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 boilingwater 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 1

H Total Sensitivity Profiles from MG and CE TSUNAMI-3D................................ 4-6

Figure 4-2 10B (n,α) 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 (%Δk/k) Due to Nuclear Data Uncertainty, Detailed 

Application Models..................................................................................................7-2

Table 7-2

Table 7-3

Uncertainty in keff (%Δk/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/CR7109. 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 TSUNAMIIP 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 LEUCOMP-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 

lattice—a two-dimensional (2D) slice of the assembly—neutron 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 energydependent 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). 

ExpApp

2

AppExp

k c

σσ

σ = , (1)

where: ck is the similarity between an application and an experiment, 

σ2

AppExp is the covariance between the application and the experiment, 

σApp is the uncertainty in the application keff due to cross section covariances

(uncertainties), and

σExp 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 

method’s 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 TSUNAMIIP 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 LEUCOMP-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 (νν̅), and fission neutron energy distributions (χ). 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/CR7194 [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-COMPTHERM (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 νν̅, as well as 

increases in the uncertainty associated with 235U νν̅and χ. 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 χ 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 νν̅and χ and decreased uncertainty in 239Pu νν̅ [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 LCT011. 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 2σ penalty factor can likely be reduced

from approximately 0.3% Δk to 0.175% Δk.

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 (% Δkeff)

GBC-68 NUREG/CR-7109 

VAN AO VAN AFP FULL AFP SFP 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 2σ penalty factor of 0.09% Δk 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 (% Δk)

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, 151

Eu, 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% Δk 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 (% Δk)

GBC-68 NUREG/CR-7109 SFP 

VAN AFP FULL AFP 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 2σ factor drops from 0.3% Δk [3] to 

0.175% Δk. The factor for 155Gd, however, nearly doubles from 0.05% Δk to 0.09% Δk. The factor 

for MAs and major FPs is unaffected and remains at 0.06% Δk. The sum of the three factors for 

the new covariance library is 0.325% Δk, which is lower than the recommended value from 

NUREG/CR-7194 of 0.41% Δk. 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% Δk 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% Δk 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. (σ) 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. (σ) 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. (σ) 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. (σ) 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 Δk 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 Δk 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. 

(σ)

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. 

(σ)

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. 

(σ)

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. 

(σ)

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 1

H 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,α) 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 1

H Total Sensitivity Profiles from MG and CE TSUNAMI-3D

Figure 4-2 10B (n,α) 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 TSUNAMI3D. 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 × 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 margin—that is, the bias

and bias uncertainty—with 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 (Δk) Bias Uncertainty 

(Δk)

Computational 

Margin (Δk)

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 energydependent 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 BAin 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 (%Δk/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 (%Δk/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 (Δk) 0.00048 0.00054

FP and MA worth (Δk) 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 

(Δk)

0.00036 0.00042 0.00042 0.00045 0.00047 0.00049 0.00051

Worth (Δk) 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 (Δk) 0.00048 0.00047

Residual 155Gd worth (Δk) 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% Δkeff, and the bias uncertainty is

approximately ~0.6% Δkeff 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

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9-2

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(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.

EE = SSaa

TTSSee

|SSaa||SSee| (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 largerthan-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, 238

U, 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

HTC2B-009MCT001-004

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

1

H 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

LCT002-004HTC2B-009MCT001-004

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

1

H 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 (χ), which has a high degree of 

uncertainty compared to other reactions. The contribution to data-induced uncertainty from χ 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 χ 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 χ 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 1

H 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 1

H total 

sensitivities are in good agreement with the experimental cases. The nuclear data uncertainty due 

to 1

H 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 1

H 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 1

H 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