case..6-6 Figure 6-8 C/E vs Ck Trend for Experiments Applicable to the 50 GWd/MTU AFP Case...... 6-7 Figure A-1 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AO Isotope Set.............................................................. A-2 Figure A-2 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AFP Isotope Set............................................................ A-3 Figure A-3 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AO Isotope Set.............................................................. A-3 Figure A-4 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set............................................................ A-4 Figure A-5 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set............................................................ A-5 Figure A-6 Comparison of Energy Dependent 1H Sensitivities for the 50 GWd/MTU AFP Case and the LCT, HTC, and MTC Experiments......................................... A-10

ix LIST OF TABLES Table 3-1 Bias, Bias Uncertainty, and Calculational Margin from Trending Analyses............ 3-4 Table 3-2 keff Uncertainty Contributions from Major Transuranic Nuclides............................. 3-8 Table 3-3 keff Uncertainty Contribution from 155Gd.................................................................. 3-8 Table 3-4 keff Uncertainty Contribution from Major FPs and MAs........................................... 3-9 Table 4-1 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AO Isotope Set.................................... 4-2 Table 4-2 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AFP Isotope Set.................................. 4-2 Table 4-3 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AO Isotope Set................................... 4-3 Table 4-4 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AFP Isotope Set.................................. 4-3 Table 4-5 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AO Isotope Set................................... 4-4 Table 4-6 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AFP Isotope Set.................................. 4-4 Table 4-7 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AO Isotope Set................................... 4-5 Table 4-8 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AFP Isotope Set.................................. 4-5 Table 4-9 Integral Parameters Ccomparing MG and CE TSUNAMI-3D................................. 4-7 Table 6-1 Bias and Bias Uncertainty Values for all 4 Applications......................................... 6-7 Table 7-1 Uncertainty in keff (%k/k) Due to Nuclear Data Uncertainty, Detailed Application Models..................................................................................................7-2 Table 7-2 Table 7-3 Uncertainty in keff (%k/k) Due to Nuclear Data Uncertainty, Non-BA Application..7-3 Reactivity Margin for Lack of Validation of FPs and MAs for Explicit Criticality Safety Calculations................................................................................................. 7-4 Table 7-4 Reactivity Margin for Lack ofVvalidation of FPs and MAs for Non-BA Criticality Safety Calculations................................................................................................. 7-4 Table 7-5 Reactivity Margin for Lack of Validation of Residual BA 155Gd in Explicit Criticality Criticality Safety Calculations................................................................................. 7-4 Table A-1 Summary Statistics Associated with Difference Between E and ck for the Four Extended BUC Applications Examined in Sections 5-7......................................... A-4 Table A-2 Comparison of E and ck Values for the Experiments Selected for Detailed Analysis.................................................................................................................. A-7 Table A-3 Comparison of Total Sensitivities for Major BUC Nuclear Applications and Selected Experiments............................................................................................ A-7 Table A-4 Comparison of Total Uncertainties for Major BUC Nuclear for Applications and Selected Experiments............................................................................................ A-8 Table B-1 Critical Benchmark Experiments Considered......................................................... B-1 Table C-1 ck Values of at Least 0.8 for Application 1............................................................. C-1 Table C-2 ck Values of at Least 0.8 for Application 2.............................................................. C-3 Table C-3 ck Values of at Least 0.8 for Application 3............................................................. C-4 Table C-4 ck Values of at Least 0.8 for Application 4............................................................. C-6 Table D-1 Critical Experiment Parameters Used for Validation.............................................. D-1

xi EXECUTIVE

SUMMARY

Applicants for certificates of compliance for spent nuclear fuel (SNF) transportation and dry storage systems perform analyses to demonstrate that these systems are adequately subcritical per the requirements of 10 CFR Parts 71 and 72. The credit for reactivity reduction during depletion is commonly referred to as burnup credit (BUC). BUC for boiling-water reactor (BWR)

SNF is not addressed in the current interim staff guidance for pressurized-water reactor (PWR)

BUC, but NUREG/CR-7194 provides a technical basis for peak reactivity BWR BUC methods.

BWR BUC beyond the burnup of peak reactivity has not previously been evaluated. In this document, extended BWR BUC is defined as credit for the reduction in reactivity at burnups greater than the peak reactivity burnup.

Approaches for validation of keff calculations for PWR BUC analyses are provided in NUREG/CR-7109. While NUREG/CR-7194 addresses peak reactivity BUC analysis, including validation, this document presents an analysis for the validation of keff calculations for extended BWR BUC.

Validation is presented for the GBC-68 cask at burnups of 25 and 50 GWd/MTU using the actinide-only (AO) and actinide-and-major-fission-product (AFP) isotope sets. The results presented in this document include (1) the selection of potentially applicable benchmark experiments, (2) sample bias and bias uncertainty results, and (3) estimation of potential reactivity margins for unvalidated minor actinides (MAs) and fission products (FPs). The codes, methods, models, and nuclear data employed in this analysis are presented in Section 2.

Section 3 of this document reviews the impact of changes to covariance data used in the selection of applicable critical benchmark experiments for the validation of peak reactivity BUC analysis.

The primary result from the updated covariance data is an increase in the number of benchmarks that may be applicable for validating the fully flooded, peak reactivity GBC-68 model. The bias and bias uncertainty values that result from this larger set of experiments could lead to a slightly larger total computational margin than that observed in NUREG/CR-7194. The reactivity margins for unvalidated isotopes in these results are significantly lower for actinides, somewhat higher for 155Gd, and unchanged for the remaining FPs. The total margin across all three of these factors is lower than that recommended in NUREG/CR-7194.

New sensitivity data were generated to allow critical experiment selection for three-dimensional (3D) models of the flooded GBC-68 cask containing fuel depleted beyond peak reactivity. The TSUNAMI-3D sequence was used to generate the sensitivity data, which were confirmed to contain accurate sensitivities by comparison to direct perturbation calculations. Section 4 discusses the generation of these sensitivity data files (SDFs). The SDFs were used in TSUNAMI-IP calculations to assess the similarity of critical benchmark experiments for use in validation studies.

Four application cases were defined to examine the number of applicable benchmarks and to perform sample determinations of computational margin. All four cases included fuel stored in the flooded GBC-68 cask. The fuel was depleted to 25 or 50 GWd/MTU, and the AO and AFP isotope sets were analyzed. Section 5 presents a discussion of potentially applicable experiments among 1,643 available critical benchmark experiments. For the two cases with the AO isotope set, 172 experiments were identified as applicable at a burnup of 25 GWd/MTU, and 173 applicable experiments were identified as applicable at a burnup of 50 GWd/MTU. A combination of LEU-COMP-THERM (LCT) and Haut Taux de Combustion (HTC) critical experiments are identified as applicable at both burnups with AO isotope set. For the two cases with the AFP isotope set, 68 HTC cases are identified as applicable at 25 GWd/MTU, and 126 HTC cases were determined to be applicable at 50 GWd/MTU. Only HTC experiments have high enough assessed similarity for

xii validation of models with the AFP isotope set. For both isotope sets, a larger number of HTC cases is applicable to the higher burnup case because the fuel composition used in the HTC experiments is a closer match to the higher burnup fuel.

Bias and bias uncertainties were assessed for each of the application models using both nontrending and trending techniques, as discussed in Section 6. The nontrending biases and bias uncertainties were consistent across the four applications, with the biases ranging from -0.00132 to -0.00236 and the bias uncertainties ranging from 0.00530 to 0.00672. The trending techniques considered trends on the energy of the average lethargy of neutrons causing fission (EALF) and, separately, on ck. The applicable experiments bounded the EALF values of all four of the applications. The results for the trending analysis using EALF showed consistent results with biases ranging between 0.00044 and -0.00206, and bias uncertainties ranging between 0.00646 and 0.00724. The trending analysis using ck produced bias estimates ranging from -0.00047 to -0.00647. The larger variability in the ck trend results from the variation of the slope of the trend line and the amount of extrapolation necessary to a ck of 1.0. The bias uncertainties for the ck trending analysis ranged from 0.00657 to 0.01556. The bias uncertainty results were influenced strongly by the extrapolation distance noted above, and also by the number of applicable experiments.

The potentially applicable critical benchmark experiments do not contain FPs or MAs. As discussed in Section 7, a reactivity margin is needed to address the validation gap. The major actinide isotopes can be validated, so no validation gaps exist for the AO isotope set. A reactivity margin of 1% of the FP and MA worth is likely appropriate for extended BWR BUC analyses that do not credit residual Gd burnable absorber. A margin of 1.5% of the total FP and MA worth is likely appropriate for analyses that include residual 155Gd in burnable absorber rods.

xiii ABBREVIATIONS AND ACRONYMS 2D two dimensional 3D three dimensional AFP actinide and major fission product isotope set AO actinide only isotope set BA burnable absorber BLO Brookhaven, Los Alamos, and Oak Ridge BOL beginning of life BUC burnup credit BWR boiling-water reactor CE continuous-energy C/E calculation over experiment CFR US Code of Federal Regulations CRC commercial reactor critical statepoint model DOM dominant EALF energy of the average lethargy of neutrons causing fission ENDF evaluated nuclear data file FP fission product(s)

GE General Electric Company HTC Haut Taux de Combustion ICSBEP International Criticality Safety Benchmark Evaluation Project ISG Interim Staff Guidance JENDL Japanese evaluated nuclear data library LCE laboratory critical experiments LCT LEU-COMP-THERM critical experiment LEU low-enriched uranium MA minor actinide MCT MIX-COMP-THERM critical experiment MG multigroup MST MIX-SOL-THERM critical experiment MTU metric ton of uranium NEA Nuclear Energy Agency (Organisation for Economic Co-operation and Development)

NRC US Nuclear Regulatory Commission PWR pressurized water reactor SFP spent fuel pool SDF sensitivity data file SNF spent nuclear fuel S/U sensitivity and uncertainty USL upper subcritical limit (in other documents, USL is used as upper safety limit)

VAN vanished lattice WPEC Working Party on International Nuclear Data Evaluation Co-operation

1-1 1 INTRODUCTION Applicants for certificates of compliance for spent nuclear fuel (SNF) transportation and dry storage systems perform analyses to demonstrate that these systems are adequately subcritical per the requirements of Title 10 of the Code of Federal Regulations (10 CFR) Parts 71 and 72 [1].

For pressurized-water reactor (PWR) SNF, these analyses may credit the reduction in assembly reactivity caused by depletion of fissile nuclides and buildup of neutron-absorbing nuclides during power operation. This credit for reactivity reduction during depletion is commonly referred to as burnup credit (BUC). US Nuclear Regulatory Commission (NRC) staff review BUC analyses according to the guidance in the Division of Spent Fuel Storage and Transportation Interim Staff Guidance (ISG) 8, Revision 3 [2], Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transportation and Storage Casks.

BUC for boiling-water reactor (BWR) SNF is not addressed in ISG-8, but NUREG/CR-7194 [3]

provides a technical basis for peak reactivity BWR BUC methods. Peak reactivity occurs when the latticea two-dimensional (2D) slice of the assemblyneutron multiplication factor (kinf) reaches its highest value at some burnup beyond beginning of life (BOL). This is a common feature of BWR assemblies caused by depletion of the burnable absorber (BA) at a more rapid rate than depletion of the fuel. BWR BUC beyond the burnup of peak reactivity has not previously been evaluated. In this document, extended BWR BUC is defined as credit for the reduction in reactivity at burnups greater than the peak reactivity burnup. Studies assessing the impacts of axial coolant density distributions, control blade usage, and axial burnup profiles on extended BWR BUC are documented in NUREG/CR-7224 [4]. Similar studies of reactor operating conditions and assembly-specific operating histories are contained in NUREG/CR-7240 [5]. The impact of each of these phenomena was evaluated to identify limiting conditions and assumptions for use in extended BWR BUC analyses.

Approaches for validation of isotopic compositions and effective neutron multiplication factor (keff) calculations for PWR BUC analyses are provided in NUREG/CR-7108 [6] and NUREG/CR-7109

[7], respectively. Peak reactivity BUC analysis, including isotopic depletion and criticality validation aspects, is discussed in NUREG/CR-7194 [3]. Approaches to validate the isotopic compositions used in extended BWR BUC are addressed in a separate document, NUREG/CR-7251 [8].

Validation of keff calculations for extended BWR BUC are considered in this document. Validation is presented for the GBC-68 cask [9], at burnups of 25 and 50 GWd/MTU using the actinide-only (AO) and actinide-and-major-fission-product (AFP) isotope sets. The results presented in this document include (1) the selection of potentially applicable benchmark experiments, (2) sample bias and bias uncertainty results, and (3) estimation of potential reactivity margins for unvalidated minor actinides (MAs) and fission products (FPs).

Section 2 of this document describes the codes, methods, models and data used in the validation techniques addressed in the remainder of the report. As discussed in Section 2.3, new nuclear covariance data have been included in SCALE 6.2.2 [10], and the impact of the data on the validation of keff calculations at peak reactivity is assessed in Section 3. Section 4 discusses generation of the sensitivity data used here to identify the potentially applicable critical benchmark experiments documented in Section 5. Example determinations of bias and bias uncertainty are provided in Section 6, and reactivity margins for unvalidated nuclides are examined in Section 7.

Finally, Section 8 summarizes the studies included in this document and the conclusions that can be drawn from them.

2-1 2 CODES, METHODS, MODELS, AND DATA This section provides details on the codes, methods, models and data used as part of the validation efforts discussed in the remainder of the report. Codes and their methods are described in Section 2.1, while the computational models used in the validation studies are described in Section 2.2. The nuclear data, sources of critical experiments with sensitivity data, and the covariance data included in SCALE 6.2.2 [10] are discussed in Section 2.3.

2.1 Codes and Methods Critical experiment selection was performed using sensitivity/uncertainty (S/U) techniques, which require sensitivity data for each model and nuclear covariance data. The sensitivity data for the application models are generated using the TSUNAMI-3D sequence in SCALE 6.2.2 [10]; the TSUNAMI-3D code and its methods are described in Section 2.1.1. The sources of sensitivity data for the benchmark experiments are described in Section 2.3.2. The selection of potentially applicable critical experiments is based on the ck index generated with TSUNAMI-IP, which is discussed in Section 2.1.2. Nuclear covariance data used both in the selection of critical experiments (Section 5) and in the estimation of reactivity margins for unvalidated nuclides (Section 7) are discussed in Section 2.3.3. The margins proposed in Section 7 are based on nuclear covariance data propagated to keff uncertainty performed in TSUNAMI-IP. The validation techniques used to determine sample bias and bias uncertainty values presented in Section 3 and Section 6 are summarized in Section 2.1.3.

2.1.1 TSUNAMI-3D The TSUNAMI-3D sequence is used for three-dimensional (3D) cross section sensitivity generation for S/U analysis. The sequence provides automated processing of material input and cross section data, neutron transport, calculation of sensitivity coefficients (i.e., sensitivity of keff to nuclear data variation), and determination of uncertainty in keff due to cross section covariances.

Sensitivities based on the fluxes calculated by KENO are written to a sensitivity data file (SDF) containing the nuclide-, energy-, and reaction-dependent keff sensitivity coefficients. These energy-dependent sensitivities are determined for each nuclide in the model using first-order perturbation theory. SCALE 6.2.2 can generate sensitivity data using either continuous-energy (CE) or multigroup (MG) methods. Both the MG and CE methods are used here to provide a comparison of the calculated sensitivities. The CE and MG sensitivity results for the GBC-68 cask model are compared in Section 4. Further details of the CE and MG sensitivity calculation methodologies are available in Section 6 of the SCALE 6.2.2 manual [10].

2.1.2 TSUNAMI-IP The TSUNAMI-IP sequence provides a range of S/U analysis capabilities in SCALE 6.2.2 [10]. It is used for two primary purposes in these studies: (1) to calculate the integral parameter ck for critical experiment selection and (2) to propagate nuclear data uncertainties to determine an uncertainty in keff for estimation of potential reactivity margins for unvalidated isotopes. Each of these calculations relies on nuclear covariance data; the SCALE 6.2.2 covariance data libraries are discussed in Section 2.3.3. A brief discussion of each TSUNAMI-IP calculation is provided in this section. Additional details are available in Section 6.5.1 of the SCALE 6.2.2 manual.

TSUNAMI-IP is used to evaluate the similarity of critical experiments and application models and to determine uncertainties in cask reactivity due to cross section covariance data. The similarity metric calculated here is ck. ck is the correlation coefficient of the effect of nuclear data uncertainty on keff of the application and experiment and can be determined by dividing the covariance

2-2 between the experiment and application by the product of the uncertainties in the experiment and the application [11], as shown in Eq. (1).

Exp App 2

AppExp kc

=

(1) where: ck is the similarity between an application and an experiment, 2AppExp is the covariance between the application and the experiment, App is the uncertainty in the application keff due to cross section covariances (uncertainties), and Exp is the uncertainty in the experiment keff due to cross section covariances (uncertainties).

In essence, ck is the fraction of the cross section-induced uncertainty in keff that is shared by two systems. A ck value of 1 indicates that the keff values for two compared systems would be affected identically by nuclear data errors, which are the primary contributors to the computational methods bias. A ck value 0.8 is considered to have a high enough degree of similarity to be acceptable for use in validation studies [11], and it is used as the cutoff for the acceptably similar experiments identified in Section 5.

Other parameters are available within TSUNAMI-IP to quantify the similarity between an application and benchmark experiments. While only the integral parameter ck is used for experiment selection in the main body and recommendations of this report, the integral index E is discussed in Appendix A. Integral index E differs from ck in that it does not consider the uncertainties of the nuclear data; it only considers the similarity of the sensitivity data. The E parameter is used in Section 4.3 to compare application SDFs generated from MG and CE TSUNAMI-3D. It is used in that specific context because all sensitivities are given equal weight.

Differences in important isotopes with low uncertainties may not have a large impact on ck, but they should be evident based on the values of the integral index E.

The propagation of nuclear covariances to uncertainties in keff is also performed by TSUNAMI-IP.

The uncertainty contribution from each isotope and reaction is calculated by multiplying the sensitivity of keff by the uncertainty in the isotope/reaction cross section. The complete list of these results by isotope and reaction is generated by specifying the uncert_long keyword in TSUNAMI-IP input. The total isotope contribution to keff uncertainty is calculated by taking the square root of the sum of the squares of the uncertainties associated with relevant nuclear reactions.

2.1.3 Validation Methods The primary purpose of this report is to demonstrate that sufficient applicable critical experiments exist to allow validation of keff calculations in support of extended BWR BUC. A secondary purpose is to generate representative bias and bias uncertainty values for the GBC-68 cask model. Two statistical techniques for generating the bias and uncertainty values have been selected from NUREG/CR-6698 [12] for this purpose. The nontrending and unweighted lower prediction bands are used, with three different trending parameters used in the trending method.

The trending parameters are the average enrichment of the lattice (for peak reactivity only), the energy of the average lethargy of neutrons causing fission (EALF), and ck. No trending analysis on enrichment is performed for the extended BUC cases because the isotopic composition of the burned fuel assembly deviates too much from the fresh case for the results to be meaningful. The trending method used is equivalent to upper subcritical limit (USL)-1 with no administrative

2-3 margin. The desired final results of this analysis are representative values of the bias and bias uncertainty values for extended BWR BUC applications.

2.1.4 Critical Experiment Correlations A series of critical experiments is often performed with a limited number of parameters that are varied systematically to cover a range in some parameter space. Primarily, performing experiment series allows for the determination of system sensitivity to specific parameters such as lattice pitch. An additional benefit to performing experiments in series is that several related experiments can be done at lower cost per experiment and in less time than if each experiment had been performed in isolation.

The use of experiment series in validation creates additional complexities because of the correlations among the individual experiments within the series. The correlation between a pair of experiments is a result of shared experimental components that include fissile, reflector, or absorbing materials, detector systems, and procedures. Many of these shared characteristics should have very little effect on the results of the experiments or the independence of the data measured or derived from the experiments. The use of common materials, however, can create correlations among the experiments that demonstrably reduce the independence of each experiment in a series. This can impact the determination of the computational bias, but it is far more likely to affect the uncertainty in the bias. The uncertainty is increased because several measurements of the same system do not provide as much unique information as the same number of measurements of different systems. Thus, the correlation among experiments in a series acts to reduce the effective number of experiments in a validation set. The smaller number of effective experiments would lead to a larger uncertainty, so neglecting the correlations is nonconservative because it results in a lower bias uncertainty.

The impact of critical experiment correlations may be larger for BUC analyses than for other applications because a smaller number of experiments are applicable for performing the validation. For peak reactivity BWR BUC validation, for instance, most of the applicable experiments are drawn from the LEU-COMP-THERM-008, LEU-COMP-THERM-011, and LEU-COMP-THERM-051 evaluations [3] in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook [13]. These experiments are documented in three different series, but all three were performed at the Babcock and Wilcox Lynchburg Research Center using the same fuel rods and the same fuel rod pitch. The HTC experiments [14] are another set of experiments which may be highly correlated and are used in BUC validation. The fissile material is the same in all 156 cases, and is a specific mix of actinides intended to represent PWR fuel near discharge from the reactor. The experiments were carried out over a range of fuel rod pitches and with different absorbers and reflectors. These variations will reduce the correlations among the experiments, but it is not clear by how much. Experiments using the same pitch are likely to be moderately to highly correlated. The small number of applicable experiments from different series and facilities makes BUC validation particularly vulnerable to the effects of critical experiment correlations.

The challenge facing criticality safety practitioners and regulators is to establish a reliable method of determining the correlations among the critical experiments and ultimately to determine methods to incorporate them into usable validation techniques. Further information on the determination of correlation coefficients is available in Hoefer et al. [15] and in Marshall, Rearden, and Pevey [16]. One proposed validation technique incorporating correlations into trending

2-4 analysis is also available [17]. Further work is needed to develop correlation coefficients and validation techniques that are defensible in a regulatory proceeding, and to assess the impact of these new methods on BUC validation.

2.2 Models The GBC-68 computational benchmark model was developed in NUREG/CR-7157 [9] as a generic BUC cask for modeling BWR SNF. The KENO model of the fuel loaded in the cask explicitly represents each fuel rod in the General Electric Company (GE) 14 fuel assemblies, including the gap and cladding. Part-length rods are truncated at the appropriate elevation so that both the full lattice (referred to as full or dominant and abbreviated as DOM) and the vanished lattice (VAN) are included explicitly in the KENO model. The fuel assembly channel model is simplified in KENO and is represented with constant thickness and squared corners. All fuel assemblies in the GBC-68 cask model are assumed to contain fuel with identical compositions and irradiation histories. A single average fuel composition is used for fuel pins without gadolinium, and seven unique compositions are used for the rings modeling the gadolinium fuel pins in each axial node.

All KENO models contain 25 axial nodes, each 6 inches in length (15.24 cm). Figure 2-1 shows a radial view of the GBC-68 half-cask model depicting the cask body, basket, and fuel assemblies.

Figure 2-2 provides an axial view of the model with each unique axial fuel composition shown in a different color.

Figure 2-1 Radial View of the GBC-68 Cask Model in KENO in the VAN Lattice Stainless steel Water

2-5 Figure 2-2 Axial View of the GBC-68 Cask KENO Model VAN lattice 66 in (167.64 cm)

DOM lattice 84 in (213.36 cm)

2-6 2.3 Data A range of different data types is used in this work. Nuclear data are used for the neutron transport calculations, sensitivity data generated with TSUNAMI-3D for both experiments and the application models are used in conjunction with covariance (uncertainty) data for critical experiment selection and the determination of reactivity margins for unvalidated isotopes. These data sets are described in the following subsections.

2.3.1 Nuclear Data The nuclear data used in the transport calculations consist of reaction cross sections, fission multiplicities (), and fission neutron energy distributions (). All these data are contained in the nuclear data libraries distributed with SCALE [10]. The libraries based on ENDF/B-VII.1 [18] are used here, and most results presented are based on the CE data. Some results are generated using the MG libraries; any MG data will be explicitly identified.

2.3.2 Sensitivity Data S/U methods are used to identify potentially applicable experiments for validating keff calculations in extended BWR BUC analyses. Sensitivity data are therefore needed for the applications and the experiments being considered. The sensitivity data for the applications are generated as a part of this work, as discussed in Section 4.

A set of 1,643 critical experiments with available SDFs was generated for use in NUREG/CR-7194 [3]. The same suite of experiments is considered here. This set includes all experiments considered in NUREG/CR-7109 [7] except for the French fission product experiments, all the experiments in the VALID suite [19], and a number of experiments with sensitivity data generated by the Nuclear Energy Agency (NEA) [20]. The NEA experiments are drawn from the LEU-COMP-THERM (LCT), MIX-COMP-THERM (MCT) and MIX-SOL-THERM (MST) categories. Almost 1,400 LCT experiments and more than 500 MIX experiments are included in the ICSBEP Handbook [13]; a subset of these experiments have SDFs available on the Handbook. The complete suite of experiments consists of over 1,100 low-enriched uranium (LEU) experiments and more than 475 MIX experiments; the entire list of experiments is provided in Appendix B. The SDFs for the experiments are generally based on ENDF/B-VII.0 libraries with 238 energy groups.

The SDFs were generated in SCALE 6 or SCALE 6.1 and are acceptable when screening experiment similarity. The sensitivities do not change dramatically with different cross section libraries, so the similarity assessment between the application and experiments is unaffected. This was demonstrated in sensitivity studies using ENDF/B-V and ENDF/B-VI in NUREG/CR-7109 [7].

The keff values associated with the SDFs generated with different cross section libraries should not be used in validation.

2.3.3 Covariance Data Two different sets of nuclear covariance data are used in aspects of this work. These libraries express the uncertainties in the nuclear data which result primarily from measurement and evaluation. The primary covariance library used is the 56-group library developed for SCALE 6.2

[10]. The 44-group covariance library originally developed for SCALE 6 is used here only for comparison with results for the peak reactivity validation results presented in NUREG/CR-7194

[3]. Brief descriptions of each of these libraries are presented in this section.

2-7 2.3.3.1 56-group covariance library The default covariance library in SCALE 6.2 [10] is the 56-group library based primarily on ENDF/B-VII.1. The complete list of sources of covariance data for the library are provided in Table 10.2.1 of the SCALE 6.2 manual. They originate from one of six sources:

1.

ENDF/B-VII.1 evaluations [18],

2.

updates to erroneous ENDF/B-VII.1 evaluations [10],

3.

ENDF/B-VI evaluations, 4.

low-fidelity evaluations from the Brookhaven, Los Alamos, and Oak Ridge (BLO) collaboration [21],

5.

the NEA Working Party on International Nuclear Data Evaluation Co-operation (WPEC) subgroup 26 [22], and 6.

Japanese evaluated nuclear data library (JENDL)-4.0 [23].

The source of the covariance data for each nuclide is identified in Table 10.2.1 of the SCALE 6.2 manual [10]. Many nuclides have the same covariance data from the previous SCALE 6/SCALE 6.1 44-group covariance library, but the major isotopes have been updated, along with all the fission energy spectrum uncertainties. Testing of the new covariance library is discussed in Marshall et al. [24], where some of the major differences are highlighted. The most relevant changes for validation of SNF include a large reduction in the uncertainty of 239Pu, as well as increases in the uncertainty associated with 235U and. Taken together, these changes will reduce the importance of 239Pu sensitivity and will increase the importance of 235U sensitivity in determining ck [24]. This is discussed further in Section 3, which addresses the impact of the updated covariance data on validation of keff calculations using the peak reactivity method.

2.3.3.2 44-group covariance library The 44-group covariance library distributed with SCALE 6.0 and SCALE 6.1 [25] is also distributed with SCALE 6.2 to allow for comparisons with the new covariance data. The sources for data in the older library include the following:

1.

ENDF/B-VII evaluations, 2.

ENDF/B-VI evaluations, 3.

JENDL-3.3 evaluations [26],

4.

low-fidelity BLO evaluations [21], and 5.

WPEC subgroup 26 evaluations [22].

Energy-dependent uncertainties for are based on the method developed in Broadhead and Wagschal [27]. The source of the covariance data for each isotope is provided in Table 10.2.6 of the SCALE 6.2 manual [10]. As mentioned previously, the 44-group covariance library is used in this work only to provide an assessment of the impact of implementing the new covariance library on the keff validation results presented in NUREG/CR-7194 [3] for peak reactivity analyses.

3-1 3 IMPACT OF NEW COVARIANCE DATA ON PEAK REACTIVITY VALIDATION An assessment of the validation of keff calculations using the peak reactivity methodology is provided in Section 4 of NUREG/CR-7194 [3]. Critical experiment benchmarks were selected for that assessment based on similarity indicated by the integral parameter ck. As mentioned in the previous section, changes to the covariance data included in SCALE 6.2 impact the similarity determinations and therefore the entire validation assessment. The impact of the change in covariance data on the calculated ck values was first reported by Marshall et al. [24], but without further analysis of the impact on the validation itself. This section provides ck results for the AFP isotope set and VAN lattice in the GBC-68 cask, validation based on the experiments selected from these results, and estimated reactivity allowances for unvalidated isotopes. These results are generated with the new 56-group covariance library and compared with the prior results from NUREG/CR-7194 that were generated using the 44-group covariance library to demonstrate the impact of the new covariance library on the validation of peak reactivity BWR BUC.

3.1 Potentially Applicable Experiments The same SDFs used in NUREG/CR-7194 [3] are used here to isolate the changes coming from the differences in covariance data. The application model is a 2D slice of the GBC-68 cask, including the VAN lattice at a burnup of approximately 7.5 GWd/MTU. Assuming each assembly has an initial loading of 6 rods containing 2 wt% Gd2O3, this burnup is very near the reactivity peak for this lattice. The depleted fuel is modeled using the AFP isotope set. All 1,643 experiments are represented with SDFs from a range of sources, as discussed in Section 2.3.2.

The ck values calculated for all 1,643 experiments compared to the GBC-68 peak reactivity model are shown in Figure 3-1. The results with the 44-group covariance library use the same closed, color-coded markers that are used in Figure 4.3 of NUREG/CR-7194. The results with the new 56-group covariance library are black open markers of the same shape. The figure clearly shows that the new covariance library increases ck values for LCT experiments and generally lowers the ck values for mixed uranium/plutonium systems. The MCT and MST experiments are significantly lower, while most of the HTC cases remain largely unchanged. These ck changes are the result of increased uncertainty in 235U and and decreased uncertainty in 239Pu [24]. Larger uncertainties essentially result in higher weights for reactions in determining the ck value. The similarities between the uranium sensitivities in the LCT experiments are therefore emphasized more with the new covariance data, and the similarity in plutonium sensitivities is emphasized less. These changes result in a net increase in the number of experiments which have a ck of 0.8 or more in comparison to the GBC-68 computational benchmark with fuel at peak reactivity.

Of the 1,643 experiments, 111 have a ck value in excess of 0.8 for the GBC-68 cask with the VAN lattice at a burnup of approximately 7.5 GWd/MTU. This is an increase from 67 cases meeting the same criterion with the 44-group covariance data, as reported in NUREG/CR-7194. Forty-two cases have a ck value greater than 0.9; no cases met this higher criterion with the 44-group covariance data. The most similar experiments are still identified as LCT-008, LCT-051, and LCT-011. The most similar experiments all come from LCT-008, followed by LCT-051 and LCT-011.

The top 42 experiments are drawn from these three evaluations and represent all cases with ck values above 0.9.

3-2 Figure 3-1 ck Values for Critical Experiments Compared to GBC-68 with Vanished Lattice and AFP Isotope Set Of the 111 experiments, 8 are not used in the sample validation for the reasons discussed below.

The single case from LCT-003 is excluded because of large uncertainties in the gadolinium concentration in the water used in the experiment. The three cases from LCT-033 are omitted because the fissile material is UF4 instead of UO2. The two LCT-045 cases are excluded because the fissile material is U3O8 instead of UO2. Lastly, two cases from LCT-051 are omitted because there are large uncertainties about the boron content of the absorber plates used in those cases.

The ck values for the remaining 103 cases used in the sample validation are shown in Figure 3-2.

3-3 Figure 3-2 ck Values Greater than 0.8 with Vanished Lattice and AFP Isotope Set 3.2 Bias and Bias Uncertainty Determination The purpose of validation is to quantify the suitability of a computational method for a particular criticality safety application [28]. Guidance for performing validation is provided in Dean and Tayloe [12]. This section presents sample bias and bias uncertainty determinations for peak reactivity keff calculations using a nontrending method and a linear regression trending method with a variety of trending parameters. Fuel enrichment and EALF are the traditional trending parameters used here, and the ck parameter is also used. The methods and trending parameters are the same as those used in NUREG/CR-7194 [3]. They are regenerated here to assess the impact of the new covariance data in SCALE 6.2 [10] on the validation results.

3.2.1 Nontrending Analysis The bias and bias uncertainty are determined using the inverse variance weighted nontrending method discussed in [12], which results in a lower tolerance limit. Considering the 103 experiments identified previously in Section 3.1, the bias is -0.00319, and the bias uncertainty is 0.00553. The bias and bias uncertainty reported in Section 4.5.1 of NUREG/CR-7194 for the set of 62 experiments are -0.00354 and 0.00526, respectively. The resulting bias from the larger set of experiments is slightly smaller, but the magnitude of the difference between the identified experiment sets is negligible. The uncertainty in the bias is slightly larger with the larger data set, which is contrary to initial expectations. A larger data set reduces the one-sided multiplier used to create a 95/95 tolerance limit. The multiplier is reduced from 2.022 with 62 experiments to 1.927 with 103 experiments, so the increased number of experiments has only a small impact on the one-sided multiplier. In this case, the larger set of experiments has a higher variability than the smaller set, and the resulting confidence interval is therefore wider. As with the bias, however, the magnitude of the change is small and indicates no significant differences between the validation

3-4 analyses. The sum of bias and bias uncertainty, or the calculational margin [28], for the 103 experiment suite is -0.00872. This is essentially equal to the calculational margin of -0.00879 reported in NUREG/CR-7194.

The USL resulting from this sample validation would subtract the calculational margin, administrative margin, and margins for unvalidated isotopes from 1. The administrative margin is typically 0.05 for dry storage and transportation systems [29]. An additional reactivity margin for unvalidated isotopes is needed because none of the identified applicable experiments contain any of the actinides present in SNF other than uranium or any FPs. These reactivity margins are discussed further in Section 3.3. There do not appear to be any significant impacts to the calculational margin resulting from the use of the new covariance library in selecting applicable benchmark experiments for peak reactivity keff validation using the nontrending approach.

3.2.2 Traditional Trending Analysis The trending analysis of the 103 experiments identified in Section 3.1 is presented here for comparison with the validation results presented in Section 4.5.2 of NUREG/CR-7194. As before, enrichment and EALF are used as the trending parameters. The bias, bias uncertainty, and calculational margin values for both trends and both experiment sets are shown below in Table 3-1. The enrichment trend is shown in Figure 3-3, and the EALF trend is shown in Figure 3-4. The critical experiment results are presented as a ratio of calculated keff result divided by expected benchmark keff, referred to as a C/E ratio or C/E value.

Table 3-1 Bias, Bias Uncertainty, and Calculational Margin from Trending Analyses Parameter Application value Experiment set Bias Bias uncertainty Calculational margin Enrichment 3.51 wt% 235U 62

-0.00136 0.00604

-0.00740 103

-0.00069 0.00660

-0.00729 EALF 0.2217 eV 62

-0.00396 0.00577

-0.00973 103

-0.00314 0.00765

-0.01080 The enrichment trend results are similar between the two experiment sets. The 103 experiment set has a smaller bias but a larger uncertainty, yielding an equivalent calculational margin. The higher uncertainty is also observed in the nontrending analysis discussed in the previous section.

The bias is somewhat lower for the 103 experiment set, but it is not reduced enough to indicate a significant difference between the experiment sets.

The bias resulting from the EALF trend is also slightly smaller for the 103 experiment set than it is for the 62 experiment set. The magnitude of the difference is larger for the EALF trend, but it is still not a significant difference. The bias uncertainty is larger for the EALF trend, as it is for the enrichment trend and the nontrending method. The increase in the bias uncertainty is larger than the reduction in the bias, so the resulting calculational margin is larger. The calculational margin is significantly larger for the EALF trend than for the enrichment trend in both experiment sets. There do not appear to be any significant impacts to the calculational margin resulting from the use of the new covariance library in selecting applicable benchmark experiments for peak reactivity keff validation via traditional trending techniques.

3-5 Figure 3-3 C/E Trend as a Function of Enrichment Figure 3-4 C/E Trend as a Function of EALF 3.2.3 ck Trending The use of ck as a trending parameter is recommended as part of TSUNAMI validation [11], and ck was used as a trending parameter in NUREG/CR-7194 [3]. The ck trend using the 103 experiment set and the ck values from the 56-group covariance library are shown in Figure 3-5. The changes in the ck values induce a significant shift in the trend compared to that shown in Figure 4.11 of NUREG/CR-7194. The bias and bias uncertainty are determined by extrapolation to a ck value of 1 because this value represents an exact match to the application system. For the 103 experiment

3-6 set with the new ck values, the bias is -0.00587, and the bias uncertainty is 0.00654. Therefore, the calculational margin is -0.01241, which is significantly larger than the margin determined in the previous section for enrichment and EALF trends. The calculational margin is also significantly larger than that from the ck trend of the 62 experiment set.

Figure 3-5 C/E Trend for the 103 experiment Set as a Function of ck Value The bias and bias uncertainty are examined for the 62 experiment set using the ck values from the 56-group library. This isolates the difference in the ck values from the difference in the experiments included in the validation set. The trend is shown in Figure 3-6. The resulting bias is -0.00355, the bias uncertainty is 0.00580, and the calculational margin is -0.00935. These values are similar to the values presented in NUREG/CR-7194. Therefore, it can be concluded that changing the experiments included in the validation is responsible for a larger share of the difference in bias and bias uncertainty than the change in the ck values. Note that the difference is driven by higher C/E values in experiments with lower ck values. These less similar experiments have higher C/E values and cause the trend with a negative slope shown in Figure 3-5 as compared to the flat extrapolation shown in Figure 3-6.

3-7 Figure 3-6 C/E Trend for the 62 experiment Set as a Function of 56-group Covariance ck Value 3.3 Reactivity Margins for Unvalidated Isotopes Validation gaps and weaknesses must be addressed [28], and the same gaps exist in the sample validations presented here as those present in NUREG/CR-7194 [3]. Namely, none of the applicable experiments identified in Section 3.1 contain actinides other than uranium. Also, none of the experiments contain gadolinium or any other FPs or MAs. The S/U-based approach to estimating reactivity margins for the unvalidated isotopes is used here exactly as it was in NUREG/CR-7194, but the updated 56-group covariance data released with SCALE 6.2 is used instead of the older 44-group data. All four application models used in NUREG/CR-7194 are analyzed again here to investigate the impact of the covariance data change on the potentially bounding factors that were previously recommended. These models include three GBC-68 loadings and a BWR spent fuel pool (SFP) rack model.

The uncertainty in keff due to uncertainty in plutonium isotopes and 241Am is shown for all four models in Table 3-2. The uncertainty drops significantly for 238Pu, 239Pu, and 240Pu relative to the 44-group covariance library. The uncertainty contribution increases for 241Pu, 242Pu, and 241Am.

The uncertainty contribution from 239Pu dominates the other contributions so that essentially all of the uncertainty comes from the single isotope. The total uncertainty is therefore reduced by a factor of ~2 with the new covariance data. Therefore, the 2 penalty factor can likely be reduced from approximately 0.3% k to 0.175% k.

The change in the Pu covariance data was particularly large in SCALE 6.2 and future variations are expected to be smaller [24]. It is conservative, however, to maintain the higher penalty factor.

The impact of other covariance data releases, like ENDF/B-VIII [30], should be evaluated to ensure that a conservative estimate of the penalty factor is applied.

3-8 Table 3-2 keff Uncertainty Contributions from Major Transuranic Nuclides Nuclide 1 sigma uncertainty (% keff)

GBC-68 NUREG/CR-7109 SFP AFP VAN AO VAN AFP FULL AFP 44 grp 56 grp 44 grp 56 grp 44 grp 56 grp 44 grp 56 grp 238Pu 6.55E-5 2.60E-4 6.27E-5 2.39E-4 8.76E-5 2.96E-4 1.24E-4 3.65E-4 239Pu 1.38E-1 7.20E-2 1.33E-1 7.03E-2 1.53E-1 7.94E-2 1.54E-1 8.03E-2 240Pu 7.83E-3 3.03E-3 7.34E-3 2.84E-3 9.10E-3 3.49E-3 1.13E-2 4.44E-3 241Pu 1.67E-3 2.49E-3 1.64E-3 2.48E-3 1.99E-3 3.18E-3 3.28E-3 6.06E-3 242Pu 1.77E-4 1.97E-4 1.65E-4 1.88E-4 2.58E-4 2.98E-4 4.96E-4 5.73E-4 241Am 8.88E-4 1.92E-3 8.27E-4 1.78E-3 1.17E-3 2.38E-3 1.07E-4 2.05E-4 Total 0.138 0.072 0.134 0.070 0.153 0.080 0.155 0.081 The uncertainty contribution of residual Gd is shown for the three application models containing Gd in Table 3-3. As noted in NUREG/CR-7194, only 155Gd is considered because only traces of the naturally occurring 157Gd remain at peak reactivity. The larger neutron absorption cross section of 157Gd causes it to burn out much more quickly than 155Gd, and there is no appreciable FP generation of 157Gd. The uncertainty contribution from 155Gd nearly doubles with the new covariance library. A conservative 2 penalty factor of 0.09% k is recommended based on the new data. As with the Pu factor, evaluation of future covariance data libraries is recommended to ensure conservative factors are used.

Table 3-3 keff Uncertainty Contribution from 155Gd Model Uncertainty (% k) 44 group 56 group GBC-68 VAN 0.015 0.034 GBC-68 FULL 0.019 0.038 NUREG/CR-7109 SFP 0.024 0.044 The uncertainty contribution from the MAs and FPs is shown in Table 3-4 for both the 56-and 44-group covariance libraries for the three application systems with MAs and FPs modeled in the fuel composition. The MAs considered are 236U, 237Np, and 243Am. The top 15 FPs typically used in BUC [7] are included, and they are 95Mo, 99Tc, 101Ru, 103Rh, 109Ag, 133Cs, 147Sm, 149Sm, 150Sm, 151Sm, 152Sm, 143Nd, 145Nd, 151Eu, and 153Eu. 155Gd is also typically included as a FP, but here it is treated separately because it is inseparable in the fuel composition from residual burnable absorber Gd. The uncertainty contributions from the MAs and major FPs are small because of the relatively low concentrations at the low burnup associated with peak reactivity. Many of the nuclides in this set have the same low-fidelity covariance evaluations in both libraries and therefore have the same uncertainty contribution from both libraries. The major contributors to uncertainty are 149Sm, which is unchanged, and 143Nd, which has a slightly higher uncertainty contribution with the new library. Overall, the same reactivity margin of 0.06% k recommended in NUREG/CR-7194 appears appropriate for the new covariance data library. It is unlikely that new covariance evaluations will impact the overall uncertainty from these isotopes significantly, especially considering their low sensitivities at low burnups.

3-9 Table 3-4 keff Uncertainty Contribution from Major FPs and MAs Nuclide 1 sigma uncertainty (% k)

GBC-68 NUREG/CR-7109 SFP AFP VAN AFP FULL AFP 44-group 56-group 44-group 56-group 44-group 56-group 95Mo 1.31E-03 1.26E-03 1.62E-03 1.56E-03 1.70E-03 1.63E-03 99Tc 1.96E-03 2.75E-03 2.14E-03 3.07E-03 2.99E-03 4.22E-03 101Ru 1.65E-03 1.66E-03 2.05E-03 2.07E-03 3.23E-03 3.22E-03 103Rh 5.38E-03 5.50E-03 6.75E-03 6.91E-03 8.32E-03 8.48E-03 109Ag 1.95E-04 1.99E-04 2.65E-04 2.71E-04 3.98E-04 3.86E-04 133Cs 4.33E-03 4.38E-03 5.25E-03 5.31E-03 7.74E-03 7.70E-03 147Sm 1.60E-03 1.60E-03 1.90E-03 1.90E-03 4.77E-04 4.75E-04 149Sm 1.09E-02 1.09E-02 1.13E-02 1.13E-02 1.01E-02 9.98E-03 150Sm 1.02E-03 1.02E-03 1.14E-03 1.15E-03 1.65E-03 1.64E-03 151Sm 6.02E-03 6.05E-03 5.97E-03 6.01E-03 6.06E-03 6.08E-03 152Sm 1.62E-03 1.63E-03 1.95E-03 1.96E-03 2.96E-03 2.96E-03 143Nd 9.94E-03 1.03E-02 1.04E-02 1.08E-02 1.37E-02 1.44E-02 145Nd 4.09E-03 4.48E-03 5.10E-03 5.48E-03 7.89E-03 8.34E-03 151Eu 1.13E-04 1.13E-04 1.23E-04 1.23E-04 6.71E-06 6.66E-06 153Eu 7.86E-04 9.40E-04 1.00E-03 1.13E-03 1.65E-03 1.80E-03 236U 8.05E-03 6.72E-03 9.79E-03 8.30E-03 1.33E-02 1.03E-02 237Np 1.00E-03 1.47E-03 1.26E-03 1.88E-03 1.46E-03 2.14E-03 243Am 1.92E-06 2.46E-06 3.58E-06 4.62E-06 7.63E-06 9.77E-06 Total 0.020 0.020 0.022 0.022 0.027 0.026 The reactivity margin for major actinides are significantly lower with the new covariance library than the same margin resulting from the old library. The 2 factor drops from 0.3% k [3] to 0.175% k. The factor for 155Gd, however, nearly doubles from 0.05% k to 0.09% k. The factor for MAs and major FPs is unaffected and remains at 0.06% k. The sum of the three factors for the new covariance library is 0.325% k, which is lower than the recommended value from NUREG/CR-7194 of 0.41% k. Both factors are fairly small, especially in comparison to the bias uncertainty and administrative margins associated with criticality safety validation.

3.4 Summary This section has presented a brief overview of the impact of the new 56-group covariance library released with SCALE 6.2 [10]. The validation assessment presented in NUREG/CR-7194 [3] for peak reactivity analyses was performed again with the new covariance library, and the results are presented here. The assessment focuses on identification of and selection of potentially applicable experiments, sample determinations of bias and bias uncertainty, and estimation of reactivity margins for unvalidated isotopes.

The new covariance library tends to increase the importance of uranium while decreasing the importance of plutonium in assessing similarity of critical experiments with SNF applications [24].

For low burnup, peak reactivity BWR fuel, this generally results in LCT experiments having higher ck values for GBC-68 applications. Therefore, more experiments may be applicable for validation with the new covariance library: 103 experiments compared to 62 for the VAN lattice model with the AFP isotope set. These results are discussed in Section 3.1.

3-10 Sample bias and bias uncertainty values for the 103 experiment set were generated and are discussed in Section 3.2. Various nontrending and trending approaches were used, and the results are comparable with the values generated in NUREG/CR-7194. The resulting bias and bias uncertainty are significantly different for the ck trend, although this appears to be a result of the change in experiment set and not the variation in ck values.

Reactivity margins for unvalidated isotopes are discussed in Section 3.3. These factors are needed because the experiments identified as being potentially applicable do not contain plutonium, americium, or FPs. The S/U methods use the uncertainty induced in keff by nuclear data uncertainty to provide estimates of the magnitude of the error that could be present and undetected because of the lack of benchmark experiments. The sum of the independent factors for major actinides, 155Gd, MAs, and FPs is lower with the new covariance library than with the old library. This is primarily a result of large reductions in the uncertainty associated with 239Pu. The uncertainty in 155Gd is larger, but the smaller sensitivity to 155Gd reduces the overall impact of this change. Similar assessments of the impact of new covariance data should be performed as new data are released.

4-1 4 SENSITIVITY DATA GENERATION The validation of extended BWR BUC keff calculations relies on S/U methods, which allow rigorous assessment of critical experiment applicability and quantification of any necessary allowances for isotopes absent from the validation suite. The use of these methods requires sensitivity data for the application and for the critical experiment models which might be used in the validation.

Covariance data are also needed for similarity assessments and uncertainty analysis of unvalidated isotopes. The 56-group covariance data from SCALE 6.2 [10] are used in all analyses of extended BWR BUC presented in this report. A brief description of this data library is presented in Section 2.3.3, and a more complete description is provided in the SCALE 6.2 manual [10].

This section focuses on the generation of the sensitivity data used in the validation analyses. As discussed in Section 2.1.1, sensitivity data are generated using the TSUNAMI-3D sequence within SCALE. Prior to SCALE 6.2, TSUNAMI-3D employed only MG methods to generate sensitivity data. New CE methods are available beginning with SCALE 6.2, and these methods are used in this report. Few published reports provide comparisons of the CE and MG methods in TSUNAMI-3D [31, 32], so SDFs are generated using both techniques. A comparison of the two methods is summarized here, providing confidence that the SDFs generated by CE TSUNAMI can be used in this work.

The validation of keff calculations for extended BWR BUC analysis is evaluated in this report at two different burnups, 25 and 50 GWd/MTU, and with the AO and AFP isotope sets. Unique SDFs are required for each of the four combinations to allow comparisons to benchmark model SDFs. The comparisons are performed using TSUNAMI-IP to identify potentially applicable benchmark experiments. The selection of potentially applicable experiments is documented in Section 5.

4.1 MG TSUNAMI-3D Models The MG TSUNAMI-3D models are half-cask models with a reflective boundary condition applied on the -Y face. Explicit modeling of only half the cask allows a finer mesh to be used for collection of flux moments within memory constraints. The mesh used has 62 mesh intervals in the X direction, 31 in the Y direction, and 33 in the Z direction. The radial mesh is essentially a uniform square mesh that is 3 cm on each side. The axial mesh is varied with finer mesh near the ends of the fuel assemblies and larger mesh along the central axial portion of the assemblies. The water in the vanished rod locations within the VAN lattice is divided into 6-inch axial segments for better resolution of the flux moments within this lattice.

SDFs were generated at both 25 and 50 GWd/MTU with both the AO and AFP isotope sets. The forward Monte Carlo calculations used 11,000 particles per generation and ran until an uncertainty of 0.025% k was achieved. The first 25 generations were discarded, and a total of 700-1,600 generations were required to achieve the desired statistical uncertainty. The adjoint Monte Carlo calculations used 33,000 particles per generation and were run until a statistical uncertainty of 0.125% k was achieved. This required 2,600-3,900 adjoint generations per calculation.

Direct perturbation calculations were performed using MG KENO to confirm that the sensitivity data generated by TSUNAMI-3D was accurate. Separate calculations were performed for each burnup and isotope set. Direct perturbations were performed for the water mixture in the axial zone with the highest sensitivity, the water mixture in the vanished lattice positions, fuel isotopes in the axial zone with the highest sensitivity, and 10B in the absorber panels. These mixtures and isotopes were chosen because of their high sensitivities and corresponding importance to the overall reactivity of the model. Summaries of the comparisons of TSUNAMI-3D sensitivities and

4-2 direct perturbation sensitivities are provided in Table 4-1 for 25 GWd/MTU and the AO isotope set, Table 4-2 for 25 GWd/MTU and the AFP isotope set, Table 4-3 for 50 GWd/MTU and the AO isotope set, and Table 4-4 for 50 GWd/MTU and the AFP isotope set. Agreement between TSUNAMI and direct perturbations is generally good. The relative difference between the two estimates of the moderator sensitivity in the fuel rod unit cell is higher than the desired targets of 5% and 2 standard deviations [33].The absolute differences are small enough, less than 0.01

[33], that the discrepancies are acceptable and the SDF can be used for analysis.

Table 4-1 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AO Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff.

(%)

Rel. Diff. ()

Abs. Diff.

H2O, fuel rod cell 2.95E-02 8.26E-04 2.74E-02 4.45E-04 7.48 2.19 0.0021

H2O, VAN cell 5.77E-02 1.93E-03 5.83E-02 8.77E-04

-1.03 0.28

-0.0006 10B

-5.11E-02 6.06E-05

-5.03E-02 8.06E-04 1.78 1.10

-0.0009 235U 3.88E-02 1.31E-04 3.80E-02 5.78E-04 2.23 1.43 0.0008 238U

-1.65E-02 1.00E-04

-1.62E-02 2.49E-04 1.61 0.97

-0.0003 239Pu 1.27E-02 4.94E-05 1.26E-02 1.95E-04 0.97 0.61 0.0001 Table 4-2 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AFP Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff.

(%)

Rel. Diff. ()

Abs. Diff.

H2O, fuel rod cell 2.12E-02 1.14E-03 2.01E-02 3.61E-04 5.76 0.96 0.0012

H2O, VAN cell 5.52E-02 2.52E-03 5.34E-02 9.42E-04 3.43 0.68 0.0018 10B

-5.11E-02 8.55E-05

-5.03E-02 8.35E-04 1.59 0.95

-0.0008 235U 2.96E-02 1.16E-04 3.02E-02 4.94E-04

-2.00 1.19

-0.0006 238U

-1.14E-02 1.35E-04

-1.15E-02 1.95E-04

-0.86 0.42 0.0001 239Pu 1.53E-02 7.18E-05 1.48E-02 5.26E-04 3.57 0.99 0.0005

4-3 Table 4-3 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AO Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff.

(%)

Rel. Diff. ()

Abs. Diff.

H2O, fuel rod cell 4.51E-02 1.32E-03 4.28E-02 6.08E-04 5.30 1.56 0.0023

H2O, VAN cell 6.23E-02 2.09E-03 6.13E-02 7.96E-04 1.60 0.44 0.0010 10B

-5.07E-02 7.16E-05

-5.08E-02 6.86E-04

-0.16 0.12 0.0001 235U 5.23E-02 1.48E-04 5.02E-02 6.68E-04 4.19 3.07 0.0021 238U

-2.28E-02 1.42E-04

-2.27E-02 3.03E-04 0.36 0.25

-0.0001 239Pu 2.50E-02 8.34E-05 2.48E-02 3.16E-04 0.69 0.52 0.0002 Table 4-4 Summary of Comparisons of MG TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AFP Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff.

(%)

Rel. Diff. ()

Abs. Diff.

H2O, fuel rod cell 4.65E-02 1.38E-03 4.42E-02 8.61E-04 5.14 1.40 0.0023

H2O, VAN cell 6.11E-02 2.36E-03 5.92E-02 1.12E-03 3.12 0.71 0.0018 10B

-5.07E-02 7.82E-05

-4.93E-02 9.30E-04 2.87 1.51

-0.0014 235U 5.61E-02 1.52E-04 5.46E-02 1.01E-03 2.77 1.48 0.0015 238U

-1.95E-02 1.44E-04

-1.92E-02 3.55E-04 1.55 0.78

-0.0003 239Pu 3.34E-02 9.08E-05 3.40E-02 6.14E-04

-1.68 0.92

-0.0006 4.2 CE TSUNAMI-3D Models The CE TSUNAMI-3D models are half-cask models, with a reflective boundary condition applied on the -Y face. Both the MG and CE TSUNAMI-3D models are based on the same KENO models.

The CLUTCH method [31] is used to generate sensitivity data in CE TSUNAMI. This method uses an F*(r) function as the importance function in calculating sensitivities, with a recommended cubic mesh of 1-2 cm on a side [31]. The mesh implemented in the CE TSUNAMI models used 140 mesh intervals in the X direction, 80 in the Y direction, and 25 in the Z direction. The radial mesh is rectangular with 1.35 cm in the X direction and 1.19 cm in the Y direction. The axial mesh is 31.5 cm over the bottom portion of the cask model and 6 cm over the top 90 cm of the model. The finer axial mesh is used in the upper portion of the cask model because the majority of the fissions occur in this region.

SDFs were generated at both 25 and 50 GWd/MTU with both the AO and AFP isotope sets. The CE TSUNAMI methods only require a single forward calculation with no separate adjoint calculation. The calculations used 30,000 particles per generation. The first 1,000 generations, which were skipped for the keff calculation, are used to tally the F*(r) function.

4-4 The Monte Carlo uncertainty in the calculated keff was approximately 0.00005 k for all 4 simulations. Three of the calculations completed 11,000 total generations; 10,000 of these generations were active. The calculation at a burnup of 50 GWd/MTU with the AO isotope set reached a keff uncertainty of less than 0.00005 k and terminated after 10,341 total, or 9,341 active, generations.

Direct perturbation calculations were performed using CE KENO to confirm that the sensitivity data generated by TSUNAMI-3D was accurate. Direct perturbations are needed for confirmation because there is no guidance on the required uncertainty distribution of the F*(r) function. The available evidence [32] indicates that there is no generic distribution of uncertainties that guarantees accurate sensitivity calculations. As for the MG TSUNAMI-3D calculations, separate calculations were performed for each burnup and isotope set. Direct perturbations were performed for all water in the fuel rod unit cell and all the 235U, 238U, 239Pu, and 240Pu in the SNF. Again, these mixtures and isotopes were chosen because of their high sensitivities and corresponding importance to the overall reactivity of the model. Summaries of the comparisons of TSUNAMI-3D sensitivities and direct perturbation sensitivities are provided in Table 4-5 for 25 GWd/MTU and the AO isotope set, Table 4-6 for 25 GWd/MTU and the AFP isotope set, Table 4-7 for 50 GWd/

MTU and the AO isotope set, and Table 4-8 for 50 GWd/MTU and the AFP isotope set.

Agreement between TSUNAMI and direct perturbations is generally good. The relative difference between the two estimates of the 238U and 240Pu sensitivities is larger than desired in the AO cases, with relative differences over 5% and 2 standard deviations [33]. As with the MG discrepancies, the absolute differences are acceptable because they are less than 0.01 [33].

Table 4-5 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AO Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff. (%)

Rel. Diff.

()

Abs. Diff.

H2O, fuel rod cell 1.94E-01 2.54E-03 1.99E-01 2.57E-03

-2.76 1.52

-0.0055 235U 1.88E-01 5.98E-05 1.87E-01 2.62E-03 0.67 0.48 0.0012 238U

-8.18E-02 1.80E-04

-7.77E-02 1.16E-03 5.38 3.56

-0.0042 239Pu 6.43E-02 5.07E-05 6.25E-02 9.07E-04 2.80 1.93 0.0018 240Pu

-1.98E-02 8.73E-06

-1.88E-02 2.78E-04 5.51 3.71

-0.0010 Table 4-6 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 25 GWd/MTU Burnup and AFP Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff. (%)

Rel. Diff.

()

Abs. Diff.

H2O, fuel rod cell 1.93E-01 2.57E-03 1.96E-01 2.81E-03

-1.54 0.79

-0.0030 235U 2.08E-01 6.15E-05 2.10E-01 3.23E-03

-1.30 0.85

-0.0027 238U

-7.58E-02 1.86E-04

-7.43E-02 1.18E-03 2.01 1.25

-0.0015 239Pu 9.94E-02 1.17E-04 9.73E-02 1.53E-03 2.18 1.38 0.0021 240Pu

-2.54E-02 1.04E-05

-2.55E-02 3.91E-04

-0.50 0.32 0.0001

4-5 Table 4-7 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AO Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff. (%)

Rel. Diff.

()

Abs. Diff.

H2O, fuel rod cell 2.15E-01 2.82E-03 2.23E-01 3.19E-03

-3.42 1.79

-0.0076 235U 1.79E-01 6.50E-05 1.81E-01 2.68E-03

-0.68 0.46

-0.0012 238U

-7.95E-02 1.92E-04 8.69E-02 1.39E-03 2.86 1.80

-0.0022 239Pu 9.01E-02 5.85E-05

-7.72E-02 1.21E-03 3.71 2.32 0.0032 240Pu

-2.76E-02 1.09E-05

-2.63E-02 4.16E-04 4.74 3.00

-0.0012 Table 4-8 Summary of Comparisons of CE TSUNAMI-3D and Direct Perturbation Sensitivities for 50 GWd/MTU Burnup and AFP Isotope Set Material TSUNAMI-3D Direct perturbation Comparison Sensitivity Unc.

Sensitivity Unc.

Rel. Diff. (%)

Rel. Diff.

()

Abs. Diff.

H2O, fuel rod cell 2.23E-01 2.76E-03 2.24E-01 3.64E-03

-0.65 0.32

-0.0015 235U 2.05E-01 6.64E-05 2.10E-01 3.41E-03

-2.07 1.27

-0.0043 238U

-6.84E-02 1.92E-04 1.16E-01 1.98E-03 1.84 1.05

-0.0012 239Pu 1.17E-01 6.09E-05

-6.71E-02 1.16E-03 1.40 0.81 0.0016 240Pu

-2.89E-02 2.01E-05

-2.81E-02 4.70E-04 2.71 1.62

-0.0008 4.3 Comparison of MG and CE Sensitivities Two integral parameters were used to compare the sensitivity data generated by the MG and CE TSUNAMI-3D calculations: ck and E. The integral parameter ck is used as it is the most common parameter for comparing systems. As discussed in Section 2.1.2, E is used as an additional parameter because all sensitivities are given equal weight in determining this parameter. Direct comparisons of high sensitivity isotopes and reactions are also made. The resulting total sensitivity profile for 1H in the fuel rod unit cell with the highest sensitivity at 25 GWd/MTU burnup and the AO isotope set is provided in Figure 4-1 from both MG and CE TSUNAMI-3D. The 10B (n,) sensitivity profiles are provided in Figure 4-2 from both TSUNAMI-3D calculations for the 25 GWd/MTU burnup and the AFP isotope set. The comparisons for the total sensitivity of 235U from the highest sensitivity axial zone are provided in Figure 4-3 for the AO isotope set at 50 GWd/MTU burnup and in Figure 4-4 for 239Pu for the AFP isotope set at the same burnup. All of these comparisons show excellent agreement.

4-6 Figure 4-1 1H Total Sensitivity Profiles from MG and CE TSUNAMI-3D Figure 4-2 10B (n,) Sensitivity Profiles from MG and CE TSUNAMI-3D Figure 4-3 235U Total Sensitivity Profiles from MG and CE TSUNAMI-3D

4-7 Figure 4-4 239Pu Total Sensitivity Profiles from MG and CE TSUNAMI-3D The results of the ck and E calculations are provided in Table 4-9. All 4 ck values are in excess of 0.98, and all 4 E values are in excess of 0.999. These results also indicate excellent agreement between the two methods for the same application systems. The higher values for E likely indicate that the differences between the SDFs occur in isotopes and reactions with relatively large uncertainties. The larger uncertainty reactions receive a higher weight in the calculation of ck, but these reactions are also generally of low sensitivity.

Table 4-9 Integral Parameters Comparing MG and CE TSUNAMI-3D Isotope set 25 GWd/MTU 50 GWd/MTU ck E

ck E

AO 0.9831 0.9994 0.9831 0.9994 AFP 0.9828 0.9996 0.9833 0.9995 TSUNAMI-IP calculates an individual ck for each isotope and reaction. This quantity is calculated in the same way as the integral ck, shown in Eq. (1) in Section 2.1.2, except it is not integrated over all isotopes and all reactions. An examination of individual ck values for the comparison of MG and CE sensitivity data at 50 GWd/MTU burnup and the AFP isotope set revealed only one reaction from the top 50 contributors to overall ck with an individual ck less than 0.95. This reaction is elastic scatter in 56Fe in the stainless steel basket. The two sensitivity profiles in Figure 4-5 show a much larger sensitivity for the CE calculation than the MG calculation. Direct perturbation calculations were performed for the total sensitivity of 56Fe in the basket; these calculations confirmed that the CE TSUNAMI-3D calculation was more accurate than the MG calculation. The cause of the poor sensitivity prediction from the MG TSUNAMI calculation was not investigated extensively. It is most likely related to the difficulty in collecting accurate flux moments for the thin basket regions with the mesh size used in the model. A finer mesh spacing with planes deliberately located in the stainless steel basket regions would likely improve the MG sensitivity prediction.

4-8 Figure 4-5 56Fe Elastic Scattering Sensitivity Profiles from MG and CE TSUNAMI-3D The comparisons of sensitivity data generated from MG and CE TSUNAMI-3D show excellent agreement for the GBC-68 application cases used in this work at both burnups considered with both isotope sets. One reaction/isotope combination with a discrepancy was identified, and the CE method was shown to be more accurate. The SDFs calculated using CE TSUNAMI-3D will be used for experiment selection (see Section 5) and reactivity margin assessments (see Section 7) because they have been shown to be more accurate than the SDFs generated by MG TSUNAMI-3D. However, the MG sensitivities are highly similar and are also acceptable for use in these applications.

4.4 Comparison to GBC-32 The SDFs for the GBC-68 cask containing fuel depleted to a burnup of 50 GWd/MTU were compared to the GBC-32 cask containing Westinghouse 17 x 17 optimized fuel assemblies depleted to the same burnup. The GBC-32 SDFs were used in NUREG/CR-7109 [7]. Both the AO and AFP isotope sets were considered. The purpose of this comparison is to determine if there are significant differences between the generic cask systems or the fuel depleted in different reactor types that would impact validation of SNF systems. The two systems have a high degree of similarity. The ck value for the two casks with the AO isotope set is 0.94, and 0.97 for the AFP isotope set. This result indicates that, at least at typical discharge burnups, the BWR and PWR systems are similar. Thus, the same experiments that are useful for PWR BUC validation [7]

should also apply to extended BWR BUC validation. Results also indicate that the challenges regarding the lack of applicable validation experiments with FPs will apply to BWR BUC validation as well.

5-1 5 POTENTIALLY APPLICABLE EXPERIMENTS As mentioned in previous sections, the application models used to examine keff validation for extended BWR BUC are the GBC-68 computational benchmark cask [9] at burnups of 25 and 50 GWd/MTU with both the AO and AFP isotopes sets. Each application also had five years of cooling time after irradiation. The models are described in Section 2.2, and the GBC-68 cask model is defined in NUREG/CR-7157 [9]. The two selected burnups are intended to bracket the range of burnups over which extended BWR BUC is likely to be applied. Burnups lower than 25 GWd/MTU are likely to be governed by peak reactivity analysis, and assembly average burnups for BWR fuel are unlikely to be significantly greater than 50 GWd/MTU.

TSUNAMI-IP is used to calculate the ck integral parameter assessing similarity of each of a suite of 1,643 laboratory critical experiments (LCEs) to each of the four application models. This method of assessing similarity is discussed in Section 2.1.2 and is based on guidance provided in Rearden et al. [11] and Scaglione et al. [7]. The experiment suite is discussed in Section 2.3.2. It is the same suite that was used for investigations of keff validation of the peak reactivity method in NUREG/CR-7194 [3]. The application SDFs were generated using CE TSUNAMI-3D, as discussed in Section 4. The experiment SDFs were all generated with MG TSUNAMI-3D. The difference in SDF generation methods will not significantly impact the assessed similarity of the experiments, because, as shown in Section 4.3, the two methods yield very similar sensitivity data. No commercial reactor critical statepoint models (CRCs) are used in this work.

5.1 Application 1: 25 GWd/MTU and AO Isotope Set The full suite of 1,643 critical experiment SDFs was compared to the SDF from the GBC-68 model, which had an assembly average burnup of 25 GWd/MTU and the AO isotope set. A plot of the resulting ck values is provided in Figure 5-1. Each category of experiments is shown as a different data series to help illustrate which types of experiments are most applicable. No distinctions are made in the figure to indicate the source of each individual experiment SDF. As shown in the figure, a number of LCT experiments and a large number of HTC experiments show sufficient similarity with this application to be used in validation. A total of 174 experiments have a ck greater than 0.8; 73 are LCT experiments, and the remaining 101 are HTC experiments. Figure 5-2 shows the ck values greater than 0.8, highlighting the different series of experiments. The ck values are provided for these 174 experiments in Appendix C, Table C-1. Two cases from the LCT-051 evaluation (Cases 13 and 14) are excluded due to the large uncertainties in the boron content of the poison plates used in those experiments. The two cases use the same poison plates, and they are the only two cases that used those particular plates. Therefore, the final set of potentially applicable experiments consists of 71 LCT experiments and 101 HTC experiments, for a total of 172 experiments. A number of LCT series are represented, including a large number of cases from the LCT-008, LCT-011, and LCT-051 evaluations. Forty-eight of the 71 LCT experiments identified as potentially applicable are from these three series.

5-2 Figure 5-1 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AO Isotope Set Figure 5-2 ck Values Greater than 0.8 at 25 GWd/MTU Burnup with the AO Isotope Set 5.2 Application 2: 25 GWd/MTU and AFP Isotope Set The SDF from the GBC-68 model with an assembly average burnup of 25 GWd/MTU and the AFP isotope set was compared to the full suite of 1,643 critical experiment SDFs. A plot of the resulting ck values is provided in Figure 5-3. Each category of experiments is shown as a different data series to help identify which types of experiments are most applicable. No distinctions are made in the figure to indicate the source of each individual experiment SDF. As shown in the

5-3 figure, only some HTC, and no LCT experiments, show sufficient similarity with this application to be used in validation. A total of 68 experiments has a ck greater than 0.8. Figure 5-4 shows the ck values greater than or equal to 0.8, highlighting the different HTC phases from which applicable experiments are drawn. The ck values are provided for these 68 experiments in Appendix C, Table C-2.

A comparison of Figure 5-1 and Figure 5-3 shows that ck values are lower with the AFP isotope set than with the AO isotope set. This is the result of the addition of MAs and major FPs to the application model. None of the experiments contain these isotopes in the quantity and distribution that occurs in SNF. Some MCT experiments show modest increases in ck despite the change in compositions. This is a result of the spectral hardening induced by the thermal absorption in FPs; the EALF increases from 0.225 eV with the AO isotopes to 0.275 eV with the AFP set. These are modest increases, and the ck values for all MCT experiments (not including the HTC experiments) remain below 0.7. The ck values for the HTC experiments are relatively low for this application because the fissile material was designed to represent PWR fuel at a burnup of approximately 37.5 GWd/MTU. The HTC experiments have been shown to be poor for validation of low burnup PWR [7] and BWR [3] fuel. A number of the HTC cases are applicable in the lower end of the burnup range, as expected for extended BWR BUC.

Figure 5-3 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AFP Isotope Set

5-4 Figure 5-4 ck Values Not Less than 0.8 at 25 GWd/MTU Burnup with the AFP Isotope Set 5.3 Application 3: 50 GWd/MTU and AO Isotope Set The suite of critical experiment SDFs was compared to the SDF from the GBC-68 model with an assembly average burnup of 50 GWd/MTU and the AO isotope set. A plot of the resulting ck values is provided in Figure 5-5. Each category of experiments is shown as a different data series to help identify which types of experiments are most applicable. No distinctions are made in the figure to indicate the source of each individual experiment SDF. As shown in the figure, a few LCT experiments and the majority of the HTC experiments show sufficient similarity with this application to be used in validation. A total of 175 experiments have a ck greater than 0.8; 28 of the experiments are LCT experiments, and the remaining 147 are HTC experiments. Figure 5-6 shows the ck values greater than 0.8, highlighting the different series of experiments. The ck values are provided for these 175 experiments in Appendix C, Table C-3. As mentioned in Section 5.1, LCT-051 Cases 13 and 14 are excluded because of large uncertainties associated with the poison plates used in those cases. Therefore, the final set of potentially applicable experiments consists of a total of 173 experiments, including 26 LCT experiments and 147 HTC experiments.

A comparison of Figure 5-1 and Figure 5-5 shows lower ck values for the LCT experiments and higher values for the HTC experiments. The application case at 50 GWd/MTU has more Pu and a lower U enrichment, both of which make the LCT experiments less applicable. The higher burnup SNF is more similar to the HTC actinide composition than the lower burnup applications. At 25 GWd/MTU, the volume average uranium enrichment is 2.35 wt% 235U, and it drops to 1.10 wt%

235U at 50 GWd/MTU. The enrichment of the HTC actinide composition is 1.57 wt% 235U [14], 0.47 wt% higher than the 50 GWd/MTU application, and 0.78 wt% lower than the 25 GWd/MTU application. Similarly, the fraction of Pu that is 239Pu drops from 70.77 wt% at 25 GWd/MTU to 53.76 wt% at 50 GWd/MTU. The HTC fuel composition has 59.2 wt% of Pu as 239Pu, again in significantly better agreement with the higher burnup actinide composition.

5-5 Figure 5-5 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AO Isotope Set Figure 5-6 ck Values Not Less than 0.8 at 50 GWd/MTU Burnup with the AO Isotope Set 5.4 Application 4: 50 GWd/MTU and AFP Isotope Set The SDF from the GBC-68 model with an assembly average burnup of 50 GWd/MTU and the AFP isotope set was compared to the suite of critical experiment SDFs. A plot of the resulting ck values is provided in Figure 5-7. Each category of experiments is shown as a different data series to help identify which types of experiments are most applicable. No distinctions are made in the figure to indicate the source of each individual experiment SDF. As shown in the figure, only HTC

5-6 experiments show sufficient similarity with this application to be used in validation. A total of 126 HTC cases have a ck greater than 0.8. Figure 5-8 shows the ck values greater than 0.8, highlighting the different HTC phases from which applicable experiments are drawn. The ck values are provided for these 126 experiments in Appendix C, Table C-4.

A comparison of Figure 5-5 and Figure 5-7 shows that ck values are lower with the AFP isotope set than with the AO isotopes. This is simply the result of the addition of MAs and major FPs to the application model. As mentioned previously, only HTC experiments retain sufficient similarity for use in validation. A larger number of cases are applicable than identified at a burnup of 25 GWd/MTU because of the better actinide composition agreement, as described in the previous section.

Figure 5-7 ck Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set

5-7 Figure 5-8 ck Values Not Less than 0.8 at 50 GWd/MTU Burnup with the AFP Isotope Set

6-1 6 BIAS AND BIAS UNCERTAINTY DETERMINATION The primary purpose of validation is to quantify the suitability of a computational method for use in a criticality safety analysis [28]. Typically, this involves the determination of a code bias and a bias uncertainty to estimate a lower bound on the calculated keff for a critical system. Some validation approaches determine a single calculational margin which represents a combination of the bias and bias uncertainty. The USL is derived by combining the calculational marginthat is, the bias and bias uncertaintywith an additional administrative margin and any additional margins required to account for gaps or weaknesses in the validation set. The USL is the highest calculated keff that can be assumed to represent a subcritical system [28]. A discussion of margins for extended BWR BUC validation is presented in Section 7 to account for the gadolinium, MAs, and FPs not present in critical experiments identified in Section 5 as potentially applicable. This section provides sample bias and bias uncertainty determinations for the four application models considering the applicable experiments identified in the previous section. As discussed in Section 2.1.3, a nontrending method and a trending method with a range of trending parameters is used in these calculations. For the extended burnup credit cases, trends on EALF and ck were considered. The enrichment trend used for the peak reactivity cases was not considered because the burnups of the models that were included depart significantly from fresh fuel compositions. A summary of the sample bias and bias uncertainty values is provided in Table 6-1 in Section 6.4 for all 4 applications.

6.1 Application 1: 25 GWd/MTU and AO Isotope Set Using the set of 172 critical experiments (101 HTCs and 71 LCTs) that were determined to be applicable in Section 5.1, three sets of biases and bias uncertainties were generated. Bias and bias uncertainty were determined using a nontrending analysis, and they were also determined for trends on EALF and ck. The nontrending bias for the 25 GWd/MTU case with the AO isotope set was developed using the inverse variance weighted nontrending method discussed in Section 2.1.3. The nontrended bias was found to be -0.00172, and the associated bias uncertainty was found to be 0.00530. The nontrending calculational margin for the AO isotope set is -0.00702.

Trending analyses were performed with EALF and ck serving as the trending variables. The trend evaluations are shown in Figure 6-1 for the EALF case and Figure 6-2 for the ck case. The 25 GWd/MTU AO model has an EALF of 0.2279 eV, which is within the range of EALFs of the applicable benchmarks of 0.08755 eV to 1.4962 eV, with the majority of the applicable benchmarks being in the near vicinity of the application case. Evaluation of the trend at the application EALF yields a bias of -0.00182 and a bias uncertainty of 0.00649, which results in a combined calculational margin of -0.00831. The trend on ck is extrapolated to a value of 1.0 to evaluate the bias and bias uncertainty. The values of the bias and bias uncertainty for a ck trending evaluation are -0.00674 and 0.00762, which results in a combined calculational margin of

-0.01436. The bias and bias uncertainty are higher than the values found for peak reactivity with ck trending. The bias and bias uncertainty for the ck trend are heavily influenced by the extrapolation of the data from a mean ck of 0.843 to a value of 1.0. The relatively large extrapolation results because ck values for the 25 GWd/MTU cases are greater than the threshold value of 0.8 but are still relatively low for the LCT and HTC cases. The slope of the best estimate C/E vs. ck trend line is negative, so the extrapolation of the bias results in a larger magnitude bias than the nontrending evaluation.

6-2 Figure 6-1 C/E vs EALF Trend for Experiments Applicable to the 25 GWd/MTU AO Case Figure 6-2 C/E vs Ck Trend for Experiments Applicable to the 25 GWd/MTU AO Case

6-3 6.2 Application 2: 25 GWd/MTU and AFP Isotope Set Using the set of 68 critical experiments (all HTCs) that were determined to be applicable in Section 5.2, three sets of biases and bias uncertainties were generated. The bias and bias uncertainty were determined for a nontrending analysis, and they were also determined for trends on EALF and ck. The untrended bias for the 25 GWd/MTU case with the AFP isotope set was developed using the inverse variance weighted nontrending method discussed in Section 2.1.3.

The untrended bias was found to be -0.00236, and the associated bias uncertainty was found to be 0.00672. The untrended calculational margin for the AFP isotope set is -0.00908.

Trending analyses were performed with EALF and ck serving as the trending variables. The trend evaluations are shown in Figure 6-3 for the EALF case and Figure 6-4 for the ck case. The 25 GWd/MTU AFP model has an EALF of 0.2766 eV, which is within the range of EALFs of the applicable benchmarks of 0.09114 eV to 0.29172 eV, with the majority of the applicable benchmarks being lower in EALF but still in the vicinity of the application case. Evaluation of the trend at the application EALF yields a best estimate bias of 0.00044, which would be conservatively set to 0 to avoid taking credit for a positive bias and a bias uncertainty of 0.00724, which results in a combined calculational margin of -0.00724. The trend on ck is extrapolated to a value of 1.0 to evaluate the bias and bias uncertainty. The values of the bias and bias uncertainty for a ck trending evaluation are -0.00050 and 0.01556, which results in a combined calculational margin of -0.01606. The bias and bias uncertainty for the ck trend are heavily influenced by the extrapolation of the data from a mean ck of 0.816 to a value of 1.0. The relatively large extrapolation is necessary because ck values for the 25 GWd/MTU AFP cases are greater than the threshold value of 0.8 but still relatively low for the HTC cases. The slope of the best estimate trend line is slightly positive, but the small number of points and the large extrapolation to a ck value of 1 leads to a wide statistical prediction band.

Figure 6-3 C/E vs EALF Trend for Experiments Applicable to the 25 GWd/MTU AFP Case

6-4 Figure 6-4 C/E vs Ck Trend for Experiments Applicable to the 25 GWd/MTU AFP Case 6.3 Application 3: 50 GWd/MTU and AO Isotope Set Using the set of 173 critical experiments (26 LCTs and 147 HTCs) that were determined to be applicable in Section 5.3, three sets of biases and bias uncertainties were generated. Bias and bias uncertainty were determined for a nontrending analysis, and they were also determined for trends on EALF and ck. The nontrending bias for the 50 GWd/MTU case with the AO isotope set was developed using the inverse variance weighted nontrending method discussed earlier. The untrended bias was found to be -0.00173, and the associated bias uncertainty was found to be 0.00581. The untrended calculational margin for the AO isotope set is -0.00754.

Trending analyses were performed with EALF and ck serving as the trending variables. The trend evaluations are shown in Figure 6-5 for the EALF case and Figure 6-6 for the ck case. The 50 GWd/MTU AO model has an EALF of 0.2259 eV, which is within the range of EALFs of the applicable benchmarks of 0.06748 eV to 0.29172 eV, with the majority of the applicable benchmarks being lower in EALF but still in the vicinity of the application case. Evaluation of the trend at the application EALF yields a best estimate bias of -0.00206 and a bias uncertainty of 0.00646, which results in a combined calculational margin of -0.00852. The trend on ck is extrapolated to a value of 1.0 to evaluate the bias and bias uncertainty. The values of the bias and bias uncertainty for a ck trending evaluation are -0.00047 and 0.00657, which result in a combined calculational margin of -0.00704. The combined bias and bias uncertainty for the ck trend are reduced for the 50 GWd/MTU AO compared to 25 GWd/MTU AO and AFP cases because the extrapolation of the data is from a higher mean ck of 0.865, the trend of the best estimate bias line is upward sloped, and there are a larger number of available experiments, resulting in a smaller statistical uncertainty.

6-5 Figure 6-5 C/E vs EALF Trend for Experiments Applicable to the 50 GWd/MTU AO Case Figure 6-6 C/E vs Ck Trend for Experiments Applicable to the 50 GWd/MTU AO Case

6-6 6.4 Application 4: 50 GWd/MTU and AFP Isotope Set Using the set of 126 critical experiments (only HTCs), determined to be applicable in Section 5.4, three sets of biases and bias uncertainties were generated. Bias and bias uncertainty were determined for a nontrending analysis, and they were also determined for trends on EALF and ck.

The nontrending bias for the 50 GWd/MTU case with the AFP isotope set was developed using the inverse variance weighted nontrending method discussed earlier. The untrended bias was found to be -0.00132, and the associated bias uncertainty was found to be 0.00562. The untrended calculational margin for the AFP isotope set is -0.00694.

Trending analyses were performed with EALF and ck serving as the trending variables. The trend evaluations are shown in Figure 6-7 for the EALF case and Figure 6-8 for the ck case. The 50 GWd/MTU AFP model has an EALF of 0.2779 eV, which is within the range of EALFs of the applicable benchmarks of 0.06748 eV to 0.29172 eV, with the majority of the applicable benchmarks being lower in EALF but still in the vicinity of the application case. Evaluation of the trend at the application EALF yields a best estimate bias of -0.00120 and a bias uncertainty of 0.00680, which results in a combined calculational margin of 0.00800. The trend on ck is extrapolated to a value of 1.0 to evaluate the computational margin. The values of the bias and bias uncertainty are -0.00502 and 0.00723, which result in a calculational margin of -0.01225. The mean of the critical experiment ck values for this application is 0.850. The computational margin for the ck trend for this case is reduced compared to the 25 GWd/MTU AO and AFP cases, but by less than for the AO case. The uncertainty in the bias is about half the 25 GWd/MTU AO case because the extrapolation distance is significantly less and the number of data points is larger.

The best estimate trend line has a negative slope, thus resulting in a large negative bias.

Figure 6-7 C/E vs EALF Trend for Experiments Applicable to the 50 GWd/MTU AFP Case

6-7 Figure 6-8 C/E vs Ck Trend for Experiments Applicable to the 50 GWd/MTU AFP Case Table 6-1 Bias and Bias Uncertainty Values for All 4 Applications Application Technique Bias (k)

Bias Uncertainty (k)

Computational Margin (k) 1: 25 GWd/MTU and AO Isotope Set Nontrending

-0.00172 0.00530

-0.00702 EALF Trend

-0.00182 0.00649

-0.00831 ck Trend

-0.00674 0.00762

-0.01436 2: 25 GWd/MTU and AFP Isotope Set Nontrending

-0.00236 0.00672

-0.00908 EALF Trend 0.00044 0.00724

-0.00724 ck Trend

-0.00050 0.01556

-0.01606 3: 50 GWd/MTU and AO Isotope Set Nontrending

-0.00173 0.00581

-0.00754 EALF Trend

-0.00206 0.00646

-0.00852 ck Trend

-0.00047 0.00657

-0.00704 4: 50 GWd/MTU and AFP Isotope Set Nontrending

-0.00132 0.00562

-0.00694 EALF Trend

-0.00120 0.00680

-0.00800 ck Trend

-0.00502 0.00723

-0.01225

7-1 7 REACTIVITY MARGINS FOR UNVALIDATED ISOTOPES As discussed in NUREG/CR-7109 [7] and NUREG/CR-7194 [3], a challenge associated with implementing credit for FPs and MAs (236U, 243Am, and 237Np) in burnup credit analyses is the lack of applicable LCEs that contain these nuclides. Relevant guidance on the validation of criticality safety calculations recommends the inclusion of an appropriate reactivity margin, or penalty, for the presence of any nuclides that cannot be validated explicitly. A method of estimating the bias associated with the FPs is to use the nuclear data-induced uncertainty in keff instead of explicit validation of the MAs and FPs. As discussed in Section 2.1.2, TSUNAMI-IP combines the energy-dependent sensitivity data for each reaction and the covariance data to produce the nuclear data-induced uncertainty in keff for each reaction (capture, elastic scatter, etc.) for each isotope. These uncertainties are then combined for all of the nuclides that are not explicitly validated by calculating the root sum square of the uncertainties. Historically, the penalty associated with lack of validation of MAs and FPs has also been expressed as a fraction of the worth of the unvalidated nuclides [7]. Both the absolute and fractional reactivity margins were developed and are provided in this section.

These calculations were performed for two sets of burnup credit models that might be implemented by practitioners. The first set of calculations, consistent with the other sections of the document, used a detailed representation of the fuel, including 25 axial nodes, with 8 fuel compositions for each elevation. A single fuel composition was used for the non-gadolinia rods, and 7 equal volume rings were used for gadolinia-bearing rods. The explicit models contained the total 155Gd concentration resulting from any residual burnable absorber material and from FP gadolinium. This burnable absorber modeling strategy is typical of current peak reactivity methods used in BWR SFP analyses. In anticipation of applications that would use an extended burnup credit approach which would ignore the presence of any gadolinium from residual BA, similar to what is commonly practiced with PWRs, a second model was used. The second model has a single fuel composition for each of the 25 axial elevations, and only includes the concentration of 155Gd produced as a FP while neglecting the presence of any remaining BA gadolinium. The second model is referred to as the non-BA model.

The nuclear data-induced uncertainty for the major actinides, MAs, FPs, and nonfuel materials are presented in Table 7-1 for the detailed model and in Table 7-2 for the non-BA model. The detailed model considered 155Gd separately from the FPs because the majority of the 155Gd absorptions are due to residual BA. The nuclear data uncertainties for the FPs and MAs are slightly larger in the detailed model than in the non-BA model. The presence of residual BA in the upper portion of the fuel assembly forces the flux distribution into lower portions of the assembly that are more heavily burned. The sensitivity of keff to the FPs is greater in these regions because of the higher FP concentrations. This higher sensitivity leads to the observed larger keff uncertainties. The total uncertainty is also slightly lower in the non-BA application models shown in Table 7-2 because less gadolinium is present and credited in the models.

The combined nuclear data uncertainties for the FPs and MAs are tabulated in Table 7-3 and Table 7-4 for the detailed and non-BA models. Each table contains the absolute reactivity uncertainty and the uncertainty as a fraction of the FP and MA worth. The detailed model exhibits a large reactivity suppression from residual BA 155Gd. Critical experiments with gadolinium contain natural gadolinium, and the absorption is dominated by 157Gd. Therefore, these experiments do not provide significant validation for 155Gd, so a separate reactivity margin is developed for 155Gd in the detailed model and is provided in Table 7-5.

7-2 Table 7-1 Uncertainty in keff (%k/k) Due to Nuclear Data Uncertainty, Detailed Application Models Burnup 25 GWd/MTU 50 GWd/MTU All nuclides 0.42783 0.43205 Major actinides (9) 0.38650 0.38635 234U 0.00321 0.00301 235U 0.26975 0.24766 238U 0.18232 0.18365 238Pu 0.00686 0.01200 239Pu 0.20105 0.22160 240Pu 0.01648 0.02006 241Pu 0.03710 0.05044 242Pu 0.00830 0.01261 241Am 0.03442 0.04289 MAs (3) 0.01936 0.02202 243Am 0.01592 0.01709 237Np 0.01099 0.01382 236U 0.00068 0.00144 FPs (16) 0.04411 0.04978 95Mo 0.00344 0.00383 99Tc 0.00717 0.00835 101Ru 0.00569 0.00658 109Rh 0.01538 0.01673 109Ag 0.00154 0.00197 133Cs 0.01279 0.01427 147Sm 0.00495 0.00531 149Sm 0.01259 0.01326 150Sm 0.00339 0.00418 151Sm 0.01085 0.01169 152Sm 0.00478 0.00520 143Nd 0.03014 0.03471 145Nd 0.01272 0.01433 151Eu 0.00022 0.00023 153Eu 0.00652 0.00822 155Gd 0.04847 0.04708 Nonfuel materials 0.17024 0.17949

7-3 Table 7-2 Uncertainty in keff (%k/k) Due to Nuclear Data Uncertainty, Non-BA Application Burnup 20 GWd/MTU 25 GWd/MTU 30 GWd/MTU 35 GWd/MTU 40 GWd/MTU 45 GWd/MTU 50 GWd/MTU All nuclides 0.42611 0.42480 0.42299 0.42314 0.42394 0.42534 0.42690 Major actinides (9) 0.38872 0.38507 0.38302 0.38198 0.38152 0.38176 0.38212 234U 0.00361 0.00349 0.00341 0.00333 0.00327 0.00322 0.00317 235U 0.31513 0.30345 0.29399 0.28602 0.27913 0.27289 0.26756 238U 0.17678 0.17744 0.17853 0.17985 0.18100 0.18264 0.18367 238Pu 0.00176 0.00257 0.00350 0.00449 0.00543 0.00647 0.00756 239Pu 0.14107 0.15377 0.16385 0.17226 0.17958 0.18625 0.19205 240Pu 0.00775 0.00918 0.01041 0.01151 0.01248 0.01339 0.01420 241Pu 0.01799 0.02352 0.02862 0.03329 0.03758 0.04175 0.04540 242Pu 0.00262 0.00387 0.00510 0.00629 0.00744 0.00857 0.00961 241Am 0.01530 0.01986 0.02397 0.02774 0.03112 0.03434 0.03728 MAs (3) 0.01281 0.01412 0.01530 0.01645 0.01738 0.01826 0.01906 243Am 0.01140 0.01221 0.01290 0.01361 0.01410 0.01454 0.01493 237Np 0.00585 0.00709 0.00823 0.00923 0.01013 0.01100 0.01179 236U 0.00016 0.00028 0.00043 0.00060 0.00078 0.00098 0.00119 FPs (16) 0.03412 0.03922 0.03922 0.04137 0.04329 0.04514 0.04684 95Mo 0.00213 0.00263 0.00263 0.00282 0.00298 0.00314 0.00327 99Tc 0.00430 0.00540 0.00540 0.00585 0.00625 0.00662 0.00695 101Ru 0.00329 0.00421 0.00421 0.00458 0.00492 0.00524 0.00551 109Rh 0.00985 0.01193 0.01193 0.01269 0.01333 0.01389 0.01436 109Ag 0.00071 0.00104 0.00104 0.00119 0.00132 0.00145 0.00156 133Cs 0.00787 0.00973 0.00973 0.01046 0.01107 0.01165 0.01212 147Sm 0.00277 0.00341 0.00341 0.00367 0.00389 0.00410 0.00428 149Sm 0.02084 0.02021 0.02021 0.01979 0.01938 0.01894 0.01864 150Sm 0.00196 0.00266 0.00266 0.00292 0.00317 0.00340 0.00362 151Sm 0.00954 0.01061 0.01061 0.01102 0.01136 0.01168 0.01195 152Sm 0.00294 0.00358 0.00358 0.00381 0.00403 0.00418 0.00434 143Nd 0.01824 0.02291 0.02291 0.02479 0.02642 0.02794 0.02926 145Nd 0.00764 0.00952 0.00952 0.01027 0.01091 0.01150 0.01203 151Eu 0.00018 0.00020 0.00020 0.00021 0.00022 0.00022 0.00023 153Eu 0.00302 0.00445 0.00445 0.00509 0.00563 0.00620 0.00669 155Gd 0.00503 0.00769 0.00769 0.00902 0.01025 0.01155 0.01275 Nonfuel materials 0.17069 0.17447 0.17447 0.17651 0.17886 0.18112 0.18350

7-4 Table 7-3 Reactivity Margin for Lack of Validation of FPs and MAs for Explicit Criticality Safety Calculations Burnup GWd/MTU 25 50 FP and MA uncertainty (k) 0.00048 0.00054 FP and MA worth (k) 0.03495 0.04256 Uncertainty/worth (%)

1.37%

1.27%

Table 7-4 Reactivity Margin for Lack of Validation of FPs and MAs for Non-BA Criticality Safety Calculations Burnup GWd/MTU 20 25 30 35 40 45 50 FP and MA uncertainty (k) 0.00036 0.00042 0.00042 0.00045 0.00047 0.00049 0.00051 Worth (k) 0.03903 0.04135 0.04371 0.04567 0.04704 0.04847 0.04953 Uncertainty/

worth (%)

0.92%

1.02%

0.96%

0.99%

1.00%

1.01%

1.03%

Table 7-5 Reactivity Margin for Lack of Validation of Residual BA 155Gd in Explicit Criticality Safety Calculations Burnup GWd/MTU 25 50 Residual 155Gd uncertainty (k) 0.00048 0.00047 Residual 155Gd worth (k) 0.08282 0.07845 Uncertainty/worth (%)

0.59%

0.60%

8-1 8

SUMMARY

AND CONCLUSIONS This document provides an assessment of validation of keff calculations for BWR BUC analyses.

The examination of the validation of peak reactivity cask keff calculations, originally assessed in NUREG/CR-7194 [3], is discussed in Section 3. The generation of sensitivity data for the GBC-68 cask at multiple burnups beyond peak reactivity, including multiple isotope sets, is discussed in Section 4. Section 5 identifies potentially applicable experiments for use in validation based on these sensitivity data. Example determinations of bias and bias uncertainty for both burnups and both isotope sets are presented in Section 6. Finally, reactivity allowances to account for unvalidated isotopes are included in Section 7. Summaries of these discussions are presented in Section 8.1, and relevant conclusions are provided in Section 8.2.

8.1 Assessment Summary The validation of keff calculations in the peak reactivity method were initially assessed in NUREG/CR-7194 [3] using SCALE 6.1 [25]. As discussed in Section 2.3.3, SCALE 6.2 [10]

includes a significant revision to the nuclear covariance data. The impact of this change is reviewed in detail in Section 3. The primary result of the updated covariance data is an increase in the number of LCEs with a ck of 0.8 or higher compared to the peak reactivity GBC-68 model. The bias and bias uncertainty values that result from this larger set of experiments may lead to a slightly larger total computational margin than that observed in NUREG/CR-7194. The reactivity margins for unvalidated isotopes are significantly lower for actinides, are somewhat larger for 155Gd, and are unchanged for the remaining FPs. The total margin across all three of these factors is somewhat lower than that recommended in NUREG/CR-7194.

New sensitivity data were generated using TSUNAMI-3D models of the GBC-68 cask containing fuel depleted beyond peak reactivity to allow S/U-based critical experiment selection. The TSUNAMI-3D sequence was used in both MG and CE modes, and both the MG and CE SDFs were confirmed to contain accurate sensitivities by comparison to direct perturbation calculations.

The discussion of the generation and comparison of these SDFs is contained in Section 4. The sensitivity data calculated from both techniques were very similar. The SDFs generated using CE TSUNAMI were used for determinations of critical benchmark similarity and reactivity margins for unvalidated isotopes. The SDFs resulting from the MG TSUNAMI calculations for the applications were not used in this report. The existing critical experiment SDFs were all generated with MG TSUNAMI.

A set of four application cases was defined to examine the number of available applicable benchmarks and to perform sample determinations of bias and bias uncertainty. All four cases included SNF in a flooded GBC-68 cask. The fuel was depleted to 25 and 50 GWd/MTU, and the AO and AFP isotope sets were considered for both burnups. The discussion of potentially applicable experiments is contained in Section 5. For the two cases with the AO isotope set, 172 experiments were identified as applicable at a burnup of 25 GWd/MTU, and 173 applicable experiments were identified for the 50 GWd/MTU case. A combination of LCT and HTC cases are identified as applicable at both burnups; nearly three times as many LCTs appear to be applicable at 25 GWd/MTU than at 50 GWd/MTU. For the two cases with the AFP isotope set, 68 HTC cases are identified as applicable at 25 GWd/MTU, and 126 HTC cases were determined to be applicable at 50 GWd/MTU. For both isotope sets, more HTC cases are applicable at higher burnup because the fuel used in the HTC experiments is a closer match to higher burnup discharged fuel.

8-2 Bias and bias uncertainties were assessed for each of the four application models using trending and nontrending techniques. The trending techniques considered trends on EALF and on ck. The nontrending biases and bias uncertainties were consistent, with the biases ranging from -0.00132 to -0.00236, and the bias uncertainties ranging from 0.00530 to 0.00672, with the highest values occurring for the 25 GWd/MTU AFP case. The combined calculational margin ranged from 0.00694 to 0.00908 for the untrended analysis. The applicable experiments also bounded all four of the applications EALF values, which were tightly clustered between 0.22 eV (AO cases) and 0.28 eV (AFP cases). The results for the trending analysis using EALF as the independent variable also showed consistent results, with biases ranging between 0 (best estimate value of

+0.00044) and -0.00206, and the bias uncertainties ranging between 0.00646 and 0.00724. The total calculational margin for the EALF trending evaluation ranged between 0.00724 and 0.00852.

The trending analysis using ck as the independent variable produced bias estimates ranging from

-0.00047 to -0.00647, resulting from the variation of the slope of the trend line describing that data and the amount of extrapolation necessary to obtain a ck of 1.0. The bias uncertainty results for the ck trending analysis ranged from 0.00657 to 0.01556. The bias uncertainty results were influenced by the previously mentioned extrapolation distance and number of applicable experiments. The biases and bias uncertainties found here compare reasonably well with those found for PWR fuel in NUREG/CR-7109 [7], where the bias and bias uncertainty were found to be

~-0.00150 and ~0.01500 when evaluated with a trend on EALF (Table 7.3 of NUREG/CR-7109

[7]) and the bias varied from ~-0.00150 to ~0.00630 and the bias uncertainty varied from

~0.00850 to ~0.01500 when evaluated with a trend on ck (Table 7.6 of NUREG/CR-7109 [7]).

The identified potentially applicable critical benchmark experiments do not contain FPs or MAs, so a reactivity margin is needed to address the validation gap as discussed in Section 7. The major actinide isotopes can be validated, so no additional margins are necessary for analyses using the AO isotope set. A reactivity margin of 1% of the FP and MA worth is likely appropriate for extended BWR BUC analyses that do not credit any residual Gd burnable absorber. A margin of 1.5% of the total FP and MA worth is applicable to models which do credit residual 155Gd in BA rods, along with FP 155Gd.

8.2 Conclusions Several conclusions can be drawn regarding the validation of keff calculations associated with BWR BUC analyses.

Sufficient laboratory critical experiments exist to perform adequate validation of keff calculations for peak reactivity and extended BWR BUC analyses.

Changes in covariance data can impact the applicable critical benchmark experiments to be used in validation. New covariance data should be investigated as they become available to establish their impact on benchmark applicability.

Accurate sensitivity data for BWR storage and transportation systems can be generated in the TSUNAMI-3D sequence using both the MG and CE modes.

SNF storage and transportation systems containing BWR or PWR fuel in the typical discharge burnup range share a high degree of similarity. Similar experiments are used for validation of BUC analyses for both PWR and BWR fuel, and similar gaps exist for validating FPs and MAs.

Validation of extended BWR BUC keff calculations can be accomplished with LCT and HTC experiments for the AO isotope set and with HTC experiments for the AFP isotope set.

8-3 The bias and bias uncertainty values generated for extended BWR BUC are similar to those for peak reactivity analysis. Values vary somewhat based on validation technique, but the bias tends to be approximately ~0.2% keff, and the bias uncertainty is approximately ~0.6% keff for traditional methods. Results varied substantially more in ck based trending analysis, with bias and bias uncertainty values being generally higher. The bias values for the ck trends range from -0.00050 to -0.00674 and the uncertainties range from 0.00657 to 0.01556. The magnitude of the uncertainties is driven primarily by the amount of extrapolation needed to reach a ck value of 1.

Reactivity margins for unvalidated MAs and FPs can be estimated using S/U techniques.

A margin of 1% of the MA and FP worth is likely appropriate for extended BWR BUC models that do not credit residual 155Gd from the BAs. Note that crediting FP 155Gd is accounted for in the 1% margin. Crediting residual BA gadolinium increases the necessary margin to 1.5% of the MA and FP worth.

9-1 9 REFERENCES 1.

US Code of Federal Regulations Title 10, Energy, US Nuclear Regulatory Commission, Washington, DC (2018).

2.

Division of Spent Fuel Storage and Transportation, Interim Staff Guidance8, Revision 3, Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transportation and Storage Casks, US Nuclear Regulatory Commission (2012).

3.

W. J. Marshall, B. J. Ade, S. M. Bowman, I. C. Gauld, G. Ilas, U. Mertyurek, and G. Radulescu, Technical Basis for Peak Reactivity Burnup Credit for BWR Spent Nuclear Fuel in Storage and Transportation Systems, NUREG/CR-7194 (ORNL/TM-2014/240),

prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2015).

4.

W. J. Marshall, B. J. Ade, S. M. Bowman, and J. S. Martinez-Gonzalez, Axial Moderator Density Distributions, Control Blade Usage, and Axial Burnup Distributions for Extended BWR Burnup Credit, NUREG/CR-7224 (ORNL/TM-2015/544), prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2016).

5.

B. J. Ade, W. J. Marshall, G. Ilas, B. R. Betzler, and S. M. Bowman, Impact of Operating Parameters on Extended BWR Burnup Credit, NUREG/CR-7240 (ORNL/TM-2017/46),

prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2018).

6.

G. Radulescu, I. C. Gauld, G. Ilas, and J. C. Wagner, An Approach for Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses-Isotopic Composition Predictions, NUREG/CR-7108 (ORNL/TM-2011/509), prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2012).

7.

J. M. Scaglione, D. E. Mueller, J. C. Wagner, and W. J. Marshall, An Approach for Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses-Criticality (keff) Predictions, NUREG/CR-7109 (ORNL/TM-2011/514), prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2012).

8.

I. C. Gauld and U. Mertyurek, Margins for Uncertainty in the Predicted Spent Fuel Isotopic Inventories for BWR Burnup Credit, NUREG/CR-7251 (ORNL/TM-2018/782) prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2018).

9.

D. E. Mueller, J. M. Scaglione, J. C. Wagner, and S. M. Bowman, Computational Benchmark for Estimated Reactivity Margin from Fission Products and Minor Actinides in BWR Burnup Credit, NUREG/CR-7157 (ORNL/TM-2012/96), prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (February 2013).

10. B. T. Rearden and M. A. Jessee, Editors, SCALE Code System, ORNL/TM-2005/39, Version 6.2.2, Oak Ridge National Laboratory (2017).

11. B. T. Rearden, M. L. Williams, M. A. Jessee, D. E. Mueller, and D. A. Wiarda, Sensitivity and Uncertainty Analysis Capabilities and Data in SCALE, Nucl. Technol. 174 (2), pp.

236-288 (2011).

9-2

12. J. C. Dean and R. W. Tayloe, Jr., Guide for Validation of Nuclear Criticality Safety Calculational Methodology, prepared for the US Nuclear Regulatory Commission by Science Applications International Corporation, Oak Ridge, TN (2001).

13. International Handbook of Evaluated Criticality Safety Benchmark Experiments, NEA/NSC/DOC(95)03, NEA Nuclear Science Committee (2016).

14. D. E. Mueller, K. R. Elam, and P. B. Fox, Evaluation of the French Haut Taux de Combustion (HTC) Critical Experiment Data, NUREG/CR-6979 (ORNL/TM-2007/083) prepared for the US Nuclear Regulatory Commission by Oak Ridge National Laboratory, Oak Ridge, TN (2008).

15. Axel Hoefer et al., Proposal for Benchmark Phase IV Role of Integral Experiment Covariance Data for Criticality Safety, Benchmark Proposal, OECD/NEA (2015).

16. W. J. Marshall, B. T. Rearden, and R. E. Pevey, Determination of Critical Experiment Correlations for Experiments Involving Arrays of Low-Enriched Fuel Rods, Proceedings of NCSD 2017: Criticality Safety - pushing boundaries by modernizing and integrating data, methods, and regulations, Carlsbad, NM (2017).

17. V. Sobes, B. T. Rearden, D. E. Mueller, W. J. Marshall, J. M. Scaglione, and M. E. Dunn, Upper Subcritical Limit Calculations Based on Correlated Experimental Data, International Conference on Nuclear Criticality Safety (ICNC 2015), Charlotte, NC (2015).

18. M. B. Chadwick et al., ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields, and Decay Data, Nucl. Data Sheets 112(12), 2887-2996 (2011).

19. W. J. Marshall and B. T. Rearden, The SCALE Verified, Archived Library of Inputs and Data - VALID, ANS Nuclear Criticality Safety Division Topical Meetings (NCSD2013),

Wilmington, NC (2013).

20. I. Hill, J. Gulliford, J. B. Briggs, B. T. Rearden, and T. Ivanova, Generation of 1800 New Sensitivity Data Files for ICSBEP Using SCALE 6.0, Trans. of the American Nuclear Society 109(1), pp. 867-869 (2013).

21. R. Little, T. Kawano, G. D. Hale, M. T. Pigni, M. Herman, P. Oblozinsky, M. L. Williams, M.

E. Dunn, G. Arbanas, D. Wiarda, R. D. McKnight, J. N. McKamy, and J. R. Felty, Low-Fidelity Covariance Project, Nucl. Data Sheets 109(12), pp. 2828-2833 (2008).

22. M. Salvatores and R. Jacqmin, Uncertainty and Target Accuracy Assessment for Innovative Systems Using Recent Covariance Data Evaluations, NEA/WPEC-26, Nuclear Energy Agency (2008).

23. K. Shibata, O. Iwamoto, T. Nakagawa, N. Iwamoto, A. Ichihara, S. Kunieda, S. Chiba, K.

Furutaka, N. Otuka, T. Ohsawa, T. Murata, H. Matsunobu, A. Zukeran, S. Kamada, and J.

Katakura: "JENDL-4.0: A New Library for Nuclear Science and Engineering," J. Nucl. Sci.

Technol.. 48(1), pp. 1-30 (2011).

24. W. J. Marshall, M. L. Williams, D. Wiarda, B. T. Rearden, M. E. Dunn, D. E. Mueller, J. B.

Clarity, and E. L. Jones, Development and Testing of Neutron Cross Section Covariance Data for SCALE 6.2, Proceedings of International Conference on Nuclear Criticality Safety, Charlotte, NC (2015).

25. SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, (2011).

9-3

26. K. Shibata, T. Kawano, T. Nakagawa, O. Iwamoto, J. Katakura, T. Fukahori, S. Chiba, A.

Hasegawa, T. Murata, H. Matsunobu, T. Ohsawa, Y. Nakajima, T. Yoshida, A. Zukeran, M. Kawai, M. Baba, M. Ishikawa, T. Asami, T. Watanabe, Y. Watanabe, M. Igashira, N.

Yamamuro, H. Kitazawa, N. Yamano and H. Takano: "Japanese Evaluated Nuclear Data Library Version 3 Revision-3: JENDL-3.3," J. Nucl. Sci. Technol. 39, 1125 (2002).

27. B. L. Broadhead and J. J. Wagschal, The Fission Spectrum Uncertainty, 95821.pdf in Proc. of PHYSOR 2004The Physics of Fuel Cycles and Advanced Nuclear Systems:

Global Developments, Chicago, IL (2004).

28. Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations, ANSI/ANS-8.24-2017, American Nuclear Society, La Grange Park, IL (2017).

29. Standard Review Plan for Spent Fuel Dry Storage Systems at a General License Facility, NUREG-1536, Revision 1, US Nuclear Regulatory Commission, Washington, DC (2010).

30. D. A. Brown et al., ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Library with CIELO-project Cross Sections, New Standards and Thermal Scattering Data, Nucl. Data Sheets 148, pp. 1-142 (2018).

31. C. M. Perfetti, B. T. Rearden, and W. R. Martin, SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations, Nucl. Sci. Eng., 182, 3, 332-353 (2016).

32. E. L. Jones, User Perspective and Analysis of the Continuous-Energy Sensitivity Methods in SCALE 6.2 using TSUNAMI-3D, M.S. Thesis, University of Tennessee-Knoxville (2015).

33. W. J. Marshall, E. L. Jones, B. T. Rearden, and M. E. Dunn, A Case Study in the Application of TSUNAMI-3D - Part 1, Multigroup, Trans. Am. Nucl. Soc. 115, 673-676 (2016).

APPENDIX A ASSESSMENT OF INTEGRAL PARAMETER E

A-1 Historically, ck (see Section 2.1.2) has been the integral parameter used for S/U based validation of computational methods for criticality safety. The calculation of ck is performed by combining the sensitivity profiles of the application of interest with the profiles of each experiment considered in the validation study and weighting both sensitivity profiles with the neutron cross section covariance data. Combining the sensitivity data with the covariance data produces a measure of the correlation of the nuclear data-induced uncertainty in keff between each experiment and application. Theoretically, cross sections with the greatest uncertainty are most likely to contribute to the calculational bias of a system, providing a justification for using ck values to select representative experiments (Sections 3.1 and 5) and as the independent variable in trending analysis (Sections 3.2.3 and 6).

Neutron cross section covariance data has become an area of interest only in the past 20 years for the validation of criticality safety computational methods and is therefore maturing much more rapidly than the underlying cross section data. An update to the covariance data was performed as part of the release of SCALE 6.2. A subsequent assessment of the updated covariance data performed by Marshall et al. [24] showed that the values of ck using the new data had changed significantly for PWR and BWR BUC systems compared to values generated with the previous version of the covariance library. This topic is discussed extensively in Section 3 with respect to the validation of peak reactivity BWR BUC.

Another approach that has been discussed is the development of alternative integral indices that use weighting functions that are independent of the covariance data. One of the simplest approaches is to consider the unweighted overlap in the sensitivity profiles. The integral parameter E is calculated by combining the sensitivity for the application with the experiments without including a weighting function. Just as ck represents the fraction of uncertainty in keff that is shared between an application and an experiment, E represents the fraction of the sensitivity coefficients that is shared between an application and an experiment. The definition of E is provided in Equation A-1, where Sa is the nuclide-and energy-dependent sensitivity profile for the applications, and Se is the sensitivity profile for the experiment. Like ck, E is calculated by the TSUNAMI-IP module available in SCALE.

=

llll (A-1)

This appendix begins to examine the potential application of E as a validation parameter. The analysis of the integral parameter E compared to ck is divided in two segments. The first segment examines the general trends in the parameters for each of the four applications used for the extended BUC validation study. The second segment analyzes the individual differences in sensitives and nuclear data-induced uncertainties for the application cases and selected critical experiments.

This appendix documents an initial investigation into the use of E and should not be construed as an endorsement or indictment of the use of E as an experimental selection or trending parameter for validation. E is used along with ck in Section 4.3 to compare different methods of sensitivity profile generation. It is appropriate for this purpose because it is simply being used to show the aggregate equivalence of two methods being used with the same system rather than as a metric of demonstrating the neutronic similarity of two systems.

APPENDIX A ASSESSMENT OF INTEGRAL PARAMETER E

A-2 A.1 General Trend Analysis Similarity of the critical experiments is assessed for each of the four extended BUC cases using the E integral parameter. Figures A-1 through A-4 are plots of E that are directly comparable to the plots in Section 5 which used ck as the parameter of interest:

Figure A-1 presents the values of E found for the 25 GWd/MTU AO case and is directly comparable to Figure 5-1.

Figure A-2 presents the values of E for the 25 GWd/MTU AFP case is and directly comparable to Figure 5-3.

Figure A-3 presents the values of E for the 50 GWd/MTU AO case and is directly comparable to Figure 5-5.

Figure A-4 presents values of E for the 50 GWd/MTU case and is directly comparable to Figure 5-7.

A red line corresponding to an E value of 0.8 in each figure provides perspective to the Section 5 plots. While guidance is available on what values of ck should be used as a cutoff of the inclusion in a validation study, such guidance is essentially nonexistent for E. Rearden et al. [11] state that

[b]cause of the similarity of ck and E, the same limits developed for ck should be applicable to the use of the E parameter.

The average and standard deviation of E, ck, and the difference between E and ck are tabulated in Table A-1. The experimental types included in Table A-1 are limited to the LCT, MCT, and HTC types. This data reduction is introduced because the LEU-MISC-THERM and LEU-SOL-THERM experiments behave in a manner similar to that of the LEU-COMP-THERM experiments, and the MIX-SOL-THERM experiments behave in a manner similar to that of the MIX-COMP-THERM.

Figure A-1 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AO Isotope Set

A-3 Figure A-2 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 25 GWd/MTU and the AFP Isotope Set Figure A-3 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AO Isotope Set

A-4 Figure A-4 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set Table A-1 Summary Statistics Associated with Difference Between E and ck for the Four Extended BUC Applications Examined in Sections 5-7 25 GWd/MTU AO 25 GWd/MTU AFP Experiment Set E

ck E-ck E

ck E-ck LCT 0.907 +/- 0.024 0.674 +/- 0.079 0.233 +/- 0.078 0.853 +/- 0.022 0.560 +/- 0.088 0.294 +/- 0.086 MCT 0.436 +/- 0.127 0.491 +/- 0.103 -0.055 +/- 0.057 0.514 +/- 0.118 0.526 +/- 0.089

-0.012 +/- 0.065 HTC 0.923 +/- 0.011 0.808 +/- 0.037 0.116 +/- 0.033 0.942 +/- 0.013 0.782 +/- 0.038 0.160 +/- 0.035 50 GWd/MTU AO 50 GWd/MTU AFP LCT 0.861 +/- 0.024 0.670 +/- 0.065 0.191 +/- 0.063 0.824 +/- 0.022 0.592 +/- 0.070 0.232 +/- 0.069 MCT 0.527 +/- 0.126 0.584 +/- 0.110 -0.058 +/- 0.054 0.562 +/- 0.119 0.592 +/- 0.098

-0.030 +/- 0.059 HTC 0.955 +/- 0.012 0.869 +/- 0.038 0.086 +/- 0.034 0.954 +/- 0.014 0.837 +/- 0.037 0.117 +/- 0.034 Figures A-1 through A-4 and Table A-1 show that the values of the integral parameter E vary substantially for each of the four application cases when compared to the values of ck. The average values of E for the LCT experiments range between 0.907 and 0.824 for each of four cases of the extended BUC cases, with a consistent standard deviation of approximately 0.024.

This represents an increase of the integral parameter ranging from 0.191 to 0.294 between ck and E. The E values for the LCT experiments are greater for the 25 GWd/MTU cases than they are for

A-5 the 50 GWd/MTU cases, and they are also higher for the AO cases than they are for the AFP cases. The E values are higher for the 25 GWd/MTU cases because the fuel composition in the 25 GWd/MTU cases more closely resembles fresh fuel than the fuel composition in the 50 GWd/MTU case. The E values are higher for the AO cases than the AFP cases because the AFP cases include a number of fission products that do not have any sensitivity profiles associated with them in the LCT critical experiments. Also, there is a substantial amount of 155Gd BA remaining in the AFP cases. The remaining 155Gd is preferentially located in the upper portion of the fuel assemblies in the fuel with lower burnup, causing the flux distribution to be shifted lower in the fuel assembly to nodes with higher burnup. The fuel assembly thus appears more heavily burned with the AFP isotope set than with the AO set. A plot of the relative fission density as a function of axial elevation is given in Figure A-5. Figure A-5 shows that the middle of the fuel assembly, which has higher relative burnups, is more important for the AFP cases than for the AO cases, with the effect being significantly more pronounced for the 25 GWd/MTU case than the 50 GWd/MTU case. It is also noted that the standard deviation of the E values is about one quarter of the standard deviation of the ck values for each of the cases considered. It is noted that a similar trend with burnup and isotope set was observed for the ck values.

Figure A-5 E Values for Critical Experiments Compared to GBC-68 with Fuel at a Burnup of 50 GWd/MTU and the AFP Isotope Set The MCT experiments were also examined. Figures A-1 through A-4 and Table A-1 show that the MCT cases have the lowest similarity to the application cases, with the values of E ranging from 0.436 for the 25 GWd/MTU AO case to 0.562 for the 50 GWd/MTU AFP case. The AFP cases show greater similarity to the MCT cases than the AO cases, and the 50 GWd/MTU cases show a higher similarity to the MCT cases than the 25 GWd/MTU cases. This is consistent with the increased dependence of the keff of the system on the plutonium cross sections with increased burnup of the assembly. The E and ck values for each of the cases are relatively close, with the difference ranging from -0.012 to -0.058. Of the three types of experiments considered in this work, the MCT experiments are the only ones for which the value of E is consistently below the

A-6 value of ck, indicating that removal of the covariance weighting results in lower assessed similarity.

The low similarity in terms of both integral indices is not surprising given the nearly complete lack of 235U in the MCT cases and the modest burnup of the upper nodes of the fuel assembly in the cask models.

The HTC cases were also examined. Figures A-1 through A-4 and Table A-1 show that the HTC cases have average values of E ranging 0.923 to 0.955. The values of E are generally high, and they increase from the 25 GWd/MTU cases to the 50 GWd/MTU cases, as would be expected given that the HTCs are intended to mimic the actinide composition of 4.5 wt% enriched fuel, with a burnup of 37.5 GWd/MTU. The axial fission density weighted burnups of the cases correspond to 16.9 GWd/MTU and 23.3 GWd/MTU for the 25 GWd/MTU AO and AFP cases, and 26.4 and 28.6 for the 50 GWd/MTU AO and AFP cases. The values of E are higher for the AFP isotope set than for the AO isotope set for the 25 GWd/MTU, but they were essentially the same for the 50 GWd/MTU cases. E was higher than ck for both of the isotope sets at both burnups. It is also noted that the standard deviation of the values of E is about one third of the standard deviation of the ck values.

A.2 Detailed Analysis of Selected Experiments It is clear that there are substantial changes in the values of E and ck based on the general trends of those parameters with respect to the four extended BUC cases investigated. To gain better insight into what is causing the differences between E and ck, a more detailed examination must be made of one experiment for each of the LCT, MCT, and HTC sets. As discussed earlier, ck is a measure of the amount of nuclear data-induced uncertainty that is shared between the application and experiment. The shared uncertainty is calculated by weighting the shared sensitivity of the application and experiment by the covariance data. The E parameter is the unweighted shared sensitivity between the two experiments. To identify areas where E and ck differ, a comparison of the sensitivities and nuclear data induced uncertainties was performed.

The test cases identified to examine the differences between ck and E were LCT-002-004, MCT-001-004, and HTC-2B-009. The E and ck values for the selected experiments are provided in Table A-2 for comparison. Among all of the experiments considered, LCT-002-004 has a larger-than-average change between ck and E when compared to other LCT experiments, MCT-001-004 has a representative change between ck and E when compared to other MCT experiments and HTC-2B-009 has a smaller-than-average change when compared to other experiments.

A-7 Table A-2 Comparison of E and ck Values for the Experiments Selected for Detailed Analysis Experiment Parameter 25 GWd/MTU AO 25 GWd/MTU AFP 50 GWd/MTU AO 50 GWd/MTU AFP LCT-002-004 ck 0.59620 0.47090 0.60790 0.52010 E

0.90570 0.84870 0.86200 0.82010 MCT-001-004 ck 0.43340 0.47820 0.52970 0.54370 E

0.34870 0.42790 0.45120 0.48510 HTC-2B-009 ck 0.86620 0.85910 0.92020 0.90130 E

0.92140 0.94530 0.95320 0.95660 Tables A-3 and A-4 show the total sensitivities and nuclear data-induced uncertainties, respectively, for the nuclides important to BWR BUC applications, including 235U, 238U, 239Pu, 1H, 10B, and 155Gd. Analysis of the similarities and differences between an application and the experiments should improve understanding of the practical differences between E and ck.

Table A-3 Comparison of Total Sensitivities for Major BUC Nuclides for the Applications and Selected Experiments Nuclide 25 GWd/MTU AO 25 GWd/MTU AFP 50 GWd/MTU AO 50 GWd/MTU AFP LCT-002-004 HTC-2B-009 MCT-001-004 235U 0.1884 0.2077 0.1793 0.2054 0.2038 0.1630 0.0025 238U

-0.0818

-0.0758

-0.0795

-0.0684

-0.0588

-0.0971

-0.0052 239Pu 0.0643 0.0991 0.0901 0.1174 0.1238 0.1221 1H 0.1938 0.1933 0.2150 0.2225 0.1715 0.1224 0.1930 10B

-0.0507

-0.0509

-0.0501

-0.0502

-0.1190 155Gd

-0.0144

-0.0142

A-8 Table A-4 Comparison of Total Uncertainties for Major BUC Nuclides for the Applications and Selected Experiments Nuclide 25 GWd/MTU AO 25 GWd/MTU AFP 50 GWd/MTU AO 50 GWd/MTU AO LCT-002-004 HTC-2B-009 MCT-001-004 235U 0.3010 0.2698 0.2644 0.2477 0.6089 0.2202 0.0142 238U 0.1830 0.1823 0.1923 0.1837 0.3113 0.2400 0.0858 239Pu 0.1596 0.2011 0.2003 0.2216 0.2627 0.6610 1H 0.1066 0.0987 0.1175 0.1081 0.2583 0.1257 0.2635 10B 0.0087 0.0089 0.0085 0.0086 0.0099 155Gd 0.0485 0.0471 The 235U total sensitivities range between 0.1793 and 0.2077 for each of the application cases, and the nuclear data induced uncertainty ranges between 0.2477 and 0.3010. Both the total sensitivity and uncertainty for 235U are within relatively narrow bands, though the sensitivity and uncertainty do not increase and decrease together. The values of 235U sensitivity appear to be similar among the application cases and are also similar between the LCT experiment (0.2038) and the HTC experiment (0.1630). This is also true of the nuclear data-induced uncertainty in the HTC experiment, with its value falling slightly below the range of the application cases. The smaller sensitivities and uncertainties for the HTC case are logical, given that the applications behave as though they are less burned than the HTC experiment and therefore have higher contributions from 235U than shown in the experiment. Despite having a similar 235U sensitivity to the applications, the LCT experiment has a nuclear data-induced uncertainty of 0.6089, which is more than twice the application cases. A more detailed inspection of the LCT experiment uncertainty output revealed that there is a much larger sensitivity of the LCT experiment to the energy dependence of the neutrons emerging from fission (), which has a high degree of uncertainty compared to other reactions. The contribution to data-induced uncertainty from for the application cases is virtually zero. Discussions with M. L. Williams indicated that large uncertainties are associated with geometrically small systems in which leakage plays an important role. Examining the underlying sensitivity revealed that the sensitivity is 500 times greater in the LCT experiment than in the applications. The LCT experiment is a reasonably small geometry relative to the application case. It is noted that this conclusion is in conflict with the results from the HTC case, which is a similar size system to the LCT case but does not have a large uncertainty.

This topic needs further investigation to be fully understood. The MCT case contains very little 235U and therefore does not have a substantial sensitivity or nuclear data-induced uncertainty associated with 235U.

The 238U total sensitivities range from -0.0684 to -0.0818, and the nuclear data-induced uncertainties range from 0.1823 to 0.1923 for all the application cases. For the HTC experiment, both the sensitivity and nuclear data-induced uncertainty are larger than in any of the application cases. The LCT experiment has a smaller total sensitivity to 238U than any of the application cases, but the nuclear data-induced uncertainty is nearly twice that of any of the application cases. The 238U uncertainty is driven by a large contribution from inelastic scattering for the LCT experiment. This contribution to the uncertainty is much smaller for the application cases, which derive most of their sensitivity and uncertainty from radiative capture. The MCT experiment has

A-9 relatively little uranium present, so it does not have a substantial sensitivity to the 238U cross sections; the uncertainty contributed is approximately half that of the application cases. The disproportionately high contribution of uncertainty is present because inelastic scattering is the primary contributor among the 238U reactions for the MCT experiment.

The 239Pu total cross section sensitivities range from 0.0643 to 0.1174, and the nuclear data-induced uncertainties ranged from 0.1596 to 0.2216 for each of the applications cases. The LCT experiment considered has no Pu present, and therefore it has no sensitivity or nuclear data-induced uncertainty due to the Pu cross sections. The HTC experiment considered has a slightly higher sensitivity and nuclear data-induced uncertainty than any of the application cases. This is because the HTC cases are designed to have the actinide composition of fuel that is slightly more burned than the fission density weighted burnup of the applications used in the analysis.

Furthermore, the nuclear data-induced uncertainty increase for the HTC cases compared to the applications is approximately proportional to the increased sensitivity. The total sensitivity to 239Pu is approximately the same for the MCT case as it is for the HTC case, which is slightly elevated compared to the application cases. However, the nuclear data-induced uncertainty for the MCT case is more than three times that of any of the applications. The contributions to nuclear data uncertainty for fission and radiative capture are about three times higher for the MCT case than for the application cases, and an additional contribution to uncertainty from is also present, which is not in the application cases. Therefore, it appears that the sensitivity of the MCT cases is small since it is a sum of large negative and positive contributions which both increase the nuclear data induced uncertainty but cancel in the sum of sensitivities.

The sensitivities to 1H range between 0.1933 and 0.2225, and the nuclear data-induced uncertainties range between 0.0987 and 0.1175 for each of the application cases. The 1H total sensitivities are in good agreement with the experimental cases. The nuclear data uncertainty due to 1H for the LCT and MCT cases is about twice the value for the applications. Differences in nuclear data-induced uncertainty are due to how they influence the other reactions in the problem. A plot of the energy-dependent 1H total sensitivity is provided in Figure A-6, which shows the 50 GWd/MTU application case and HTC experiment have relatively flat sensitivity profiles when compared to the MCT and LCT experiments. The LCT and MCT experiments have strong positive sensitivities in the fast region and strong negative sensitivities in the thermal region, while the HTC and application have lesser contributions in both regions. The large sensitivities in the MCT and LCT fast region are likely the cause of the increased uncertainty due to the large cross section uncertainties in that energy range.

In the AFP cases, the absorbers in the application case included 10B in the absorber panels and 155Gd in the fuel. Despite the moderate sensitivity of the boron in the absorber plates, there is very little contribution to total uncertainty due to the low small cross section uncertainty. The 155Gd contribution to the nuclear data-induced uncertainty is modest considering that it has a relatively small sensitivity.

A-10 Figure A-6 Comparison of Energy Dependent 1H Sensitivities for the 50 GWd/MTU AFP Case and the LCT, HTC, and MTC Experiments

APPENDIX B LIST OF CRITICAL BENCHMARK EXPERIMENTS CONSIDERED

B-1 Table B-1 of this appendix contains the full list of critical benchmark experiments considered as candidates for use in criticality code validation. This list was compiled from the three sources discussed in Section 2.3.2 and contains data from 1,643 unique critical experiments.

Table B-1 Critical Benchmark Experiments Considered List of critical benchmark experiments considered LEU-COMP-THERM-001-001 LEU-COMP-THERM-033-025 LEU-COMP-THERM-090-007 LEU-COMP-THERM-001-002 LEU-COMP-THERM-033-026 LEU-COMP-THERM-090-008 LEU-COMP-THERM-001-003 LEU-COMP-THERM-033-027 LEU-COMP-THERM-090-009 LEU-COMP-THERM-001-004 LEU-COMP-THERM-033-028 LEU-COMP-THERM-091-001 LEU-COMP-THERM-001-005 LEU-COMP-THERM-033-029 LEU-COMP-THERM-091-002 LEU-COMP-THERM-001-006 LEU-COMP-THERM-033-030 LEU-COMP-THERM-091-003 LEU-COMP-THERM-001-007 LEU-COMP-THERM-033-031 LEU-COMP-THERM-091-004 LEU-COMP-THERM-001-008 LEU-COMP-THERM-033-032 LEU-COMP-THERM-091-005 LEU-COMP-THERM-002-001 LEU-COMP-THERM-033-033 LEU-COMP-THERM-091-006 LEU-COMP-THERM-002-002 LEU-COMP-THERM-033-034 LEU-COMP-THERM-091-007 LEU-COMP-THERM-002-003 LEU-COMP-THERM-033-035 LEU-COMP-THERM-091-008 LEU-COMP-THERM-002-004 LEU-COMP-THERM-033-036 LEU-COMP-THERM-091-009 LEU-COMP-THERM-002-005 LEU-COMP-THERM-033-037 LEU-COMP-THERM-092-001 LEU-COMP-THERM-003-001 LEU-COMP-THERM-033-038 LEU-COMP-THERM-092-002 LEU-COMP-THERM-003-002 LEU-COMP-THERM-033-039 LEU-COMP-THERM-092-003 LEU-COMP-THERM-003-003 LEU-COMP-THERM-033-040 LEU-COMP-THERM-092-004 LEU-COMP-THERM-003-004 LEU-COMP-THERM-033-041 LEU-COMP-THERM-092-005 LEU-COMP-THERM-003-005 LEU-COMP-THERM-033-042 LEU-COMP-THERM-092-006 LEU-COMP-THERM-003-006 LEU-COMP-THERM-033-043 LEU-COMP-THERM-094-001 LEU-COMP-THERM-003-007 LEU-COMP-THERM-033-044 LEU-COMP-THERM-094-002 LEU-COMP-THERM-003-008 LEU-COMP-THERM-033-045 LEU-COMP-THERM-094-003 LEU-COMP-THERM-003-009 LEU-COMP-THERM-033-046 LEU-COMP-THERM-094-004 LEU-COMP-THERM-003-010 LEU-COMP-THERM-033-047 LEU-COMP-THERM-094-005 LEU-COMP-THERM-003-011 LEU-COMP-THERM-033-048 LEU-COMP-THERM-094-006 LEU-COMP-THERM-003-012 LEU-COMP-THERM-033-049 LEU-COMP-THERM-094-007 LEU-COMP-THERM-003-013 LEU-COMP-THERM-033-050 LEU-COMP-THERM-094-008 LEU-COMP-THERM-003-014 LEU-COMP-THERM-033-051 LEU-COMP-THERM-094-009 LEU-COMP-THERM-003-015 LEU-COMP-THERM-033-052 LEU-COMP-THERM-094-010 LEU-COMP-THERM-003-016 LEU-COMP-THERM-034-001 LEU-COMP-THERM-094-011 LEU-COMP-THERM-003-017 LEU-COMP-THERM-034-002 LEU-MISC-THERM-005-001 LEU-COMP-THERM-003-018 LEU-COMP-THERM-034-003 LEU-MISC-THERM-005-002 LEU-COMP-THERM-003-019 LEU-COMP-THERM-034-004 LEU-MISC-THERM-005-003 LEU-COMP-THERM-003-020 LEU-COMP-THERM-034-005 LEU-MISC-THERM-005-004 LEU-COMP-THERM-003-021 LEU-COMP-THERM-034-006 LEU-MISC-THERM-005-005 LEU-COMP-THERM-003-022 LEU-COMP-THERM-034-007 LEU-MISC-THERM-005-006 LEU-COMP-THERM-004-001 LEU-COMP-THERM-034-008 LEU-MISC-THERM-005-007 LEU-COMP-THERM-004-002 LEU-COMP-THERM-034-009 LEU-MISC-THERM-005-008 LEU-COMP-THERM-004-003 LEU-COMP-THERM-034-010 LEU-MISC-THERM-005-009 LEU-COMP-THERM-004-004 LEU-COMP-THERM-034-011 LEU-MISC-THERM-005-010 LEU-COMP-THERM-004-005 LEU-COMP-THERM-034-012 LEU-MISC-THERM-005-011 LEU-COMP-THERM-004-006 LEU-COMP-THERM-034-013 LEU-MISC-THERM-005-012 LEU-COMP-THERM-004-007 LEU-COMP-THERM-034-014 LEU-SOL-THERM-002-001 LEU-COMP-THERM-004-008 LEU-COMP-THERM-034-015 LEU-SOL-THERM-002-002 APPENDIX B LIST OF CRITICAL BENCHMARK EXPERIMENTS CONSIDERED

B-2 List of critical benchmark experiments considered LEU-COMP-THERM-004-009 LEU-COMP-THERM-034-016 LEU-SOL-THERM-002-003 LEU-COMP-THERM-004-010 LEU-COMP-THERM-034-017 LEU-SOL-THERM-003-001 LEU-COMP-THERM-004-011 LEU-COMP-THERM-034-018 LEU-SOL-THERM-003-002 LEU-COMP-THERM-004-012 LEU-COMP-THERM-034-019 LEU-SOL-THERM-003-003 LEU-COMP-THERM-004-013 LEU-COMP-THERM-034-020 LEU-SOL-THERM-003-004 LEU-COMP-THERM-004-014 LEU-COMP-THERM-034-021 LEU-SOL-THERM-003-005 LEU-COMP-THERM-004-015 LEU-COMP-THERM-034-022 LEU-SOL-THERM-003-006 LEU-COMP-THERM-004-016 LEU-COMP-THERM-034-023 LEU-SOL-THERM-003-007 LEU-COMP-THERM-004-017 LEU-COMP-THERM-034-024 LEU-SOL-THERM-003-008 LEU-COMP-THERM-004-018 LEU-COMP-THERM-035-001 LEU-SOL-THERM-003-009 LEU-COMP-THERM-004-019 LEU-COMP-THERM-035-002 LEU-SOL-THERM-004-001 LEU-COMP-THERM-004-020 LEU-COMP-THERM-035-003 LEU-SOL-THERM-004-002 LEU-COMP-THERM-005-001 LEU-COMP-THERM-036-001 LEU-SOL-THERM-004-003 LEU-COMP-THERM-005-002 LEU-COMP-THERM-036-002 LEU-SOL-THERM-004-004 LEU-COMP-THERM-005-003 LEU-COMP-THERM-036-003 LEU-SOL-THERM-004-005 LEU-COMP-THERM-005-004 LEU-COMP-THERM-036-004 LEU-SOL-THERM-004-006 LEU-COMP-THERM-005-005 LEU-COMP-THERM-036-005 LEU-SOL-THERM-004-007 LEU-COMP-THERM-005-006 LEU-COMP-THERM-036-006 MIX-COMP-THERM-001-001 LEU-COMP-THERM-005-007 LEU-COMP-THERM-036-007 MIX-COMP-THERM-001-002 LEU-COMP-THERM-005-008 LEU-COMP-THERM-036-008 MIX-COMP-THERM-001-003 LEU-COMP-THERM-005-009 LEU-COMP-THERM-036-009 MIX-COMP-THERM-001-004 LEU-COMP-THERM-005-010 LEU-COMP-THERM-036-010 MIX-COMP-THERM-002-001S LEU-COMP-THERM-005-011 LEU-COMP-THERM-036-011 MIX-COMP-THERM-002-002S LEU-COMP-THERM-005-012 LEU-COMP-THERM-036-012 MIX-COMP-THERM-002-003S LEU-COMP-THERM-005-013 LEU-COMP-THERM-036-013 MIX-COMP-THERM-002-004S LEU-COMP-THERM-005-014 LEU-COMP-THERM-036-014 MIX-COMP-THERM-002-005S LEU-COMP-THERM-005-015 LEU-COMP-THERM-036-015 MIX-COMP-THERM-002-006S LEU-COMP-THERM-005-016 LEU-COMP-THERM-036-016 MIX-COMP-THERM-003-001 LEU-COMP-THERM-006-001 LEU-COMP-THERM-036-017 MIX-COMP-THERM-003-002 LEU-COMP-THERM-006-002 LEU-COMP-THERM-036-018 MIX-COMP-THERM-003-003 LEU-COMP-THERM-006-003 LEU-COMP-THERM-036-019 MIX-COMP-THERM-003-004 LEU-COMP-THERM-006-004 LEU-COMP-THERM-036-020 MIX-COMP-THERM-003-005 LEU-COMP-THERM-006-005 LEU-COMP-THERM-036-021 MIX-COMP-THERM-003-006 LEU-COMP-THERM-006-006 LEU-COMP-THERM-036-022 MIX-COMP-THERM-004-001 LEU-COMP-THERM-006-007 LEU-COMP-THERM-036-023 MIX-COMP-THERM-004-002 LEU-COMP-THERM-006-008 LEU-COMP-THERM-036-024 MIX-COMP-THERM-004-003 LEU-COMP-THERM-006-009 LEU-COMP-THERM-036-025 MIX-COMP-THERM-004-004 LEU-COMP-THERM-006-010 LEU-COMP-THERM-036-026 MIX-COMP-THERM-004-005 LEU-COMP-THERM-006-011 LEU-COMP-THERM-036-027 MIX-COMP-THERM-004-006 LEU-COMP-THERM-006-012 LEU-COMP-THERM-036-028 MIX-COMP-THERM-004-007 LEU-COMP-THERM-006-013 LEU-COMP-THERM-036-029 MIX-COMP-THERM-004-008 LEU-COMP-THERM-006-014 LEU-COMP-THERM-036-030 MIX-COMP-THERM-004-009 LEU-COMP-THERM-006-015 LEU-COMP-THERM-036-031 MIX-COMP-THERM-004-010 LEU-COMP-THERM-006-016 LEU-COMP-THERM-036-032 MIX-COMP-THERM-004-011 LEU-COMP-THERM-006-017 LEU-COMP-THERM-036-033 MIX-COMP-THERM-005-01 LEU-COMP-THERM-006-018 LEU-COMP-THERM-036-034 MIX-COMP-THERM-005-02 LEU-COMP-THERM-008-001 LEU-COMP-THERM-036-035 MIX-COMP-THERM-005-03 LEU-COMP-THERM-008-002 LEU-COMP-THERM-036-036 MIX-COMP-THERM-005-04 LEU-COMP-THERM-008-003 LEU-COMP-THERM-036-037 MIX-COMP-THERM-005-05 LEU-COMP-THERM-008-004 LEU-COMP-THERM-036-038 MIX-COMP-THERM-005-06

B-3 List of critical benchmark experiments considered LEU-COMP-THERM-008-005 LEU-COMP-THERM-036-039 MIX-COMP-THERM-005-07 LEU-COMP-THERM-008-006 LEU-COMP-THERM-036-040 MIX-COMP-THERM-006-001 LEU-COMP-THERM-008-007 LEU-COMP-THERM-036-041 MIX-COMP-THERM-006-002 LEU-COMP-THERM-008-008 LEU-COMP-THERM-036-042 MIX-COMP-THERM-006-003 LEU-COMP-THERM-008-009 LEU-COMP-THERM-036-043 MIX-COMP-THERM-006-004 LEU-COMP-THERM-008-010 LEU-COMP-THERM-036-044 MIX-COMP-THERM-006-005 LEU-COMP-THERM-008-011 LEU-COMP-THERM-036-045 MIX-COMP-THERM-006-006 LEU-COMP-THERM-008-012 LEU-COMP-THERM-036-046 MIX-COMP-THERM-006-007 LEU-COMP-THERM-008-013 LEU-COMP-THERM-036-047 MIX-COMP-THERM-006-008 LEU-COMP-THERM-008-014 LEU-COMP-THERM-036-048 MIX-COMP-THERM-006-009 LEU-COMP-THERM-008-015 LEU-COMP-THERM-036-049 MIX-COMP-THERM-006-010 LEU-COMP-THERM-008-016 LEU-COMP-THERM-036-050 MIX-COMP-THERM-006-011 LEU-COMP-THERM-008-017 LEU-COMP-THERM-036-051 MIX-COMP-THERM-006-012 LEU-COMP-THERM-009-001 LEU-COMP-THERM-036-052 MIX-COMP-THERM-006-013 LEU-COMP-THERM-009-002 LEU-COMP-THERM-036-053 MIX-COMP-THERM-006-014 LEU-COMP-THERM-009-003 LEU-COMP-THERM-036-054 MIX-COMP-THERM-006-015 LEU-COMP-THERM-009-004 LEU-COMP-THERM-036-055 MIX-COMP-THERM-006-016 LEU-COMP-THERM-009-005 LEU-COMP-THERM-036-056 MIX-COMP-THERM-006-017 LEU-COMP-THERM-009-006 LEU-COMP-THERM-036-057 MIX-COMP-THERM-006-018 LEU-COMP-THERM-009-007 LEU-COMP-THERM-036-058 MIX-COMP-THERM-006-019 LEU-COMP-THERM-009-008 LEU-COMP-THERM-036-059 MIX-COMP-THERM-006-020 LEU-COMP-THERM-009-009 LEU-COMP-THERM-036-060 MIX-COMP-THERM-006-021 LEU-COMP-THERM-009-010 LEU-COMP-THERM-036-061 MIX-COMP-THERM-006-022 LEU-COMP-THERM-009-011 LEU-COMP-THERM-036-062 MIX-COMP-THERM-006-023 LEU-COMP-THERM-009-012 LEU-COMP-THERM-036-063 MIX-COMP-THERM-006-024 LEU-COMP-THERM-009-013 LEU-COMP-THERM-036-064 MIX-COMP-THERM-006-025 LEU-COMP-THERM-009-014 LEU-COMP-THERM-036-065 MIX-COMP-THERM-006-026 LEU-COMP-THERM-009-015 LEU-COMP-THERM-036-066 MIX-COMP-THERM-006-027 LEU-COMP-THERM-009-016 LEU-COMP-THERM-036-067 MIX-COMP-THERM-006-028 LEU-COMP-THERM-009-017 LEU-COMP-THERM-036-068 MIX-COMP-THERM-006-029 LEU-COMP-THERM-009-018 LEU-COMP-THERM-036-069 MIX-COMP-THERM-006-030 LEU-COMP-THERM-009-019 LEU-COMP-THERM-037-001 MIX-COMP-THERM-006-031 LEU-COMP-THERM-009-020 LEU-COMP-THERM-037-002 MIX-COMP-THERM-006-032 LEU-COMP-THERM-009-021 LEU-COMP-THERM-037-003 MIX-COMP-THERM-006-033 LEU-COMP-THERM-009-022 LEU-COMP-THERM-037-004 MIX-COMP-THERM-006-034 LEU-COMP-THERM-009-023 LEU-COMP-THERM-037-005 MIX-COMP-THERM-006-035 LEU-COMP-THERM-009-024 LEU-COMP-THERM-037-006 MIX-COMP-THERM-006-036 LEU-COMP-THERM-009-025 LEU-COMP-THERM-037-007 MIX-COMP-THERM-006-037 LEU-COMP-THERM-009-026 LEU-COMP-THERM-037-008 MIX-COMP-THERM-006-038 LEU-COMP-THERM-009-027 LEU-COMP-THERM-037-009 MIX-COMP-THERM-006-039 LEU-COMP-THERM-010-001 LEU-COMP-THERM-037-010 MIX-COMP-THERM-006-040 LEU-COMP-THERM-010-002 LEU-COMP-THERM-037-011 MIX-COMP-THERM-006-041 LEU-COMP-THERM-010-003 LEU-COMP-THERM-038-001 MIX-COMP-THERM-006-042 LEU-COMP-THERM-010-004 LEU-COMP-THERM-038-002 MIX-COMP-THERM-006-043 LEU-COMP-THERM-010-005 LEU-COMP-THERM-038-003 MIX-COMP-THERM-006-044 LEU-COMP-THERM-010-006 LEU-COMP-THERM-038-004 MIX-COMP-THERM-006-045 LEU-COMP-THERM-010-007 LEU-COMP-THERM-038-005 MIX-COMP-THERM-006-046 LEU-COMP-THERM-010-008 LEU-COMP-THERM-038-006 MIX-COMP-THERM-006-047 LEU-COMP-THERM-010-009 LEU-COMP-THERM-038-007 MIX-COMP-THERM-006-048 LEU-COMP-THERM-010-010 LEU-COMP-THERM-038-008 MIX-COMP-THERM-006-049

B-4 List of critical benchmark experiments considered LEU-COMP-THERM-010-011 LEU-COMP-THERM-038-009 MIX-COMP-THERM-006-050 LEU-COMP-THERM-010-012 LEU-COMP-THERM-038-010 MIX-COMP-THERM-007-001 LEU-COMP-THERM-010-013 LEU-COMP-THERM-038-011 MIX-COMP-THERM-007-002 LEU-COMP-THERM-010-014 LEU-COMP-THERM-038-012 MIX-COMP-THERM-007-003 LEU-COMP-THERM-010-015 LEU-COMP-THERM-038-013 MIX-COMP-THERM-007-004 LEU-COMP-THERM-010-016 LEU-COMP-THERM-038-014 MIX-COMP-THERM-007-005 LEU-COMP-THERM-010-017 LEU-COMP-THERM-039-001 MIX-COMP-THERM-007-006 LEU-COMP-THERM-010-018 LEU-COMP-THERM-039-002 MIX-COMP-THERM-007-007 LEU-COMP-THERM-010-019 LEU-COMP-THERM-039-003 MIX-COMP-THERM-007-008 LEU-COMP-THERM-010-020 LEU-COMP-THERM-039-004 MIX-COMP-THERM-007-009 LEU-COMP-THERM-010-021 LEU-COMP-THERM-039-005 MIX-COMP-THERM-007-010 LEU-COMP-THERM-010-022 LEU-COMP-THERM-039-006 MIX-COMP-THERM-007-011 LEU-COMP-THERM-010-023 LEU-COMP-THERM-039-007 MIX-COMP-THERM-007-012 LEU-COMP-THERM-010-024 LEU-COMP-THERM-039-008 MIX-COMP-THERM-007-013 LEU-COMP-THERM-010-025 LEU-COMP-THERM-039-009 MIX-COMP-THERM-007-014 LEU-COMP-THERM-010-026 LEU-COMP-THERM-039-010 MIX-COMP-THERM-007-015 LEU-COMP-THERM-010-027 LEU-COMP-THERM-039-011 MIX-COMP-THERM-007-016 LEU-COMP-THERM-010-028 LEU-COMP-THERM-039-012 MIX-COMP-THERM-007-017 LEU-COMP-THERM-010-029 LEU-COMP-THERM-039-013 MIX-COMP-THERM-007-018 LEU-COMP-THERM-010-030 LEU-COMP-THERM-039-014 MIX-COMP-THERM-007-019 LEU-COMP-THERM-011-001 LEU-COMP-THERM-039-015 MIX-COMP-THERM-007-020 LEU-COMP-THERM-011-002 LEU-COMP-THERM-039-016 MIX-COMP-THERM-007-021 LEU-COMP-THERM-011-003 LEU-COMP-THERM-039-017 MIX-COMP-THERM-007-022 LEU-COMP-THERM-011-004 LEU-COMP-THERM-040-001 MIX-COMP-THERM-007-023 LEU-COMP-THERM-011-005 LEU-COMP-THERM-040-002 MIX-COMP-THERM-007-024 LEU-COMP-THERM-011-006 LEU-COMP-THERM-040-003 MIX-COMP-THERM-007-025 LEU-COMP-THERM-011-007 LEU-COMP-THERM-040-004 MIX-COMP-THERM-007-026 LEU-COMP-THERM-011-008 LEU-COMP-THERM-040-005 MIX-COMP-THERM-007-027 LEU-COMP-THERM-011-009 LEU-COMP-THERM-040-006 MIX-COMP-THERM-008-001 LEU-COMP-THERM-011-010 LEU-COMP-THERM-040-007 MIX-COMP-THERM-008-002 LEU-COMP-THERM-011-011 LEU-COMP-THERM-040-008 MIX-COMP-THERM-008-003 LEU-COMP-THERM-011-012 LEU-COMP-THERM-040-009 MIX-COMP-THERM-008-004 LEU-COMP-THERM-011-013 LEU-COMP-THERM-040-010 MIX-COMP-THERM-008-005 LEU-COMP-THERM-011-014 LEU-COMP-THERM-042-001 MIX-COMP-THERM-008-006 LEU-COMP-THERM-011-015 LEU-COMP-THERM-042-002 MIX-COMP-THERM-008-007 LEU-COMP-THERM-012-001 LEU-COMP-THERM-042-003 MIX-COMP-THERM-008-008 LEU-COMP-THERM-012-002 LEU-COMP-THERM-042-004 MIX-COMP-THERM-008-009 LEU-COMP-THERM-012-003 LEU-COMP-THERM-042-005 MIX-COMP-THERM-008-010 LEU-COMP-THERM-012-004 LEU-COMP-THERM-042-006 MIX-COMP-THERM-008-011 LEU-COMP-THERM-012-005 LEU-COMP-THERM-042-007 MIX-COMP-THERM-008-012 LEU-COMP-THERM-012-006 LEU-COMP-THERM-043-001 MIX-COMP-THERM-008-013 LEU-COMP-THERM-012-007 LEU-COMP-THERM-043-002 MIX-COMP-THERM-008-014 LEU-COMP-THERM-012-008 LEU-COMP-THERM-043-003 MIX-COMP-THERM-008-015 LEU-COMP-THERM-012-009 LEU-COMP-THERM-043-004 MIX-COMP-THERM-008-016 LEU-COMP-THERM-012-010 LEU-COMP-THERM-043-005 MIX-COMP-THERM-008-017 LEU-COMP-THERM-013-001 LEU-COMP-THERM-043-006 MIX-COMP-THERM-008-018 LEU-COMP-THERM-013-002 LEU-COMP-THERM-043-007 MIX-COMP-THERM-008-019 LEU-COMP-THERM-013-003 LEU-COMP-THERM-043-008 MIX-COMP-THERM-008-020 LEU-COMP-THERM-013-004 LEU-COMP-THERM-043-009 MIX-COMP-THERM-008-021 LEU-COMP-THERM-013-005 LEU-COMP-THERM-044-001 MIX-COMP-THERM-008-022

B-5 List of critical benchmark experiments considered LEU-COMP-THERM-013-006 LEU-COMP-THERM-044-002 MIX-COMP-THERM-008-023 LEU-COMP-THERM-013-007 LEU-COMP-THERM-044-003 MIX-COMP-THERM-008-024 LEU-COMP-THERM-014-001 LEU-COMP-THERM-044-004 MIX-COMP-THERM-008-025 LEU-COMP-THERM-014-002 LEU-COMP-THERM-044-005 MIX-COMP-THERM-008-026 LEU-COMP-THERM-014-005 LEU-COMP-THERM-044-006 MIX-COMP-THERM-008-027 LEU-COMP-THERM-014-006 LEU-COMP-THERM-044-007 MIX-COMP-THERM-008-028 LEU-COMP-THERM-014-007 LEU-COMP-THERM-044-008 MIX-COMP-THERM-009-01 LEU-COMP-THERM-015-001 LEU-COMP-THERM-044-009 MIX-COMP-THERM-009-02 LEU-COMP-THERM-015-002 LEU-COMP-THERM-044-010 MIX-COMP-THERM-009-03 LEU-COMP-THERM-015-003 LEU-COMP-THERM-045-001 MIX-COMP-THERM-009-04 LEU-COMP-THERM-015-004 LEU-COMP-THERM-045-002 MIX-COMP-THERM-009-05 LEU-COMP-THERM-015-005 LEU-COMP-THERM-045-003 MIX-COMP-THERM-009-06 LEU-COMP-THERM-015-006 LEU-COMP-THERM-045-004 MIX-COMP-THERM-011-01 LEU-COMP-THERM-015-007 LEU-COMP-THERM-045-005 MIX-COMP-THERM-011-02 LEU-COMP-THERM-015-008 LEU-COMP-THERM-045-006 MIX-COMP-THERM-011-03 LEU-COMP-THERM-015-009 LEU-COMP-THERM-045-007 MIX-COMP-THERM-011-04 LEU-COMP-THERM-015-010 LEU-COMP-THERM-045-008 MIX-COMP-THERM-011-05 LEU-COMP-THERM-015-011 LEU-COMP-THERM-045-009 MIX-COMP-THERM-011-06 LEU-COMP-THERM-015-012 LEU-COMP-THERM-045-010 MIX-COMP-THERM-012-001 LEU-COMP-THERM-015-013 LEU-COMP-THERM-045-011 MIX-COMP-THERM-012-002 LEU-COMP-THERM-015-014 LEU-COMP-THERM-045-012 MIX-COMP-THERM-012-003 LEU-COMP-THERM-015-015 LEU-COMP-THERM-045-013 MIX-COMP-THERM-012-004 LEU-COMP-THERM-015-016 LEU-COMP-THERM-045-014 MIX-COMP-THERM-012-005 LEU-COMP-THERM-015-017 LEU-COMP-THERM-045-015 MIX-COMP-THERM-012-006 LEU-COMP-THERM-015-018 LEU-COMP-THERM-045-016 MIX-COMP-THERM-012-007 LEU-COMP-THERM-015-019 LEU-COMP-THERM-045-017 MIX-COMP-THERM-012-008 LEU-COMP-THERM-015-020 LEU-COMP-THERM-045-018 MIX-COMP-THERM-012-009 LEU-COMP-THERM-015-021 LEU-COMP-THERM-045-019 MIX-COMP-THERM-012-010 LEU-COMP-THERM-015-022 LEU-COMP-THERM-045-020 MIX-COMP-THERM-012-011 LEU-COMP-THERM-015-023 LEU-COMP-THERM-045-021 MIX-COMP-THERM-012-012 LEU-COMP-THERM-015-024 LEU-COMP-THERM-046-001 MIX-COMP-THERM-012-013 LEU-COMP-THERM-015-025 LEU-COMP-THERM-046-002 MIX-COMP-THERM-012-014 LEU-COMP-THERM-015-026 LEU-COMP-THERM-046-003 MIX-COMP-THERM-012-015 LEU-COMP-THERM-015-027 LEU-COMP-THERM-046-004 MIX-COMP-THERM-012-016 LEU-COMP-THERM-015-028 LEU-COMP-THERM-046-005 MIX-COMP-THERM-012-017 LEU-COMP-THERM-015-029 LEU-COMP-THERM-046-006 MIX-COMP-THERM-012-018 LEU-COMP-THERM-015-030 LEU-COMP-THERM-046-007 MIX-COMP-THERM-012-019 LEU-COMP-THERM-015-031 LEU-COMP-THERM-046-008 MIX-COMP-THERM-012-020 LEU-COMP-THERM-015-032 LEU-COMP-THERM-046-009 MIX-COMP-THERM-012-021 LEU-COMP-THERM-015-033 LEU-COMP-THERM-046-010 MIX-COMP-THERM-012-022 LEU-COMP-THERM-015-034 LEU-COMP-THERM-046-011 MIX-COMP-THERM-012-023 LEU-COMP-THERM-015-035 LEU-COMP-THERM-046-012 MIX-COMP-THERM-012-024 LEU-COMP-THERM-015-036 LEU-COMP-THERM-046-013 MIX-COMP-THERM-012-025 LEU-COMP-THERM-015-037 LEU-COMP-THERM-046-014 MIX-COMP-THERM-012-026 LEU-COMP-THERM-015-038 LEU-COMP-THERM-046-015 MIX-COMP-THERM-012-027 LEU-COMP-THERM-015-039 LEU-COMP-THERM-046-016 MIX-COMP-THERM-012-028 LEU-COMP-THERM-015-040 LEU-COMP-THERM-046-017 MIX-COMP-THERM-012-029 LEU-COMP-THERM-015-041 LEU-COMP-THERM-046-018 MIX-COMP-THERM-012-030 LEU-COMP-THERM-015-042 LEU-COMP-THERM-046-019 MIX-COMP-THERM-012-031 LEU-COMP-THERM-015-043 LEU-COMP-THERM-046-020 MIX-COMP-THERM-012-032

B-6 List of critical benchmark experiments considered LEU-COMP-THERM-015-044 LEU-COMP-THERM-046-021 MIX-COMP-THERM-012-033 LEU-COMP-THERM-015-045 LEU-COMP-THERM-046-022 MIX-COMP-THERM-013-001 LEU-COMP-THERM-015-046 LEU-COMP-THERM-047-001 MIX-COMP-THERM-013-002 LEU-COMP-THERM-015-047 LEU-COMP-THERM-047-002 MIX-COMP-THERM-013-003 LEU-COMP-THERM-015-048 LEU-COMP-THERM-047-003 MIX-COMP-THERM-013-004 LEU-COMP-THERM-015-049 LEU-COMP-THERM-048-001 MIX-COMP-THERM-013-005 LEU-COMP-THERM-015-050 LEU-COMP-THERM-048-002 MIX-COMP-THERM-013-006 LEU-COMP-THERM-015-051 LEU-COMP-THERM-048-003 MIX-COMP-THERM-013-007 LEU-COMP-THERM-015-052 LEU-COMP-THERM-048-004 MIX-COMP-THERM-013-008 LEU-COMP-THERM-015-053 LEU-COMP-THERM-048-005 MIX-COMP-THERM-013-009 LEU-COMP-THERM-015-054 LEU-COMP-THERM-050-001 MIX-COMP-THERM-013-010 LEU-COMP-THERM-015-055 LEU-COMP-THERM-050-002 MIX-COMP-THERM-013-011 LEU-COMP-THERM-015-056 LEU-COMP-THERM-050-003 MIX-COMP-THERM-013-012 LEU-COMP-THERM-015-057 LEU-COMP-THERM-050-004 MIX-COMP-THERM-013-013 LEU-COMP-THERM-015-058 LEU-COMP-THERM-050-005 MIX-COMP-THERM-013-014 LEU-COMP-THERM-015-059 LEU-COMP-THERM-050-006 MIX-COMP-THERM-013-015 LEU-COMP-THERM-015-060 LEU-COMP-THERM-050-007 MIX-COMP-THERM-013-016 LEU-COMP-THERM-015-061 LEU-COMP-THERM-050-008 MIX-COMP-THERM-013-017 LEU-COMP-THERM-015-062 LEU-COMP-THERM-050-009 MIX-COMP-THERM-013-018 LEU-COMP-THERM-015-063 LEU-COMP-THERM-050-010 MIX-COMP-THERM-013-019 LEU-COMP-THERM-015-064 LEU-COMP-THERM-050-011 MIX-COMP-THERM-013-020 LEU-COMP-THERM-015-065 LEU-COMP-THERM-050-012 MIX-COMP-THERM-013-021 LEU-COMP-THERM-015-066 LEU-COMP-THERM-050-013 MIX-COMP-THERM-013-022 LEU-COMP-THERM-015-067 LEU-COMP-THERM-050-014 MIX-COMP-THERM-013-023 LEU-COMP-THERM-015-068 LEU-COMP-THERM-050-015 MIX-COMP-THERM-013-024 LEU-COMP-THERM-015-069 LEU-COMP-THERM-050-016 MIX-COMP-THERM-013-025 LEU-COMP-THERM-015-070 LEU-COMP-THERM-050-017 MIX-COMP-THERM-013-026 LEU-COMP-THERM-015-071 LEU-COMP-THERM-050-018 MIX-COMP-THERM-013-027 LEU-COMP-THERM-015-072 LEU-COMP-THERM-051-001 MIX-COMP-THERM-013-028 LEU-COMP-THERM-015-073 LEU-COMP-THERM-051-002 MIX-COMP-THERM-013-029 LEU-COMP-THERM-015-074 LEU-COMP-THERM-051-003 MIX-COMP-THERM-013-030 LEU-COMP-THERM-015-075 LEU-COMP-THERM-051-004 MIX-COMP-THERM-014-001 LEU-COMP-THERM-015-076 LEU-COMP-THERM-051-005 MIX-COMP-THERM-014-002 LEU-COMP-THERM-015-077 LEU-COMP-THERM-051-006 MIX-COMP-THERM-014-003 LEU-COMP-THERM-015-078 LEU-COMP-THERM-051-007 MIX-COMP-THERM-014-004 LEU-COMP-THERM-015-079 LEU-COMP-THERM-051-008 MIX-COMP-THERM-014-005 LEU-COMP-THERM-015-080 LEU-COMP-THERM-051-009 MIX-COMP-THERM-014-006 LEU-COMP-THERM-015-081 LEU-COMP-THERM-051-010 MIX-COMP-THERM-014-007 LEU-COMP-THERM-015-082 LEU-COMP-THERM-051-011 MIX-COMP-THERM-014-008 LEU-COMP-THERM-015-083 LEU-COMP-THERM-051-012 MIX-COMP-THERM-014-009 LEU-COMP-THERM-015-084 LEU-COMP-THERM-051-013 MIX-COMP-THERM-014-010 LEU-COMP-THERM-015-085 LEU-COMP-THERM-051-014 MIX-COMP-THERM-014-011 LEU-COMP-THERM-015-086 LEU-COMP-THERM-051-015 MIX-COMP-THERM-014-012 LEU-COMP-THERM-015-087 LEU-COMP-THERM-051-016 MIX-COMP-THERM-014-013 LEU-COMP-THERM-015-088 LEU-COMP-THERM-051-017 MIX-COMP-THERM-014-014 LEU-COMP-THERM-015-089 LEU-COMP-THERM-051-018 MIX-COMP-THERM-014-015 LEU-COMP-THERM-015-090 LEU-COMP-THERM-051-019 MIX-COMP-THERM-014-016 LEU-COMP-THERM-015-091 LEU-COMP-THERM-052-001 MIX-COMP-THERM-014-017 LEU-COMP-THERM-015-092 LEU-COMP-THERM-052-002 MIX-COMP-THERM-014-018 LEU-COMP-THERM-015-093 LEU-COMP-THERM-052-003 MIX-COMP-THERM-014-019

B-7 List of critical benchmark experiments considered LEU-COMP-THERM-015-094 LEU-COMP-THERM-052-004 MIX-COMP-THERM-014-020 LEU-COMP-THERM-015-095 LEU-COMP-THERM-052-005 MIX-COMP-THERM-014-021 LEU-COMP-THERM-015-096 LEU-COMP-THERM-052-006 MIX-COMP-THERM-014-022 LEU-COMP-THERM-015-097 LEU-COMP-THERM-053-001 MIX-COMP-THERM-016-001 LEU-COMP-THERM-015-098 LEU-COMP-THERM-053-002 MIX-COMP-THERM-016-002 LEU-COMP-THERM-015-099 LEU-COMP-THERM-053-003 MIX-COMP-THERM-016-003 LEU-COMP-THERM-015-100 LEU-COMP-THERM-053-004 MIX-COMP-THERM-016-004 LEU-COMP-THERM-015-101 LEU-COMP-THERM-053-005 MIX-COMP-THERM-016-005 LEU-COMP-THERM-015-102 LEU-COMP-THERM-053-006 MIX-COMP-THERM-016-006 LEU-COMP-THERM-015-103 LEU-COMP-THERM-053-007 MIX-COMP-THERM-016-007 LEU-COMP-THERM-015-104 LEU-COMP-THERM-053-008 MIX-COMP-THERM-016-008 LEU-COMP-THERM-015-105 LEU-COMP-THERM-053-009 MIX-COMP-THERM-016-009 LEU-COMP-THERM-015-106 LEU-COMP-THERM-053-010 MIX-COMP-THERM-016-010 LEU-COMP-THERM-015-107 LEU-COMP-THERM-053-011 MIX-COMP-THERM-016-011 LEU-COMP-THERM-015-108 LEU-COMP-THERM-053-012 MIX-COMP-THERM-016-012 LEU-COMP-THERM-015-109 LEU-COMP-THERM-053-013 MIX-COMP-THERM-016-013 LEU-COMP-THERM-015-110 LEU-COMP-THERM-053-014 MIX-COMP-THERM-016-014 LEU-COMP-THERM-015-111 LEU-COMP-THERM-054-001 MIX-COMP-THERM-016-015 LEU-COMP-THERM-015-112 LEU-COMP-THERM-054-002 MIX-COMP-THERM-016-016 LEU-COMP-THERM-015-113 LEU-COMP-THERM-054-003 MIX-COMP-THERM-016-017 LEU-COMP-THERM-015-114 LEU-COMP-THERM-054-004 MIX-COMP-THERM-016-018 LEU-COMP-THERM-015-115 LEU-COMP-THERM-054-005 MIX-COMP-THERM-016-019 LEU-COMP-THERM-015-116 LEU-COMP-THERM-054-006 MIX-COMP-THERM-017-001 LEU-COMP-THERM-015-117 LEU-COMP-THERM-054-007 MIX-COMP-THERM-017-002 LEU-COMP-THERM-015-118 LEU-COMP-THERM-054-008 MIX-COMP-THERM-017-003 LEU-COMP-THERM-015-119 LEU-COMP-THERM-055-001 MIX-COMP-THERM-017-004 LEU-COMP-THERM-015-120 LEU-COMP-THERM-055-002 MIX-COMP-THERM-017-005 LEU-COMP-THERM-015-121 LEU-COMP-THERM-057-001 MIX-COMP-THERM-017-006 LEU-COMP-THERM-015-122 LEU-COMP-THERM-057-002 MIX-COMP-THERM-017-007 LEU-COMP-THERM-015-123 LEU-COMP-THERM-057-003 MIX-COMP-THERM-017-008 LEU-COMP-THERM-015-124 LEU-COMP-THERM-057-004 MIX-COMP-THERM-017-009 LEU-COMP-THERM-015-125 LEU-COMP-THERM-057-005 MIX-COMP-THERM-017-010 LEU-COMP-THERM-015-126 LEU-COMP-THERM-057-006 MIX-COMP-THERM-017-011 LEU-COMP-THERM-015-127 LEU-COMP-THERM-057-007 MIX-COMP-THERM-017-012 LEU-COMP-THERM-015-128 LEU-COMP-THERM-057-008 MIX-COMP-THERM-017-013 LEU-COMP-THERM-015-129 LEU-COMP-THERM-057-009 MIX-COMP-THERM-017-014 LEU-COMP-THERM-015-130 LEU-COMP-THERM-057-010 MIX-COMP-THERM-017-015 LEU-COMP-THERM-015-131 LEU-COMP-THERM-057-011 MIX-COMP-THERM-017-016 LEU-COMP-THERM-015-132 LEU-COMP-THERM-057-012 MIX-COMP-THERM-017-017 LEU-COMP-THERM-015-133 LEU-COMP-THERM-057-013 MIX-COMP-THERM-017-018 LEU-COMP-THERM-015-134 LEU-COMP-THERM-057-014 MIX-COMP-THERM-017-019 LEU-COMP-THERM-015-135 LEU-COMP-THERM-057-015 HTC1_001 LEU-COMP-THERM-015-136 LEU-COMP-THERM-057-016 HTC1_002 LEU-COMP-THERM-015-137 LEU-COMP-THERM-057-017 HTC1_003 LEU-COMP-THERM-015-138 LEU-COMP-THERM-057-018 HTC1_004 LEU-COMP-THERM-015-139 LEU-COMP-THERM-057-019 HTC1_005 LEU-COMP-THERM-015-140 LEU-COMP-THERM-057-020 HTC1_006 LEU-COMP-THERM-015-141 LEU-COMP-THERM-057-021 HTC1_007 LEU-COMP-THERM-015-142 LEU-COMP-THERM-057-022 HTC1_008 LEU-COMP-THERM-015-143 LEU-COMP-THERM-057-023 HTC1_009

B-8 List of critical benchmark experiments considered LEU-COMP-THERM-015-144 LEU-COMP-THERM-057-024 HTC1_010 LEU-COMP-THERM-015-145 LEU-COMP-THERM-057-025 HTC1_011 LEU-COMP-THERM-015-146 LEU-COMP-THERM-057-026 HTC1_012 LEU-COMP-THERM-015-147 LEU-COMP-THERM-057-027 HTC1_013 LEU-COMP-THERM-015-148 LEU-COMP-THERM-057-028 HTC1_014 LEU-COMP-THERM-015-149 LEU-COMP-THERM-057-029 HTC1_015 LEU-COMP-THERM-015-150 LEU-COMP-THERM-057-030 HTC1_016 LEU-COMP-THERM-015-151 LEU-COMP-THERM-057-031 HTC1_017 LEU-COMP-THERM-015-152 LEU-COMP-THERM-057-032 HTC1_018 LEU-COMP-THERM-015-153 LEU-COMP-THERM-057-033 HTC2B_001 LEU-COMP-THERM-015-154 LEU-COMP-THERM-057-034 HTC2B_002 LEU-COMP-THERM-015-155 LEU-COMP-THERM-057-035 HTC2B_003 LEU-COMP-THERM-015-156 LEU-COMP-THERM-057-036 HTC2B_004 LEU-COMP-THERM-015-157 LEU-COMP-THERM-058-001 HTC2B_005 LEU-COMP-THERM-015-158 LEU-COMP-THERM-058-002 HTC2B_006 LEU-COMP-THERM-015-159 LEU-COMP-THERM-058-003 HTC2B_007 LEU-COMP-THERM-015-160 LEU-COMP-THERM-058-004 HTC2B_008 LEU-COMP-THERM-015-161 LEU-COMP-THERM-058-005 HTC2B_009 LEU-COMP-THERM-015-162 LEU-COMP-THERM-058-006 HTC2B_010 LEU-COMP-THERM-015-163 LEU-COMP-THERM-058-007 HTC2B_011 LEU-COMP-THERM-015-164 LEU-COMP-THERM-058-008 HTC2B_012 LEU-COMP-THERM-015-165 LEU-COMP-THERM-058-009 HTC2B_014 LEU-COMP-THERM-016-001 LEU-COMP-THERM-061-001 HTC2B_015 LEU-COMP-THERM-016-002 LEU-COMP-THERM-061-002 HTC2B_016 LEU-COMP-THERM-016-003 LEU-COMP-THERM-061-003 HTC2B_017 LEU-COMP-THERM-016-004 LEU-COMP-THERM-061-004 HTC2B_018 LEU-COMP-THERM-016-005 LEU-COMP-THERM-061-005 HTC2B_019 LEU-COMP-THERM-016-006 LEU-COMP-THERM-061-006 HTC2B_020 LEU-COMP-THERM-016-007 LEU-COMP-THERM-061-007 HTC2B_021 LEU-COMP-THERM-016-008 LEU-COMP-THERM-061-008 HTC2G_001 LEU-COMP-THERM-016-009 LEU-COMP-THERM-061-009 HTC2G_002 LEU-COMP-THERM-016-010 LEU-COMP-THERM-061-010 HTC2G_003 LEU-COMP-THERM-016-011 LEU-COMP-THERM-062-001 HTC2G_004 LEU-COMP-THERM-016-012 LEU-COMP-THERM-062-002 HTC2G_005 LEU-COMP-THERM-016-013 LEU-COMP-THERM-062-003 HTC2G_006 LEU-COMP-THERM-016-014 LEU-COMP-THERM-062-004 HTC2G_007 LEU-COMP-THERM-016-015 LEU-COMP-THERM-062-005 HTC2G_008 LEU-COMP-THERM-016-016 LEU-COMP-THERM-062-006 HTC2G_009 LEU-COMP-THERM-016-017 LEU-COMP-THERM-062-007 HTC2G_010 LEU-COMP-THERM-016-018 LEU-COMP-THERM-062-008 HTC2G_011 LEU-COMP-THERM-016-019 LEU-COMP-THERM-062-009 HTC2G_012 LEU-COMP-THERM-016-020 LEU-COMP-THERM-062-010 HTC2G_013 LEU-COMP-THERM-016-021 LEU-COMP-THERM-062-011 HTC2G_014 LEU-COMP-THERM-016-022 LEU-COMP-THERM-062-012 HTC2G_015 LEU-COMP-THERM-016-023 LEU-COMP-THERM-062-013 HTC2G_016 LEU-COMP-THERM-016-024 LEU-COMP-THERM-062-014 HTC2G_017 LEU-COMP-THERM-016-025 LEU-COMP-THERM-062-015 HTC2G_018 LEU-COMP-THERM-016-026 LEU-COMP-THERM-065-001 HTC2G_019 LEU-COMP-THERM-016-027 LEU-COMP-THERM-065-002 HTC2G_020 LEU-COMP-THERM-016-028 LEU-COMP-THERM-065-003 HTC3_001

B-9 List of critical benchmark experiments considered LEU-COMP-THERM-016-029 LEU-COMP-THERM-065-004 HTC3_002 LEU-COMP-THERM-016-030 LEU-COMP-THERM-065-005 HTC3_003 LEU-COMP-THERM-016-031 LEU-COMP-THERM-065-006 HTC3_004 LEU-COMP-THERM-016-032 LEU-COMP-THERM-065-007 HTC3_005 LEU-COMP-THERM-017-001 LEU-COMP-THERM-065-008 HTC3_006 LEU-COMP-THERM-017-002 LEU-COMP-THERM-065-009 HTC3_007 LEU-COMP-THERM-017-003 LEU-COMP-THERM-065-010 HTC3_008 LEU-COMP-THERM-017-004 LEU-COMP-THERM-065-011 HTC3_009 LEU-COMP-THERM-017-005 LEU-COMP-THERM-065-012 HTC3_010 LEU-COMP-THERM-017-006 LEU-COMP-THERM-065-013 HTC3_011 LEU-COMP-THERM-017-007 LEU-COMP-THERM-065-014 HTC3_012 LEU-COMP-THERM-017-008 LEU-COMP-THERM-065-015 HTC3_013 LEU-COMP-THERM-017-009 LEU-COMP-THERM-065-016 HTC3_014 LEU-COMP-THERM-017-010 LEU-COMP-THERM-065-017 HTC3_015 LEU-COMP-THERM-017-011 LEU-COMP-THERM-066-004 HTC3_016 LEU-COMP-THERM-017-012 LEU-COMP-THERM-066-005 HTC3_017 LEU-COMP-THERM-017-013 LEU-COMP-THERM-066-006 HTC3_018 LEU-COMP-THERM-017-014 LEU-COMP-THERM-066-007 HTC3_019 LEU-COMP-THERM-017-015 LEU-COMP-THERM-066-008 HTC3_020 LEU-COMP-THERM-017-016 LEU-COMP-THERM-066-009 HTC3_021 LEU-COMP-THERM-017-017 LEU-COMP-THERM-066-010 HTC3_022 LEU-COMP-THERM-017-018 LEU-COMP-THERM-069-001 HTC3_023 LEU-COMP-THERM-017-019 LEU-COMP-THERM-069-002 HTC3_024 LEU-COMP-THERM-017-020 LEU-COMP-THERM-069-003 HTC3_025 LEU-COMP-THERM-017-021 LEU-COMP-THERM-069-004 HTC3_026 LEU-COMP-THERM-017-022 LEU-COMP-THERM-069-005 HTC4FE_001 LEU-COMP-THERM-017-023 LEU-COMP-THERM-070-001 HTC4FE_002 LEU-COMP-THERM-017-024 LEU-COMP-THERM-070-002 HTC4FE_003 LEU-COMP-THERM-017-025 LEU-COMP-THERM-070-003 HTC4FE_004 LEU-COMP-THERM-017-026 LEU-COMP-THERM-070-004 HTC4FE_005 LEU-COMP-THERM-017-027 LEU-COMP-THERM-070-005 HTC4FE_006 LEU-COMP-THERM-017-028 LEU-COMP-THERM-070-006 HTC4FE_007 LEU-COMP-THERM-017-029 LEU-COMP-THERM-070-007 HTC4FE_008 LEU-COMP-THERM-018-001 LEU-COMP-THERM-070-008 HTC4FE_009 LEU-COMP-THERM-020-001 LEU-COMP-THERM-070-009 HTC4FE_010 LEU-COMP-THERM-020-002 LEU-COMP-THERM-070-010 HTC4FE_011 LEU-COMP-THERM-020-003 LEU-COMP-THERM-070-011 HTC4FE_012 LEU-COMP-THERM-020-004 LEU-COMP-THERM-070-012 HTC4FE_013 LEU-COMP-THERM-020-005 LEU-COMP-THERM-071-001 HTC4FE_014 LEU-COMP-THERM-020-006 LEU-COMP-THERM-071-002 HTC4FE_015 LEU-COMP-THERM-020-007 LEU-COMP-THERM-071-003 HTC4FE_016 LEU-COMP-THERM-021-001 LEU-COMP-THERM-071-004 HTC4FE_017 LEU-COMP-THERM-021-002 LEU-COMP-THERM-072-001 HTC4FE_018 LEU-COMP-THERM-021-003 LEU-COMP-THERM-072-002 HTC4FE_019 LEU-COMP-THERM-021-004 LEU-COMP-THERM-072-003 HTC4FE_020 LEU-COMP-THERM-021-005 LEU-COMP-THERM-072-004 HTC4FE_021 LEU-COMP-THERM-021-006 LEU-COMP-THERM-072-005 HTC4FE_022 LEU-COMP-THERM-022-001 LEU-COMP-THERM-072-006 HTC4FE_023 LEU-COMP-THERM-022-002 LEU-COMP-THERM-072-007 HTC4FE_024 LEU-COMP-THERM-022-003 LEU-COMP-THERM-072-008 HTC4FE_025

B-10 List of critical benchmark experiments considered LEU-COMP-THERM-022-004 LEU-COMP-THERM-072-009 HTC4FE_026 LEU-COMP-THERM-022-005 LEU-COMP-THERM-073-001 HTC4FE_027 LEU-COMP-THERM-022-006 LEU-COMP-THERM-073-002 HTC4FE_028 LEU-COMP-THERM-022-007 LEU-COMP-THERM-073-003 HTC4FE_029 LEU-COMP-THERM-023-001 LEU-COMP-THERM-073-004 HTC4FE_030 LEU-COMP-THERM-023-002 LEU-COMP-THERM-073-005 HTC4FE_031 LEU-COMP-THERM-023-003 LEU-COMP-THERM-073-006 HTC4FE_032 LEU-COMP-THERM-023-004 LEU-COMP-THERM-073-007 HTC4FE_033 LEU-COMP-THERM-023-005 LEU-COMP-THERM-073-008 HTC4PB_001 LEU-COMP-THERM-023-006 LEU-COMP-THERM-073-009 HTC4PB_002 LEU-COMP-THERM-024-001 LEU-COMP-THERM-073-010 HTC4PB_003 LEU-COMP-THERM-024-002 LEU-COMP-THERM-073-011 HTC4PB_004 LEU-COMP-THERM-026-001 LEU-COMP-THERM-073-012 HTC4PB_005 LEU-COMP-THERM-026-002 LEU-COMP-THERM-073-013 HTC4PB_006 LEU-COMP-THERM-026-003 LEU-COMP-THERM-073-014 HTC4PB_007 LEU-COMP-THERM-026-004 LEU-COMP-THERM-074-001 HTC4PB_008 LEU-COMP-THERM-026-005 LEU-COMP-THERM-074-002 HTC4PB_009 LEU-COMP-THERM-026-006 LEU-COMP-THERM-074-003 HTC4PB_010 LEU-COMP-THERM-027-001 LEU-COMP-THERM-074-004 HTC4PB_011 LEU-COMP-THERM-027-002 LEU-COMP-THERM-075-001 HTC4PB_012 LEU-COMP-THERM-027-003 LEU-COMP-THERM-075-002 HTC4PB_013 LEU-COMP-THERM-027-004 LEU-COMP-THERM-075-003 HTC4PB_014 LEU-COMP-THERM-028-001 LEU-COMP-THERM-075-004 HTC4PB_015 LEU-COMP-THERM-028-002 LEU-COMP-THERM-075-005 HTC4PB_016 LEU-COMP-THERM-028-003 LEU-COMP-THERM-075-006 HTC4PB_017 LEU-COMP-THERM-028-004 LEU-COMP-THERM-076-001 HTC4PB_018 LEU-COMP-THERM-028-005 LEU-COMP-THERM-076-002 HTC4PB_019 LEU-COMP-THERM-028-006 LEU-COMP-THERM-076-003 HTC4PB_020 LEU-COMP-THERM-028-007 LEU-COMP-THERM-076-004 HTC4PB_021 LEU-COMP-THERM-028-008 LEU-COMP-THERM-076-005 HTC4PB_022 LEU-COMP-THERM-028-009 LEU-COMP-THERM-076-006 HTC4PB_023 LEU-COMP-THERM-028-010 LEU-COMP-THERM-076-007 HTC4PB_024 LEU-COMP-THERM-028-011 LEU-COMP-THERM-077-001 HTC4PB_025 LEU-COMP-THERM-028-012 LEU-COMP-THERM-077-002 HTC4PB_026 LEU-COMP-THERM-028-013 LEU-COMP-THERM-077-003 HTC4PB_027 LEU-COMP-THERM-028-014 LEU-COMP-THERM-077-004 HTC4PB_028 LEU-COMP-THERM-028-015 LEU-COMP-THERM-077-005 HTC4PB_029 LEU-COMP-THERM-028-016 LEU-COMP-THERM-078-001 HTC4PB_030 LEU-COMP-THERM-028-017 LEU-COMP-THERM-078-002 HTC4PB_031 LEU-COMP-THERM-028-018 LEU-COMP-THERM-078-003 HTC4PB_032 LEU-COMP-THERM-028-019 LEU-COMP-THERM-078-004 HTC4PB_033 LEU-COMP-THERM-028-020 LEU-COMP-THERM-078-005 HTC4PB_034 LEU-COMP-THERM-029-001 LEU-COMP-THERM-078-006 HTC4PB_035 LEU-COMP-THERM-029-002 LEU-COMP-THERM-078-007 HTC4PB_036 LEU-COMP-THERM-029-003 LEU-COMP-THERM-078-008 HTC4PB_037 LEU-COMP-THERM-029-004 LEU-COMP-THERM-078-009 HTC4PB_038 LEU-COMP-THERM-029-005 LEU-COMP-THERM-078-010 MIX-SOL-THERM-001-001 LEU-COMP-THERM-029-006 LEU-COMP-THERM-078-011 MIX-SOL-THERM-001-002 LEU-COMP-THERM-029-007 LEU-COMP-THERM-078-012 MIX-SOL-THERM-001-003 LEU-COMP-THERM-029-008 LEU-COMP-THERM-078-013 MIX-SOL-THERM-001-004

B-11 List of critical benchmark experiments considered LEU-COMP-THERM-029-009 LEU-COMP-THERM-078-014 MIX-SOL-THERM-001-005 LEU-COMP-THERM-029-010 LEU-COMP-THERM-078-015 MIX-SOL-THERM-001-006 LEU-COMP-THERM-029-011 LEU-COMP-THERM-079-001 MIX-SOL-THERM-001-007 LEU-COMP-THERM-029-012 LEU-COMP-THERM-079-002 MIX-SOL-THERM-001-008 LEU-COMP-THERM-030-001 LEU-COMP-THERM-079-003 MIX-SOL-THERM-001-009 LEU-COMP-THERM-030-002 LEU-COMP-THERM-079-004 MIX-SOL-THERM-001-010 LEU-COMP-THERM-030-003 LEU-COMP-THERM-079-005 MIX-SOL-THERM-001-011 LEU-COMP-THERM-030-004 LEU-COMP-THERM-079-006 MIX-SOL-THERM-001-012 LEU-COMP-THERM-030-005 LEU-COMP-THERM-079-007 MIX-SOL-THERM-001-013 LEU-COMP-THERM-030-006 LEU-COMP-THERM-079-008 MIX-SOL-THERM-002-001 LEU-COMP-THERM-030-007 LEU-COMP-THERM-079-009 MIX-SOL-THERM-002-002 LEU-COMP-THERM-030-008 LEU-COMP-THERM-079-010 MIX-SOL-THERM-002-003 LEU-COMP-THERM-030-009 LEU-COMP-THERM-080-001 MIX-SOL-THERM-003-001 LEU-COMP-THERM-030-010 LEU-COMP-THERM-080-002 MIX-SOL-THERM-003-002 LEU-COMP-THERM-030-011 LEU-COMP-THERM-080-003 MIX-SOL-THERM-003-003 LEU-COMP-THERM-030-012 LEU-COMP-THERM-080-004 MIX-SOL-THERM-003-004 LEU-COMP-THERM-031-001 LEU-COMP-THERM-080-005 MIX-SOL-THERM-003-005 LEU-COMP-THERM-031-002 LEU-COMP-THERM-080-006 MIX-SOL-THERM-003-006 LEU-COMP-THERM-031-003 LEU-COMP-THERM-080-007 MIX-SOL-THERM-003-007 LEU-COMP-THERM-031-004 LEU-COMP-THERM-080-008 MIX-SOL-THERM-003-008 LEU-COMP-THERM-031-005 LEU-COMP-THERM-080-009 MIX-SOL-THERM-003-009 LEU-COMP-THERM-031-006 LEU-COMP-THERM-080-010 MIX-SOL-THERM-003-010 LEU-COMP-THERM-032-001 LEU-COMP-THERM-080-011 MIX-SOL-THERM-004-001 LEU-COMP-THERM-032-002 LEU-COMP-THERM-082-002 MIX-SOL-THERM-004-002 LEU-COMP-THERM-032-003 LEU-COMP-THERM-082-003 MIX-SOL-THERM-004-003 LEU-COMP-THERM-032-004 LEU-COMP-THERM-082-004 MIX-SOL-THERM-004-004 LEU-COMP-THERM-032-005 LEU-COMP-THERM-082-005 MIX-SOL-THERM-004-005 LEU-COMP-THERM-032-006 LEU-COMP-THERM-082-006 MIX-SOL-THERM-004-006 LEU-COMP-THERM-032-007 LEU-COMP-THERM-083-001 MIX-SOL-THERM-004-007 LEU-COMP-THERM-032-008 LEU-COMP-THERM-083-002 MIX-SOL-THERM-004-008 LEU-COMP-THERM-032-009 LEU-COMP-THERM-083-003 MIX-SOL-THERM-004-009 LEU-COMP-THERM-033-001 LEU-COMP-THERM-084-001 MIX-SOL-THERM-005-001 LEU-COMP-THERM-033-002 LEU-COMP-THERM-085-001 MIX-SOL-THERM-005-002 LEU-COMP-THERM-033-003 LEU-COMP-THERM-085-002 MIX-SOL-THERM-005-003 LEU-COMP-THERM-033-004 LEU-COMP-THERM-085-003 MIX-SOL-THERM-005-004 LEU-COMP-THERM-033-005 LEU-COMP-THERM-085-004 MIX-SOL-THERM-005-005 LEU-COMP-THERM-033-006 LEU-COMP-THERM-085-005 MIX-SOL-THERM-005-006 LEU-COMP-THERM-033-007 LEU-COMP-THERM-085-006 MIX-SOL-THERM-005-007 LEU-COMP-THERM-033-008 LEU-COMP-THERM-085-007 MIX-SOL-THERM-007-001 LEU-COMP-THERM-033-009 LEU-COMP-THERM-085-008 MIX-SOL-THERM-007-002 LEU-COMP-THERM-033-010 LEU-COMP-THERM-085-009 MIX-SOL-THERM-007-003 LEU-COMP-THERM-033-011 LEU-COMP-THERM-085-010 MIX-SOL-THERM-007-004 LEU-COMP-THERM-033-012 LEU-COMP-THERM-085-011 MIX-SOL-THERM-007-005 LEU-COMP-THERM-033-013 LEU-COMP-THERM-085-012 MIX-SOL-THERM-007-006 LEU-COMP-THERM-033-014 LEU-COMP-THERM-085-013 MIX-SOL-THERM-007-007 LEU-COMP-THERM-033-015 LEU-COMP-THERM-089-001 MIX-SOL-THERM-010-001 LEU-COMP-THERM-033-016 LEU-COMP-THERM-089-002 MIX-SOL-THERM-010-002 LEU-COMP-THERM-033-017 LEU-COMP-THERM-089-003 MIX-SOL-THERM-010-003 LEU-COMP-THERM-033-018 LEU-COMP-THERM-089-004 MIX-SOL-THERM-010-004 LEU-COMP-THERM-033-019 LEU-COMP-THERM-090-001 MIX-SOL-THERM-010-005

B-12 List of critical benchmark experiments considered LEU-COMP-THERM-033-020 LEU-COMP-THERM-090-002 MIX-SOL-THERM-010-006 LEU-COMP-THERM-033-021 LEU-COMP-THERM-090-003 MIX-SOL-THERM-010-007 LEU-COMP-THERM-033-022 LEU-COMP-THERM-090-004 MIX-SOL-THERM-010-008 LEU-COMP-THERM-033-023 LEU-COMP-THERM-090-005 MIX-SOL-THERM-010-009 LEU-COMP-THERM-033-024 LEU-COMP-THERM-090-006

APPENDIX C EXPERIMENTS WITH CK VALUES OF AT LEAST 0.8

C-1 This appendix provides the ck values of at least 0.8 for critical experiments compared to each of the 4 applications presented in Section 5. Table C-1 contains results for the GBC-68 cask containing fuel assemblies with a burnup of 25 GWd/MTU modeled with the AO isotope set. The results for the same fuel modeled with the AFP isotope set is provided in Table C-2. Table C-3 and Table C-4 contain the results for a burnup of 50 GWd/MTU modeled with the AO isotope set and the AFP isotope set, respectively.

Table C-1 ck Values of at Least 0.8 for Application 1 Experiment ck Experiment ck LEU-COMP-THERM-008-001 0.83910 MIX-HTC3_001 0.82240 LEU-COMP-THERM-008-002 0.84590 MIX-HTC3_002 0.82830 LEU-COMP-THERM-008-003 0.84660 MIX-HTC3_003 0.83030 LEU-COMP-THERM-008-004 0.84770 MIX-HTC3_004 0.82590 LEU-COMP-THERM-008-005 0.84740 MIX-HTC3_005 0.83060 LEU-COMP-THERM-008-006 0.85060 MIX-HTC3_006 0.83430 LEU-COMP-THERM-008-007 0.84940 MIX-HTC3_007 0.82730 LEU-COMP-THERM-008-008 0.85740 MIX-HTC3_008 0.83640 LEU-COMP-THERM-008-009 0.85740 MIX-HTC3_009 0.83360 LEU-COMP-THERM-008-010 0.84600 MIX-HTC3_010 0.83300 LEU-COMP-THERM-008-011 0.84560 MIX-HTC3_011 0.83270 LEU-COMP-THERM-008-012 0.84620 MIX-HTC3_016 0.80270 LEU-COMP-THERM-008-013 0.84630 MIX-HTC3_017 0.80830 LEU-COMP-THERM-008-014 0.84390 MIX-HTC3_018 0.81540 LEU-COMP-THERM-008-015 0.84500 MIX-HTC3_019 0.81130 LEU-COMP-THERM-008-016 0.85040 MIX-HTC3_020 0.81250 LEU-COMP-THERM-008-017 0.85770 MIX-HTC3_025 0.80840 LEU-COMP-THERM-011-002 0.84700 MIX-HTC4FE_001 0.83900 LEU-COMP-THERM-011-003 0.85410 MIX-HTC4FE_002 0.83800 LEU-COMP-THERM-011-004 0.85510 MIX-HTC4FE_003 0.83860 LEU-COMP-THERM-011-005 0.85380 MIX-HTC4FE_004 0.83700 LEU-COMP-THERM-011-006 0.85330 MIX-HTC4FE_005 0.83590 LEU-COMP-THERM-011-007 0.85080 MIX-HTC4FE_006 0.83160 LEU-COMP-THERM-011-008 0.84810 MIX-HTC4FE_007 0.82970 LEU-COMP-THERM-011-009 0.84640 MIX-HTC4FE_008 0.83680 LEU-COMP-THERM-011-010 0.85090 MIX-HTC4FE_009 0.83660 LEU-COMP-THERM-011-011 0.84670 MIX-HTC4FE_010 0.83550 LEU-COMP-THERM-011-012 0.84090 MIX-HTC4FE_011 0.83520 LEU-COMP-THERM-011-013 0.83810 MIX-HTC4FE_012 0.84300 LEU-COMP-THERM-011-014 0.83150 MIX-HTC4FE_013 0.84340 LEU-COMP-THERM-011-015 0.82120 MIX-HTC4FE_014 0.84220 LEU-COMP-THERM-014-005 0.82880 MIX-HTC4FE_015 0.83660 LEU-COMP-THERM-015-151 0.81620 MIX-HTC4FE_016 0.83830 LEU-COMP-THERM-015-158 0.81130 MIX-HTC4FE_017 0.84400 LEU-COMP-THERM-017-004 0.80260 MIX-HTC4FE_018 0.84100 LEU-COMP-THERM-017-026 0.83020 MIX-HTC4FE_019 0.83730 LEU-COMP-THERM-017-027 0.81680 MIX-HTC4FE_020 0.83430 LEU-COMP-THERM-017-028 0.80900 MIX-HTC4FE_021 0.83610 LEU-COMP-THERM-017-029 0.80200 MIX-HTC4FE_022 0.83600 LEU-COMP-THERM-042-002 0.80540 MIX-HTC4FE_023 0.83630 LEU-COMP-THERM-042-003 0.81190 MIX-HTC4FE_024 0.83390 APPENDIX C EXPERIMENTS WITH CK VALUES OF AT LEAST 0.8

C-2 Experiment ck Experiment ck LEU-COMP-THERM-042-004 0.81110 MIX-HTC4FE_025 0.83150 LEU-COMP-THERM-042-005 0.81100 MIX-HTC4FE_026 0.82980 LEU-COMP-THERM-042-007 0.80460 MIX-HTC4FE_027 0.80190 LEU-COMP-THERM-047-001 0.84730 MIX-HTC4FE_028 0.80540 LEU-COMP-THERM-051-001 0.83620 MIX-HTC4FE_029 0.80960 LEU-COMP-THERM-051-002 0.86660 MIX-HTC4FE_030 0.81880 LEU-COMP-THERM-051-003 0.86480 MIX-HTC4FE_031 0.81820 LEU-COMP-THERM-051-004 0.86440 MIX-HTC4FE_032 0.81220 LEU-COMP-THERM-051-005 0.86120 MIX-HTC4FE_033 0.80420 LEU-COMP-THERM-051-006 0.86100 MIX-HTC4PB_002 0.81030 LEU-COMP-THERM-051-007 0.86260 MIX-HTC4PB_003 0.81060 LEU-COMP-THERM-051-008 0.85560 MIX-HTC4PB_004 0.81000 LEU-COMP-THERM-051-009 0.86010 MIX-HTC4PB_005 0.80970 LEU-COMP-THERM-051-010 0.84760 MIX-HTC4PB_006 0.84550 LEU-COMP-THERM-051-011 0.84800 MIX-HTC4PB_007 0.84470 LEU-COMP-THERM-051-012 0.84850 MIX-HTC4PB_008 0.84590 LEU-COMP-THERM-051-013 0.84790 MIX-HTC4PB_009 0.84520 LEU-COMP-THERM-051-014*

0.84600 MIX-HTC4PB_010 0.84340 LEU-COMP-THERM-051-015*

0.84980 MIX-HTC4PB_011 0.84420 LEU-COMP-THERM-051-016 0.84730 MIX-HTC4PB_012 0.84190 LEU-COMP-THERM-051-017 0.84910 MIX-HTC4PB_013 0.84100 LEU-COMP-THERM-051-018 0.84820 MIX-HTC4PB_014 0.83900 LEU-COMP-THERM-051-019 0.83740 MIX-HTC4PB_015 0.83990 LEU-COMP-THERM-055-001 0.81200 MIX-HTC4PB_016 0.83840 LEU-COMP-THERM-055-002 0.80260 MIX-HTC4PB_017 0.84600 LEU-COMP-THERM-076-001 0.81380 MIX-HTC4PB_018 0.84210 LEU-COMP-THERM-076-002 0.81950 MIX-HTC4PB_019 0.84980 LEU-COMP-THERM-076-003 0.81630 MIX-HTC4PB_020 0.84730 LEU-COMP-THERM-076-004 0.80820 MIX-HTC4PB_021 0.84380 LEU-COMP-THERM-076-005 0.82130 MIX-HTC4PB_022 0.84180 LEU-COMP-THERM-076-006 0.81530 MIX-HTC4PB_023 0.84080 LEU-COMP-THERM-076-007 0.82410 MIX-HTC4PB_024 0.83880 MIX-HTC2B_004 0.80760 MIX-HTC4PB_025 0.83700 MIX-HTC2B_005 0.82080 MIX-HTC4PB_026 0.84120 MIX-HTC2B_006 0.81950 MIX-HTC4PB_027 0.81210 MIX-HTC2B_007 0.83100 MIX-HTC4PB_028 0.81460 MIX-HTC2B_008 0.84260 MIX-HTC4PB_029 0.82080 MIX-HTC2B_009 0.86620 MIX-HTC4PB_030 0.82070 MIX-HTC2B_010 0.85190 MIX-HTC4PB_031 0.81940 MIX-HTC2B_011 0.83380 MIX-HTC4PB_032 0.81880 MIX-HTC2B_012 0.81580 MIX-HTC4PB_033 0.81730 MIX-HTC2B_016 0.81910 MIX-HTC4PB_034 0.83150 MIX-HTC2B_017 0.84130 MIX-HTC4PB_035 0.83360 MIX-HTC2B_018 0.86150 MIX-HTC4PB_036 0.82950 MIX-HTC2B_020 0.83930 MIX-HTC4PB_037 0.82370 MIX-HTC2B_021 0.81300 MIX-HTC4PB_038 0.81790

• LEU-COMP-THERM-051 cases 13 and 14 are excluded because of large uncertainties

C-3 Table C-2 ck Values of at Least 0.8 for Application 2 Experiment ck Experiment ck MIX-HTC2B_005 0.80170 MIX-HTC4FE_017 0.82130 MIX-HTC2B_006 0.80000 MIX-HTC4FE_018 0.81780 MIX-HTC2B_007 0.81610 MIX-HTC4FE_019 0.81300 MIX-HTC2B_008 0.83290 MIX-HTC4FE_020 0.80910 MIX-HTC2B_009 0.85910 MIX-HTC4FE_021 0.81140 MIX-HTC2B_010 0.83750 MIX-HTC4FE_022 0.81110 MIX-HTC2B_011 0.81220 MIX-HTC4FE_023 0.81150 MIX-HTC2B_017 0.82240 MIX-HTC4FE_024 0.80830 MIX-HTC2B_018 0.85270 MIX-HTC4FE_025 0.80550 MIX-HTC2B_020 0.82620 MIX-HTC4FE_026 0.80340 MIX-HTC3_002 0.80140 MIX-HTC4PB_006 0.82360 MIX-HTC3_003 0.80430 MIX-HTC4PB_007 0.82260 MIX-HTC3_005 0.80460 MIX-HTC4PB_008 0.82420 MIX-HTC3_006 0.80940 MIX-HTC4PB_009 0.82300 MIX-HTC3_008 0.81120 MIX-HTC4PB_010 0.82070 MIX-HTC3_009 0.80780 MIX-HTC4PB_011 0.82170 MIX-HTC3_010 0.80710 MIX-HTC4PB_012 0.81880 MIX-HTC3_011 0.80650 MIX-HTC4PB_013 0.81770 MIX-HTC4FE_001 0.81570 MIX-HTC4PB_014 0.81510 MIX-HTC4FE_002 0.81440 MIX-HTC4PB_015 0.81600 MIX-HTC4FE_003 0.81530 MIX-HTC4PB_016 0.81400 MIX-HTC4FE_004 0.81320 MIX-HTC4PB_017 0.82540 MIX-HTC4FE_005 0.81190 MIX-HTC4PB_018 0.82020 MIX-HTC4FE_006 0.80640 MIX-HTC4PB_019 0.82850 MIX-HTC4FE_007 0.80400 MIX-HTC4PB_020 0.82530 MIX-HTC4FE_008 0.81310 MIX-HTC4PB_021 0.82060 MIX-HTC4FE_009 0.81270 MIX-HTC4PB_022 0.81810 MIX-HTC4FE_010 0.81120 MIX-HTC4PB_023 0.81700 MIX-HTC4FE_011 0.81080 MIX-HTC4PB_024 0.81450 MIX-HTC4FE_012 0.82120 MIX-HTC4PB_025 0.81220 MIX-HTC4FE_013 0.82180 MIX-HTC4PB_026 0.81720 MIX-HTC4FE_014 0.82010 MIX-HTC4PB_034 0.80430 MIX-HTC4FE_015 0.81280 MIX-HTC4PB_035 0.80700 MIX-HTC4FE_016 0.81510 MIX-HTC4PB_036 0.80130

C-4 Table C-3 ck Values of at Least 0.8 for Application 3 Experiment ck Experiment ck LEU-COMP-THERM-011-003 0.80370 MIX-HTC3_011 0.89500 LEU-COMP-THERM-011-004 0.80400 MIX-HTC3_012 0.84200 LEU-COMP-THERM-011-005 0.80340 MIX-HTC3_013 0.84840 LEU-COMP-THERM-011-006 0.80350 MIX-HTC3_014 0.85920 LEU-COMP-THERM-011-007 0.80280 MIX-HTC3_015 0.86280 LEU-COMP-THERM-011-008 0.80180 MIX-HTC3_016 0.86660 LEU-COMP-THERM-011-009 0.80130 MIX-HTC3_017 0.87090 LEU-COMP-THERM-011-010 0.80460 MIX-HTC3_018 0.87560 LEU-COMP-THERM-011-011 0.80330 MIX-HTC3_019 0.87150 LEU-COMP-THERM-011-012 0.80060 MIX-HTC3_020 0.87220 LEU-COMP-THERM-047-001 0.80660 MIX-HTC3_021 0.85290 LEU-COMP-THERM-051-002 0.81770 MIX-HTC3_022 0.84170 LEU-COMP-THERM-051-003 0.81700 MIX-HTC3_023 0.83530 LEU-COMP-THERM-051-004 0.81710 MIX-HTC3_024 0.85490 LEU-COMP-THERM-051-005 0.81580 MIX-HTC3_025 0.87200 LEU-COMP-THERM-051-006 0.81600 MIX-HTC3_026 0.86020 LEU-COMP-THERM-051-007 0.81670 MIX-HTC4FE_001 0.89980 LEU-COMP-THERM-051-008 0.81360 MIX-HTC4FE_002 0.89890 LEU-COMP-THERM-051-009 0.81610 MIX-HTC4FE_003 0.89920 LEU-COMP-THERM-051-010 0.80150 MIX-HTC4FE_004 0.89760 LEU-COMP-THERM-051-011 0.80160 MIX-HTC4FE_005 0.89670 LEU-COMP-THERM-051-012 0.80150 MIX-HTC4FE_006 0.89300 LEU-COMP-THERM-051-013*

0.80000 MIX-HTC4FE_007 0.89140 LEU-COMP-THERM-051-014*

0.80150 MIX-HTC4FE_008 0.89750 LEU-COMP-THERM-051-015 0.80060 MIX-HTC4FE_009 0.89740 LEU-COMP-THERM-051-016 0.80190 MIX-HTC4FE_010 0.89650 LEU-COMP-THERM-051-017 0.80020 MIX-HTC4FE_011 0.89630 LEU-COMP-THERM-051-018 0.80200 MIX-HTC4FE_012 0.90230 MIX-HTC1_001 0.83200 MIX-HTC4FE_013 0.90260 MIX-HTC1_002 0.82930 MIX-HTC4FE_014 0.90170 MIX-HTC1_003 0.82960 MIX-HTC4FE_015 0.89720 MIX-HTC1_004 0.84180 MIX-HTC4FE_016 0.89860 MIX-HTC1_005 0.84070 MIX-HTC4FE_017 0.90410 MIX-HTC1_006 0.84070 MIX-HTC4FE_018 0.90140 MIX-HTC1_007 0.83310 MIX-HTC4FE_019 0.89810 MIX-HTC1_008 0.83190 MIX-HTC4FE_020 0.89550 MIX-HTC1_009 0.83240 MIX-HTC4FE_021 0.89730 MIX-HTC1_010 0.82410 MIX-HTC4FE_022 0.89720 MIX-HTC1_011 0.82390 MIX-HTC4FE_023 0.89750 MIX-HTC1_012 0.82480 MIX-HTC4FE_024 0.89560 MIX-HTC1_013 0.83320 MIX-HTC4FE_025 0.89330 MIX-HTC1_014 0.83130 MIX-HTC4FE_026 0.89190 MIX-HTC1_015 0.83150 MIX-HTC4FE_027 0.86820 MIX-HTC1_016 0.83880 MIX-HTC4FE_028 0.87100 MIX-HTC1_017 0.84120 MIX-HTC4FE_029 0.87410 MIX-HTC1_018 0.83520 MIX-HTC4FE_030 0.88070 MIX-HTC2B_001 0.84720 MIX-HTC4FE_031 0.87980 MIX-HTC2B_002 0.84680 MIX-HTC4FE_032 0.87490

C-5 Experiment ck Experiment ck MIX-HTC2B_003 0.85850 MIX-HTC4FE_033 0.86820 MIX-HTC2B_004 0.86970 MIX-HTC4PB_001 0.86280 MIX-HTC2B_005 0.88050 MIX-HTC4PB_002 0.87460 MIX-HTC2B_006 0.87950 MIX-HTC4PB_003 0.87500 MIX-HTC2B_007 0.88870 MIX-HTC4PB_004 0.87440 MIX-HTC2B_008 0.89770 MIX-HTC4PB_005 0.87420 MIX-HTC2B_009 0.92020 MIX-HTC4PB_006 0.90570 MIX-HTC2B_010 0.90980 MIX-HTC4PB_007 0.90500 MIX-HTC2B_011 0.89530 MIX-HTC4PB_008 0.90590 MIX-HTC2B_012 0.88010 MIX-HTC4PB_009 0.90510 MIX-HTC2B_014 0.84660 MIX-HTC4PB_010 0.90360 MIX-HTC2B_015 0.85980 MIX-HTC4PB_011 0.90440 MIX-HTC2B_016 0.88130 MIX-HTC4PB_012 0.90250 MIX-HTC2B_017 0.89960 MIX-HTC4PB_013 0.90160 MIX-HTC2B_018 0.91490 MIX-HTC4PB_014 0.89990 MIX-HTC2B_019 0.86420 MIX-HTC4PB_015 0.90070 MIX-HTC2B_020 0.89240 MIX-HTC4PB_016 0.89950 MIX-HTC2B_021 0.87160 MIX-HTC4PB_017 0.90490 MIX-HTC2G_001 0.83990 MIX-HTC4PB_018 0.90190 MIX-HTC2G_002 0.84000 MIX-HTC4PB_019 0.90940 MIX-HTC2G_003 0.83100 MIX-HTC4PB_020 0.90720 MIX-HTC2G_004 0.82990 MIX-HTC4PB_021 0.90420 MIX-HTC2G_005 0.82940 MIX-HTC4PB_022 0.90260 MIX-HTC2G_006 0.81110 MIX-HTC4PB_023 0.90170 MIX-HTC2G_007 0.81000 MIX-HTC4PB_024 0.90000 MIX-HTC2G_015 0.83040 MIX-HTC4PB_025 0.89840 MIX-HTC2G_016 0.83000 MIX-HTC4PB_026 0.90210 MIX-HTC2G_017 0.82630 MIX-HTC4PB_027 0.87770 MIX-HTC2G_018 0.80960 MIX-HTC4PB_028 0.87970 MIX-HTC2G_020 0.82850 MIX-HTC4PB_029 0.88460 MIX-HTC3_001 0.88540 MIX-HTC4PB_030 0.88450 MIX-HTC3_002 0.89100 MIX-HTC4PB_031 0.88340 MIX-HTC3_003 0.89220 MIX-HTC4PB_032 0.88290 MIX-HTC3_004 0.88840 MIX-HTC4PB_033 0.88150 MIX-HTC3_005 0.89280 MIX-HTC4PB_034 0.89280 MIX-HTC3_006 0.89530 MIX-HTC4PB_035 0.89450 MIX-HTC3_007 0.89010 MIX-HTC4PB_036 0.89170 MIX-HTC3_008 0.89820 MIX-HTC4PB_037 0.88720 MIX-HTC3_009 0.89550 MIX-HTC4PB_038 0.88250 MIX-HTC3_010 0.89490

• LEU-COMP-THERM-051 cases 13 and 14 are excluded because of large uncertainties

C-6 Table C-4 ck Values of at Least 0.8 for Application 4 Experiment ck Experiment ck MIX-HTC1_001 0.80900 MIX-HTC4FE_009 0.86620 MIX-HTC1_002 0.80590 MIX-HTC4FE_010 0.86510 MIX-HTC1_003 0.80640 MIX-HTC4FE_011 0.86490 MIX-HTC1_004 0.80290 MIX-HTC4FE_012 0.87260 MIX-HTC1_005 0.80170 MIX-HTC4FE_013 0.87300 MIX-HTC1_006 0.80170 MIX-HTC4FE_014 0.87170 MIX-HTC2B_001 0.81200 MIX-HTC4FE_015 0.86600 MIX-HTC2B_002 0.81170 MIX-HTC4FE_016 0.86790 MIX-HTC2B_003 0.82620 MIX-HTC4FE_017 0.87390 MIX-HTC2B_004 0.84020 MIX-HTC4FE_018 0.87070 MIX-HTC2B_005 0.85430 MIX-HTC4FE_019 0.86660 MIX-HTC2B_006 0.85300 MIX-HTC4FE_020 0.86350 MIX-HTC2B_007 0.86520 MIX-HTC4FE_021 0.86550 MIX-HTC2B_008 0.87780 MIX-HTC4FE_022 0.86540 MIX-HTC2B_009 0.90130 MIX-HTC4FE_023 0.86580 MIX-HTC2B_010 0.88600 MIX-HTC4FE_024 0.86340 MIX-HTC2B_011 0.86660 MIX-HTC4FE_025 0.86070 MIX-HTC2B_012 0.84720 MIX-HTC4FE_026 0.85890 MIX-HTC2B_014 0.80620 MIX-HTC4FE_027 0.82970 MIX-HTC2B_015 0.82150 MIX-HTC4FE_028 0.83300 MIX-HTC2B_016 0.84820 MIX-HTC4FE_029 0.83690 MIX-HTC2B_017 0.87200 MIX-HTC4FE_030 0.84560 MIX-HTC2B_018 0.89430 MIX-HTC4FE_031 0.84480 MIX-HTC2B_019 0.82680 MIX-HTC4FE_032 0.83890 MIX-HTC2B_020 0.86830 MIX-HTC4FE_033 0.83100 MIX-HTC2B_021 0.83980 MIX-HTC4PB_001 0.82460 MIX-HTC2G_001 0.80970 MIX-HTC4PB_002 0.83750 MIX-HTC2G_002 0.80980 MIX-HTC4PB_003 0.83790 MIX-HTC2G_003 0.80850 MIX-HTC4PB_004 0.83720 MIX-HTC2G_004 0.80700 MIX-HTC4PB_005 0.83690 MIX-HTC2G_005 0.80650 MIX-HTC4PB_006 0.87620 MIX-HTC2G_020 0.80170 MIX-HTC4PB_007 0.87530 MIX-HTC3_001 0.85140 MIX-HTC4PB_008 0.87650 MIX-HTC3_002 0.85820 MIX-HTC4PB_009 0.87540 MIX-HTC3_003 0.85980 MIX-HTC4PB_010 0.87350 MIX-HTC3_004 0.85500 MIX-HTC4PB_011 0.87440 MIX-HTC3_005 0.86040 MIX-HTC4PB_012 0.87200 MIX-HTC3_006 0.86370 MIX-HTC4PB_013 0.87100 MIX-HTC3_007 0.85650 MIX-HTC4PB_014 0.86890 MIX-HTC3_008 0.86640 MIX-HTC4PB_015 0.86980 MIX-HTC3_009 0.86330 MIX-HTC4PB_016 0.86820 MIX-HTC3_010 0.86260 MIX-HTC4PB_017 0.87620 MIX-HTC3_011 0.86260 MIX-HTC4PB_018 0.87220 MIX-HTC3_013 0.80700 MIX-HTC4PB_019 0.88030 MIX-HTC3_014 0.81970 MIX-HTC4PB_020 0.87760 MIX-HTC3_015 0.82400 MIX-HTC4PB_021 0.87380 MIX-HTC3_016 0.82880 MIX-HTC4PB_022 0.87170 MIX-HTC3_017 0.83420 MIX-HTC4PB_023 0.87070

C-7 Experiment ck Experiment ck MIX-HTC3_018 0.84080 MIX-HTC4PB_024 0.86870 MIX-HTC3_019 0.83640 MIX-HTC4PB_025 0.86670 MIX-HTC3_020 0.83760 MIX-HTC4PB_026 0.87110 MIX-HTC3_021 0.81300 MIX-HTC4PB_027 0.84070 MIX-HTC3_024 0.81410 MIX-HTC4PB_028 0.84310 MIX-HTC3_025 0.83470 MIX-HTC4PB_029 0.84890 MIX-HTC3_026 0.82080 MIX-HTC4PB_030 0.84880 MIX-HTC4FE_001 0.86910 MIX-HTC4PB_031 0.84750 MIX-HTC4FE_002 0.86800 MIX-HTC4PB_032 0.84690 MIX-HTC4FE_003 0.86850 MIX-HTC4PB_033 0.84520 MIX-HTC4FE_004 0.86660 MIX-HTC4PB_034 0.85920 MIX-HTC4FE_005 0.86550 MIX-HTC4PB_035 0.86130 MIX-HTC4FE_006 0.86090 MIX-HTC4PB_036 0.85740 MIX-HTC4FE_007 0.85890 MIX-HTC4PB_037 0.85180 MIX-HTC4FE_008 0.86650 MIX-HTC4PB_038 0.84600

APPENDIX D VALIDATION DATA FOR LCT EXPERIMENTS

D-1 The relevant critical experiment parameters used for the example validations provided in Section 6 are provided in Table D-1 for the LCT experiments. No data are provided here for the HTC experiments because the data are proprietary.

Table D-1 Critical Experiment Parameters Used for Validation Experiment C/E C/E Uncertainty Enrichment (wt% 235U)

EALF (eV)

LEU-COMP-THERM-008-001 0.99893 0.00120 2.46 0.279 LEU-COMP-THERM-008-002 0.99956 0.00120 2.46 0.246 LEU-COMP-THERM-008-003 1.00019 0.00120 2.46 0.246 LEU-COMP-THERM-008-004 0.99957 0.00120 2.46 0.247 LEU-COMP-THERM-008-005 0.99882 0.00120 2.46 0.247 LEU-COMP-THERM-008-006 0.99970 0.00120 2.46 0.246 LEU-COMP-THERM-008-007 0.99884 0.00120 2.46 0.246 LEU-COMP-THERM-008-008 0.99829 0.00120 2.46 0.244 LEU-COMP-THERM-008-009 0.99877 0.00120 2.46 0.244 LEU-COMP-THERM-008-010 0.99938 0.00120 2.46 0.249 LEU-COMP-THERM-008-011 1.00001 0.00120 2.46 0.255 LEU-COMP-THERM-008-012 0.99956 0.00120 2.46 0.249 LEU-COMP-THERM-008-013 0.99977 0.00120 2.46 0.248 LEU-COMP-THERM-008-014 0.99942 0.00120 2.46 0.251 LEU-COMP-THERM-008-015 0.99939 0.00120 2.46 0.250 LEU-COMP-THERM-008-016 0.99950 0.00120 2.46 0.228 LEU-COMP-THERM-008-017 0.99867 0.00120 2.46 0.199 LEU-COMP-THERM-011-002 0.99749 0.00319 2.46 0.248 LEU-COMP-THERM-011-003 0.99775 0.00319 2.46 0.195 LEU-COMP-THERM-011-004 0.99827 0.00319 2.46 0.195 LEU-COMP-THERM-011-005 0.99807 0.00319 2.46 0.196 LEU-COMP-THERM-011-006 0.99789 0.00319 2.46 0.197 LEU-COMP-THERM-011-007 0.99786 0.00319 2.46 0.198 LEU-COMP-THERM-011-008 0.99825 0.00319 2.46 0.199 LEU-COMP-THERM-011-009 0.99794 0.00319 2.46 0.200 LEU-COMP-THERM-011-010 0.99415 0.00169 2.46 0.189 LEU-COMP-THERM-011-011 0.99416 0.00169 2.46 0.165 LEU-COMP-THERM-011-012 0.99398 0.00169 2.46 0.170 LEU-COMP-THERM-011-013 0.99524 0.00169 2.46 0.149 LEU-COMP-THERM-011-014 0.99505 0.00169 2.46 0.153 LEU-COMP-THERM-011-015 0.99689 0.00180 2.46 0.140 LEU-COMP-THERM-014-005 1.00333 0.00692 4.31 0.586 LEU-COMP-THERM-015-151 0.99951 0.00300 3.56 0.178 LEU-COMP-THERM-015-158 0.99797 0.00300 3.56 0.211 LEU-COMP-THERM-017-004 0.99764 0.00309 2.35 0.205 LEU-COMP-THERM-017-026 0.99588 0.00279 2.35 0.376 LEU-COMP-THERM-017-027 0.99797 0.00280 2.35 0.323 LEU-COMP-THERM-017-028 0.99858 0.00280 2.35 0.282 LEU-COMP-THERM-017-029 0.99854 0.00280 2.35 0.254 LEU-COMP-THERM-042-002 0.99771 0.00160 2.35 0.178 LEU-COMP-THERM-042-003 0.99851 0.00160 2.35 0.185 LEU-COMP-THERM-042-004 0.99930 0.00170 2.35 0.183 LEU-COMP-THERM-042-005 0.99922 0.00330 2.35 0.180 APPENDIX D VALIDATION DATA FOR LCT EXPERIMENTS

D-2 Experiment C/E C/E Uncertainty Enrichment (wt% 235U)

EALF (eV)

LEU-COMP-THERM-042-007 0.99752 0.00180 2.35 0.176 LEU-COMP-THERM-047-001 1.00043 0.00200 3.01 0.168 LEU-COMP-THERM-051-001 0.99782 0.00200 2.46 0.149 LEU-COMP-THERM-051-002 0.99818 0.00240 2.46 0.196 LEU-COMP-THERM-051-003 0.99817 0.00240 2.46 0.196 LEU-COMP-THERM-051-004 0.99795 0.00239 2.46 0.198 LEU-COMP-THERM-051-005 0.99765 0.00239 2.46 0.198 LEU-COMP-THERM-051-006 0.99778 0.00239 2.46 0.199 LEU-COMP-THERM-051-007 0.99743 0.00239 2.46 0.200 LEU-COMP-THERM-051-008 0.99776 0.00239 2.46 0.201 LEU-COMP-THERM-051-009 0.99709 0.00190 2.46 0.167 LEU-COMP-THERM-051-010 0.99680 0.00189 2.46 0.192 LEU-COMP-THERM-051-011 0.99409 0.00189 2.46 0.193 LEU-COMP-THERM-051-012 0.99285 0.00189 2.46 0.195 LEU-COMP-THERM-051-015 0.99206 0.00238 2.46 0.200 LEU-COMP-THERM-051-016 0.99167 0.00198 2.46 0.169 LEU-COMP-THERM-051-017 0.99348 0.00268 2.46 0.201 LEU-COMP-THERM-051-018 0.99323 0.00209 2.46 0.169 LEU-COMP-THERM-051-019 0.99313 0.00189 2.46 0.150 LEU-COMP-THERM-055-001 0.99948 0.00250 3.01 1.217 LEU-COMP-THERM-055-002 0.99906 0.00250 3.01 1.482 LEU-COMP-THERM-076-001 0.99847 0.00250 3.00 1.485 LEU-COMP-THERM-076-002 0.99847 0.00250 3.00 1.485 LEU-COMP-THERM-076-003 0.99850 0.00250 3.00 1.403 LEU-COMP-THERM-076-004 0.99779 0.00250 3.00 1.483 LEU-COMP-THERM-076-005 1.00171 0.00251 3.00 1.480 LEU-COMP-THERM-076-006 0.99949 0.00250 3.00 1.496 LEU-COMP-THERM-076-007 1.00325 0.00251 3.00 1.368

NUREG/CR-7252 ORNL/TM-2018/797 W.J. Marshall J.B. Clarity S.M. Bowman Oak Ridge National Laboratory Managed by UT-Battelle, LLC Oak Ridge, TN 37831-6170 Division of System Analysis and Regulatory Effectiveness Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, D.C. 20555-0001 The validation of numerical methods used in criticality safety analyses is required by the Code of Federal Regulations. Validation requires the comparison of computational results with measurements of physical systems, and these systems must be similar to the safety analysis being performed. This document examines methods available to generate sensitivity data to facilitate the identification of similar systems. A large number of critical benchmark experiments are surveyed using sensitivity/uncertainty (S/U) techniques to assess their applicability to boiling-water reactor (BWR) burnup credit (BUC) beyond the burnup of peak reactivity. Multiple burnups of BWR assemblies are considered, as well as both the actinide-only (AO) and actinide and major fission product (AFP) isotope sets. Sample validations are completed for representative application models to demonstrate that appropriate validation is possible and to provide an indication of the bias and bias uncertainty values that should be expected for related applications.

Validation Burnup credit Boiling-water reactor December 2018 Technical Validation of keff Calculations for Extended BWR Burnup Credit

NUREG/CR-7252 Validation of keff Calculations for Extended BWR Burnup Credit December 2018