An Approach for Validating 

Actinide and Fission Product 

Burnup Credit Criticality Safety 

Analyses—Criticality (keff ) 

Predictions

Office of Nuclear Regulatory Research

NUREG/CR-7109 

ORNL/TM-2011/514
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An Approach for Validating 

Actinide and Fission Product 

Burnup Credit Criticality Safety 

Analyses—Criticality (keff ) 

Predictions

Manuscript Completed: December 2011

Date Published: April 2012

Prepared by

J. M. Scaglione

D. E. Mueller

J. C. Wagner

W. J. Marshall

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6170

Don Algama, NRC Project Manager

Prepared for

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code V6005

Office of Nuclear Regulatory Research

 NUREG/CR-7109

ORNL/TM-2011/514

iii

ABSTRACT 

Taking credit for the reduced reactivity of spent nuclear fuel (SNF) in criticality analyses is 

referred to as burnup credit (BUC). Criticality safety evaluations require validation of the 

computational methods with critical experiments that are as similar as possible to the safety 

analysis models, and for which the keff values are known. This poses a challenge for validation 

of BUC criticality analyses, as critical experiments with actinide and fission product (FP) 

nuclides similar to SNF are not available. To address the issue of validation for nuclides that 

lack experimental data (e.g., minor actinides and FPs) the US Nuclear Regulatory Commission 

initiated a project with the Oak Ridge National Laboratory to establish and demonstrate an 

approach that could be used for commercial SNF criticality safety evaluations based on bestavailable data and methods. This report describes how model-specific sensitivity data can be 

used to translate nuclear data uncertainties into uncertainty in the model keff value.

v 

TABLE OF CONTENTS 

Section Page 

ABSTRACT .................................................................................................................................. iii

LIST OF FIGURES ..................................................................................................................... vii

LIST OF TABLES ......................................................................................................................... ix

EXECUTIVE SUMMARY ............................................................................................................ xiii

ACKNOWLEDGMENTS ............................................................................................................. xv

ACRONYMS AND UNITS .......................................................................................................... xvii

1. INTRODUCTION ................................................................................................................... 1

2. BACKGROUND ..................................................................................................................... 3

3. ANALYSIS METHODS .......................................................................................................... 5

3.1 COMPUTER CODES AND DATA USED ..................................................................... 7

3.1.1 Depletion Analyses ........................................................................................... 8

3.1.2 Criticality Analyses ............................................................................................ 9

3.1.3 Sensitivity/Uncertainty Analyses ....................................................................... 9

3.2 DESCRIPTION OF ANALYSIS .................................................................................... 9

3.2.1 Application and Critical Experiment Modeling ................................................ 10

3.2.2 Similarity of Application and Critical Experiment Models ................................ 10

3.2.3 Sensitivity Analysis of Application and Critical Experiment Models ................ 11

3.2.4 Similarity Analysis Using Sensitivity Data ....................................................... 11

3.2.5 Model-Specific keff Uncertainties Due to Nuclear Data Uncertainties ............. 12

3.2.6 Trending Analysis and Bias and Bias Uncertainty Determination ................... 19

3.2.7 Fission Product Bias Analysis Techniques ..................................................... 21

4. APPLICATION MODELS ..................................................................................................... 25

4.1 PWR SPENT NUCLEAR FUEL POOL APPLICATIONS ............................................ 26

4.2 CASK APPLICATION ................................................................................................. 29

4.3 BWR SPENT NUCLEAR FUEL POOL APPLICATION .............................................. 32

5. CRITICAL EXPERIMENTS .................................................................................................. 37

5.1 LOW-ENRICHMENT URANIUM EXPERIMENTS ...................................................... 37

5.2 MIXED URANIUM AND PLUTONIUM EXPERIMENTS ............................................. 39

5.3 HAUT TAUX DE COMBUSTION MOX EXPERIMENTS ............................................ 41

5.4 FRENCH FISSION PRODUCT PROGRAM EXPERIMENTS .................................... 41

6. BIAS AND BIAS UNCERTAINTY ........................................................................................ 43

6.1 BIAS AND BIAS UNCERTAINTY DETERMINATION ................................................ 43

6.2 BIAS AND BIAS UNCERTAINTY USING S/U ANALYSIS FOR SIMILARITY 

AND cK TRENDING .................................................................................................... 47

6.2.1 Similarity Determination Using Sensitivity and Uncertainty Analysis .............. 47

6.2.2 Bias and Bias Uncertainty Using Sensitivity and Uncertainty Analysis ........... 51

6.3 COMPARISON OF BIAS AND UNCERTAINTY WITH NUCLEAR DATA 

UNCERTAINTY VALUES ........................................................................................... 53

6.4 BIAS AND BIAS UNCERTAINTY FOR FISSION PRODUCTS .................................. 57

6.4.1 Fission Product Experiment Analysis ............................................................. 61
vi 

TABLE OF CONTENTS 

(Continued) 

Section Page

6.4.2 Application of Fission Product Bias and Bias Uncertainty .............................. 77

6.5 CONCLUSIONS ON CALCULATION OF BIAS AND BIAS UNCERTAINTY ............. 80

7. BIAS AND BIAS UNCERTAINTY SENSITIVITY STUDY .................................................... 83

7.1 PARAMETRIC EVALUATION .................................................................................... 83

7.2 REFERENCE MODEL PARAMETERS ...................................................................... 83

7.3 PARAMETRIC APPLICATIONS ................................................................................. 83

7.4 SENSITIVITY ANALYSIS RESULTS AND DISCUSSION ......................................... 88

7.4.1 Conventional Bias and Bias Uncertainty Assessment Impacts ...................... 88

7.4.2 Sensitivity and Uncertainty Based Benchmark Selection Bias and Bias 

Uncertainty Impacts ........................................................................................ 96

7.4.3 Nonapplicable LCE Nuclide Validation Assessment ..................................... 101

7.5 SENSITIVITY ANALYSIS SUMMARY ...................................................................... 106

8. CONCLUSIONS AND RECOMMENDATIONS .................................................................. 107

9. REFERENCES .................................................................................................................. 109

APPENDIX A. SPENT NUCLEAR FUEL ASSEMBLY BENCHMARK DATA SUMMARY 

OF EXPERIMENTAL AND CALCULATED RESULTS .................................... A-1

APPENDIX B. SIMILARITY ASSESSMENT RESULTS .......................................................... B-1

APPENDIX C. BIAS AND BIAS UNCERTAINTY USING GLLSM ........................................... C-1

APPENDIX D. EXAMPLE TRITON DEPLETION CODE INPUT ............................................. D-1
vii 

LIST OF FIGURES 

Figure Page 

Figure 3.1 Overview of burnup credit validation process. ........................................................ 6

Figure 3.2 Comparison of calculated biases and experiment-specific nuclear data 

uncertainty in keff for 124 LEU LCEs. .................................................................... 15

Figure 3.3 Comparison of calculated biases and experiment-specific nuclear data 

uncertainty in keff for 194 Pu+U LCEs. .................................................................. 16

Figure 3.4 Comparison of calculated biases and experiment-specific nuclear data 

uncertainty in keff for 156 French HTC LCEs. ........................................................ 17

Figure 3.5 Comparison of calculated biases and experiment-specific nuclear data 

uncertainty in keff for 135 French FP LCEs. ......................................................... 18

Figure 3.6 (Top) samarium-149 keff sensitivity, (center) (n,) cross sections, and 

(bottom) (n,) cross-section uncertainty. ............................................................... 22

Figure 3.7 Samarium-149 (n,) cross-section correlation matrix. ........................................... 23

Figure 4.1 PWR SFP application model. ................................................................................ 27

Figure 4.2 Burnup credit loading curves for PWR SFP application models. .......................... 28

Figure 4.3 Cutaway view of the GBC-32 cask showing the cask bottom half with a 

quarter of the model removed. .............................................................................. 30

Figure 4.4 Burnup credit loading curves for GBC-32 application models. ............................. 31

Figure 4.5 Burnup credit and BWR peak SCCG k∞. .............................................................. 33

Figure 4.6 Relationship between hot full-power k∞ and SCCG k∞. ......................................... 34

Figure 4.7 BWR SFP application model. ................................................................................ 35

Figure 6.1 Similarity of 10 GWd/MTU PWR SFP model and each critical experiment. ......... 48

Figure 6.2 Similarity of 40 GWd/MTU PWR SFP model and each critical experiment. ......... 49

Figure 6.3 Similarity of 10 GWd/MTU GBC-32 cask model and each critical 

experiment. ........................................................................................................... 49

Figure 6.4 Similarity of 40 GWd/MTU GBC-32 cask model and each critical 

experiment. ........................................................................................................... 50

Figure 6.5 Similarity of BWR SFP model at peak SCCG burnup (11 GWd/MTU) and 

each critical experiment. ....................................................................................... 50

Figure 6.6 FP experiment keff values. ..................................................................................... 60
viii 

LIST OF FIGURES 

(Continued) 

Figure Page 

Figure 6.7 Reference HNO3 trending of keff versus EALF. ..................................................... 61

Figure 6.8 Reference HNO3 trending of keff versus leakage fraction. ..................................... 62

Figure 6.9 Reference HNO3 trending of keff versus neutron mean free path. ......................... 62

Figure 6.10 Reference HNO3 trending of keff versus critical water height. ............................... 63

Figure 6.11 Reference HNO3 trending of keff versus fuel rod number. ..................................... 63

Figure 6.12 Trending analysis of keff versus EALF. .................................................................. 65

Figure 6.13 Trending analysis of keff versus neutron leakage fraction. .................................... 66

Figure 6.14 Trending analysis of keff versus mean free path. ................................................... 67

Figure 6.15 Trending analysis of keff versus water level. .......................................................... 68

Figure 6.16 Trending analysis of keff versus rod number. ........................................................ 69

Figure 6.17 Net FP bias and uncertainty using reported experimental uncertainty. ................ 76

Figure 6.18 Net FP bias and uncertainty using adjusted experimental uncertainty. ................ 76

Figure 6.19 FP bias and uncertainty comparison against cross-section covariance as a 

function of burnup for PWR SFP application model. ............................................. 80

Figure 7.1 Percentage change in bias as a function of decay time. ....................................... 92

Figure 7.2 Percentage change in bias from rack design variations. ...................................... 93

Figure 7.3 Percentage change in bias for different soluble boron concentrations. ................ 94

Figure 7.4 Percentage change in bias for assembly and cross-section library 

parameter variations. ............................................................................................ 95

Figure C.1 Net FP bias and bias uncertainty compared against bounding FP 

covariance uncertainty. ..................................................................................... C-14

 
ix 

LIST OF TABLES 

Table Page 

Table 4.1 Key parameters from PWR SFP application models ........................................... 28

Table 4.2 Key parameters from application models (GBC-32) ............................................ 31

Table 6.1 Bias and uncertainty as a function of EALF using only IHECSBE 

experiments ......................................................................................................... 44

Table 6.2 Bias and uncertainty as a function of EALF using IHECSBE and HTC 

experiments ......................................................................................................... 44

Table 6.3 Bias and uncertainty as a function of final enrichment using IHECSBE 

experiments ......................................................................................................... 45

Table 6.4 Bias and uncertainty as a function of final enrichment using HTC and 

IHECSBE experiments ........................................................................................ 45

Table 6.5 Bias and uncertainty as a function of final Pu content 

[wt %, g Pu/(g Pu + g U)] using IHECSBE experiments ...................................... 46

Table 6.6 Bias and uncertainty as a function of final Pu content 

[wt %, g Pu/(g Pu + g U)] using HTC and IHECSBE experiments ...................... 46

Table 6.7 Similarity assessment summary .......................................................................... 48

Table 6.8 Bias and bias uncertainty results using S/U analysis .......................................... 52

Table 6.9 Nonparametric bias and bias uncertainty ............................................................ 52

Table 6.10 Uncertainty in keff due to uncertainty in nuclear data for BUC 

application models ............................................................................................... 54

Table 6.11 Uncertainty in keff due to uncertainty in nuclear data for SFP 

model as a function of burnup ............................................................................. 55

Table 6.12 keff uncertainty due to uncertainty in nuclear data for ENDF/B-V, 

-VI, and -VII nuclear data libraries ....................................................................... 56

Table 6.13 FP experiment evaluation data ............................................................................ 58

Table 6.14 Rhodium-103 bias evaluation .............................................................................. 71

Table 6.15 Cesium-133 bias evaluation ................................................................................ 72

Table 6.16 Samarium-149 bias evaluation ............................................................................ 73

Table 6.17 Samarium-152 bias evaluation ............................................................................ 73

Table 6.18 Gadolinium-155 bias evaluation .......................................................................... 74
x 

LIST OF TABLES 

(Continued) 

Table Page 

Table 6.19 Neodymium bias evaluation ................................................................................ 74

Table 6.20 FP experiment bias and bias uncertainty (k) (reported experimental 

uncertainty) .......................................................................................................... 75

Table 6.21 FP experiment bias and bias uncertainty (k) (adjusted experimental 

uncertainty) .......................................................................................................... 75

Table 6.22 PWR SFP application model sensitivity-adjusted FP bias (EALF) and 

uncertainty (k) ................................................................................................... 78

Table 6.23 PWR SFP application model sensitivity-adjusted FP bias (leakage 

fraction) and uncertainty (k) .............................................................................. 78

Table 6.24 PWR SFP application model sensitivity-adjusted FP bias (mean free path) 

and uncertainty (k) ............................................................................................ 78

Table 6.25 PWR SFP application model sensitivity-adjusted FP bias (water height) 

and uncertainty (k) ............................................................................................ 79

Table 6.26 PWR SFP application model sensitivity-adjusted FP bias (fuel rods) and 

uncertainty (k) ................................................................................................... 79

Table 6.27 Summary bias and uncertainty results for actinide-only validation ...................... 81

Table 6.28 Uncertainty in keff due to minor actinide and fission product nuclear data 

uncertainties ........................................................................................................ 81

Table 6.29 Summary bias and uncertainty results for actinide and fission product 

BUC validation ..................................................................................................... 82

Table 7.1 Parameters selected for sensitivity analyses....................................................... 83

Table 7.2 Sensitivity case key parameters .......................................................................... 85

Table 7.3 Bias and uncertainty as a function of EALF ......................................................... 89

Table 7.4 Bias and uncertainty as a function of final uranium enrichment .......................... 90

Table 7.5 Bias and uncertainty as a function of final plutonium content .............................. 91

Table 7.6 Bias and uncertainty based on ck trending .......................................................... 97

Table 7.7 Bias and uncertainty based on EALF trending .................................................... 98

Table 7.8 Bias and uncertainty based on final plutonium content trending ......................... 99
xi 

LIST OF TABLES 

(Continued) 

Table Page 

Table 7.9 Bias and uncertainty based on final uranium enrichment trending .................... 100

Table 7.10 Summary of one sigma uncertainty results for PWR SFP parametric 

application models ............................................................................................. 102

Table 7.11 Unvalidated nuclide uncertainty-to-worth ratios (k) results for PWR SFP 

application model using all isotopes BUC ......................................................... 105

Table 7.12 Unvalidated nuclide uncertainty to worth ratios (k) results for GBC32 

application models ............................................................................................. 105

Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library 

results ................................................................................................................ A-1

Table B.1 Critical experiment similarity assessment ck values for applications ................. B-1

Table C.1 TSURFER results using actinide + 16 FP isotopes ........................................... C-3

Table C.2 TSURFER total bias and bias uncertainty (1) ................................................. C-4

Table C.3 TSURFER FP isotope bias ................................................................................ C-5

Table C.4 TSURFER FP residual uncertainty (1) ............................................................ C-8

Table C.5 TSUNAMI-IP seven FP bounding uncertainty in keff at 1 confidence ............ C-11

xiii 

EXECUTIVE SUMMARY

One of the most significant remaining challenges associated with expanded implementation of 

burnup credit in the United States is the validation of depletion and criticality calculations used in 

the safety evaluation—in particular, the availability and use of applicable measured data to 

support validation, especially for fission products. This report presents an approach for 

addressing validation of minor actinides and fission products in burnup credit criticality safety 

analyses of commercial spent nuclear fuel (SNF) storage and transportation systems. 

This approach (1) uses available laboratory critical experiment (LCE) data from the International 

Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE) and the French 

Haut Taux de Combustion (HTC) program to demonstrate use of existing laboratory critical 

experiments for validation of the major actinide isotopes, and (2) uses calculated sensitivities 

and nuclear data uncertainties to predict individual biases for relevant nuclides (e.g., minor 

actinides and fission products) where applicable critical experiments are unavailable. 

The methodology for determining the nuclide biases based on nuclear data uncertainties is 

described in Section 3.2.5, results are provided in Sections 6.3 and 7.4.3, and 

recommendations for applying the cross section uncertainty data to minor actinides and fission 

products are provided in Section 8. 

Reference bias and bias uncertainty results are provided for representative criticality safety 

analyses of pressurized water reactor (PWR) and boiling water reactor SFP systems and a 

representative PWR storage cask. 

Mixed plutonium-uranium oxide configurations from the IHECSBE and the HTC experiment 

configurations, collectively, provide sufficient data for validation of burnup credit analyses with 

major actinides and hence should be used for validation. LEU critical configurations should not 

be used in a conventional validation analysis to validate spent fuel systems because they do not 

include any bias contribution from the plutonium present in burned fuel. For minor actinide and 

fission product nuclides for which adequate critical experiment data are not available, 

calculations of keff uncertainty due to nuclear data uncertainties can be used to establish a 

bounding bias value which was approximately 1.5% of the worth of the minor actinides and 

fission products for the representative safety analyses used in this report. This value is 

considered applicable when using the ENDF/B-V, -VI, or –VII cross-section libraries. 

xv 

ACKNOWLEDGMENTS 

This work was performed under contract with the US Nuclear Regulatory Commission (NRC) 

Office of Nuclear Regulatory Research. The authors thank D. Algama, the NRC Project 

Manager, M. Aissa and R. Y. Lee of the Office of Nuclear Research (RES), K. A. L. Wood of the 

Office of Nuclear Reactor Regulation (NRR), A. B. Barto and Z. Li of the Office of Nuclear 

Material Safety and Safeguards (NMSS), and C. N. Van Wert of the Office of New Reactors 

(NRO) for their support and guidance. Many valuable review comments were received from 

NRC staff members of RES, NRR, NMSS, and NRO. The authors also wish to thank Chris 

Perfetti and Georgeta Radulescu for their reviews, and D. Counce, A. Harkey, and D. Weaver 

for assistance in editing, formatting, and preparing the final document. 

xvii 

ACRONYMS AND UNITS 

1D 

2D 

3D 

One-dimensional 

Two-dimensional 

Three-dimensional 

BA burnable absorber 

BNL Brookhaven National Laboratory 

BPR burnable poison rod

BUC burnup credit

B&W Babcock and Wilcox Company

BWR boiling water reactor

CFR Code of Federal Regulations 

DOE 

DUN 

US Department of Energy 

depleted uranyl-nitrate 

EALF energy of average lethargy of neutrons causing fission (unit of neutron energy)

ENDF/B Evaluated Nuclear Data Files, Part B 

EOL end of life 

eV electron volts (unit of energy)

FP fission product

GLLSM generalized linear least squares method (e.g., TSURFER)

GWd/MTU gigawatt-days per metric ton of uranium (unit of fuel burnup)

HTC Haut Taux de Combustion experiments, French for high burnup experiments

H/X ratio of hydrogen to fissile nuclide atoms 

IHECSBE International Handbook of Evaluated Criticality Safety Benchmark Experiments 

IRSN Institut de Radioprotection et de Sûreté Nucléaire

keV kilo-electron volts (unit of energy)

LANL Los Alamos National Laboratory

LCE Laboratory Critical Experiment

LEU low-enrichment uranium

LWR light water reactor

MeV megaelectron volts (unit of energy)

MOX mixed uranium and plutonium oxides

NRC US Nuclear Regulatory Commission

OFA optimized fuel assembly 

ORNL Oak Ridge National Laboratory

ppm parts per million

PWR 

RCA 

ROP

pressurized water reactor 

radiochemical analysis 

range of parameters

SCALE Standardized Computer Analyses for Licensing Evaluation

SCCG standard cold core geometry 

SDF sensitivity data file 

SFP spent nuclear fuel pool

SNF spent nuclear fuel

SRP standard review plan 

S/U sensitivity and uncertainty

USL upper subcritical limit
xviii 

W Westinghouse Electric Company

WABA wet annular burnable absorber rods
1 

1. INTRODUCTION 

Criticality safety analyses are performed to show that a proposed fuel storage or transport 

configuration meets the applicable requirements of Title 10, Code of Federal Regulations (CFR), 

Parts 50, 52, 70, 71, and 72 (Ref. 1) and that it includes calculations to demonstrate that the 

proposed configuration will meet the maximum effective neutron multiplication factor (keff) limits 

specified in the applicable requirements and guidance. For commercial spent nuclear fuel 

(SNF), the reduced reactivity associated with the net depletion of fissile isotopes and the 

creation of neutron-absorbing isotopes when the fuel is irradiated in the reactor can reduce the 

criticality potential of the SNF configurations. Taking credit for the reduced reactivity potential of 

SNF in criticality analyses is referred to as burnup credit (BUC). 

Consistent with applicable industry standards (i.e., ANSI/ANS-8 [Refs. 2 and 3]) and regulatory 

guidance (Refs. 4 and 5), criticality safety evaluations require validation of the calculational 

method with critical experiments that are as similar as possible to the safety analysis models, 

and for which the keff values are known. This poses a challenge for validation of BUC criticality 

analyses, as critical experiments with actinide and fission product (FP) nuclides similar to SNF 

are not available. As a result, validation for SNF pools (SFPs) has typically relied on critical 

experiments without FPs (Ref. 6), and BUC for transportation has been limited to actinide-only, 

based on Ref. 5. Credit for FPs is needed for high-density SNF storage in SFPs and is 

beneficial for enabling storage and transportation of most discharged SNF assemblies in casks 

(i.e., dry storage casks and transportation packages) (Ref. 7). Therefore, this report explores a 

physics-based, defensible approach to establishing a bounding estimate for bias in keff

prediction for cases in which critical experiment data are lacking or nonexistent. 

The purpose of this report is to establish a validation approach for nuclides that lack 

experimental data (minor actinides and FPs) for commercial SNF criticality safety evaluations. 

Some additional information is provided to demonstrate acceptable methods for determining keff

bias and bias uncertainty for major actinide nuclides using existing experimental data. This 

report uses the best-available data and methods and applies the approach to representative 

SNF storage and transport configurations/conditions to demonstrate its usage and applicability, 

as well as to provide reference bias results. Validation of SNF composition calculations is 

addressed in a companion report (Ref. 8). 

The work presented in this report involved (1) validation of several representative BUC safety 

analysis models, hereafter also referred to as “applications,” (2) consideration of selecting 

appropriate critical experiments for the application, (3) examination of the variation in bias and 

bias uncertainty with variation of some analysis parameters, (4) examination of the potential 

impacts of validation gaps and weaknesses (most notably inadequate validation of FPs), and (5) 

establishment of a methodology on how to address the validation gaps and weaknesses. This 

report is organized with sections on analysis methods (Section 3), representative safety analysis 

models considered (Section 4), critical experiments used for validation (Section 5), validation of 

the safety analysis models (Section 6), evaluation of the potential impact of poor FP and minor 

actinide validation (Sections 6.3 and 6.4), a parametric evaluation of SFP application model 

differences and associated impacts on calculated biases and uncertainties (Section 7), and 

conclusions and recommendations for BUC validation (Section 8). The specific methodology for 

calculating keff uncertainties from the nuclear data uncertainties is described in Section 3.2.5, 

results are provided in Sections 6.3 and 7.4.3, and recommendations for applying the minor 

actinide and FP cross-section uncertainty data are provided in Section 8. 

3 

2. BACKGROUND 

Ideally, computer calculations would yield results that predict reality. However, computational 

modeling of real-world systems requires the use of simplified and approximate descriptions of 

the systems being modeled to facilitate attaining solutions on available computing systems. For 

keff calculations, the nuclear data used include errors associated with data measurement, 

evaluation, and representation in forms usable by computer programs. As a result, calculated 

results typically do not exhibit exact agreement with expectations. Hence, the goal of validation 

is to establish a predictable relationship between calculated results and reality. The main goal of 

a validation study is a quantitative understanding of the difference or “bias” between calculated 

and expected results and the uncertainty in this difference (bias uncertainty). 

Critical experiments, which are used to validate criticality (keff) calculations, are arrangements of 

fissionable and structural materials in various forms and configurations that are carefully 

assembled to approach a critical state (i.e., keff ≈ 1). Information describing critical experiments 

is found in a variety of sources, such as technical reports generated to support the criticality 

safety of nuclear operations and the International Handbook of Evaluated Criticality Safety 

Benchmark Experiments (IHECSBE [Ref. 9]). 

Criticality validation will yield an appropriate bias for the safety application only if the critical 

experiments and the safety application model are similar (i.e., use the same nuclear data in a 

similar energy-dependent manner). The same computational method must be used for both 

experiments and applications; otherwise, differences in the computational methods could 

produce biased results. The computational method is the combination of the computer code, the 

data used by the computer code, and the calculational options selected by the user. Materials 

present in only one of either the experiments or the applications could result in determination 

and application of an incorrect bias. Even if the same materials are present in an experiment 

and in an application, local variations in the energy-dependent neutron spectrum could cause 

different energy-ranges of the nuclear data to be exercised, resulting in an incorrect bias. It is 

not enough to simply have the same materials in both the experiments and the application. For 

example, in a water-moderated sphere of 235U, the 235U will not have the same neutron spectrum 

that a sphere of 235U metal reflected by water would have; consequently, the bias is likely to be 

different. The high-energy 235U nuclear data are very important in the metal sphere, whereas the 

thermal data are the most important in the water-moderated 235U system. 

A significant part of the bias and bias uncertainty calculated using critical experiment models is 

a result of deficiencies and errors in experiment descriptions. This can clearly be seen in 

comparing results from critical experiment models from different critical experiment series or 

different critical experiment facilities. Section 4 of the IHECSBE evaluations includes critical 

experiment model results prepared by the evaluation authors. In some cases, such as MIXCOMP-THERM-012 and PU-COMP-MIXED-001, the sample results are so far from critical that 

it is clear that a significant part of the variation from critical is caused by deficiencies in the 

experiment descriptions. This observation should not be read as a criticism of the experiments, 

experimentalists, or IHECSBE evaluators. These experiments were designed and performed 

consistent with the standards of the day and for the purposes of their time. The existence of bias 

components associated with critical experiment descriptions highlights the importance of using 

critical experiments from multiple sources to ensure that the bias calculated is not overly 

influenced by systematic deficiencies or errors in critical experiment descriptions. For example, 

the 156 critical configurations described in the French Haut Taux de Combustion (HTC) 
4 

experiment reports (Refs. 10, 11, 12, and 13) all use the same fuel rods. An error in determining 

the 235U content would affect all 156 configurations and would contribute to the computational 

method bias even though this bias component has nothing to do with how well the 

computational method predicts reality. The intent of computational method validation is to 

quantify how well the method predicts reality. Inclusion of the bias and uncertainty associated 

with critical experiment descriptions increases the overall computational bias uncertainty, but 

this is an unavoidable aspect of using critical experiments for validation. 
5 

3. ANALYSIS METHODS 

A general overview of the process for implementing BUC is outlined in Figure 3.1. This report 

focuses on the criticality code validation process and provides a validation approach for 

developing the information provided in the orange-shaded boxes. Examples for development of 

the unshaded boxes are also provided, but they are application-specific and need to be 

developed for each specific license application. The demonstration of adequate BUC validation 

involves development of an allowable neutron multiplication factor. For the sake of facilitating 

this discussion with a common terminology, the terms from ANSI/ANS-8.27 (Ref. 2) are being 

used in a slightly modified format as presented in Eq. (3.1). 

 kp + kp + i + ki +β + k + kx + km ≤ klimit (3.1) 

where 

kp is the calculated multiplication factor of the model for the system being evaluated. 

kp is an allowance for 

 statistical or convergence uncertainties, or both, in the determination of kp, 

 material and fabrication tolerances, 

 uncertainties due to geometric or material representation limitations of the 

models used in the determination of kp. 

i is the bias in kp due to depletion code bias in the calculated nuclide compositions 

(this component is described in Ref. 8). 

ki is the uncertainty in kp due to depletion code bias uncertainty in the calculated 

nuclide compositions (this component is described in Ref. 8). 

 is the bias that results from the calculation of the benchmark criticality experiments 

using a particular calculation method and nuclear cross-section data. 

k is bias uncertainty that includes 

 statistical or convergence uncertainties, or both, in the computation of , 

 uncertainties in the benchmark criticality experiments, 

 uncertainty in the bias resulting from application of the linear least-squares fitting 

technique to the critical experiment results, 

 a tolerance interval multiplier to yield a single-sided 95% probability and 95% 

confidence level. 

kx is a supplement to  and k that may be included to provide an allowance for the 

bias and uncertainty from nuclide cross-section data that might not be adequately 

accounted for in the benchmark criticality experiments used for calculating . 

km is a margin for unknown uncertainties and is deemed adequate to ensure 

subcriticality of the physical system being modeled. This term is typically referred to 

as an administrative margin. 

klimit is the upper limit on the keff value for which the system is considered acceptable. 
6

Figure 3.1 Overview of burnup credit validation process. 

Safety Analysis Isotopic Validation Criticality Validation Licensing
7 

BUC computational validation starts with identification of a safety analysis model (Box 1 of 

Figure 3.1). Representative safety analysis models used in this report are described in Section 

4. The safety analysis model is developed by an analyst using depletion and criticality 

computational tools and data of the analyst’s choosing. Calculations are completed and relevant 

parameters of interest characterizing the application model are collected (Box 2; see Section 4 

for representative examples in this report). The values for kp and kp (Box 3) are used for the 

licensing criterion (Box 16). Box 4 provides other parameters defining the application model that 

are used in the process steps identified as Boxes 6 and 9. Box 6 uses the range of parameters 

(ROP) data (Box 4) and the radiochemical assay (RCA) data (Box 5) to propagate isotopic 

uncertainties to keff; it is the subject of Ref. 8. The output from Box 6 are the i and ki (Box 7) 

factors for the licensing criterion (Box 16). Box 9 uses information from the ROP (Box 4) for 

selecting applicable critical benchmark experiments (Box 10). Sections 3.2.2 and 3.2.4 provide 

a discussion of the benchmark selection process. Box 11 uses the critical benchmark 

experiments from Box 10 and establishes  and k. The values for  and k (Box 12) are used 

for the licensing criterion (Box 16). Methods for calculating these terms and example values are 

provided in Sections 6.1, 6.2, and 7.4. Note that  and k will be application-specific and need 

to be developed by the analyst with the tools that are being validated. Applicable critical 

benchmarks are available only for the major actinide isotopes. Therefore, if additional isotopes 

are being credited in the application model (Box 13), or if the neutron energy spectrum in which 

the common nuclides are present varies significantly between the application and laboratory 

critical experiments (LCEs), then Box 14 is implemented to establish kx (Box 15a). (A method 

of determining this value is described in Section 3.2.5 with representative values presented in 

Sections 6.3 and 7.4.3). If additional isotopes are not being credited, then kx is set to zero 

(Box 15b). 

Applications crediting fuel burnup typically include some nuclides in the SNF material 

compositions for which little or no applicable critical experiment data is available (for SNF 

applications, typically FPs and minor actinides such as 243Am, 237Np, and 236U). Therefore, a 

means of accounting for the unvalidated nuclides is necessary. This report demonstrates how 

the cross-section uncertainty data can be used to establish a bounding value using the following 

derivation to establish the kx term in Eq. (3.1) above: 

∆k୶ ൌ ඥ∑ ߪ௜

௜ߪ ∑ ൅ ்஼஺ ଶ

ଶ ி௉ (3.2) 

where 

௜ߪ ∑

ଶ

஺஼் = sum of the squares of the uncertainty in keff due to the uncertainty in nuclear 

data for unvalidated and poorly validated actinide nuclides; 

௜ߪ ∑

ଶ

ி௉ = sum of the squares of the uncertainty in keff due to the uncertainty in nuclear 

data for unvalidated and poorly validated FP nuclides. 

3.1 COMPUTER CODES AND DATA USED 

A variety of computer codes and nuclear data sets have been and are being used by industry to 

perform BUC criticality safety analyses. Fuel depletion calculations are typically performed using 

flux solutions from either a cylindrical one-dimensional (1D) or two-dimensional (2D) lattice 

model, approximating an assembly, coupled with a zero-dimensional code used to calculate fuel 

compositions. Commonly used codes include SCALE (Ref. 14), CASMO (Ref. 15), and 

PARAGON (Ref. 16). Future methods are likely to include flux solutions from three-dimensional 

(3D) models. Access to some of the commonly used computer codes is controlled as proprietary 
8 

information. Burnup-dependent fuel compositions are then used in criticality codes such as 

SCALE or MCNP (Ref. 17) to determine keff for the system of interest. 

The calculations performed for the work presented in this report were generated using a qualityassurance-controlled pre-release version of SCALE 6.1. All calculations were not updated with 

the version distributed through the Radiation Safety Information Computational Center, as 

differences in results were not expected. 

3.1.1 Depletion Analyses 

All depletion calculations were performed using either the TRITON (Ref. 14, Section T01) t-depl 

sequence or the STARBUCS (Ref. 14, Section C10) sequence. Model development is 

discussed in Section 4. Both the STARBUCS and TRITON sequences use the ORIGEN-S 

(Ref. 14, Section F07) program to calculate fuel compositions. The nuclear data in the 

ORIGEN-S libraries can be broadly classified as decay data, cross-section data, FP yields, 

photon emission data, and neutron emission data. In SCALE the nuclear decay data are derived 

from ENDF/B-VII.0 (hereinafter referred to as ENDF/B-VII), including the half-lives, branching 

fractions, and recoverable energy per disintegration. Decay branching fractions are included for 

the following decay modes: beta, electron capture and positron emission, isomeric transition, 

alpha, spontaneous fission, delayed neutron (β ̄, n) emission, and double β ̄ decay. 

The TRITON t-depl sequence uses the NEWT (Ref. 14, Section F21) computer code to obtain 

the detailed 2D flux solutions that are used in multiple ORIGEN-S depletion calculations to 

calculate fuel compositions that can be used directly in a criticality calculation and/or to generate 

ORIGEN/ARP libraries that are used by STARBUCS. The NEWT calculations were performed 

using the SCALE 238-energy-group ENDF/B-VII library (Ref. 14, Section M4). 

The STARBUCS sequence was used to calculate fuel compositions for all pressurized water 

reactor (PWR) models. The automated fuel depletion built into STARBUCS was used to model 

fuel compositions that varied axially along the fuel assembly. The STARBUCS loading curve 

search options were used to determine the maximum acceptable initial fuel enrichment for a 

given fuel assembly burnup and target keff value. This process is discussed in the description of 

the model development in Section 4. STARBUCS uses the ORIGEN/ARP method, described in 

Section D01 of Ref. 14, to rapidly generate pointwise-specific fuel compositions for a range of 

conditions that are consistent with conditions used to generate the generic ORIGEN/ARP 

libraries. In other words, generic ORIGEN/ARP libraries are generated from TRITON 

calculations over a range of relevant enrichment and burnup values. The TRITON calculations 

required to generate the ORIGEN/ARP libraries can take several hours to complete. 

STARBUCS uses ORIGEN/ARP to give the specific enrichment and burnup isotopic 

compositions (e.g., initial enrichment of 2.63 wt % 235U at 22.43 GWd/MTU burnup) with a few 

seconds of computer run-time based on the pregenerated ORIGEN/ARP libraries. The reason 

STARBUCS uses the ORIGEN/ARP code as opposed to TRITON is to reduce the total 

computational time needed. STARBUCS then uses the fuel compositions in CSAS5 (Ref. 14, 

Section C05) calculations with the SCALE ENDF/B-VII 238-energy-group library to determine 

keff. The boiling water reactor (BWR) application model fuel compositions were calculated 

directly with TRITON. 
9 

3.1.2 Criticality Analyses 

Criticality or keff calculations were performed using the CSAS5 (Ref. 14, Section C05) or 

CSAS6 (Ref. 14, Section C06) sequences and the ENDF/B-VII 238-energy-group library. 

CSAS5 and CSAS6 use the KENO V.a and KENO-VI Monte Carlo transport codes, 

respectively. Both sequences were operated in multigroup mode. The primary difference 

between CSAS5 and CSAS6 is that the KENO-VI geometry inputs support more complex 

geometry descriptions. CSAS5 was used for all calculations with the exception of the BWR SFP 

model and some of the proprietary FP experiments. 

3.1.3 Sensitivity/Uncertainty Analyses 

The TSUNAMI-3D (Ref. 14, Section C09) analysis sequence was used to compute the 

sensitivity of keff to energy-dependent cross-section data for each reaction of each nuclide in a 

system model using linear perturbation theory as described in Sections C09 and F22 of Ref. 14. 

The 3D forward and adjoint calculations are performed with KENO V.a or KENO-VI. The 

energy-dependent sensitivity data are stored in a sensitivity data file (SDF) for subsequent 

analysis. TSUNAMI-3D was used to generate sensitivity data for all critical experiments and 

application models. 

The TSUNAMI-IP (Ref. 14, Section M18) program was used to evaluate the similarity of critical 

experiments to application models and to compute the uncertainty in each system’s keff value 

due to the cross-section uncertainty data (i.e., cross-section covariance data). Similarity and 

uncertainty analysis is discussed in more detail in following sections of this report. 

TSURFER (Ref. 14, Section M21) is a bias and bias uncertainty prediction tool that implements 

the generalized linear least-squares method (GLLSM) approach to data assimilation and crosssection data adjustment. The data adjustments produced by TSURFER are not used to produce 

adjusted cross-section data libraries for subsequent use; rather, they are used to infer biases in 

application systems. The TSURFER tool was used with sensitivity data for the critical 

experiments and the application models to estimate biases associated with some FPs for a 

confirmatory analysis as described in Appendix C. 

The TSUNAMI sequences and TSURFER program use energy-, nuclide-, and reactiondependent nuclear data uncertainty information contained in the SCALE 44-neutron-energygroup cross-section covariance data file distributed with SCALE. The covariance data file is 

described in Section M19 of Ref. 14. 

A final piece of software used was the USLSTATS computer code, which was used to calculate 

bias and bias uncertainty for application models using keff results for sets of critical experiment 

models. The USLSTATS program, which has been distributed with SCALE, was used to 

perform trending analysis and to calculate upper subcritical limits (USLs) from which the bias 

and bias uncertainties presented in this report were calculated. The USLSTATS program was 

derived from the V_STATS program (Ref. 18). The input for USLSTATS is described in 

Appendix C of Ref. 19. 

3.2 DESCRIPTION OF ANALYSIS 

The analyses performed to support the objective of this report involved the following: 
10 

 preparation of typical or representative safety analysis models, also referred to in this report 

as applications, and critical experiment models 

 identification of critical experiments that are appropriate for use in validation studies for the 

applications 

 generation of keff sensitivity data for the applications and for the critical experiments 

 use of the sensitivity data to assess the neutronic similarity of the critical experiments and 

applications 

 use of sensitivity data and nuclear data uncertainties to estimate the potential impact of 

nuclear data uncertainties on application keff values 

 use of critical experiment calculated keff values to calculate bias and bias uncertainty as a 

function of trending parameters 

 examination of FP critical experiment results to estimate FP biases 

Note that the last analysis uses proprietary FP critical experiments only to confirm the approach 

of using nuclear data uncertainty information to address validation gaps and weaknesses. 

3.2.1 Application and Critical Experiment Modeling 

Application model development is described in Section 4 of this report. Critical experiment 

model development is described in Section 5. With the exception of the HTC [IRSN Proprietary 

Refs. 10, 11, 12, and 13] and French Fission Product Programme [IRSN Proprietary Refs. 20, 

21, 22, 23, and 24] critical experiments, all critical experiments used in this work are described 

in the IHECSBE (Ref. 9). Section 5 provides a complete list of experiments used. 

3.2.2 Similarity of Application and Critical Experiment Models 

The primary objective of computational method validation is to establish the relationship 

between reality and calculated results. For validation of criticality calculations, this is 

accomplished with comparisons between measured critical conditions and calculated keff values 

of LCEs. The generally accepted guidance for critical experiment selection is that the critical 

experiments should be as similar to the application model as is practical and that the same 

computational method should be used for both critical experiment and application models. 

Unfortunately, a high degree of similarity occurs only in cases in which critical experiments were 

designed to simulate the real operational situation. Much more frequently, the analyst is 

confronted with validating an application model that varies from available critical experiment 

descriptions. This is particularly true for BUC application models because there are no LCEs 

that include enriched uranium, plutonium, other actinides, and FPs in the same proportions 

contained in commercial SNF. Hence, a combination of LCEs is necessary to yield an accurate 

calculation of the bias and bias uncertainty. 

BUC application models involve fuel compositions that include low-enrichment uranium (LEU) 

and, especially at moderate to high burnup values, a significant amount of plutonium, which 

includes a significant 240Pu fraction. Beyond the fuel composition issues, the fuel storage and 
11 

transport application models typically include steel and aluminum as structural materials and 

may include neutron absorbers. No LCEs are driven primarily by burned nuclear fuel; 

consequently, BUC critical experiment validation sets are typically composed of low-enrichment 

UO2 critical experiments and mixed uranium and plutonium oxide (MOX) critical experiments. 

Unless one uses sensitivity and uncertainty (S/U) analysis techniques, the traditional approach 

is often used to determine which critical experiments are similar to a given application model, 

which is based primarily on qualitative characteristics, such as the presence of certain 

fissionable, moderating, and/or neutron-absorbing nuclides; the form and geometry of the 

fissionable material; and global quantitative characteristics such as the ratio of hydrogen to 

fissile nuclide atoms (H/X), fuel pin lattice pitch, and energy of average lethargy of neutrons 

causing fission (EALF). 

3.2.3 Sensitivity Analysis of Application and Critical Experiment 

Models 

The SCALE computer code system includes calculational sequences (i.e., TSUNAMI-1D, -2D, 

and -3D) that can be used to calculate the sensitivity of the keff value of a system to variation of 

the nuclear data used in the keff calculation. The fundamental principle evaluated, which can be 

evaluated with any criticality code, is how the response (e.g., system keff) changes with minor 

variations (i.e., perturbations) to input parameters used to calculate keff. The SCALE-generated 

sensitivities are calculated as a function of nuclide, nuclear reaction, and neutron energy group 

using first-order linear perturbation theory (Ref. 14, Section F22). As calculated by TSUNAMI, 

sensitivity is the fractional change in keff due to a fractional change in a nuclear data value, or 

S ≡ (∆k/k) / (∆σ/σ). A sensitivity of +1.0 means a 1.0 % increase in the value of the nuclear data 

will result in a 1.0% increase in the system keff value. A feature unique to the SCALE sensitivity 

calculations is that the effects of the sensitivity of the multigroup problem-dependent resonance 

calculations to variations in data used in the resonance calculations are included and are 

referred to as the “implicit” contribution to sensitivity. For example, in water-moderated lowenrichment lattices, the 238U resonance calculations are sensitive to the hydrogen-scattering 

cross sections. Consequently, the sensitivity of hydrogen scattering includes an explicit 

component related to its ability to thermalize neutrons and an implicit component that reflects 

hydrogen-scattering impact on 238U resonance calculations. 

TSUNAMI-3D calculations were performed for all application and critical experiment models. 

Direct perturbation calculations were used to confirm the adequacy of the sensitivity data. Direct 

perturbation calculations involve manually varying the composition information around the 

nominal value and using the resulting keff value variations to calculate the total sensitivity. Direct 

perturbation results were compared with TSUNAMI sensitivity results to confirm the adequacy of 

the sensitivity data. 

3.2.4 Similarity Analysis Using Sensitivity Data 

A technique implemented in the SCALE S/U tools can be used to perform detailed comparisons 

of application and critical experiment models. The technique compares the detailed sensitivity 

data for the two systems, giving greater weight to comparisons of sensitivities for nuclides and 

reactions with the highest nuclear data uncertainties. For each model, TSUNAMI-IP combines 

the sensitivity data and the cross-section covariance data to generate nuclide-, reaction-, and 

energy-dependent keff uncertainty data. A correlation coefficient, identified as the ck value, is 

calculated and indicates the degree to which each application and critical experiment model pair 
12 

share keff uncertainty. A high ck value, approaching one, indicates that the two compared 

systems share a similar sensitivity to the same nuclear data uncertainty. Based on the 

assumption that computational biases are due primarily to nuclear data errors and that the 

nuclear data uncertainty values should indicate the potential for such nuclear data errors, two 

highly correlated systems should exhibit the same computational bias. 

Oak Ridge National Laboratory (ORNL) experience (Ref. 25) with the SCALE S/U tools has 

indicated that a critical experiment is similar to an application model if the ck value ≥ 0.9. Critical 

experiments with ck values between 0.8 and 0.9 are considered marginally similar, and use of 

experiments with ck values below 0.8 is not recommended. The use of S/U techniques to assess 

similarity is discussed in more detail in Section 6.2.1. 

3.2.5 Model-Specific keff Uncertainties Due to Nuclear Data 

Uncertainties 

All nuclear data used in criticality calculations have some uncertainty. The amount of uncertainty 

varies with the type of data; the experimental apparatus used to measure the data; the quality 

and amount of measured data from which the nuclear data are derived; and the evaluation 

technique used to convert the experimental data into formats suitable for use in the 

computational method. Uncertainty associated with the latter includes uncertainties related to 

fitting sometimes conflicting data from multiple sources, interpolation between measurements, 

use of nuclear models to fill in gaps between sometimes sparse data, fitting of resonance data 

to nuclear data library formats, and creation of multigroup data from pointwise evaluated data. 

This nuclear data uncertainty can be correlated among different neutron energy groups, 

different nuclear reactions, and different nuclides. To quantify the degree of correlation and 

effects, covariance matrices are needed. 

High-fidelity covariance data are available for only a limited number of nuclides. A collaborative 

effort involving nuclear data experts from Brookhaven National Laboratory (BNL), Los Alamos 

National Laboratory (LANL), and ORNL has developed approximate covariance data for nearly 

all other nuclides and reactions of interest. These high- and low-fidelity covariance data are 

combined in the SCALE 44-group covariance data file, which is a comprehensive covariance 

library representing 401 materials (Ref. 14, Section M19.1), including those relevant to BUC 

calculations. This information is in the form of variance and covariance information, where 

covariance is the degree to which different data and their uncertainties are related to each other. 

Model-specific sensitivity data, in units of (∆k/k)/(∆σ/σ), can be used to translate nuclear data 

uncertainties, which are in units of ∆σ/σ, into uncertainty in the model keff value. 

Frequently, the use of 44-group covariance data with 238-group neutron transport calculations 

is questioned. Use of the 44-group data is acceptable because, whereas the nuclear data vary 

significantly within the 238 neutron-energy-group structure, the fractional uncertainty does not. 

Nuclear data uncertainties are more a product of the measurement and evaluation processes 

and do not vary as much over a broader range (see Section 3.2.7.1 for an illustrative example). 

The SCALE TSUNAMI-IP module (Ref. 14, Section M18.1) was used to calculate detailed keff

uncertainty information for each application model using the process described in 

Section F22.2.5 of Ref. 14. Note that the uncertainty calculation incorporates correlations in 

uncertainties among energy groups, among reactions, and, in some cases, among nuclides. 

Such correlations may exist because a measurement technique has been calibrated using one 

nuclide to measure the value for another. A different type of correlation is one in which nuclear 
13 

data are not measured but are calculated from two other measured quantities (e.g., the 

scattering cross section could be determined from the difference between the total cross section 

and the absorption cross section). 

Conventional validation analyses use LCEs that are as similar as possible to the safety analysis 

models, and statistical analysis of the LCE results, to determine bias and bias uncertainty. 

Attention to the range of applicability of the LCEs is necessary to identify weaknesses in the 

validation. Such weaknesses may consist of missing materials, materials not present in the 

correct proportions, extra materials present only in the LCEs, geometry differences, neutron 

energy spectra differences, and others. Historically, when an analyst could not validate a 

particular material in a safety analysis model, the analyst typically either removed the material or 

used a ∆k penalty or uncertainty based on engineering judgment (Ref. 6). The S/U analysis 

tools calculate the uncertainty in keff due to nuclear data uncertainties, creating a way to 

quantify keff bias associated with errors in the nuclear data in order to address these validation 

weaknesses using a quantifiable basis (Ref. 26). 

Figures 3.2 through 3.5 present the individual calculated biases for 609 LCEs described and 

used in this report, along with the uncertainty in keff due to nuclear data for each experiment. In 

these figures, the Bias is the calculated keff minus the critical experiment evaluator expected keff

(e.g., from IHECSBE); the experiment uncertainty is the evaluator-reported uncertainty for the 

expected keff value (e.g., from IHECSBE); and the cross-section uncertainty is the SCALE 

TSUNAMI-IP calculated keff uncertainty due to the cross-section uncertainties. Note that the 

Monte Carlo calculation uncertainty is not shown but would follow the bias and would be 

negligible compared with the uncertainties illustrated. Ignoring the contribution of experimental 

uncertainty to the bias and thereby assuming that the bias is due entirely to nuclear data errors, 

one would expect that around 67% of the individual critical experiment biases would be within 

one standard deviation of nuclear data uncertainty. Including the effect of critical experiment 

design and measurement uncertainty should spread the distribution of experiment-specific bias 

values somewhat. Figure 3.2 shows the results for 124 LEU LCEs. Note that 98% of the 

calculated bias values are within one standard deviation of the uncertainty in keff due to nuclear 

data uncertainty. This suggests that the nuclear data uncertainties are overestimated. The 

extreme outliers, such as experiment number 57, are probably the result of poor experiment 

description. Figures 3.3 through 3.5 show similar information for the 194 mixed Pu+U LCEs, the 

156 French HTC LCEs, and the 135 French FP experiments. In the Pu+U configurations, 71% 

of the calculated biases are within one standard deviation. The average over the four sets, 

containing 609 LCEs, is that 90% of the LCE-calculated biases fall within one standard deviation 

of the expected value. 

The purpose of these comparisons is to provide confidence that the uncertainty in keff due to 

nuclear data uncertainties can be used to provide bounding estimates of the actual bias values. 

Since each critical experiment uses the same nuclear data set, there is a significant source of 

common or systematic error. The impact of the systematic error is best quantified using the 

average or trended bias. The variability around the average bias reflects the variability in the 

critical experiment systems and does not reflect the ability of the computational method to 

accurately calculate keff for a safety analysis model. Based on Figures 3.2 through 3.5, the 

nuclear data uncertainty, even at the one-standard-deviation level, provides a good estimate for 

how large the computational bias could be, and using two or three standard deviations would 

provide a conservative bounding estimate for the bias. 
14 

The estimated bias values from the nuclear data uncertainties are related to the cross-section 

data measurements and evaluations. Since the various ENDF versions are derived from the 

same nuclear data measurements it is reasonable to believe that using other criticality codes 

with the same nuclear data should yield similar biases. Consequently, use of nuclear data 

uncertainties to provide a conservative estimate of the bias for commonly used criticality codes 

is appropriate. Cross-section processing may be different (e.g., continuous energy) for other 

criticality codes, but this will be captured through the validation process with applicable critical 

benchmark experiments. Confirmation of the applicability of this approach (i.e., the use of 

uncertainties in keff due to nuclear data uncertainties as a conservative estimate of the actual 

bias for unvalidated nuclides) for use with other criticality code systems could be demonstrated 

with nuclide worth comparisons. 

This method will be applied below to the application models to yield information on the 

uncertainty in keff due to nuclear data uncertainty for the application models. 
15

Figure 3.2 Comparison of calculated biases and experiment-specific nuclear data uncertainty in keff for 124 LEU LCEs. 

‐8.0E‐03

‐6.0E‐03

‐4.0E‐03

‐2.0E‐03

2.0E

0.0E+00

‐03

4.0E‐036.0E‐038.0E‐031.0E‐021.2E‐021.4E‐02

0 10 20 30 40 50 60 70 80 90 100 110 120 130

eff

kΔ

Experiment Number

Cross‐Section Uncertainty (+1 σ)Experiment Uncertainty (+1 σ)Zero BiasBias (calculated ‐ expected)Experiment Uncertainty (‐1 σ)Cross‐Section Uncertainty (‐1 σ)

98% within 1 σ

cross‐section uncertainty
16

Figure 3.3 Comparison of calculated biases and experiment-specific nuclear data uncertainty in keff for 194 Pu+U LCEs. 

‐3.0E‐02

‐2.5E‐02

‐2.0E‐02

‐1.5E‐02

‐1.0E‐02

‐5.0E‐03

5.0E

0.0E+00

‐03

1.0E‐021.5E‐022.0E‐022.5E‐023.0E‐02

0 20 40 60 80 100 120 140 160 180 200

eff

kΔ

Experiment Number

Cross‐Section Uncertainty (+1 σ)Experiment Uncertainty (+1 σ)Zero BiasBias (calculated ‐ expected)Experiment Uncertainty (‐1 σ)Cross‐Section Uncertainty (‐1 σ)

71% within 1 σ

cross‐section uncertainty
17

Figure 3.4 Comparison of calculated biases and experiment-specific nuclear data uncertainty in keff for 156 French HTC 

LCEs. 

‐8.0E‐03‐6.0E‐03

‐4.0E‐03‐2.0E‐03

2.0E

0.0E+00

‐03

4.0E‐036.0E‐038.0E‐031.0E‐02

1.2E‐02

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

eff

kΔ

Experiment Number

Cross‐Section Uncertainty (+1 σ)Experiment Uncertainty (+1 σ)Zero BiasBias (calculated ‐ expected)Experiment Uncertainty (‐1 σ)Cross‐Section Uncertainty (‐1 σ)

98% within 1 σ

cross‐section uncertainty
18

Figure 3.5 Comparison of calculated biases and experiment-specific nuclear data uncertainty in keff for 135 French FP 

LCEs. 

‐8.0E‐03

‐6.0E‐03

‐4.0E‐03

‐2.0E‐03

2.0E

0.0E+00

‐03

4.0E‐036.0E‐038.0E‐031.0E‐021.2E‐02

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

eff

kΔ

Experiment Number

Cross‐Section Uncertainty (+1 σ)Experiment Uncertainty (+1 σ)Zero BiasBias (calculated ‐ expected)Experiment Uncertainty (‐1 σ)Cross‐Section Uncertainty (‐1 σ)

100% within 1 σ

cross‐section uncertainty
19 

3.2.6 Trending Analysis and Bias and Bias Uncertainty Determination 

Computational method validation includes determination of bias and bias uncertainty based on 

statistical analysis of critical experiment simulation results. The bias and bias uncertainty 

sometimes vary significantly as a function of one or more characteristics of the critical 

experiments. For example, the bias and bias uncertainty may vary as a function of the soluble 

boron concentration used in the experiments, or as the neutron energy spectrum shifts to lower 

or higher energies. According to applicable standards and guidance (e.g., Refs. 3 and 27), the 

statistical analysis should include evaluation of the LCE results for trends occurring as functions 

of relevant parameters such as soluble boron concentration, EALF, fuel pin pitch, fissile 

concentration/enrichment, H/X atom ratios, and plutonium weight fraction (i.e., g Pu per g U+Pu) 

that may affect the bias and bias uncertainty. Since BUC analyses typically include fuel 

compositions that have a varying U to Pu ratio, and the biases associated with U and Pu may 

be significantly different, trending analysis for BUC validation should include a trend reflecting 

the in-growth of plutonium with fuel burnup. 

Typically, trending analysis is performed by calculating a linear fit of the critical experiment 

results as a function of the trend parameters. Fits should include weighting with the uncertainty 

associated with each critical experiment result. NUREG/CR-6698, Guide for Validation of 

Nuclear Criticality Safety Calculational Methodology (Ref. 28), provides recipes and guidance 

that may be useful for trending analysis. For the work documented in this report, the USLSTATS 

(Refs. 18 and 19) computer code was used for single-parameter trending analyses. 

An issue frequently encountered in examining trends is that the process yields multiple values 

for bias and bias uncertainty from the various fits, and it is not clear which bias and bias 

uncertainty should be used. Generally, to be conservative, the most restrictive bias and bias 

uncertainty resulting from the trending analyses is used. Exceptions should be thoroughly 

researched and justified. 

An additional trending parameter, ck, is used in this report. As discussed in Section 3.2.4, the ck

parameter is a correlation coefficient indicating how similar an experiment is to an application 

model. If the validation set includes a significant number of high-ck-value critical experiments, 

trending and extrapolation of the bias and bias uncertainty to a ck value of 1.0 should yield the 

most accurate value for the bias and bias uncertainty. A strength of the ck value trending 

technique is that it includes the effects of all trends at the same time. Many other trending 

techniques either are 1D, considering only variation of the targeted parameter, or, as in the case 

of EALF, trend only global quantities. One might object to the extrapolation of the ck trend to a 

value of 1.0 because extrapolation is typically not permitted unless the source of the trend is 

thoroughly understood. However, extrapolation of ck to 1.0 is not really extrapolation, but rather 

interpolation to the center of an n-dimensional space. It can be thought of in three dimensions 

as interpolating to the center of a sphere along different rays. The ck trending method should not 

be used unless there are a significant number of experiments with ck values of no less than 0.9. 

Otherwise, the interpolation would be over too large a range. Reference 25 discusses how to 

determine what a significant number of experiments is, and recommends 25 to 40 experiments 

with ck values of 0.8 or higher including 15 to 20 with ck values of 0.9 or higher. 

The bias is the best-estimate difference between calculated and expected keff values. A bias is 

called positive when the computational method calculates higher keff values than are expected. 

In general, credit is not taken for positive biases in safety analyses. This does not mean that 
20 

every positive contributor toward the bias should be discarded. The overall bias is a combination 

of many positive and negative biases. Discarding positive partial biases just because they have 

been explicitly quantified is not appropriate. 

There are two components to the bias uncertainty: (1) the uncertainty in the mean bias value 

and (2) the sometimes overlooked uncertainty associated with spread of the critical experiment 

results. Including the uncertainty associated with the population variance is required to address 

the following requirements from 10 CFR 50.68 (b)(4): 

(4) If no credit for soluble boron is taken, the k-effective of the spent fuel storage racks 

loaded with fuel of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 

percent probability, 95 percent confidence level, if flooded with unborated water. If credit 

is taken for soluble boron, the k-effective of the spent fuel storage racks loaded with fuel 

of the maximum fuel assembly reactivity must not exceed 0.95, at a 95 percent 

probability, 95 percent confidence level, if flooded with borated water, and the k-effective 

must remain below 1.0 (subcritical), at a 95 percent probability, 95 percent confidence 

level, if flooded with unborated water. 

Inclusion of the population variance is required because the probability and confidence level 

cited in 10 CFR 50.68(b)(4) is associated with a single configuration, which is assumed to be 

from the same population as the critical experiments, meeting the applicable keff criterion. It is 

required that if one additional calculation, assumed to be from the same distribution, is 

performed, the keff must be low enough that there is a 95% probability with a 95% confidence 

level that the keff value is below the applicable limit. Thus, ignoring the impact of discarded 

positive biases, the 95/95 bias and uncertainty should be below 95% of the critical experiment 

values; and it should be far enough below to support a 95% confidence band on the 95% 

probability level. Similar guidance is provided in the standard review plans (SRPs) for SNF dry 

storage facilities (Ref. 29), dry cask storage systems (Ref. 30), and transportation packages for 

SNF (Ref. 31). 

Many techniques can be used to calculate bias and bias uncertainty. Some examples are 

provided in NUREG/CR-6698 (Ref. 28); the work presented in this report used the USLSTATS 

computer program (Refs. 18 and 19). Care must be taken to ensure that the application of the 

statistical method meets all assumptions and prerequisites associated with the method. For 

example, many methods rely on an assumption that the population of critical experiments is 

normally distributed. If the distribution is not normal, the uncertainty associated with the 95% 

probability and 95% confidence levels may be significantly in error. Typically, nonparametric 

methods are used when distribution normality cannot be established. 

For the purposes of this report, the bias is the difference between the best-estimate fit of the 

adjusted calculated keff values and 1.0. The calculated keff values are adjusted by dividing each 

value by the “expected” value for the critical experiment model. The expected values, where 

available, include adjustments for modeling simplifications and approximations on the measured 

or inferred keff value. The IHECSBE (Ref. 9) evaluations describe recommended models and 

provide expected keff and experimental uncertainty values. Bias uncertainty values presented in 

this report will be either the 95/95 uncertainty, which includes the population variance and 

tolerance factor, or the uncertainty on the mean bias value. 
21 

3.2.7 Fission Product Bias Analysis Techniques 

Laboratory critical experiments, including those with FPs, are described in Section 5. The FP 

LCEs are driven solely or primarily by 235U fission, include insufficient or no plutonium, and/or 

include FPs in compositions that do not approximate those found in SNF. Hence, the FP LCEs 

do not support FP bias calculations with typical trending analysis techniques as described in 

Section 3.2.6. Consequently, it is necessary to use alternative techniques to estimate biases 

associated with FP nuclear data. These techniques include the use of nuclear data uncertainty 

information, qualitative examination of FP critical experiments for biases, and FP bias estimates 

using the GLLSM implemented in TSURFER, as described in Appendix C. 

3.2.7.1 Fission Product Nuclear Data Uncertainty 

The use of nuclear data uncertainty to estimate actual bias values is described in Section 3.2.5. 

Fission products do not fission and have an insignificant neutron scattering contribution 

compared with other materials present. They are also present only at low densities in 

commercial light water reactor (LWR) SNF, so the only relevant nuclear reaction is neutron 

capture (i.e., neutron absorption followed by  emission). The neutron absorption contribution is 

primarily from thermal neutron absorption and absorption in a few resonances. Figure 3.6 shows 

the sensitivity of keff to the 149Sm neutron capture cross section, the 149Sm neutron capture 

cross sections, and the neutron capture cross-section uncertainties without associated 

covariances (note how the 44-group cross-section uncertainties are constant over the energy 

range where the 238-group cross-section data varies significantly, demonstrating the 

acceptability of using the 44-group covariance data with 238-group neutron transport 

calculations). Quantification of the uncertainty in keff due to 149Sm nuclear data uncertainty 

involves combining the sensitivity data from the top plot in the figure with the uncertainty data in 

the bottom plot, including consideration of the nuclear data covariances. Figure 3.7 shows how 

the cross-section uncertainties are correlated among energy groups for the n, reaction data for 

149Sm. A mathematical description of how the uncertainties are calculated is included in Section 

F22.2.5 of Ref. 14. 

Figure 3.7 shows that in the thermal neutron energy range (energy groups 25 to 44) and in the 

resonance region energy range (energy groups 15 to 24), cross-section uncertainties within 

each range are 100% correlated in the SCALE covariance library. In the fast neutron energy 

range (energy groups 1 to 14), the uncertainties are less correlated and negative correlations 

exist between some of the fast neutron energy groups. The combination of the keff sensitivity 

data and the nuclear data uncertainty information yields the uncertainty in the keff value for the 

application model due to the uncertainty in the 149Sm cross sections. This uncertainty can then 

be used to provide a bounding estimate for how large the keff bias due to 149Sm nuclear data 

errors could be. 
22 

Figure 3.6 (Top) samarium-149 keff sensitivity, (center) (n,) cross sections, and 

(bottom) (n,) cross-section uncertainty. 
23 

Figure 3.7 Samarium-149 (n,) cross-section correlation matrix. 

3.2.7.2 Examination of FP LCE Results 

Critical experiments that include FPs are described in Section 5. Although none of the existing 

critical experiments is directly applicable for bias determination for the BUC application models, 

the results can be examined for trends that may be useful in estimating FP biases. For example, 

examination of the LEU-COMP-THERM-050 149Sm LCE cases shows that as the amount of 

samarium is increased, the difference between calculated and experimental keff values rises. If 

there were no competing effects, this would indicate that the 149Sm capture cross section is too 

small and that there is an increasingly positive (i.e., kcalc – kexpected > 0) computational bias 

associated with an increasing presence of 149Sm in a thermal neutron energy spectrum. It 

should then be possible to estimate how much the computational bias changes as the amount 

of 149Sm changes and thus to determine a bias applicable to the safety analysis model. The 

results for sets of FP critical experiments, appropriate for application to the BUC application 

models, were examined for trends and biases. Determination of FP biases from FP LCEs is 

discussed in detail in Section 6.4. 

 

25 

4. APPLICATION MODELS 

Application models were generated representing PWR and BWR SFP configurations and a 

PWR cask configuration. The PWR configurations included a Westinghouse 17×17 optimized 

fuel assembly (OFA) burned from 0 to 70 GWd/MTU, whereas the BWR configuration included 

a generic 10×10 assembly design burned to about 11 GWd/MTU. These assembly designs 

were selected because they are used in many reactors and are considered to be representative 

of limiting fuel assembly designs in criticality safety applications. Example TRITON input files 

are provided in Appendix D showing the representative depletion parameters used for the PWR 

and BWR assemblies. The PWR SFP application models were generated without soluble boron 

in the SFP and a target keff value of 0.99. The 1% ∆k reduction from 1.0 was included to 

approximate the impact of including bias and bias uncertainty. The GBC-32 target keff value was 

0.94 and was represented as being flooded with full-density water. The BWR SFP configuration 

was representative of limiting SFP conditions (i.e., an assembly at peak reactivity). 

PWR application models were developed for the following six cases: 

 Actinides only 

– BUC with SNF composition consisting of actinide nuclides only (i.e., 234U, 235U, 236U, 238U, 

237Np, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, and 243Am). SFP model developed for 0 

ppm soluble boron in the SFP with a target keff value of 0.99. 

– BUC in a cask configuration with a target keff value of 0.94. 

 Actinides and 16 FPs 

– BUC with SNF composition consisting of “actinides-only” nuclides and 16 FPs (i.e., 95Mo, 

99Tc, 101Ru, 103Rh, 109Ag, 133Cs, 143Nd, 145Nd, 147Sm, 149Sm, 150Sm, 151Sm, 152Sm, 151Eu, 

153Eu, and 155Gd). SFP model developed for 0 ppm soluble boron in the SFP with a 

target keff value of 0.99. 

– BUC in a cask configuration with a target keff of 0.94. 

 Actinides and all FPs 

– BUC with SNF composition consisting of all nuclides supported by the SCALE code 

system. SFP model developed for 0 ppm soluble boron in the SFP with a target keff value 

of 0.99. 

– BUC in a cask configuration with a target keff of 0.94. 

The cask application model assumed a 5-year cooling period as is typical for dry storage cask 

and transportation package evaluations. The PWR SFP application models assumed a 3-day 

postirradiation decay period. 

A single BWR SFP application BUC model was also developed using “actinides and all FPs” 

BUC for 0 ppm soluble boron at peak reactivity. The BWR SFP application assumed a 3-day 

postirradiation decay period. 
26 

Details of the application models are provided below. The application models are considered to 

be similar to or representative of models that applicants use in their criticality analyses. 

4.1 PWR SPENT NUCLEAR FUEL POOL APPLICATIONS 

The PWR fuel storage rack is modeled as a laterally infinite array of loaded fuel storage cells 

reflected on the top and bottom by 30 cm of full-density water. Each storage cell is a stainless 

steel box having an internal dimension of 22.352 cm (8.8 in.) and a wall thickness of 0.292 cm 

(0.115 in.). One 0.203-cm-thick (0.080-in.-thick) Boral® plate with a 0.020 g 10B/cm2

 loading is 

modeled between each storage cell. The center-to-center spacing for this model is 23.139 cm 

(9.110 in.). The 17 × 17 OFA is modeled as centered in the storage cell. Only the 365.76 cm 

(12 ft) of active fuel length of the assembly is modeled. The poison panels are also modeled to 

the same axial length. 

Figure 4.1 shows an overhead view of the model, and Figure 4.2 shows three BUC loading 

curves, Actinides-only, Actinides & 16 FP, and Actinides & all FP. The numbers in the grid in 

Figure 4.2 identify the number of PWR assemblies within a given burnup and enrichment range 

as taken from the RW-859 database (Ref. 32), which includes data on the US commercial LWR 

SNF inventory as of 2002. Table 4.1 shows some key parameters for the application models at 

two burnups, 10 and 40 GWd/MTU, for evaluations of the potential for variation in biases as a 

function of burnup. The final uranium enrichment and plutonium fraction vary axially as a result 

of the use of axial burnup profiles. Two averages are presented for these parameters. One is 

the simple average from each of the 18 axial zones. The second uses the axial fission density 

fraction as a weighting factor, thus giving increased weight to the axial zones having the most 

impact on system neutron multiplication. For bias and bias uncertainty determination, use of the 

fission density weighted values is more appropriate. 

The burned fuel compositions used in the SFP models were generated using the SCALE 

STARBUCS sequence and an ORIGEN/ARP library generated using TRITON and the 

ENDF/B-VII 238 energy group library. It included 24 wet annular burnable absorber (WABA) 

rods for the entire depletion. The WABA rods were included throughout the depletion because 

they cause the neutron spectrum to be harder during irradiation, resulting in a conservative 

representation of the SNF residual reactivity level. The STARBUCS loading curve search 

options were used to find the initial 235U enrichment that, when depleted to the target assembly 

average burnup value, produced a rack model keff value of 0.99. 
27 

Figure 4.1 PWR SFP application model. 

Fuel pin unit cell 

Guide tube unit cell 

Moderator 

Neutron absorber panel 

Steel 
28 

Figure 4.2 Burnup credit loading curves for PWR SFP application models. 

Table 4.1 Key parameters from PWR SFP application models 

Simple average Fission density 

weighted average 

BUC type 

Initial enr. 

(w/o 235U) 

BU 

(GWd/MTU) 

EALF 

(eV) 

Final enr. 

(w/o 235U)

Pu/(Pu+U) 

(w/o Pu) 

Final enr. 

(w/o 235U) 

Pu/(Pu+U) 

(w/o Pu) 

Actinides-only 2.25 10 0.190 1.440 0.579 1.548 0.507

Actinides-only 3.72 40 0.233 1.072 1.303 1.330 1.182

Actinides &16 FP 2.50 10 0.199 1.658 0.566 1.848 0.447

Actinides &16 FP 4.74 40 0.277 1.712 1.299 2.188 1.114

Actinides & all FP 2.59 10 0.202 1.735 0.562 1.956 0.427

Actinides & all FP 5.15 40 0.295 1.995 1.298 2.227 1.212

Note: w/o = weight percent 

0

10

20

30

40

50

60

70

1.5 2 2.5 3 3.5 4 4.5 5

Final Assembly Average Burnup (GWd/MTU)

Initial Enrichment (wt % 235U)

Actinides-only

Actinides & 16 FP

Actinides & all FP

Acceptable

Not Acceptable
29 

4.2 CASK APPLICATION 

A generic cask model with a 32-PWR assembly capacity, referred to as the GBC-32 and 

described in NUREG/CR-6747 (Ref. 33), was previously developed to serve as a computational 

benchmark. The features of the GBC-32 model include 32 cells with 365.76-cm-tall and 

19.05-cm-wide Boral® (0.0225 g 10B/cm2

) panels between and on the external faces of each cell. 

The cells have inner dimensions of 22 by 22 cm and are spaced on 23.76 cm centers. The cell 

walls are constructed of stainless steel. The cells sit 15 cm above the bottom of a stainless steel 

cask having an inner radius of 87.5 cm and internal height of 410.76 cm. The radial thickness of 

the side walls is 20 cm, and the cask bottom and lid are 30 cm thick. Figure 4.3 shows a 

cutaway view of the KENO V.a cask model, and Figure 4.4 shows the three BUC loading curves 

for the GBC-32 superimposed over the RW-859 database PWR inventory. 

The cask was modeled as loaded with Westinghouse 17×17 OFA assemblies with assembly 

average burnups of up to 70 GWd/MTU. The fuel compositions were generated using the 

SCALE STARBUCS sequence and an ORIGEN/ARP library generated using TRITON and the 

ENDF/B-VII 238 energy group library. They included 24 WABA rods for the entire depletion. The 

STARBUCS loading curve search options were used to find the initial 235U enrichment that, 

when depleted to the target assembly average burnup value, produced a keff value of 0.94. The 

target keff value was reduced from 0.95 by 0.01 ∆k to leave margin for bias and bias uncertainty. 

Separate loading curves were determined and models generated for actinide-only BUC, actinide 

plus 16 FP BUC, and BUC using all actinides and FPs available in the SCALE ORIGEN and 

ENDF/B-VII 238-energy-group libraries. Table 4.2 shows some key parameters for the 32 PWR 

GBC application models at two burnups, 10 and 40 GWd/MTU, for evaluation of the potential for 

variation in biases as a function of burnup. The final uranium enrichment and plutonium fraction 

vary axially as a result of the use of axial burnup profiles. Two averages are presented for these 

parameters. One is the simple average from each of the 18 axial zones. The second uses the 

axial fission density fraction as a weighting factor, thus giving increased weight to the axial 

zones having the most impact on system neutron multiplication. As discussed earlier, for bias 

and bias uncertainty determination, use of the fission density weighted values is more 

appropriate. 
30 

Figure 4.3 Cutaway view of the GBC-32 cask showing the cask bottom half with a 

quarter of the model removed. 
31 

Figure 4.4 Burnup credit loading curves for GBC-32 application models. 

Table 4.2 Key parameters from application models (GBC-32) 

Simple average Fission density 

weighted average 

BUC type Initial enr. 

(w/o 235U) 

BU 

(GWd/MTU)

EALF 

(eV) 

Final enr.

(w/o 235U)

Pu/ (Pu+U) 

(w/o Pu) 

Final enr. 

(w/o 235U) 

Pu/(Pu+U)

(w/o Pu) 

Actinides-only 2.04 10 0.190 1.262 0.588 1.480 0.433

Actinides-only 3.49 40 0.229 0.942 1.278 1.181 1.162

Actinides & 16FP 2.34 10 0.200 1.511 0.572 1.748 0.418

Actinides & 16FP 4.68 40 0.285 1.663 1.268 1.985 1.146

Actinides & all FP 2.37 10 0.201 1.540 0.570 1.780 0.416

Actinides & all FP 4.90 40 0.295 1.815 1.267 2.150 1.144
32 

4.3 BWR SPENT NUCLEAR FUEL POOL APPLICATION 

In BWRs, the fuel bundles typically include some fuel rods in which gadolinia (Gd2O3) is mixed 

with the UO2 in the fuel pellets. Gadolinium is a strong neutron absorber that burns out relatively 

quickly. Gadolinium depletion causes the fuel bundle reactivity to rise to a peak value that, for 

the limiting fuel assemblies, occurs at assembly average burnup values below 20 GWd/MTU. 

Since reactivity initially increases with burnup, using the fresh fuel bundle in the fuel storage 

analysis would not be conservative if the gadolinium rods were modeled. However, analyses in 

which the gadolinium fuel rods are substituted with fresh, unpoisoned fuel rods will provide 

conservative results that are very restrictive over the first cycle of burnup. Consequently, 

criticality analyses of BWR fuel storage pools are usually performed with fuel at the maximum or 

“peak” reactivity point. Although some applicants have been working to credit fuel burnup 

beyond the peak reactivity point, this has not typically been done in BWR fuel storage rack 

analyses. 

BWR fuel assemblies have initial 235U enrichments that may vary axially and radially. The 

number of fuel rods with Gd2O3 and the weight fraction of the Gd2O3 in these rods may also 

vary. Modern BWR fuel assembly designs also use part-length fuel rods, allowing for additional 

water in the upper parts of the assembly. Because of the number of assembly lattice variations, 

BWR criticality analyses characterize each lattice, depleted in hot reactor conditions, according 

to its maximum 2D k∞ in standard cold core geometry (SCCG) (i.e., an infinite lattice of 

assemblies with a 6 in. pitch at 20°C moderator temperature with no voids or control absorbers) 

(Ref. 34). After the peak k∞ is identified, the fuel compositions from the peak k∞ burnup are 

typically decayed for 3 days, to allow xenon decay, and then used in a fuel storage rack model 

to establish the relationship between peak SCCG k∞ and the keff for the fuel storage rack model. 

This relationship identifies the maximum SCCG k∞ that will result in a fuel storage rack keff that 

meets the regulatory requirement. 

The red curve in Figure 4.5 shows the burnup-dependent behavior of the SCCG k∞ for an 

assembly that contains eight Gd2O3 rods. The green curve shows the SCCG k∞ for the same 

assembly without Gd2O3. The purpose of the figure is to illustrate the credit taken for fuel burnup 

in the BWR fuel storage rack analysis. Figure 4.6 shows the relationship between the SCCG k∞

and the k∞ at hot full-power reactor conditions. 

The BWR application model is shown in Figure 4.7. Note that there are many variants of BWR 

assembly designs that could have been modeled, but the application model in this report is 

provided to be representative of commonly used BWR designs and will not exactly match an 

actual design. The modeled assembly is a 10×10 array of 5 wt % 235U fuel rods burned to about 

11 GWd/MTU. The assembly included eight 3 wt % Gd2O3 in UO2 fuel rods and two water rods 

that displace eight fuel rods. The Gd2O3+UO2 rods are modeled using five equal-volume radial 

regions to accurately model the gadolinium depletion. The assembly is stored in a 0.2-cm-thick 

Zircaloy fuel channel having an inner dimension of 12.95 cm. Each fuel storage rack cell is 

modeled as a square tube of steel that is 0.18 cm thick and has an inner dimension of 14.75 cm. 

A single B4C plus aluminum plate (representative of Boral®) is placed between each storage 

cell. Each neutron-absorbing plate is 0.203 cm thick and 11.64 cm wide and has a neutron 

absorber loading of 0.020 g 10B/cm2

. The model has reflected boundary conditions on all sides 

and so is effectively infinite in all directions. The initial enrichment, number of gadolinium rods, 

gadolinium rod enrichment, and storage cell pitch were selected so that when the fuel is 

depleted to peak reactivity, the fuel storage rack model has a calculated keff value of 0.94. The 

target keff value was reduced from 0.95 by 0.01 ∆k to leave margin for bias and bias uncertainty. 
33 

The peak SCCG was indentified and the burned fuel compositions calculated using the SCALE 

TRITON 2D depletion sequence. The in-rack keff value was calculated using the SCALE CSAS6 

sequence. The EALF for the BWR application model is 0.456 eV. The burned fuel fissiondensity-weighted average composition included uranium with a 235U enrichment of 3.82 wt % 

and a plutonium-to-uranium ratio of 0.331 wt % Pu. 

Figure 4.5 Burnup credit and BWR peak SCCG k∞. 

1.2

1.25

1.3

1.35

1.4

1.45

0 5 10 15 20

Lattice kinfinity in Reactor Geometry

Lattice Average Burnup (GWd/MTU)

In-Reactor, SCCG kinf

In-Reactor, No Gd, SCCG kinf

Residual Gd Credit

Burnup Credit
34 

Figure 4.6 Relationship between hot full-power k∞ and SCCG k∞. 

1.23

1.24

1.25

1.26

1.27

1.28

1.29

1.3

1.31

1.32

0 5 10 15 20

Lattice kinfinity in Reactor Geometry

Lattice Average Burnup (GWd/MTU)

In-Reactor, SCCG

In-Reactor, Hot
35 

Figure 4.7 BWR SFP application model. 

 

Fuel pin unit cell 

Gd rod unit cell 

Channel 

Steel 

Moderator 

Water rod 

Neutron absorber panel 

37 

5. CRITICAL EXPERIMENTS 

A total of 609 critical experiments were used as the initial validation set. As described below, the 

SCALE S/U analysis tools were used to down-select the validation set based on the ck similarity 

correlation coefficient. The initial set included 124 LEU and 194 mixed uranium and plutonium 

critical configurations from the IHECSBE (Ref. 9). The critical configurations used are from the 

following IHECSBE evaluations: 

 LEU-COMP-THERM-001, 002, 010, 017, 022, 023, 024, 026, 042, 050, and 079 

 LEU-MISC-THERM-005 

 LEU-SOL-THERM-002, 003, and 004 

 MIXED-COMP-THERM-001, 002, 003, 004, 005, 006, 007, 008, 009, 011, and 012 

 MIXED-SOL-THERM-001, 002, 004, and 005 

Some of the configurations from LEU-COMP-THERM-050 and 079, and LEU-MISC-THERM005 contain FPs. 

The validation set also included 156 configurations from the HTC experiment set that includes 

actinide nuclides in proportions similar to those for a fuel assembly with an initial enrichment of 

4.5 wt % 235U burned to 37.5 GWd/MTU. The HTC experiment data were published in a series 

of four reports by the French Institut de Radioprotection et de Sûreté Nucléaire (IRSN). The 

experiment descriptions for this set are provided in Refs. 10 through 13 and are considered 

commercial proprietary. There are currently restrictions on who may use the data and for what 

purposes. Data recipients are required to sign a nondisclosure agreement, which includes 

provisions for release of the data to the US Nuclear Regulatory Commission (NRC) and the US 

Department of Energy. 

The validation set also included 135 configurations from the French Fission Product Program 

experiments described in Refs. 20 through 24. The critical experiment descriptions are 

commercial proprietary and are not expected to be released for applicant use. 

Summary descriptions are provided below for the critical experiments. All 609 critical 

configurations were modeled and analyzed with SCALE. Appendix A presents data derived from 

the experiment descriptions and from the calculational results for each critical configuration. 

Note that proprietary data are intentionally excluded from this report. 

The ranges for the key parameters for these critical configurations are as follows: 

 0.0338 ≤ EALF ≤ 1.0 eV 

 0.145 ≤ U enrichment ≤ 59.7 wt % 235U 

 0 ≤ Pu/(Pu + U) ≤ 96.8 wt % Pu 

 0 ≤ Sol. boron concentration ≤ 5030 ppm of B by weight 

5.1 LOW-ENRICHMENT URANIUM EXPERIMENTS 

Included in the initial validation set were 124 LEU critical configurations because applicants 

frequently include LEU configurations in their benchmarking analyses. These configurations are 

all documented in the IHECSBE. 
38 

The LEU configurations considered include the following: 

 8 configurations (cases 1–8) from LEU-COMP-THERM-001. These configurations are watermoderated U(2.35 wt %)O2 fuel rods in 2.032-cm square-pitched arrays. 

 5 configurations (cases 1–5) from LEU-COMP-THERM-002. These configurations are watermoderated U(4.31 wt %)O2 fuel rods in 2.54-cm square-pitched arrays. 

 5 configurations from LEU-COMP-THERM-010. These configurations are water-moderated 

U(4.31 wt %)O2 fuel rods in square pitched arrays reflected by depleted uranium (case 5) or 

steel (cases 16–19). 

 24 configurations from LEU-COMP-THERM-017. These configurations are water-moderated 

U(2.35 wt %)O2 fuel rods in square-pitched arrays reflected by lead (cases 3 and 23–25), 

depleted uranium (cases 4–9 and 28–29), or steel (cases 10–17 and 19–22). 

 7 configurations (cases 1–7) from LEU-COMP-THERM-022. These configurations are 

uniform water-moderated hexagonally pitched lattices of U(10 wt %)O2 fuel rods. 

 6 configurations (cases 1–6) from LEU-COMP-THERM-023. These configurations are 

partially flooded, water-moderated hexagonally pitched lattices of U(10 wt %)O2 fuel rods. 

 2 configurations (cases 1–2) from LEU-COMP-THERM-024. These configurations are watermoderated square-pitched lattices of U(10 wt %)O2 fuel rods. 

 1 configuration (case 3) from LEU-COMP-THERM-026. This configuration is a watermoderated hexagonally pitched lattice of U(4.92 wt %)O2 fuel rods. 

 7 configurations (cases 1–7) from LEU-COMP-THERM-042. These configurations are watermoderated square-pitched arrays of U(2.35 wt %)O2 fuel rods separated by steel (case 1), 

borated(1.1% B)-steel (case 2), Boral (case 3), Boraflex (case 4), cadmium (case 5), copper 

(case 6), or copper with 1% cadmium (case 7) and reflected by steel walls. 

 18 configurations (cases 1–18) from LEU-COMP-THERM-050. These configurations are 

water-moderated, square-pitched lattices of U(4.738 wt %)O2 fuel rods with a central tank 

that contains either water (cases 1–2), boron solution (cases 3–7), or one of three 

concentrations of samarium (enriched to 96.9 wt % 149Sm) solution (cases 8–18). 

 10 configurations (cases 1–10) from LEU-COMP-THERM-079. These configurations are 

water-moderated, hexagonally pitched lattices of U(4.31 wt %)O2 fuel rods with 103Rh foils 

placed between fuel pellets in a fraction of the rods. Cases 3–5 and 8–10 contain 103Rh foils. 

The LEU systems also included the following solution configurations from four IHECSBE 

evaluations: 

 12 configurations (cases 1–12) from LEU-MISC-THERM-005. These configurations are 

square-pitched arrays of U(4.98 wt %)O2 fuel rods sitting in uranyl (6 wt %) nitrate solution 

that includes one or more FP elements Sm, Cs, Rh, and Eu. 

 3 configurations (cases 1–3) from LEU-SOL-THERM-002. These configurations are uranium 

(4.9 wt %) oxyfluoride solution. Cases 1 and 3 are water reflected. 
39 

 9 configurations (cases 1–9) from LEU-SOL-THERM-003. These configurations are bare 

spherical tanks containing aqueous uranyl (10 wt % 235U) nitrate solutions. 

 7 configurations (cases 1–7) from LEU-SOL-THERM-004. These configurations are waterreflected uranyl (10 wt % 235U) nitrate solutions in a cylindrical tank. 

5.2 MIXED URANIUM AND PLUTONIUM EXPERIMENTS 

Included in the initial validation set were 194 mixed uranium and plutonium critical 

configurations. These configurations are all documented in the IHECSBE. Burned fuel with initial 

enrichments and final burnups along a typical BUC loading curve generally have LEU and 

significant plutonium content. For example, the destructive assay composition measurement 

results for Takahama-3 sample SF95-4 from NUREG/CR-6811 (Ref. 35), which had an initial 

enrichment of 4.11 wt % 235U and was burned to 36.69 GWd/MTU, show that the sample had a 

final enrichment of 1.57 wt % 235U; a plutonium content of 1.1 wt % Pu (i.e., 100%g Pu/(g Pu + 

g U)); and a plutonium isotopic vector of 59.2 wt % 239Pu, 24.3 wt % 240Pu, and 10.1 wt % 241Pu. 

All of the mixed Pu + U systems include either natural or depleted uranium, and few have a 

plutonium isotopic vector that is close to the plutonium isotopics of burned fuel. 

The mixed Pu + U systems validation set includes the following: 

 4 configurations (cases 1–4) from MIXED-COMP-THERM-001. These configurations involve 

MOX fuel pins in square-pitched lattices that are moderated and reflected by water. The fuel 

pins include natural uranium, and the plutonium was 86.2 wt % 239Pu, 11.5 wt % 240Pu, and 

1.8 wt % 241Pu. 

 6 configurations (cases 1–6) from MIXED-COMP-THERM-002. These configurations involve 

MOX fuel pins in square-pitched lattices that are moderated and reflected by water. The fuel 

pins include natural uranium, and the plutonium was 91.8 wt % 239Pu, 7.8 wt % 240Pu, and 

0.4 wt % 241Pu. 

 6 configurations (cases 1–6) from MIXED-COMP-THERM-003. These configurations involve 

MOX fuel pins in square-pitched lattices that are moderated and reflected by water. The fuel 

pins include natural uranium, and the plutonium was 90.6 wt % 239Pu, 8.6 wt % 240Pu, and 

0.8 wt % 241Pu. 

 11 configurations (cases 1–11) from MIXED-COMP-THERM-004. These configurations 

involve MOX fuel pins in square-pitched lattices that are moderated and reflected by water. 

The fuel pins include natural uranium, and the plutonium was 68.2 wt % 239Pu, 22.0 wt % 

240Pu, and 7.3 wt % 241Pu. 

 7 configurations (cases 1–7) from MIXED-COMP-THERM-005. These configurations involve 

MOX fuel pins in triangular-pitched lattices that are moderated and reflected by water. The 

fuel pins include natural uranium, and the plutonium was 75.5 wt % 239Pu, 18.2 wt % 240Pu, 

and 4.9 wt % 241Pu. 

 50 configurations (cases 1–50) from MIXED-COMP-THERM-006. These configurations 

involve MOX fuel pins in triangular-pitched lattices that are moderated and reflected by 

water. The fuel pins include natural uranium, and the plutonium was 91.6 wt % 239Pu, 

7.7 wt % 240Pu, and 0.6 wt % 241Pu. The 7th through 50th cases include a hafnium, boron, 
40 

water, or air absorber rod in the center of the array. In cases 17–28 and 39–50, a cadmium 

sleeve was installed on the absorber rod. 

 5 configurations (cases 1–5 of 27) from MIXED-COMP-THERM-007. These configurations 

involve MOX fuel pins in triangular-pitched lattices that are moderated and reflected by 

water. The fuel pins include natural uranium, and the plutonium was 81.1 wt % 239Pu, 

16.5 wt % 240Pu, and 1.8 wt % 241Pu. 

 28 configurations (cases 1–28) from MIXED-COMP-THERM-008. These configurations 

involve MOX fuel pins in triangular-pitched lattices that are moderated and reflected by 

water. The fuel pins include natural uranium, and the plutonium was 71.7 wt % 239Pu, 

23.6 wt % 240Pu, and 4.1 wt % 241Pu. The 7th through 28th cases include an aluminum, 

hafnium, boron, water, or air absorber rod in the center of the array. In cases 17–28 a 

cadmium sleeve was installed on the absorber rod. 

 6 configurations (cases 1–6) from MIXED-COMP-THERM-009. These configurations involve 

MOX fuel pins in triangular-pitched lattices that are moderated and reflected by water. The 

fuel pins include depleted uranium, and the plutonium was 91.4 wt % 239Pu, 7.9 wt % 240Pu, 

and 0.7 wt % 241Pu. 

 6 configurations (cases 1–6) from MIXED-COMP-THERM-011. These configurations involve 

MOX fuel pins in triangular-pitched lattices that are moderated and reflected by water. The 

fuel pins include uranium enriched to 59.7 wt % 235U, and the plutonium was 89.3 wt % 

239Pu, 9.8 wt % 240Pu, and 0.9 wt % 241Pu. 

 33 configurations (cases 1–33) from MIXED-COMP-THERM-012. These configurations 

involve reflected and unreflected polystyrene-moderated mixed oxide cubes and slabs. All 

cases use depleted uranium. The fuel pins in cases 1–6 include plutonium that was 

67.8 wt % 239Pu, 23.0 wt % 240Pu, and 5.6 wt % 241Pu, and in cases 7–33 the plutonium was 

91.2 wt % 239Pu, 8 wt % 240Pu, and 0.6 wt % 241Pu. 

The mixed uranium–plutonium systems also included the following solution configurations from 

four IHECSBE evaluations: 

 13 configurations (cases 1–13) from MIX-SOL-THERM-001. These configurations included 

depleted uranium nitrate mixed with plutonium nitrate in an annular tank with, in some 

cases, an additional bottle of solution located inside the annulus. The plutonium was 

91 wt % 239Pu, 8 wt % 240Pu, and 0.4 wt % 241Pu. Uranium concentrations varied from 2.3 to 

380 g U/L, and the plutonium concentrations varied from 47 to 196 g Pu/L. 

 3 configurations (cases 1–3) from MIX-SOL-THERM-002. These configurations included 

depleted or natural uranium nitrate mixed with plutonium nitrate in a cylindrical tank. The 

plutonium was 91 wt % 239Pu, 8 wt % 240Pu, and 0.4 wt % 241Pu. Uranium concentrations 

varied from 11 to 41 g U/L, and the plutonium concentrations were about 12 g Pu/L. 

 9 configurations (cases 1–9) from MIX-SOL-THERM-004. These configurations included 

depleted uranium nitrate and plutonium nitrate in a cylindrical tank that was either bare or 

reflected by water or concrete. The plutonium in these configurations was 91.1 wt % 239Pu, 

8.3 wt % 240Pu, and 0.5 wt % 241Pu. The uranium concentrations varied from 63 to 

263 g U/L, and the plutonium concentrations varied from 42 to 173 g Pu/L. 
41 

 7 configurations (cases 1–7) from MIX-SOL-THERM-005. These configurations included 

depleted uranium nitrate and plutonium nitrate in a slab tank that was either unreflected or 

reflected by water. The plutonium in these configurations was 91.1 wt % 239Pu, 8.3 wt % 

240Pu, and 0.5 wt % 241Pu. The uranium concentrations varied from 63 to 263 g U/L, and the 

plutonium concentrations varied from 41 to 173 g Pu/L. 

5.3 HAUT TAUX DE COMBUSTION MOX EXPERIMENTS 

In the 1980s, the HTC experiments were conducted by IRSN at the experimental criticality 

facility in Valduc, France. The plutonium-to-uranium ratio and the isotopic compositions of both 

the uranium and plutonium used in the simulated fuel rods were designed to be similar to what 

would be found in a typical PWR fuel assembly that initially had an enrichment of 4.5 wt % 235U 

and was burned to 37.5 GWd/MTU. The fuel material also includes 241Am, which is present from 

the decay of 241Pu. The HTC experiments include configurations designed to simulate fuel 

handling activities, pool storage, and transport in casks constructed of thick lead or steel. The 

HTC critical experiments include the 156 critical configurations described in Refs. 10–13 and 36. 

Rights of use for the HTC experiment data were purchased under an agreement that limits 

release of the information. Consequently, a detailed and complete description of the 

experiments is not presented in this report. The proprietary reports may be obtained from ORNL 

following completion of a nondisclosure agreement with UT-Battelle. An evaluation of the HTC 

experiment data is documented in NUREG/CR-6979 (Ref. 37). 

5.4 FRENCH FISSION PRODUCT PROGRAM EXPERIMENTS 

From 1998 to 2004, a series of critical experiments with FPs was conducted by IRSN at the 

experimental criticality facility in Valduc, France. The experiments focused on seven FP 

nuclides (either individually or as nuclide mixtures in various experiments): 103Rh, 133Cs, 143Nd, 

145Nd, 149Sm, 152Sm, and 155Gd. In all experiments with FPs, the test material was in the form of 

slightly acidic solutions. Three experimental phases (FP Phases 1–3) were performed, each 

distinguished by the manner in which the FP solutions were configured relative to the fuel rods. 

In some experiments, depleted uranium solution, with or without FPs, was used. Reference 

experiments (with dilute nitric acid replacing the FP solutions) were also performed. A total of 

135 experiments are described in a set of five reports (Refs. 20 through 24). The NRC provided 

ORNL staff access to these reports for use in the present work. The reports are commercial 

proprietary information belonging to IRSN. It is not anticipated that these reports will be 

available to the US nuclear industry. Reference 38 provides some useful descriptions of the 

French Fission Product Program experiments. 

In this work, these experiments were used in three ways. First, they were included in the initial 

validation set from which bias and bias uncertainty information was obtained. Second, trends in 

the calculational results for these experiments were used to estimate biases associated with 

individual FPs. Third, the experiments were used in SCALE TSURFER calculations to estimate 

FP biases as described in Appendix C. 

 

43 

6. BIAS AND BIAS UNCERTAINTY 

Bias and bias uncertainty results are presented in this section for validation of the application 

models described in Section 4 using the LCEs described in Section 5 as a function of different 

trend parameters. Comparisons are provided in Section 6.1 using LCEs selected based on 

traditional techniques as discussed in Section 3.2.2. Results are presented using benchmark 

critical experiments from the IHECSBE only, and then also including the proprietary HTC LCEs 

for the application models. Section 6.2 presents bias and bias uncertainty results based on 

benchmark critical experiments selected using the SCALE S/U analysis tools, which is a more 

physics-based approach, as discussed in Section 3.2.4. 

The keff results for the 474 HTC, IHECSBE Pu+U, and LEU critical configurations and for some 

of the subsets of configurations are not normally distributed. The distribution of the results is 

dependent upon the benchmark critical experiments selected for validation, and the nonnormality of the distribution can be accounted for using either more sophisticated statistical 

analysis techniques or nonparametric analysis techniques. For the purposes of the 

demonstrations in this report, the data are assumed to follow a normal distribution because the 

bias and bias uncertainty results are provided for reference only and for examination of trends, 

and this allows a more equal comparison. Results using nonparametric analysis techniques (as 

provided in Ref. 28) for combined bias and bias uncertainty at a 95% probability and 95% 

confidence level are also provided; they are for illustration only, as they are specific to the 

respective critical benchmark experiment population sets used and the SCALE code system on 

the ORNL computer platform. Index values for the one-sided distribution-free tolerance limits 

were taken from Ref. 39. 

6.1 BIAS AND BIAS UNCERTAINTY DETERMINATION 

The USLSTATS computer program was used to determine the bias and bias uncertainty for the 

application models as a function of various trend parameters using LEU, mixed uranium–

plutonium, and the HTC LCEs. The bias and bias uncertainty values presented in this section do 

not use S/U analysis tools and are representative of what would be developed in traditional 

analyses. In the tables that follow, “bias” is calculated as keff minus expected keff (i.e., 1.0 

because calculated keff values were normalized to the experimental values). Thus a positive bias 

would imply the calculated values were higher than the expected values. Positive bias values 

are generally not credited in criticality safety analyses. The “fit uncertainty” is the one-standarddeviation uncertainty in the bias resulting from applying the linear least-squares fitting technique 

to the benchmark critical experiment results. The “bias uncertainty” includes the fit uncertainty 

and tolerance interval multiplier to yield a 95% probability and 95% confidence level. The bias 

results are presented with and without the HTC LCEs for the different trend parameters. 

Table 6.1, Table 6.3, and Table 6.5 provide results without including the HTC LCEs in the 

critical benchmarks used for the trending analysis; and Table 6.2, Table 6.4, and Table 6.6 

provide results that incorporate the HTC LCEs in the trending analysis.
44 

Table 6.1 Bias and uncertainty as a function of EALF using only IHECSBE experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/MTU)

EALF

(eV) 

keff versus EALF Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 0.190 −1.53×10−3 8.22×10−3 1.71×10−2

Actinides-only 3.72 40 0.233 −1.44×10−3

Actinides & 16 FP 2.50 10 0.199 −1.51×10−3

Actinides & 16 FP 4.74 40 0.277 −1.36×10−3

Actinides & all FP 2.59 10 0.202 −1.50×10−3

Actinides & all FP 5.15 40 0.295 −1.32×10−3

32 PWR GBC model 

Actinides-only 2.04 10 0.190 −1.53×10−3 8.22×10−3 1.71×10−2

Actinides-only 3.485 40 0.229 −1.45×10−3

Actinides & 16 FP 2.338 10 0.200 −1.51×10−3

Actinides & 16 FP 4.679 40 0.285 −1.34×10−3

Actinides & all FP 2.372 10 0.201 −1.50×10−3

Actinides & all FP 4.9 40 0.295 −1.32×10−3

BWR SFP model 

Peak SCCG 5.0 11 0.456 −1.00×10−3 8.22×10−3 1.71×10−2

Table 6.2 Bias and uncertainty as a function of EALF using IHECSBE and HTC 

experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/MTU)

EALF

(eV) 

keff versus EALF Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 0.190 −1.45×10−3 6.82×10−3 1.44×10−2

Actinides-only 3.72 40 0.233 −1.40×10−3

Actinides & 16 FP 2.50 10 0.199 −1.44×10−3

Actinides & 16 FP 4.74 40 0.277 −1.34×10−3

Actinides & all FP 2.59 10 0.202 −1.44×10−3

Actinides & all FP 5.15 40 0.295 −1.32×10−3

32 PWR GBC model 

Actinides-only 2.04 10 0.190 −1.45×10−3 6.82×10−3 1.44×10−2

Actinides-only 3.485 40 0.229 −1.40×10−3

Actinides & 16 FP 2.338 10 0.200 −1.44×10−3

Actinides & 16 FP 4.679 40 0.285 −1.33×10−3

Actinides & all FP 2.372 10 0.201 −1.44×10−3

Actinides & all FP 4.9 40 0.295 −1.32×10−3

BWR SFP model 

Peak SCCG 5.0 11 0.456 −1.11×10−3 6.82×10−3 1.44×10−2
45 

Table 6.3 Bias and uncertainty as a function of final enrichment using IHECSBE 

experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/

MTU) 

Final 

enrichment

(wt % 235U) 

keff vs. final enrichment Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 1.548 −1.79×10−3 8.21×10−3 1.71×10−2

Actinides-only 3.72 40 1.330 −1.81×10−3

Actinides & 16 FP 2.50 10 1.848 −1.77×10−3

Actinides & 16 FP 4.74 40 2.188 −1.75×10−3

Actinides & all FP 2.59 10 1.956 −1.76×10−3

Actinides & all FP 5.15 40 2.227 −1.74×10−3

32 PWR GBC model 

Actinides-only 2.04 10 1.480 −1.80×10−3 8.21×10−3 1.71×10−2

Actinides-only 3.485 40 1.181 −1.82×10−3

Actinides & 16 FP 2.338 10 1.748 −1.78×10−3

Actinides & 16 FP 4.679 40 1.985 −1.76×10−3

Actinides & all FP 2.372 10 1.780 −1.77×10−3

Actinides & all FP 4.9 40 2.150 −1.75×10−3

BWR SFP model 

Peak SCCG 5.0 11 3.820 −1.63×10−3 8.21×10−3 1.71×10−2

Table 6.4 Bias and uncertainty as a function of final enrichment using HTC and 

IHECSBE experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/

MTU) 

Final 

enrichment

(wt % 235U) 

keff vs. final enrichment Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 1.548 −1.60×10−3 6.81×10−3 1.46×10−2

Actinides-only 3.72 40 1.330 −1.61×10−3

Actinides+FP 2.50 10 1.848 −1.58×10−3

Actinides+FP 4.74 40 2.188 −1.55×10−3

Actinides & all FP 2.59 10 1.956 −1.57×10−3

Actinides & all FP 5.15 40 2.227 −1.55×10−3

32 PWR GBC model 

Actinides-only 2.04 10 1.480 −1.60×10−3 6.81×10−3 1.46×10−2

Actinides-only 3.485 40 1.181 −1.62×10−3

Actinides & 16 FP 2.338 10 1.748 −1.58×10−3

Actinides & 16 FP 4.679 40 1.985 −1.57×10−3

Actinides & all FP 2.372 10 1.780 −1.58×10−3

Actinides & all FP 4.9 40 2.150 −1.56×10−3

BWR SFP model 

Peak SCCG 5.0 11 3.820 −1.45×10−3 6.81×10−3 1.46×10−2
46 

Table 6.5 Bias and uncertainty as a function of final Pu content [wt %, g Pu/(g Pu + g U)] 

using IHECSBE experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/

MTU) 

Final Pu 

content 

(wt % Pu) 

keff vs. final Pu content Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 0.507 −2.44×10−3 8.04×10−3 1.67×10−2

Actinides-only 3.72 40 1.182 −2.36×10−3

Actinides & 16 FP 2.50 10 0.447 −2.45×10−3

Actinides & 16 FP 4.74 40 1.114 −2.37×10−3

Actinides & all FP 2.59 10 0.427 −2.45×10−3

Actinides & all FP 5.15 40 1.212 −2.35×10−3

32 PWR GBC model 

Actinide-only 2.04 10 0.433 −2.45×10−3 8.04×10−3 1.67×10−2

Actinide-only 3.485 40 1.162 −2.36×10−3

Actinide+FP 2.338 10 0.418 −2.45×10−3

Actinide+FP 4.679 40 1.146 −2.36×10−3

All 2.372 10 0.416 −2.45×10−3

All 4.9 40 1.144 −2.36×10−3

BWR SFP model 

Peak SCCG 5.0 11 0.331 −2.46×10−3 8.04×10−3 1.67×10−2

Table 6.6 Bias and uncertainty as a function of final Pu content [wt %, g Pu/(g Pu + g U)] 

using HTC and IHECSBE experiments 

BUC type 

Initial 

enrichment 

(wt % 235U) 

BU 

(GWd/

MTU) 

Final Pu 

content 

(wt % Pu) 

keff vs. final Pu content Bias 

Bias (∆k) uncertainty Fit 

uncertainty 

PWR SFP model 

Actinides-only 2.25 10 0.507 −2.04×10−3 6.69×10−3 1.42×10−2

Actinides-only 3.72 40 1.182 −1.97×10−3

Actinides & 16 FP 2.50 10 0.447 −2.05×10−3

Actinides & 16 FP 4.74 40 1.114 −1.98×10−3

Actinides & all FP 2.59 10 0.427 −2.05×10−3

Actinides & all FP 5.15 40 1.212 −1.97×10−3

32 PWR GBC model 

Actinides-only 2.04 10 0.433 −2.05×10−3 6.69×10−3 1.42×10−2

Actinides-only 3.485 40 1.162 −1.97×10−3

Actinides & 16 FP 2.338 10 0.418 −2.05×10−3

Actinides & 16 FP 4.679 40 1.146 −1.97×10−3

Actinides & all FP 2.372 10 0.416 −2.05×10−3

Actinides & all FP 4.9 40 1.144 −1.97×10−3

BWR SFP model 

Peak SCCG 5.0 11 0.331 −2.06×10−3 6.69×10−3 1.42×10−2
47 

The bias and bias uncertainty information presented in Table 6.1 through Table 6.6 was 

generated using a large set of LEU and mixed uranium–plutonium systems. No attempt was 

made to exclude critical configurations that might not be adequately similar to the application 

models. Doing so would probably be justifiable and could result in smaller 95/95 bias uncertainty 

values and data sets that are normally distributed. Applying nonparametric analysis techniques 

to account for the non-normality of the distribution resulted in a combined bias and bias 

uncertainty of −0.0306, which is nearly double the most restrictive combined bias and bias 

uncertainty based on the plutonium fraction trending parameter. The next section reports work 

that used S/U analysis tools to select critical experiments that are adequately similar to the 

application models and present the bias and bias uncertainty information for the down-selected 

sets of experiments. 

6.2 BIAS AND BIAS UNCERTAINTY USING S/U ANALYSIS FOR 

SIMILARITY AND cK TRENDING 

SCALE S/U tools were utilized to quantify the similarity of each critical experiment and 

application model pair. This technique provides a physics-based approach to benchmark critical 

experiment selection and will result in a different validation set from that used in Section 6.1. 

The selected critical experiments were then used to calculate bias and bias uncertainty in a way 

similar to the method discussed in Section 6.1. In addition to the trending parameters used in 

Section 6.1, the trending was also performed using the ck similarity index parameter. 

6.2.1 Similarity Determination Using Sensitivity and Uncertainty 

Analysis 

Calculating an accurate computational bias, one that accurately reflects the difference between 

the calculated and actual keff values for a safety analysis model, requires the use of critical 

experiments that are similar to the safety analysis model. The critical experiments need to use 

the same nuclear data in a similar energy-dependent manner. Thus the guidance usually cited 

(Ref. 3) is that the critical experiments used to validate a computational method must be as 

much like the application model as is possible. Historically, when critical experiments could not 

be created to simulate specific applications, analysts typically used qualitative and integral 

quantitative comparisons to select critical experiments as discussed in Section 3.2.2. 

Section 3.2.4 describes a methodology for using S/U analysis techniques to assess the 

similarity of one model to another for a physics-based approach to critical experiment selection. 

S/U analysis was used to quantify the similarity of each application model described in Section 4 

to each of the critical experiments identified in Section 5. A summary of the results (i.e., number 

of experiments within the ck ranges) for the LEU, mixed uranium–plutonium, and HTC 

experiments is provided in Table 6.7. All of the 124 LEU experiments had ck values below 0.8 

and thus are not considered applicable for validation of the application models. Note that the 

highest ck value for the BWR SFP application is 0.642, which was generated by comparing the 

application model to the HTC Phase 2, gadolinium solution experiment case 10. The lack of any 

experiments with ck values as high as 0.8 suggests that further study is needed to identify 

critical experiments appropriate for validation of BWR SFP models. The larger number of 

applicable experiments for the 40 GWd/MTU PWR SFP and GBC-32 models is due to the 

increasing importance of plutonium at higher burnups. Figure 6.1 through Figure 6.5 show the ck

values for each experiment for each application. 
48 

Table 6.7 Similarity assessment summary 

Burnup Number meeting ck criteria 

Model (GWd/MTU) ck < 0.8 0.8 ≤ ck < 0.9 0.9 ≤ ck 

PWR SFP 10 355 119 0

PWR SFP 40 250 128 96

GBC-32 10 318 152 4

GBC-32 40 197 122 155

BWR SFP 11 474 0 0

Figure 6.1 Similarity of 10 GWd/MTU PWR SFP model and each critical experiment. 

From the similarity assessment results, only HTC experiments generated ck values in excess of 

0.9. IHECSBE evaluations MIX-COMP-THERM-002 through -009 and -012 generated some ck

values between 0.8 and 0.9. IHECSBE evaluations MIX-COMP-THERM-001 and -011 and MIXSOL-THERM-001, -002, -004, and -005 generated some ck values in the 0.7 to 0.8 range. 

Experiments in these evaluations could be considered as candidates for validation of other BUC 

application models. 
49 

Figure 6.2 Similarity of 40 GWd/MTU PWR SFP model and each critical experiment. 

Figure 6.3 Similarity of 10 GWd/MTU GBC-32 cask model and each critical experiment. 
50 

Figure 6.4 Similarity of 40 GWd/MTU GBC-32 cask model and each critical experiment. 

Figure 6.5 Similarity of BWR SFP model at peak SCCG burnup (11 GWd/MTU) and each 

critical experiment. 
51 

6.2.2 Bias and Bias Uncertainty Using Sensitivity and Uncertainty 

Analysis 

In Section 6.2.1 S/U analysis was used to identify which critical experiments were similar to 

each application model. Results are presented in this section for calculation of the bias and bias 

uncertainty, similar to the work reported in Section 6.1, using only critical experiments that had a 

ck value of at least 0.8. Bias and bias uncertainty are also calculated as a function of the ck

similarity index. No bias and bias uncertainty is presented in this section for the BWR 

application model because none of the critical experiments had a ck value of at least 0.8 

compared with the BWR model. As the information in Table 6.1 through Table 6.6 shows, the 

bias and bias uncertainty changes little as a function of the nuclides credited, because the 

additional isotopes have a very small influence on the application model parameters used for 

trending. Therefore, the bias and bias uncertainty information provided in this section is for BUC 

with actinides and all FPs credited. Table 6.8 presents the bias and bias uncertainty results for 

the PWR SFP and GBC-32 application models. The table shows a value of “none” for bias and 

bias uncertainty for the final enrichment and plutonium content trends, indicating that the value 

of the trend parameter for the application model was outside the range of parameter values for 

the critical experiments. Table 6.9 presents combined bias and bias uncertainty results when 

nonparametric analysis techniques are used to account for the non-normality of the distribution, 

which would replace  k in Eq. (3.1). 

 
52 

Table 6.8 Bias and bias uncertainty results using S/U analysis 

Application 

model 

Initial 

enrichment 

(wt % 235U) 

Final BU 

(GWd/MTU) 

EALF 

(eV) 

keff versus EALF Bias 

Bias Fit uncertainty uncertainty 

PWR SFP 2.59 10 0.202 −1.75×10−3 2.10×10−3 7.2×10−3

5.15 40 0.295 −1.68×10−3 3.46×10−3 1.04×10−2

GBC-32 2.372 10 0.201 −1.71×10−3 1.92×10−3 6.6×10−3

4.9 40 0.295 −2.45×10−3 5.42×10−3 1.30×10−2

Application 

model 

Initial 

enrichment 

(wt % 235U) 

Final BU 

(GWd/MTU) 

Final 

enrichment 

(wt % 235U) 

keff vs. final enrichment Bias 

Bias uncertainty Fit 

uncertainty 

PWR SFP 2.59 10 1.956 none none none

5.15 40 2.227 none none none

GBC-32 2.372 10 1.780 none none none

4.9 40 2.150 none none none

Application 

model 

Initial 

enrichment 

(wt % 235U) 

Final BU 

(GWd/MTU) 

Final Pu 

content 

(wt % Pu) 

keff vs. final Pu content Bias 

Bias Fit uncertainty uncertainty 

PWR SFP 2.59 10 0.427 none none none

5.15 40 1.212 −2.03×10−3 2.95×10−3 9.5×10−3

GBC-32 2.372 10 0.416 none none none

4.9 40 1.144 −2.35×10−3 4.76×10−3 1.10×10−2

Application 

model 

Initial 

enrichment 

(wt % 235U) 

Final BU 

(GWd/MTU) 

Application 

ck value 

keff vs. ck Bias 

Bias uncertainty Fit 

uncertainty 

PWR SFP 2.59 10 1 −6.12×10−3 2.09×10−3 1.07×10−2

5.15 40 1 3.08×10−3 2.84×10−3 8.9×10−3

GBC-32 2.372 10 1 −4.03×10−3 1.91×10−3 7.47×10−3

4.9 40 1 1.92×10−3 4.68×10−3 1.08×10−2

Table 6.9 Nonparametric bias and bias uncertainty 

Model Burnup 

(GWd/MTU) 

Bias and bias 

uncertainty (k) 

PWR SFP 10 N/A

PWR SFP 40 −1.99×10-2

GBC-32 10 N/A

GBC-32 40 −3.06×10-2

N/A – not applicable because data set was normally distributed
53 

6.3 COMPARISON OF BIAS AND UNCERTAINTY WITH NUCLEAR 

DATA UNCERTAINTY VALUES 

As is discussed in Section 3.2.3, methods have been implemented in the SCALE computer 

code system to calculate model-specific sensitivity data that relate how the model keff value 

varies as nuclear data are varied. Sensitivity data are calculated for each nuclide in each 

mixture as a function of reaction and neutron energy. The model-specific keff sensitivity data can 

then be combined with the nuclear data uncertainty information contained in the SCALE crosssection covariance data file to translate the nuclear data uncertainties into uncertainties in the 

model keff value. Since the keff uncertainty data are available on a per nuclide basis, the keff

uncertainty information can be used to estimate biases for nuclides for which insufficient critical 

experiment data exist to determine the bias. Results in Section 3.2.5 demonstrate that the keff

uncertainty data can be used to provide a bounding estimate for biases for nuclides when 

sufficient critical experiment information is not available. In this section, this approach is used to 

estimate bias for the application models and evaluate the use of the approach to estimate 

biases for nuclides, such as FPs, for which applicable LCEs are not available. 

keff sensitivity data were generated for all application models described in Section 4 and for 

some variations of these models to support examination of how keff uncertainties vary with 

model variations. The keff uncertainty data were then generated for each application model with 

all actinides and FPs, using the SCALE TSUNAMI-IP program (Ref. 14, Section M18), the 

model-specific keff sensitivity data, and the SCALE 44-group cross-section covariance data. 

Table 6.10 presents the keff uncertainty data for each of the models. Table 6.11presents the keff

uncertainty data for the PWR SFP as a function of burnup. Table 6.12 presents the keff

uncertainty data for the PWR SFP pool at 10 and 40 GWd/MTU for ENDF/B-V, -VI, and -VII 238 

neutron energy group nuclear data libraries. Note that the keff uncertainty associated with the 

FPs varies with burnup but does not vary much for different models at similar burnups, or when 

different nuclear data libraries are used for keff calculations. 

Comparing the bias values from Table 6.1 though Table 6.6 with the total uncertainty value for 

“All nuclides” in Table 6.10 shows that the bias values calculated using statistical analysis of the 

critical experiment results are all within one standard deviation of the total uncertainty in keff due 

to nuclear data uncertainty. This suggests that, consistent with the study presented in 

Section 3.2.5, the uncertainty in keff due to nuclear data uncertainties could be used to 

conservatively estimate biases associated with nuclear data errors. Within Table 6.10, 

comparing the keff uncertainty for “All nuclides” with the uncertainty associated only with major 

actinides shows that the uncertainty associated with the major actinides contributes nearly all of 

the uncertainty in keff. This indicates that validation of the major actinides is most important. The 

next-highest contributor to the overall uncertainty is the category of structural materials. The 

data in Table 6.10 also indicate that bias in keff due to FP nuclear data errors is predicted to be 

small compared with the bias associated with the actinides. 

The information provided in Tables Table 6.10 to Table 6.12 was used to develop the minor 

actinide and fission product uncertainty-to-worth ratios presented in Section 7.4.3 and the kx

recommendation provided in Section 8. 

 
54 

Table 6.10 Uncertainty in keff due to uncertainty in nuclear data for BUC application 

models 

BUC model keff uncertainty (∆k) 

Model SFP SFP GBC-32 GBC-32 BWR 

Burnup (GWd/MTU) 10 40 10 40 11 

All nuclides 0.00471 0.00486 0.00468 0.00545 0.00402

Major actinides (9) 0.00463 0.00476 0.00455 0.00527 0.00393

234U 0.00000 0.00000 0.00000 0.00000 0.00000

235U 0.00270 0.00211 0.00246 0.00226 0.00293

238U 0.00250 0.00189 0.00246 0.00216 0.00211

238Pu 0.00000 0.00003 0.00000 0.00003 0.00000

239Pu 0.00281 0.00377 0.00292 0.00420 0.00154

240Pu 0.00017 0.00042 0.00018 0.00046 0.00011

241Pu 0.00008 0.00037 0.00007 0.00033 0.00003

242Pu 0.00001 0.00013 0.00001 0.00014 0.00000

241Am 0.00000 0.00002 0.00003 0.00018 0.00000

Minor actinides (3) 0.00007 0.00027 0.00007 0.00029 0.00013

243Am 0.00000 0.00001 0.00000 0.00001 0.00000

237Np 0.00002 0.00009 0.00002 0.00010 0.00001

236U 0.00007 0.00025 0.00007 0.00027 0.00013

FP (16) 0.00022 0.00052 0.00024 0.00058 0.00023

95Mo 0.00001 0.00004 0.00001 0.00006 0.00002

99Tc 0.00002 0.00007 0.00002 0.00008 0.00003

101Ru 0.00002 0.00008 0.00002 0.00008 0.00003

103Rh 0.00004 0.00019 0.00006 0.00022 0.00008

109Ag 0.00000 0.00002 0.00000 0.00002 0.00000

133Cs 0.00005 0.00016 0.00005 0.00018 0.00008

147Sm 0.00000 0.00002 0.00002 0.00006 0.00000

149Sm 0.00015 0.00018 0.00016 0.00022 0.00010

150Sm 0.00001 0.00005 0.00001 0.00006 0.00002

151Sm 0.00008 0.00013 0.00008 0.00013 0.00006

152Sm 0.00002 0.00006 0.00002 0.00007 0.00003

143Nd 0.00011 0.00033 0.00012 0.00036 0.00014

145Nd 0.00004 0.00017 0.00004 0.00018 0.00008

151Eu 0.00000 0.00000 0.00000 0.00000 0.00000

153Eu 0.00001 0.00007 0.00001 0.00008 0.00002

155Gd 0.00000 0.00000 0.00001 0.00004 *

Other actinides 0.00003 0.00003 0.00000 0.00001 0.00000

Other FP 0.00015 0.00034 0.00008 0.00027 0.00014

Structural materials 0.00081 0.00073 0.00106 0.00118 0.00080

*Gadolinium is included in structural materials because most is residual gadolinium from gadolinium fuel rods (i.e., 

gadolinium FP concentration is negligible at short decay times). 
55 

Table 6.11 Uncertainty in keff due to uncertainty in nuclear data for SFP model as a 

function of burnup 

SFP keff uncertainty (∆k) at various burnup values 

Burnup (GWd/MTU) 5 10 18 30 40 50 60 70 

All nuclides 0.00464 0.00471 0.00485 0.00489 0.00486 0.00480 0.00485 0.00487

Major actinides (9) 0.00456 0.00463 0.00477 0.00480 0.00476 0.00469 0.00472 0.00473

234U 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

235U 0.00292 0.00270 0.00235 0.00216 0.00211 0.00209 0.00188 0.00169

238U 0.00265 0.00250 0.00223 0.00201 0.00189 0.00180 0.00176 0.00172

238Pu 0.00000 0.00000 0.00001 0.00002 0.00003 0.00004 0.00006 0.00007

239Pu 0.00229 0.00281 0.00349 0.00374 0.00377 0.00373 0.00389 0.00400

240Pu 0.00011 0.00017 0.00031 0.00039 0.00042 0.00043 0.00048 0.00051

241Pu 0.00004 0.00008 0.00022 0.00035 0.00037 0.00040 0.00047 0.00054

242Pu 0.00000 0.00001 0.00005 0.00010 0.00013 0.00016 0.00020 0.00023

241Am 0.00000 0.00000 0.00000 0.00001 0.00002 0.00002 0.00003 0.00004

Minor actinides (3) 0.00005 0.00007 0.00014 0.00022 0.00027 0.00032 0.00035 0.00038

243Am 0.00000 0.00000 0.00000 0.00001 0.00001 0.00001 0.00002 0.00003

237Np 0.00001 0.00002 0.00004 0.00007 0.00009 0.00011 0.00013 0.00015

236U 0.00005 0.00007 0.00013 0.00020 0.00025 0.00030 0.00033 0.00035

FP (16) 0.00018 0.00022 0.00033 0.00046 0.00052 0.00058 0.00062 0.00064

95Mo 0.00000 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0.00006

99Tc 0.00002 0.00002 0.00004 0.00006 0.00007 0.00008 0.00008 0.00009

101Ru 0.00001 0.00002 0.00004 0.00006 0.00008 0.00009 0.00010 0.00011

103Rh 0.00002 0.00004 0.00010 0.00016 0.00019 0.00021 0.00022 0.00023

109Ag 0.00000 0.00000 0.00001 0.00002 0.00002 0.00002 0.00003 0.00003

133Cs 0.00003 0.00005 0.00009 0.00014 0.00016 0.00018 0.00020 0.00020

147Sm 0.00000 0.00000 0.00000 0.00001 0.00002 0.00002 0.00002 0.00003

149Sm 0.00015 0.00015 0.00017 0.00018 0.00018 0.00018 0.00018 0.00017

150Sm 0.00001 0.00001 0.00003 0.00004 0.00005 0.00006 0.00006 0.00007

151Sm 0.00007 0.00008 0.00010 0.00012 0.00013 0.00013 0.00014 0.00014

152Sm 0.00001 0.00002 0.00004 0.00005 0.00006 0.00007 0.00007 0.00007

143Nd 0.00006 0.00011 0.00020 0.00028 0.00033 0.00036 0.00040 0.00042

145Nd 0.00003 0.00004 0.00009 0.00014 0.00017 0.00019 0.00021 0.00022

151Eu 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

153Eu 0.00001 0.00001 0.00003 0.00006 0.00007 0.00008 0.00010 0.00011

155Gd 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

Other actinides 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00004 0.00005

Other FP 0.00016 0.00015 0.00023 0.00030 0.00034 0.00037 0.00040 0.00043

Structural materials 0.00083 0.00081 0.00076 0.00073 0.00073 0.00074 0.00075 0.00077

 
56 

Table 6.12 keff uncertainty due to uncertainty in nuclear data for ENDF/B-V, -VI, and -VII 

nuclear data libraries 

SFP keff uncertainty (∆k) for ENDF/B-V, -VI, and -VII libraries 

Library (ENDF/B-) V VI VII V VI VII 

Burnup (GWd/MTU) 10 10 10 40 40 40 

All actinides 0.00468 0.00471 0.00471 0.00483 0.00486 0.00486

Major actinides (9) 0.00462 0.00463 0.00463 0.00473 0.00475 0.00476

234U 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

235U 0.00264 0.00267 0.00270 0.00207 0.00209 0.00211

238U 0.00249 0.00252 0.00250 0.00188 0.00191 0.00189

238Pu 0.00000 0.00000 0.00000 0.00003 0.00003 0.00003

239Pu 0.00285 0.00282 0.00281 0.00377 0.00377 0.00377

240Pu 0.00018 0.00018 0.00017 0.00043 0.00042 0.00042

241Pu 0.00009 0.00008 0.00008 0.00038 0.00037 0.00037

242Pu 0.00001 0.00001 0.00001 0.00014 0.00013 0.00013

241Am 0.00000 0.00000 0.00000 0.00002 0.00002 0.00002

Minor Actinides (3) 0.00007 0.00007 0.00007 0.00028 0.00027 0.00027

243Am 0.00000 0.00000 0.00000 0.00001 0.00001 0.00001

237Np 0.00002 0.00005 0.00002 0.00010 0.00010 0.00009

236U 0.00007 0.00005 0.00007 0.00026 0.00026 0.00025

FP (16) 0.00022 0.00022 0.00022 0.00051 0.00052 0.00052

95Mo 0.00001 0.00001 0.00001 0.00004 0.00004 0.00004

99Tc 0.00002 0.00002 0.00002 0.00006 0.00006 0.00007

101Ru 0.00002 0.00002 0.00002 0.00007 0.00008 0.00008

103Rh 0.00005 0.00004 0.00004 0.00019 0.00019 0.00019

109Ag 0.00000 0.00000 0.00000 0.00002 0.00002 0.00002

133Cs 0.00004 0.00005 0.00005 0.00014 0.00016 0.00016

147Sm 0.00000 0.00000 0.00000 0.00001 0.00001 0.00002

149Sm 0.00015 0.00015 0.00015 0.00018 0.00019 0.00018

150Sm 0.00001 0.00001 0.00001 0.00005 0.00005 0.00005

151Sm 0.00008 0.00008 0.00008 0.00012 0.00013 0.00013

152Sm 0.00002 0.00002 0.00002 0.00006 0.00006 0.00006

143Nd 0.00011 0.00011 0.00011 0.00033 0.00033 0.00033

145Nd 0.00004 0.00004 0.00004 0.00016 0.00017 0.00017

151Eu 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

153Eu 0.00001 0.00001 0.00001 0.00007 0.00007 0.00007

155Gd 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

Other actinides 0.00002 0.00003 0.00003 0.00003 0.00003 0.00003

Other FP 0.00016 0.00016 0.00015 0.00038 0.00037 0.00034

Structural materials 0.00072 0.00080 0.00081 0.00065 0.00074 0.00073

 
57 

6.4 BIAS AND BIAS UNCERTAINTY FOR FISSION PRODUCTS 

Using FP LCE data (discussed in Section 5.4) for the nuclides 103Rh, 133Cs, natNd, 149Sm, 152Sm, 

and 155Gd, biases were calculated for the individual FPs. The FP experiments are being used to 

confirm the relative merits of the method described in Section 3.2.5 for determining the 

individual FP biases and propagating them to the application models appropriately. The 

numbers of available critical experiments used to assess the FP bias and uncertainty are 

 103Rh—11 experiments 

 133Cs—15 experiments 

 149Sm—9 experiments 

 152Sm—7 experiments 

 155Gd—10 experiments 

 Nd—4 experiments (which consisted of natural neodymium) 

As discussed in Section 5.4, the FP experiments were performed in three phases. Each phase 

had a number of baseline reference experiments with no FPs to test and check the experimental 

method. Phases 1 and 2 had 47 baseline experiments with a slightly acidic water (HNO3) 

moderator, and Phase 3 used depleted uranyl-nitrate (DUN). The Phase 3 FP experiments 

consisted of combined FP mixtures; therefore, the Phase 3 experiments could not be used to 

establish individual FP biases based on traditional methods for this section. 

Table 6.13 presents calculated values for the FP experiments as well as the overall FP worth 

within the experiment. For each experiment, the FP worth was calculated as the difference 

between the computed keff value for each experiment model and the computed keff value for the 

model with the FPs omitted. The phase in which they were performed is reflected in the 

experiment identifier, where FP1 indicates Phase 1, FP2 indicates Phase 2, and FP3 indicates 

Phase 3. 

ORNL conducted an assessment of the FP experiment reports, which is reported in an NRC 

internal proprietary document (Ref. 40). Several unresolved issues remain for the experimental 

descriptions contained in the reference reports, leaving some unquantified uncertainties. 

Consequently, a total keff uncertainty for each Phase 1 and 2 FP experiment model and for each 

reference experiment model was recommended (Ref. 40) as follows: 

 2.00×10−3

 for the total keff uncertainty for each FP experiment model and 

 1.00×10−3

 for each reference experiment model. 

The normalized keff (ratio of calculated to experimental [C/E]) values are presented in Figure 6.6. 

They identify a systematic bias between the Phase 1 and Phase 2 results when the FP 

benchmarks are grouped by FP and phase. In all cases except the 103Rh experiments, the 

Phase 2 FP keff values are higher. This systematic bias indicates that these two experiment sets 

should be evaluated independently in performing trending analyses. The error bars in the figure 

include the adjusted experimental uncertainty. 

Although the information presented above indicates some variability in the actual numeric 

values to be used for calculating biases and uncertainties, combined results will be presented 

using both the reported uncertainty information and the adjusted uncertainty values for 

comparative purposes. 

 
58 

Table 6.13 FP experiment evaluation data 

Experiment FP keff 

(calc)



(calc) 

FP worth 

(k) 

FP1_173_01 103Rh 1.000063 0.000100 0.0317

FP1_173_02 103Rh 1.000464 0.000099 0.0288

FP1_173_03 103Rh 0.999364 0.000099 0.0178

FP1_173_05 103Rh 0.999716 0.000100 0.0199

FP2_174_HBC_01 103Rh 0.998117 0.000099 0.0320

FP2_174_HBC_02 103Rh 0.997367 0.000099 0.0326

FP2_174_UO2_06 103Rh 0.996885 0.000099 0.0629

FP2_174_UO2_07 103Rh 0.996620 0.000099 0.0632

FP2_174_UO2_08 103Rh 0.997042 0.000099 0.0339

FP2_174_UO2_09 103Rh 0.997044 0.000099 0.0350

FP2_174_UO2_10 103Rh 0.996799 0.000099 0.0351

FP1_173_06 133Cs 0.999884 0.000099 0.0207

FP1_173_07 133Cs 0.999374 0.000099 0.0222

FP1_173_08 133Cs 0.999599 0.000099 0.0193

FP1_173_09 133Cs 0.999179 0.000100 0.0149

FP1_173_10 133Cs 0.99908 0.000099 0.0153

FP1_173_11 133Cs 0.999149 0.000099 0.0132

FP1_173_12 133Cs 0.999537 0.000099 0.0138

FP1_173_13 133Cs 0.999503 0.000100 0.0127

FP1_173_14 133Cs 0.999226 0.000100 0.0125

FP1_173_15 133Cs 0.999555 0.000099 0.0145

FP2_174_UO2_01 133Cs 1.000927 0.000099 0.0278

FP2_174_UO2_02 133Cs 1.000483 0.000099 0.0283

FP2_174_UO2_03 133Cs 1.000571 0.000099 0.0287

FP2_174_UO2_04 133Cs 1.000531 0.000099 0.0286

FP2_174_UO2_05 133Cs 1.000465 0.000099 0.0288

FP1_173_31 149Sm 0.999352 0.000100 0.0357

FP1_173_32 149Sm 0.999761 0.000099 0.0214

FP2_174_HBC_05 149Sm 1.001045 0.000099 0.0352

FP2_174_HBC_06 149Sm 1.001075 0.000100 0.0353

FP2_174_UO2_13 149Sm 1.001628 0.000100 0.0649

FP2_174_UO2_14 149Sm 1.001914 0.000099 0.0647

FP2_174_UO2_15 149Sm 1.000559 0.000099 0.0329

FP2_174_UO2_16 149Sm 1.001505 0.000100 0.0334

FP2_174_UO2_17 149Sm 1.000368 0.000100 0.0332

FP1_173_18 152Sm 0.999552 0.000099 0.0432

FP1_173_19 152Sm 0.999439 0.000099 0.0444

FP1_173_20 152Sm 0.999291 0.000099 0.0451

FP1_173_21 152Sm 1.00004 0.000099 0.0315

FP1_173_22 152Sm 1.00002 0.000100 0.0319

FP2_174_UO2_18 152Sm 1.000790 0.000098 0.0343

FP2_174_UO2_19 152Sm 1.000522 0.000099 0.0352

FP1_173_23 155Gd 0.999334 0.000100 0.0270

FP1_173_24 155Gd 0.999093 0.000099 0.0278

FP1_173_25 155Gd 0.998916 0.000099 0.0283

FP1_173_26 155Gd 0.999384 0.000099 0.0181

FP1_173_27 155Gd 0.999384 0.000099 0.0179

FP2_174_HBC_03 155Gd 1.000577 0.000099 0.0355

FP2_174_HBC_04 155Gd 1.000232 0.000100 0.0359

 
59 

Table 6.13 FP experiment evaluation data (continued) 

Experiment FP keff 

(calc)



(calc) 

FP worth 

(k) 

FP2_174_UO2_20 155Gd 1.001308 0.000099 0.0709

FP2_174_UO2_21 155Gd 0.999476 0.000099 0.0391

FP2_174_UO2_22 155Gd 0.999607 0.000099 0.0392

FP1_173_28 Mix 0.999742 0.000099 0.0291

FP1_173_29 Mix 0.999884 0.000099 0.0314

FP1_173_30 Mix 0.999881 0.000100 0.0313

FP2_174_HBC_07 Mix 1.000533 0.000099 0.0349

FP2_174_UO2_23 Mix 1.000041 0.000097 0.0361

FP2_174_UO2_24 Mix 1.000291 0.000096 0.0367

FP2_174_UO2_25 Mix 1.002539 0.000099 0.0785

FP2_174_UO2_26 Mix 1.002514 0.000100 0.0792

FP2_174_UO2_27 Mix 1.003020 0.000099 0.0806

FP2_174_UO2_28 Mix 1.002835 0.000099 0.0810

FP1_173_16 natNd 0.999678 0.000099 0.0173

FP1_173_17 natNd 0.999502 0.000099 0.0198

FP2_174_UO2_11 natNd 1.000237 0.000099 0.0173

FP2_174_UO2_12 natNd 1.000076 0.000099 0.0176

FP3_177_04 DUN Mix 1.003398 0.000099 0.0447

FP3_177_05 DUN Mix 1.003332 0.000099 0.0449

FP3_177_06 DUN Mix 1.00364 0.000100 0.0446

FP3_177_07 DUN Mix 1.003592 0.000098 0.0446

FP2_175_13 DUN Mix 1.00201 0.000099 0.0231

FP2_175_14 DUN Mix 1.001594 0.000099 0.0279

FP2_175_15 DUN Mix 1.001308 0.000099 0.0283
60

Figure 6.6 FP experiment keff values. 
61 

6.4.1 Fission Product Experiment Analysis 

As discussed in Section 3.2.6, the typical evaluation of the computational biases and 

uncertainties of the computational methods and nuclear data is developed through the use of 

trending analyses. 

The first step in the FP experiment evaluation was to evaluate for biases in the reference HNO3

experiments. Because the true bias may change significantly as the neutronic characteristics of 

a system change, single-parameter trending analysis was performed to identify whether the bias 

is changing as other key parameters change. The keff results were examined for trends as a 

function of EALF, neutron leakage fraction, neutron mean free path, critical water height, and 

fuel rod number. Plots are illustrated in Figure 6.7 through Figure 6.11. 

Figure 6.7 Reference HNO3 trending of keff versus EALF. 

y = -0.0035x + 0.9995

R2 = 0.0026

y = -0.1121x + 1.024

R2 = 0.7894

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.80E-01 1.90E-01 2.00E-01 2.10E-01 2.20E-01 2.30E-01 2.40E-01 2.50E-01 2.60E-01 2.70E-01 2.80E-01

keff C/E

EALF (eV)

Phase 1

Phase 2
62 

Figure 6.8 Reference HNO3 trending of keff versus leakage fraction. 

Figure 6.9 Reference HNO3 trending of keff versus neutron mean free path. 

y = -0.0037x + 0.9989

R2 = 0.0053

y = -0.0781x + 1.0013

R2 = 0.7943

0.993

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080

keff C/E

Leakage Fraction

Phase 1

Phase 2

y = -0.0025x + 1.0008

R2 = 0.0066

y = -0.0391x + 1.0223

R2 = 0.464

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

0.580 0.590 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670

keff C/E

Neutron Mean Free Path (cm)

Phase 1

Phase 2
63 

Figure 6.10 Reference HNO3 trending of keff versus critical water height. 

Figure 6.11 Reference HNO3 trending of keff versus fuel rod number.

R2 = 0.0119

R2 = 0.684

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

keff C/E

Critical Water Height (cm)

Phase 1

Phase 2

R2 = 0.0178

R2 = 0.0454

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

keff C/E

Number of Fuel Rods

Phase 1

Phase 2

Proprietary information not illustrated 

Proprietary information not illustrated 
64 

Examination of the FP experiment sets in Figure 6.7 through Figure 6.11 with the HNO3 solution 

mix identifies apparent systematic biases for both the Phase 1 and Phase 2 experiment sets. 

Apparent trends are identified but are not well correlated (i.e., r2

 is low) because of several outof-trend data points. In the Phase 1 data set, the data point that is consistently out of trend for 

all the parameters evaluated corresponds to a configuration with the lowest number of fuel rods 

and the highest critical water height. On average, the water level of this experiment is more than 

25 cm greater than in the rest of the non-FP Phase 1 experiments; it is possibly out of trend as a 

result of the effects of increased water reflection in the experiment. Within the Phase 2 data set, 

the trending analysis indicates a strong trend with EALF and neutron leakage fraction. Apparent 

trends are identified with the other parameters; however, the trending results indicate that the 

experiments that included MOX fuel rods from the HTC experiments (referred to as HBC) have 

a distinctly different trend from the UO2-only experiments. Therefore, the Phase 2 experiments 

will be analyzed separately when trended against neutron mean free path, critical water height, 

and number of fuel rods. 

The trending analysis was completed for each of the data sets with one data point omitted from 

the Phase 1 experiment set, as discussed above, and one data point omitted from the Phase 2 

data set. An apparent cause for this single experiment’s being out of trend is unavailable at this 

time. Omission of the Phase 2 data point changed the r2

 correlation coefficient from 0.483 to 

0.783, from 0.436 to 0.730, and from 0.455 to 0.782 in the trending analyses of mean free path, 

critical water height, and fuel rod number, respectively. The adjusted data set trending 

evaluations are provided in Figure 6.12 through Figure 6.16. 
65 

(a) Phase 1 experiments 

(b) Phase 2 experiments 

Figure 6.12 Trending analysis of keff versus EALF. 

y = -0.0528x + 1.0102

R2 = 0.7659

0.997

0.998

0.999

1.000

1.001

1.90E-01 1.95E-01 2.00E-01 2.05E-01 2.10E-01 2.15E-01 2.20E-01

keff C/E

EALF (eV)

Phase 1 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

y = -0.1127x + 1.0246

R2 = 0.7952

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.002

1.003

2.10E-01 2.20E-01 2.30E-01 2.40E-01 2.50E-01 2.60E-01

keff C/E

EALF (eV)

Phase 2 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat
66 

(a) Phase 1 experiments 

(b) Phase 2 experiments 

Figure 6.13 Trending analysis of keff versus neutron leakage fraction. 

y = -0.0369x + 1.001

R2 = 0.7434

0.997

0.998

0.999

1.000

1.001

0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

keff C/E

Leakage Fraction

Phase 1 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

y = -0.0784x + 1.0018

R2 = 0.7987

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.002

1.003

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

keff C/E

Leakage Fraction

Phase 2 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat
67 

(a) Phase 1 experiments 

(b) Phase 2 experiments with HBC rods only 

(c) Phase 2 experiments with UO2 rods only 

Figure 6.14 Trending analysis of keff versus mean free path. 

y = -0.0228x + 1.0136

R2 = 0.7495

0.998

0.998

0.999

0.999

1.000

1.000

1.001

1.001

0.590 0.600 0.610 0.620 0.630 0.640 0.650

keff C/E

Mean Free Path (cm)

Phase 1 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

y = -0.0163x + 1.0095

R2 = 0.7826

0.996

0.997

0.998

0.999

1.000

1.001

1.002

0.595 0.600 0.605 0.610 0.615 0.620 0.625 0.630 0.635

keff C/E

Mean Free Path (cm)

Phase 2 NO3 HBC

Rh-103

Sm-149

Gd-155

y = -0.0415x + 1.0234

R2 = 0.8478

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.002

1.003

0.560 0.580 0.600 0.620 0.640 0.660 0.680

keff C/E

Mean Free Path (cm)

Phase 2 NO3 UO2

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat
68 

(a) Phase 1 experiments 

(b) Phase 2 experiments with HBC rods only 

(c) Phase 2 experiments with UO2 rods only 

Figure 6.15 Trending analysis of keff versus water level. 

R2 = 0.6951

0.998

0.998

0.999

0.999

1.000

1.000

1.001

1.001

keff C/E

Water Level (cm)

Phase 1 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

R2 = 0.7303

0.996

0.997

0.998

0.999

1.000

1.001

1.002

keff C/E

Water Level (cm)

Phase 2 NO3 HBC

Rh-103

Sm-149

Gd-155

R2 = 0.786

0.9940

0.9950

0.9960

0.9970

0.9980

0.9990

1.0000

1.0010

1.0020

1.0030

keff C/E

Water Level (cm)

Phase 2 NO3 UO2

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

Proprietary information not illustrated 

Proprietary information not illustrated

Proprietary information not illustrated 
69 

(a) Phase 1 experiments 

(b) Phase 2 experiments with HBC rods only 

(c) Phase 2 experiments with UO2 rods only 

Figure 6.16 Trending analysis of keff versus rod number. 

R2 = 0.7116

0.998

0.998

0.999

0.999

1.000

1.000

1.001

1.001

keff C/E

Fuel Rods (#)

Phase 1 NO3

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

R2 = 0.7815

0.996

0.997

0.998

0.999

1.000

1.001

1.002

keff C/E

Fuel Rods (#)

Phase 2 NO3 HBC

Rh-103

Sm-149

Gd-155

R2 = 0.8492

0.994

0.995

0.996

0.997

0.998

0.999

1.000

1.001

1.002

1.003

keff C/E

Water Level (cm)

Phase 2 NO3 UO2

Rh-103

Cs-133

Sm-149

Sm-152

Gd-155

Nd-nat

Proprietary information not illustrated 

Proprietary information not illustrated

Proprietary information not illustrated 
70 

The FP experiment trending analysis evaluation results are presented in Table 6.14 through 

Table 6.19. The bias for an individual experiment was calculated by taking the difference 

between the expected keff value with no FPs, as determined from the trending analysis 

equations, and the calculated value for the experiment with FPs. Note that the bias can vary, 

depending on the trend parameter or if no trend is assumed. 

The individual bias uncertainty values, sb (referred to as “bias unc” in the tables below), were 

calculated as shown in Eq. (6.1): 

2 2

b FP fit s   

 , (6.1)

where 

 FP = the standard deviation (σi

) associated with the selected FP experiment keff values, 

 fit = the mean of the sample standard deviations calculated as shown in Eqs. (6.2) and 

(6.3) (referred to as Fit unc in the tables below); 

2 2

 i   exp  calc , (6.2)

where 

 i = 1 to the total number of samples (N), 

 exp = the experimental uncertainty, 

 calc = the calculated keff uncertainty; 

 







 









    N

i i

N

i

eff fit i

i

fit

N

k k x

N i

1

2

1

2

2

2

1 1

( ) 1

2

1







 , (6.3) 

where 

i eff k = the FP critical experiment calculated keff, 

( ) fit i k x = the trend parameter (xi) keff value.
71

Table 6.14 Rhodium-103 bias evaluation 

Phase 1 103Rh experiments 

Trending 

parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc 

FP1_173_01 6.69E-04 1.86E-04 5.43E-04 -1.76E-03 1.94E-04 5.46E-04 3.21E-04 1.92E-04 5.45E-04 -3.24E-04 2.12E-04 5.52E-04 7.03E-04 2.06E-04 5.50E-04FP1_173_02 1.63E-03 5.42E-04 -1.94E-03 5.46E-04 1.30E-03 5.45E-04 1.04E-03 5.52E-04 1.66E-03 5.50E-04FP1_173_03 5.27E-04 5.42E-04 -3.31E-03 5.46E-04 3.05E-04 5.45E-04 2.09E-04 5.52E-04 5.64E-04 5.50E-04FP1_173_05 -2.06E-05 5.43E-04 -2.11E-03 5.46E-04 -1.88E-04 5.45E-04 -6.65E-04 5.52E-04 1.48E-04 5.50E-04Phase 2 103Rh experiments FP2_174_HBC_01 -1.02E-04 5.32E-04 7.37E-04 -1.88E-03 5.28E-04 7.34E-04 -1.37E-03 1.15E-04 5.22E-04 -1.52E-03 1.28E-04 5.25E-04 -1.14E-03 1.15E-04 5.22E-04FP2_174_HBC_02 -1.73E-03 7.37E-04 -3.10E-03 7.34E-04 -2.30E-03 5.22E-04 -2.51E-03 5.25E-04 -1.99E-03 5.22E-04FP2_174_UO2_06 -5.22E-04 7.37E-04 -3.43E-03 7.34E-04 -1.57E-03 3.96E-04 6.46E-04 -3.78E-03 4.70E-04 6.93E-04 -2.17E-03 3.95E-04 6.45E-04FP2_174_UO2_07 -8.22E-04 7.37E-04 -3.77E-03 7.34E-04 -1.92E-03 6.46E-04 -4.24E-03 6.93E-04 -2.47E-03 6.45E-04FP2_174_UO2_08 -8.39E-04 7.37E-04 -2.64E-03 7.34E-04 -1.46E-03 6.46E-04 -2.22E-03 6.93E-04 -2.73E-03 6.45E-04FP2_174_UO2_09 -1.57E-03 7.37E-04 -3.19E-03 7.34E-04 -1.95E-03 6.46E-04 -3.52E-03 6.93E-04 -2.97E-03 6.45E-04FP2_174_UO2_10 -2.02E-03 7.37E-04 -3.59E-03 7.34E-04 -2.32E-03 6.46E-04 -4.11E-03 6.93E-04 -3.25E-03 6.45E-04
72

Table 6.15 Cesium-133 bias evaluation 

Phase 1 133Cs experiments 

Trending 

parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc

FP1_173_06 6.29E-04 1.86E-04 5.42E-04 -2.35E-03 1.94E-04 5.46E-04 4.05E-04 1.92E-04 5.45E-04 2.43E-04 2.12E-04 5.52E-04 6.84E-04 2.06E-04 5.50E-04FP1_173_07 -3.76E-04 5.42E-04 -2.42E-03 5.46E-04 -5.44E-04 5.45E-04 -1.08E-03 5.52E-04 -1.94E-04 5.50E-04FP1_173_08 7.64E-04 5.42E-04 -3.05E-03 5.46E-04 5.39E-04 5.45E-04 4.19E-04 5.52E-04 7.99E-04 5.50E-04FP1_173_09 -5.02E-04 5.43E-04 -2.81E-03 5.46E-04 -6.38E-04 5.45E-04 -8.63E-04 5.52E-04 -3.89E-04 5.50E-04FP1_173_10 -7.16E-04 5.42E-04 -2.74E-03 5.46E-04 -8.84E-04 5.45E-04 -1.31E-03 5.52E-04 -6.48E-04 5.50E-04FP1_173_11 3.04E-04 5.42E-04 -3.65E-03 5.46E-04 1.42E-04 5.45E-04 8.84E-05 5.52E-04 3.49E-04 5.50E-04FP1_173_12 2.78E-04 5.42E-04 -2.86E-03 5.46E-04 1.20E-04 5.45E-04 9.54E-05 5.52E-04 3.37E-04 5.50E-04FP1_173_13 6.80E-04 5.43E-04 -3.26E-03 5.46E-04 5.07E-04 5.45E-04 4.20E-04 5.52E-04 7.03E-04 5.50E-04FP1_173_14 4.06E-04 5.43E-04 -3.55E-03 5.46E-04 2.32E-04 5.45E-04 1.50E-04 5.52E-04 4.26E-04 5.50E-04FP1_173_15 -2.47E-04 5.42E-04 -2.22E-03 5.46E-04 -4.11E-04 5.45E-04 -9.23E-04 5.52E-04 -1.73E-04 5.50E-04Phase 2 133Cs experiments FP2_174_UO2_01 2.74E-03 5.32E-04 7.37E-04 1.09E-03 5.27E-04 7.34E-04 2.30E-03 3.96E-04 6.46E-04 1.31E-03 4.70E-04 6.93E-04 1.18E-03 3.95E-04 6.45E-04FP2_174_UO2_02 2.11E-03 7.37E-04 4.86E-04 7.34E-04 1.73E-03 6.46E-04 5.32E-04 6.93E-04 5.53E-04 6.45E-04FP2_174_UO2_03 1.48E-03 7.37E-04 2.54E-05 7.34E-04 1.37E-03 6.46E-04 -7.17E-04 6.93E-04 4.81E-04 6.45E-04FP2_174_UO2_04 1.87E-03 7.37E-04 3.77E-04 7.34E-04 1.57E-03 6.46E-04 6.29E-05 6.93E-04 5.21E-04 6.45E-04FP2_174_UO2_05 1.63E-03 7.37E-04 -8.06E-05 7.34E-04 1.30E-03 6.46E-04 -7.81E-04 6.93E-04 3.35E-04 6.45E-04
73

Table 6.16 Samarium-149 bias evaluation 

Phase 1 149Sm experiments 

Trending 

parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc 

FP1_173_31 -1.88E-04 1.86E-04 5.43E-04 -2.44E-03 1.94E-04 5.46E-04 -4.54E-04 1.92E-04 5.45E-04 -1.12E-03 2.12E-04 5.52E-04 7.20E-05 2.06E-04 5.50E-04FP1_173_32 4.89E-04 5.42E-04 -2.47E-03 5.46E-04 2.56E-04 5.45E-04 1.09E-04 5.52E-04 5.61E-04 5.50E-04Phase 2 149Sm experiments FP2_174_HBC_05 2.57E-03 5.32E-04 7.37E-04 9.70E-04 5.27E-04 7.34E-04 1.52E-03 1.15E-04 5.22E-04 1.39E-03 1.28E-04 5.25E-04 1.79E-03 1.15E-04 5.22E-04FP2_174_HBC_06 2.06E-03 7.37E-04 7.65E-04 7.34E-04 1.45E-03 5.23E-04 1.27E-03 5.26E-04 1.74E-03 5.23E-04FP2_174_UO2_13 3.87E-03 7.37E-04 1.32E-03 7.34E-04 3.09E-03 3.96E-04 6.46E-04 8.80E-04 4.70E-04 6.94E-04 2.50E-03 3.95E-04 6.45E-04FP2_174_UO2_14 3.95E-03 7.37E-04 1.45E-03 7.34E-04 3.25E-03 6.46E-04 7.72E-04 6.93E-04 2.74E-03 6.45E-04FP2_174_UO2_15 2.25E-03 7.37E-04 6.41E-04 7.34E-04 1.81E-03 6.46E-04 6.84E-04 6.93E-04 6.29E-04 6.45E-04FP2_174_UO2_16 2.80E-03 7.37E-04 1.19E-03 7.34E-04 2.47E-03 6.46E-04 7.52E-04 6.94E-04 1.45E-03 6.45E-04FP2_174_UO2_17 1.12E-03 7.37E-04 -2.08E-05 7.34E-04 1.20E-03 6.46E-04 -5.47E-04 6.94E-04 4.38E-04 6.45E-04

Table 6.17 Samarium-152 bias evaluation 

Phase 1 152Sm experiments 

Trending parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc 

FP1_173_18 6.71E-04 1.86E-04 5.42E-04 -2.56E-03 1.94E-04 5.46E-04 2.09E-04 1.92E-04 5.45E-04 -2.61E-04 2.12E-04 5.52E-04 7.52E-04 2.06E-04 5.50E-04FP1_173_19 4.41E-04 5.42E-04 -2.50E-03 5.46E-04 -6.60E-05 5.45E-04 -6.87E-04 5.52E-04 4.15E-04 5.50E-04FP1_173_20 1.98E-04 5.42E-04 -2.54E-03 5.46E-04 -3.16E-04 5.45E-04 -1.06E-03 5.52E-04 1.71E-04 5.50E-04FP1_173_21 7.26E-04 5.42E-04 -1.94E-03 5.46E-04 4.09E-04 5.45E-04 -1.40E-05 5.52E-04 8.40E-04 5.50E-04FP1_173_22 6.03E-04 5.43E-04 -1.81E-03 5.46E-04 2.56E-04 5.45E-04 -3.41E-04 5.52E-04 2.92E-04 5.50E-04Phase 2 152Sm experiments FP2_174_UO2_18 7.77E-04 5.32E-04 7.37E-04 8.72E-04 5.27E-04 7.33E-04 2.08E-03 3.96E-04 6.46E-04 9.12E-04 4.70E-04 6.93E-04 1.04E-03 3.95E-04 6.44E-04FP2_174_UO2_19 7.09E-06 7.37E-04 1.33E-04 7.34E-04 1.44E-03 6.46E-04 -3.87E-04 6.93E-04 5.12E-04 6.45E-04
74

Table 6.18 Gadolinium-155 bias evaluation

Phase 1 155Gd experiments 

Trending 

parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc

FP1_173_23 6.65E-05 1.86E-04 5.43E-04 -2.77E-03 1.94E-04 5.46E-04 -2.23E-04 1.92E-04 5.45E-04 -4.98E-04 2.12E-04 5.52E-04 1.34E-04 2.06E-04 5.50E-04FP1_173_24 -3.21E-04 5.42E-04 -2.82E-03 5.46E-04 -6.45E-04 5.45E-04 -1.10E-03 5.52E-04 6.90E-05 5.50E-04FP1_173_25 -6.01E-04 5.42E-04 -2.88E-03 5.46E-04 -9.31E-04 5.45E-04 -1.53E-03 5.52E-04 -6.04E-04 5.50E-04FP1_173_26 -4.69E-04 5.42E-04 -2.33E-03 5.46E-04 -6.49E-04 5.45E-04 -1.24E-03 5.52E-04 -3.44E-04 5.50E-04FP1_173_27 -3.80E-04 5.42E-04 -2.43E-03 5.46E-04 -5.73E-04 5.45E-04 -1.03E-03 5.52E-04 -2.80E-04 5.50E-04Phase 2 155Gd experiments FP2_174_HBC_03 2.22E-03 5.32E-04 7.37E-04 5.02E-04 5.27E-04 7.34E-04 1.05E-03 1.15E-04 5.22E-04 9.26E-04 1.28E-04 5.25E-04 1.32E-03 1.15E-04 5.22E-04FP2_174_HBC_04 1.36E-03 7.37E-04 -7.84E-05 7.34E-04 6.26E-04 5.23E-04 4.66E-04 5.26E-04 9.17E-04 5.22E-04FP2_174_UO2_20 3.91E-03 7.37E-04 9.19E-04 7.34E-04 2.77E-03 3.96E-04 6.46E-04 3.50E-04 4.70E-04 6.93E-04 2.30E-03 3.95E-04 6.45E-04FP2_174_UO2_21 1.15E-03 7.37E-04 -7.56E-04 7.34E-04 5.19E-04 6.46E-04 -1.11E-03 6.93E-04 -4.54E-04 6.45E-04FP2_174_UO2_22 1.07E-03 7.37E-04 -7.82E-04 7.34E-04 5.67E-04 6.46E-04 -1.34E-03 6.93E-04 -3.63E-04 6.45E-04

Table 6.19 Neodymium bias evaluation

Phase 1 Nd experiments 

Trending 

parameter 

EALF 

(keff) 

Leakage fraction 

(keff) 

Mean free path 

(keff) 

Water level 

(keff) 

Fuel rod number 

(keff) 

Experiment Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc Bias Fit unc bias unc 

FP1_173_16 8.47E-04 1.86E-04 5.42E-04 -2.98E-03 1.94E-04 5.46E-04 6.19E-04 1.92E-04 5.45E-04 5.03E-04 2.12E-04 5.52E-04 8.78E-04 2.06E-04 5.50E-04FP1_173_17 -2.29E-04 5.42E-04 -2.30E-03 5.46E-04 -4.09E-04 5.45E-04 -9.30E-04 5.52E-04 -6.60E-05 5.50E-04Phase 2 Nd experiments FP2_174_UO2_11 1.44E-03 5.32E-04 7.37E-04 -7.34E-05 5.27E-04 7.34E-04 1.07E-03 3.96E-04 6.46E-04 -5.48E-04 4.70E-04 6.93E-04 2.70E-05 3.95E-04 6.45E-04FP2_174_UO2_12 1.24E-03 7.37E-04 -3.13E-04 7.34E-04 8.29E-04 6.46E-04 -9.68E-04 6.93E-04 -1.74E-04 6.45E-04
75 

The net bias and bias uncertainty results of the FP experiment evaluations are provided in 

Table 6.20 and Table 6.21 using the reported experimental uncertainties and the adjusted 

experimental uncertainties, respectively. The combined bias in the tables is the average of the 

individual FP experiment biases, and the bias uncertainty (“bias unc”) is calculated from the 

pooled sample variance as shown in Eq. (6.4). 

 

 

k

i

i i

p N k

N s

s

1

2

2 ( 1) , (6.4) 

where 

Ni = number of samples within parameter space i,

si = mean standard deviation within parameter space i,

k = number of separate parameter spaces.

Table 6.20 FP experiment bias and bias uncertainty (k) (reported experimental 

uncertainty) 

Trending 

parameter EALF Leakage fraction Mean free path Water level Fuel rod number 

FP Bias bias unc Bias bias unc Bias bias unc Bias bias unc Bias bias unc 

103Rh -4.40E-04 6.80E-04 -2.79E-03 6.80E-04 -1.02E-03 5.90E-04 -1.97E-03 6.20E-04 -1.24E-03 6.00E-04 133Cs 7.40E-04 6.10E-04 -1.80E-03 6.10E-04 5.20E-04 5.80E-04 -1.60E-04 6.00E-04 3.30E-04 5.80E-04 149Sm 2.10E-03 7.10E-04 1.60E-04 7.10E-04 1.62E-03 6.10E-04 4.70E-04 6.50E-04 1.33E-03 6.10E-04 152Sm 4.90E-04 5.90E-04 -1.48E-03 5.90E-04 5.70E-04 5.70E-04 -2.60E-04 5.80E-04 5.70E-04 5.70E-04 155Gd 8.00E-04 6.50E-04 -8.30E-04 6.50E-04 6.70E-04 5.70E-04 -3.30E-04 5.90E-04 5.60E-04 5.70E-04 natNd 8.20E-04 6.50E-04 -1.42E-03 6.50E-04 5.30E-04 6.00E-04 -4.90E-04 6.30E-04 1.70E-04 6.00E-04

Table 6.21 FP experiment bias and bias uncertainty (k) (adjusted experimental 

uncertainty) 

Trending 

parameter EALF Leakage fraction Mean free path Water level Fuel rod number 

FP Bias bias unc Bias bias unc Bias bias unc Bias bias unc Bias bias unc

103Rh -4.40E-04 2.05E-03 -2.79E-03 2.05E-03 -1.02E-03 2.03E-03 -1.97E-03 2.03E-03 -1.24E-03 2.03E-03 133Cs 7.40E-04 2.03E-03 -1.80E-03 2.03E-03 5.20E-04 2.02E-03 -1.60E-04 2.03E-03 3.30E-04 2.02E-03 149Sm 2.10E-03 2.06E-03 1.60E-04 2.06E-03 1.62E-03 2.03E-03 4.70E-04 2.04E-03 1.33E-03 2.03E-03 152Sm 4.90E-04 2.02E-03 -1.48E-03 2.02E-03 5.70E-04 2.02E-03 -2.60E-04 2.02E-03 5.70E-04 2.02E-03 155Gd 8.00E-04 2.04E-03 -8.30E-04 2.04E-03 6.70E-04 2.02E-03 -3.30E-04 2.03E-03 5.60E-04 2.02E-03 nat

Nd 8.20E-04 2.04E-03 -1.42E-03 2.04E-03 5.30E-04 2.03E-03 -4.90E-04 2.04E-03 1.70E-04 2.03E-03

The FP bias uncertainty varies from 5.7×10−4

 to 7.1×10−4 when the reported uncertainty values 

are used, and tends to show that some of the biases are considerably larger than expected (i.e., 

more than 2 away from 0), as shown in Figure 6.17. When the adjusted uncertainty values are 

used in the analysis, the bias uncertainty varies from 2.02×10−3

 to 2.06×10−3. It is consistent with 

or exceeds the calculated experimental bias in all instances except the biases determined 

based on leakage fraction, as shown in Figure 6.18. As can be seen, the bias fluctuates with 

trending parameter, but the uncertainty remains about the same. The large fluctuations in bias 

may be an artifact of experimental uncertainties and/or recommended modeling simplifications 

that have not been sufficiently quantified. Considering that the uncertainty associated with the 

FP experiments is considered to be about 2.0×10−3

, the bias is consistent with or smaller than 

the uncertainty estimate, as shown in Figure 6.18. 
76 

Figure 6.17 Net FP bias and uncertainty using reported experimental uncertainty. 

Figure 6.18 Net FP bias and uncertainty using adjusted experimental uncertainty. 

-4.00E-03

-3.00E-03

-2.00E-03

-1.00E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

Rh-103 Cs-133 Sm-149 Sm-152 Gd-155 Nd-nat

keff Bias (

keff) with 1

 error bars

Fission Product

EALF

LF

MFP

water

rod#

-4.00E-03

-3.00E-03

-2.00E-03

-1.00E-03

0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

Rh-103 Cs-133 Sm-149 Sm-152 Gd-155 Nd-nat

keff Bias (

keff) with 1

 error bars

Fission Product

EALF

LF

MFP

water

rod#

Adjusted Experimental Uncertainty 

Adjusted Experimental Uncertainty 
77 

6.4.2 Application of Fission Product Bias and Bias Uncertainty 

As discussed in Section 3.2.7, the FP LCEs do not support bias calculations with typical 

trending analysis techniques because the same materials are not present in both the 

experiments and the application. A bias calculated for a FP using experiments that include only 

that FP, or include it in a system that is different than the application, may not be correct. 

Differences in neutron energy spectrum, as well as the presence of other FPs and other 

materials, may significantly affect the bias associated with the FP of interest. 

The bias and uncertainty is typically calculated using a single-sided lower tolerance limit 

established so that there is 95% confidence that at least 95% of the population of critical 

experiment keff values are above the limit. One possible method of accounting for the FPs in the 

application model would be to add the individual FP biases to the computational bias developed 

using the non-FP experiments when the bias is negative. However, because the bias and bias 

uncertainty is developed on a 95% probability/95% confidence interval, the individual FP 

allowance factors (kx from Section 3) would need to be similarly developed. This would result 

in very high penalties as a result of the low FP critical experiment sample sizes, requiring high 

tolerance factors to provide biases at the 95% probability/95% confidence interval. This method 

treats each FP bias independently, which is not the case in the application models. An 

alternative means of incorporating the FP biases into the application model is to adjust the 

individual FP biases by their respective keff sensitivities, as illustrated in Eq. (6.5). Using 

sensitivity data is more appropriate than using worth because some experiments could be 

saturated with the FP material and provide nonconservative adjustments. The sensitivities can 

be developed based on direct perturbation calculations or with the SCALE code system. 

࢏ࡿ ∑	 ൌ ࡼࡲࢼ

࢖࢖ࢇ

 (6.5) ,࢏ࢼ ൈ ࢖࢞ࢋ ࢏ ࢏ࡿ

where 

FP = total FP bias for the application, 

i = individual FP for which critical experiment data exist, 

Si

app = sensitivity of FP isotope (i) in application model, 

Si

exp = sensitivity of FP isotope (i) in critical experiment, 

i = individual FP isotope bias taken as difference between calculated value and 

expected value.

Sensitivity-adjusted PWR SFP application model bias and bias uncertainty terms are provided in 

Table 6.22 through Table 6.26 for the different trend parameter biases at burnups of 10, 25, 40, 

and 57 GWd/MTU. The uncertainties (“unc”) were developed using the FP experiment 

uncertainty value of 2.00×10−3

. Note that the FP experiments for neodymium were for the 

natural element. The total natNd sensitivity comprises several Nd isotopes, including 143Nd and 

145Nd. Adjusting the natNd bias by the individual isotope sensitivities approximates the 143Nd and 

145Nd isotope bias in the application model. However, because the natNd bias is within the 

experimental uncertainty estimate, it is expected that the individual isotope biases are, as well. 

The combined results are illustrated in Figure 6.19 and compared against the combined FP 

nuclear data uncertainty developed from the cross-section covariance matrices. As can be 

seen, the bias fluctuates with trending parameter, but the uncertainty remains about the same 

for each burnup. Because of the large uncertainty component (compared with the bias value), 

the results do not definitively support or refute the use of nuclear data uncertainty to bound the 

FP bias. The results do show, however, that the bias values are generally of the same order of 

magnitude and that the bias values calculated with the experimental data are subsumed within 
78 

the nuclear data uncertainty band, hence supporting the premise that nuclear data uncertainty 

can be used to bound the bias for unvalidated nuclides. Use of additional critical experiment 

data with FPs may significantly reduce the bias uncertainty and thus provide more useful bias 

and bias uncertainty estimates from which to draw definitive conclusions. 

Table 6.22 PWR SFP application model sensitivity-adjusted FP bias (EALF) and 

uncertainty (k) 

Burnup 

(GWd/MTU) 10 25 40 57 

FP FP unc FP unc FP unc FP unc 

103Rh −2.0E-05 1.6E-04 −5.0E-05 4.5E-04 −6.0E-05 6.4E-04 −8.0E-05 7.6E-04

133Cs 5.0E-05 1.9E-04 1.1E-04 4.4E-04 1.5E-04 6.1E-04 1.8E-04 7.3E-04

149Sm 6.6E-04 7.7E-04 7.5E-04 8.7E-04 8.4E-04 9.8E-04 8.5E-04 9.9E-04

152Sm 3.0E-05 1.3E-04 7.0E-05 3.0E-04 9.0E-05 3.9E-04 1.0E-04 4.3E-04

155Gd 0.0E+00 0.0E+00 0.0E+00 1.0E-05 0.0E+00 1.0E-05 0.0E+00 2.0E-05

143Nd 2.6E-04 6.5E-04 5.7E-04 1.4E-03 7.6E-04 1.9E-03 8.9E-04 2.2E-03

145Nd 2.8E-04 8.0E-04 6.2E-04 1.8E-03 8.8E-04 2.6E-03 1.1E-03 3.1E-03

Total 1.3E-03 1.3E-03 2.1E-03 2.6E-03 2.7E-03 3.5E-03 3.0E-03 4.1E-03

Table 6.23 PWR SFP application model sensitivity-adjusted FP bias (leakage fraction) 

and uncertainty (k) 

Burnup 

(GWd/MTU) 10 25 40 57 

FP FP unc FP unc FP unc FP unc 

103Rh −2.1E-04 1.6E-04 −5.8E-04 4.5E-04 −8.2E-04 6.4E-04 −9.7E-04 7.6E-04

133Cs −2.0E-04 1.9E-04 −4.6E-04 4.4E-04 −6.5E-04 6.1E-04 −7.7E-04 7.3E-04

149Sm −1.1E-04 7.7E-04 −1.2E-04 8.7E-04 −1.4E-04 9.8E-04 −1.4E-04 9.9E-04

152Sm −1.1E-04 1.3E-04 −2.4E-04 3.0E-04 −3.1E-04 3.9E-04 −3.5E-04 4.3E-04

155Gd 0.0E+00 0.0E+00 0.0E+00 1.0E-05 −1.0E-05 1.0E-05 −1.0E-05 2.0E-05

143Nd −4.7E-04 6.5E-04 −1.0E-03 1.4E-03 −1.4E-03 1.9E-03 −1.6E-03 2.2E-03

145Nd −6.7E-04 8.0E-04 −1.5E-03 1.8E-03 −2.1E-03 2.6E-03 −2.6E-03 3.1E-03

Total −1.8E-03 1.3E-03 −4.0E-03 2.6E-03 −5.5E-03 3.5E-03 −6.5E-03 4.1E-03

Table 6.24 PWR SFP application model sensitivity-adjusted FP bias (mean free path) 

and uncertainty (k) 

Burnup 

(GWd/MTU) 10 25 40 57 

FP FP unc FP unc FP unc FP unc 

103Rh −5.0E-05 1.6E-04 −1.5E-04 4.6E-04 −2.2E-04 6.5E-04 −2.6E-04 7.7E-04

133Cs 3.0E-05 1.9E-04 7.0E-05 4.3E-04 9.0E-05 6.1E-04 1.1E-04 7.3E-04

149Sm 5.0E-04 7.7E-04 5.6E-04 8.7E-04 6.3E-04 9.8E-04 6.3E-04 9.9E-04

152Sm 3.0E-05 1.3E-04 6.0E-05 3.0E-04 8.0E-05 3.9E-04 9.0E-05 4.3E-04

155Gd 0.0E+00 0.0E+00 0.0E+00 1.0E-05 0.0E+00 1.0E-05 0.0E+00 2.0E-05

143Nd 1.7E-04 6.4E-04 3.6E-04 1.4E-03 4.9E-04 1.9E-03 5.7E-04 2.2E-03

145Nd 1.7E-04 8.0E-04 3.8E-04 1.8E-03 5.5E-04 2.6E-03 6.6E-04 3.1E-03

Total 8.3E-04 1.3E-03 1.3E-03 2.6E-03 1.6E-03 3.5E-03 1.8E-03 4.1E-03
79 

Table 6.25 PWR SFP application model sensitivity-adjusted FP bias (water height) 

and uncertainty (k) 

Burnup 

(GWd/MTU) 10 25 40 57 

FP FP unc FP unc FP unc FP unc 

103Rh −1.1E-04 1.6E-04 −3.1E-04 4.6E-04 −4.4E-04 6.5E-04 −5.2E-04 7.7E-04

133Cs −2.0E-05 1.9E-04 −4.0E-05 4.4E-04 −5.0E-05 6.1E-04 −6.0E-05 7.3E-04

149Sm 1.3E-04 7.7E-04 1.5E-04 8.7E-04 1.7E-04 9.8E-04 1.7E-04 9.9E-04

152Sm −2.0E-05 1.3E-04 −4.0E-05 3.0E-04 −6.0E-05 3.9E-04 −6.0E-05 4.3E-04

155Gd 0.0E+00 0.0E+00 0.0E+00 1.0E-05 0.0E+00 1.0E-05 −1.0E-05 2.0E-05

143Nd −1.4E-04 6.5E-04 −3.1E-04 1.4E-03 −4.2E-04 1.9E-03 −4.9E-04 2.2E-03

145Nd −1.5E-04 8.0E-04 −3.4E-04 1.8E-03 −4.8E-04 2.6E-03 −5.9E-04 3.1E-03

Total −3.1E-04 1.3E-03 −9.0E-04 2.6E-03 −1.3E-03 3.5E-03 −1.6E-03 4.1E-03

Table 6.26 PWR SFP application model sensitivity-adjusted FP bias (fuel rods) 

and uncertainty (k) 

Burnup 

(GWd/MTU) 10 25 40 57 

FP FP unc FP unc FP unc FP unc 

103Rh −6.0E-05 1.6E-04 −1.7E-04 4.6E-04 −2.4E-04 6.5E-04 −2.8E-04 7.7E-04

133Cs 3.0E-05 1.9E-04 6.0E-05 4.3E-04 8.0E-05 6.1E-04 1.0E-04 7.3E-04

149Sm 4.3E-04 7.7E-04 4.8E-04 8.7E-04 5.4E-04 9.8E-04 5.5E-04 9.9E-04

152Sm 4.0E-05 1.3E-04 8.0E-05 3.0E-04 1.0E-04 3.9E-04 1.1E-04 4.3E-04

155Gd 0.0E+00 0.0E+00 0.0E+00 1.0E-05 0.0E+00 1.0E-05 0.0E+00 2.0E-05

143Nd 6.0E-05 6.4E-04 1.4E-04 1.4E-03 1.8E-04 1.9E-03 2.1E-04 2.2E-03

145Nd 9.0E-05 8.0E-04 2.1E-04 1.8E-03 3.0E-04 2.6E-03 3.6E-04 3.1E-03

Total 5.8E-04 1.3E-03 7.9E-04 2.6E-03 9.7E-04 3.5E-03 1.1E-03 4.1E-03
80 

Figure 6.19 FP bias and uncertainty comparison against cross-section covariance as a 

function of burnup for PWR SFP application model. 

6.5 CONCLUSIONS ON CALCULATION OF BIAS AND BIAS 

UNCERTAINTY 

The calculated bias and bias uncertainty values presented in Sections 6.1 and 6.2.2 can vary 

significantly with burnup, the parameter used in the trending analysis, and the set of critical 

experiments used. The temptation exists to adopt the most conservative estimate for the bias 

and bias uncertainty. However, one needs to keep in mind that, provided that the statistical 

method bases and assumptions are met and an acceptable set of applicable critical 

experiments is used, each estimate is valid. The dominant factor in the bias and bias uncertainty 

is the critical experiment population variance. The spread of the critical experiment results is 

due to the inability to accurately describe critical experiments and is not related to the ability to 

calculate keff. Consequently, use of any validly determined bias and 95/95 bias uncertainty that 

includes the population variance and consideration of keff trends in the critical experiments 

results should be acceptable. 

Table 6.27 provides a summary of the most restrictive combined bias and bias uncertainty 

results for the various application models that would be appropriate for validation of the actinideonly nuclides in the application models. These values represent the combined  and k terms 

in Eq. (3.1) in Section 3. 

 

-1.20E-02

-1.00E-02

-8.00E-03

-6.00E-03

-4.00E-03

-2.00E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

0 10 20 30 40 50 60

keff

Burnup (GWd/MTU)

EALF

LF

MFP

water height

rod#

covar 1s

covar 2s

covar 3s
81 

Table 6.27 Summary bias and uncertainty results for actinide-only validation 

BUC type Final BU 

(GWd/MTU) 

Normality assumed Nonparametric 

w/HTC wo/HTC w/HTC wo/HTC 

Values calculated based on traditional LCE selection 

PWR SFP 10 −0.0163 −0.0192 −0.0306 −0.0306 

PWR SFP 40 −0.0162 −0.0191 −0.0306 −0.0306 

PWR cask 10 −0.0163 −0.0192 −0.0306 −0.0306 

PWR cask 40 −0.0162 −0.0191 −0.0306 −0.0306 

BWR SFP 11 −0.0163 −0.0192 −0.0306 −0.0306 

Values calculated using S/U-based LCE selection 

PWR SFP 10 −0.0168 N/A 

PWR SFP 40 −0.0121 −0.0199 

PWR cask 10 −0.0115 N/A 

PWR cask 40 −0.0155 −0.0306 

N/A – not applicable because data set was normally distributed

The methodology presented in Section 3.2.5 was used to generate the results presented in 

Section 6.3 for the BUC application models. The minor actinide and FP results are provided in 

Table 6.28. The combined actinide, minor actinide, and FP bias and bias uncertainty values are 

presented in Table 6.29. 

Table 6.28 Uncertainty in keff due to minor actinide and fission product nuclear data 

uncertainties 

BUC type Final BU 

(GWd/MTU) Uncertainty 

PWR SFP 10 0.00023

PWR SFP 40 0.00059

PWR cask 10 0.00025

PWR cask 40 0.00065

BWR SFP 11 0.00027
82 

Table 6.29 Summary bias and uncertainty results for actinide and fission product BUC 

validation 

BUC type Final BU 

(GWd/MTU) 

Normality assumed Nonparametric 

w/HTC wo/HTC w/HTC wo/HTC 

Values calculated based on traditional LCE selection 

PWR SFP 10 −0.0166 −0.0195 −0.0309 −0.0309 

PWR SFP 40 −0.0169 −0.0198 −0.0313 −0.0313 

PWR cask 10 −0.0166 −0.0195 −0.0309 −0.0309 

PWR cask 40 −0.0169 −0.0198 −0.0313 −0.0313 

BWR SFP 11 −0.0166 −0.0195 −0.0309 −0.0309 

Values calculated based on S/U-based LCE selection 

PWR SFP 10 −0.0171 N/A 

PWR SFP 40 −0.0128 −0.0206 

PWR cask 10 −0.0118 N/A 

PWR cask 40 −0.0162 −0.0313 

N/A – not applicable because data set was normally distributed 
83 

7. BIAS AND BIAS UNCERTAINTY SENSITIVITY STUDY 

7.1 PARAMETRIC EVALUATION 

A parametric evaluation was conducted to determine if criticality code bias and bias uncertainty 

have any sensitivity to fuel design, SFP rack design, burnup, or other parameters important to 

criticality analyses. This section provides a parametric evaluation of SFP application model 

differences and the impacts on the calculated biases and uncertainties for a relatively wide 

range of variations that may be seen in SFP criticality safety analyses. The sensitivity of bias 

and bias uncertainty in keff was evaluated as a function of burnup for the following parameters 

important to criticality safety analyses: fuel assembly design, rack design, soluble boron 

concentration, fuel cooling time, axial representation of fuel burnup, and neutron cross-section 

data. These parameters were selected because they cover a broad range in neutron spectrum 

effects and geometric variations. 

7.2 REFERENCE MODEL PARAMETERS 

The base case SFP application model for the sensitivity studies is described in Section 4.1. The 

SNF compositions for assembly average burnups of 10, 25, 40, and 57 GWd/MTU were 

generated based on BUC with the SNF composition consisting of actinides and 16 FPs as listed 

in Section 4. Details of the parametric variation models are provided in the next section. 

7.3 PARAMETRIC APPLICATIONS 

Model parameters relevant to criticality analyses include fuel assembly design, rack design, 

SFP soluble boron concentration, fuel cooling time, axial representation of fuel burnup, and 

neutron cross-section data. The parametric variations considered in the sensitivity analysis are 

summarized in Table 7.1. 

Table 7.1 Parameters selected for sensitivity analyses 

Parameter Reference value Sensitivity analysis value 

Assembly type W 17×17 OFA B&W 15×15 depleted with burnable absorbers (BAs), W 17×17 

depleted with no BAs

Cell pitch size 9.110 in. Reference value + 0.5 in. 10B loading of Boral®

panels

0.020 g/cm2 0.022 g/cm2 (10% increase from the reference value)

0.018 g/cm2

 (10% decrease from the reference value)

0 g/cm2

 (unpoisoned)

Soluble boron 

concentration

0 ppm 1000 ppm

303 ppm (10 GWd/MTU assembly burnup)

348 ppm (25 GWd/MTU assembly burnup)

393 ppm (40 GWd/MTU assembly burnup)

424 ppm (57 GWd/MTU assembly burnup)

Cooling time 3 days 0 days

1 year

5 years

20 years 

40 years

Burnup axial 

representation

18-zone axial profile Axially uniform burnup

Cross-section data library ENDF/B-VII, 238 

energy groups

ENDF/B-V, and ENDF/B-VI, 238 energy groups
84 

The ENDF/B-V and ENDF/B-VI PWR application models were developed from the ENDF/B-VII 

cases. Nuclide compositions were omitted or modified from the original ENDF/B-VII files to be 

consistent with the different libraries. Only cases with burnups of 10 and 40 GWd/MTU were 

evaluated for comparative purposes against the ENDF/B-VII results. For actual safety analyses, 

application model bias and bias uncertainty should be developed using the same cross-section 

libraries as used in the critical benchmark evaluations. 

For the 1000 ppm soluble boron concentration cases, the base case (i.e., 0 ppm boron) was 

modified to include 1000 ppm of boron, hence resulting in keff values much lower than 0.99. The 

end-of-life (EOL) fuel composition values should have been identical to those in the base case, 

but the 1000 ppm sensitivity cases were generated using the STARBUCS automation sequence 

with a more recent set of ORIGEN-ARP libraries, which resulted in minor variations in the SNF 

isotopic compositions. The observed variations are considered to have a negligible impact on 

the calculated bias and bias uncertainties (Figure 7.3, shown later in this section, confirms this). 

The same phenomenon and conclusion also apply to the soluble boron search cases that result 

in a system keff of 0.94. 

Table 7.2 shows some key parameters for the different application models consistent with the 

results presented in Section 6. Calculated keff values are shown because at higher burnup, 

some of the variations do not result in a system keff of 0.99 without initial enrichments in excess 

of 6.0 wt % 235U. For the purposes of this study, a cap of 5.99 wt % 235U and an assembly 

average burnup of 57 GWd/MTU are used. The cap values represent the upper burnup and 

enrichment values for the base case application model to produce a keff value of 0.99. The keff

values, EALF values, uranium enrichments, Pu/(U+Pu) ratios, and axially dependent fission 

densities were extracted from the CSAS5 calculations. As described in Section 3.1, SCALE 

TSUNAMI-3D calculations were used to generate SDFs for each application model, and 

TSUNAMI-IP was used to evaluate the neutronic similarity of the critical experiments with the 

application models. 
85

Table 7.2 Sensitivity case key parameters 

Description Change from base Initial enrichment (wt % 235U) Final BU (GWd/MTU) keff / EALF (eV) 

Simple average Fission density weighted average 

Final enrichment

(wt % 235U) Pu/(Pu+U) (wt %) Final enrichment (wt % 235U) Pu/(Pu+U) (wt %) 

Base case -- 2.500 10 0.99010 / 0.000072 0.199 1.650 0.567 1.840 0.447

3.578 25 0.98989 / 0.000073 0.241 1.636 0.987 1.977 0.8294.740 40 0.99012 / 0.000071 0.277 1.701 1.301 2.179 1.1145.990 57 0.99002 / 0.000078 0.309 1.685 1.607 2.496 1.330

Assembly B&W 2.413 10 0.98998 / 0.000065 0.265 1.575 0.563 1.739 0.455design 15×15 3.502 25 0.99011 / 0.000082 0.330 1.584 0.994 1.890 0.846

4.701 40 0.98995 / 0.000069 0.386 1.678 1.309 2.123 1.1315.962 57 0.98999 / 0.000064 0.438 1.706 1.611 2.468 1.344

W 17×17 2.614 10 0.99005 / 0.000069 0.192 1.703 0.477 1.938 0.356

(no BAs) 3.765 25 0.99002 / 0.000075 0.233 1.689 0.874 2.104 0.706

4.975 40 0.99001 / 0.000069 0.266 1.746 1.161 2.321 0.9695.990 57 0.97746 / 0.000074 0.292 1.545 1.437 2.461 1.164

Rack design Unpoisoned 1.356 10 0.99017 / 0.000053 0.160 0.721 0.620 0.814 0.532

panels 1.974 25 0.98988 / 0.000057 0.184 0.598 1.011 0.787 0.872

2.719 40 0.98987 / 0.000061 0.203 0.565 1.298 0.816 1.1373.524 57 0.99019 / 0.000056 0.216 0.520 1.552 0.926 1.319

Cell pitch 2.723 10 0.99002 / 0.000079 0.178 1.844 0.548 2.044 0.430

increased 3.915 25 0.99004 / 0.000082 0.217 1.896 0.975 2.247 0.819

0.5 in. 5.177 40 0.99017 / 0.000068 0.249 2.008 1.291 2.511 1.106

5.990 57 0.97031 / 0.000073 0.268 1.724 1.588 2.528 1.315

Poison 

panel 2.536 10 0.98994 / 0.000069 0.200 1.681 0.565 1.874 0.445

10B loading 3.628 25 0.98992 / 0.000075 0.243 1.674 0.986 2.016 0.828

increased 4.808 40 0.99007 / 0.00007 0.280 1.747 1.300 2.230 1.113

10% 5.990 57 0.98646 / 0.000073 0.311 1.685 1.607 2.497 1.331
86

Description Change from base Initial enrichment (wt % 235U) Final BU (GWd/MTU) keff / EALF (eV) 

Simple average Fission density weighted average 

Final enrichment

(wt % 235U) Pu/(Pu+U) (wt %) Final enrichment (wt % 235U) Pu/(Pu+U) (wt %) 

Poison 

panel 2.460 10 0.99010 / 0.000068 0.197 1.615 0.569 1.804 0.449

10B loading 3.521 25 0.99011 / 0.000073 0.239 1.594 0.988 1.933 0.829

decreased 4.668 40 0.99000 / 0.00007 0.274 1.652 1.301 2.127 1.114

10% 5.902 57 0.98997 / 0.000072 0.306 1.632 1.606 2.435 1.330

Decay time 0 d 2.487 10 0.99014 / 0.000068 0.197 1.638 0.549 1.817 0.439

3.544 25 0.99002 / 0.000078 0.239 1.613 0.974 1.939 0.8224.690 40 0.99014 / 0.000078 0.273 1.669 1.284 2.137 1.1025.873 57 0.99002 / 0.000071 0.304 1.653 1.578 2.435 1.311

1 year 2.540 10 0.98996 / 0.000071 0.200 1.684 0.560 1.887 0.434

3.660 25 0.99002 / 0.000068 0.245 1.700 0.981 2.066 0.8124.858 40 0.98994 / 0.000066 0.282 1.783 1.291 2.295 1.0955.990 57 0.98612 / 0.000067 0.313 1.724 1.586 2.560 1.301

5 year 2.570 10 0.98996 / 0.000068 0.200 1.710 0.552 1.930 0.419

3.786 25 0.99018 / 0.000071 0.248 1.796 0.959 2.209 0.7785.088 40 0.99003 / 0.000066 0.290 1.945 1.260 2.524 1.0525.990 57 0.97132 / 0.000074 0.318 1.724 1.546 2.627 1.250

20 year 2.623 10 0.98995 / 0.000064 0.200 1.756 0.533 2.002 0.394

3.998 25 0.98997 / 0.000071 0.252 1.961 0.908 2.449 0.7185.491 40 0.98995 / 0.000073 0.302 2.237 1.186 2.928 0.9725.990 57 0.94386 / 0.000069 0.323 1.725 1.447 2.739 1.148

40 year 2.642 10 0.98980 / 0.000075 0.200 1.774 0.523 2.033 0.383

4.094 25 0.99001 / 0.000066 0.254 2.039 0.879 2.560 0.6905.670 40 0.98986 / 0.000071 0.307 2.373 1.143 3.105 0.9325.990 57 0.92800 / 0.000070 0.324 1.690 1.396 2.761 1.102

Table 7.2 Sensitivity case key parameters (continued)
87

Description Change from base Initial enrichment (wt % 235U) Final BU (GWd/MTU) keff / EALF (eV) 

Simple average Fission density weighted average 

Final enrichment

(wt % 235U) Pu/(Pu+U) (wt %) Final enrichment (wt % 235U) Pu/(Pu+U) (wt %) 

Soluble boron 1000 ppm 2.506 10 0.84285 / 0.00006 0.278 1.654 0.557 1.816 0.457

3.565 25 0.86156 / 0.000065 0.328 1.628 0.982 1.952 0.8304.731 40 0.87443 / 0.000062 0.369 1.697 1.292 2.168 1.1095.916 57 0.88311 / 0.000074 0.406 1.680 1.587 2.471 1.316

Soluble boron 303 2.506 10 0.93933 / 0.000084 0.221 1.655 0.558 1.833 0.445ppm for 348 3.565 25 0.93933 / 0.000068 0.269 1.629 0.983 1.958 0.828keff = 0.94 393 4.731 40 0.93992 / 0.000069 0.311 1.697 1.293 2.167 1.107

424 5.916 57 0.94022 / 0.000073 0.348 1.679 1.587 2.466 1.318

Cross-section ENDF/B-V 2.500 10 0.98409 / 0.000068 0.215 1.650 0.567 1.831 0.453library 4.740 40 0.98500 / 0.000073 0.300 1.701 1.301 2.159 1.112

ENDF/B-VI 2.500 10 0.98700 / 0.000076 0.204 1.650 0.567 1.839 0.448

4.740 40 0.98694 / 0.000070 0.285 1.701 1.301 2.173 1.117

Axial burnup 1 node 2.600 10 0.98997 / 0.00013 0.211 1.725 0.572 N/Aa N/A

3.773 25 0.99000 / 0.00011 0.256 1.764 0.998 N/A N/A5.084 40 0.99007 / 0.00012 0.293 1.909 1.311 N/A N/A5.990 57 0.95282 / 0.00016 0.319 1.633 1.622 N/A N/A

aN/A = not applicable. 

Table 7.2 Sensitivity case key parameters (continued) 
88 

7.4 SENSITIVITY ANALYSIS RESULTS AND DISCUSSION 

A consideration in determining biases and bias uncertainties is that the true bias may change 

significantly as the neutronic characteristics of a system change. Consequently, trending 

analysis is performed to identify whether the bias is changing as other key parameters change. 

To facilitate the evaluation in a manner applicable to real-world applications, the parameter 

change evaluations are broken down as follows. 

Section 7.4.1 provides an evaluation of bias and bias uncertainty when the critical benchmark 

experiments are selected via traditional methods as discussed in Section 3.2.2. Results are 

presented using key parameters—EALF, EOL fission density weighted 235U enrichment, and 

EOL fission density weighted plutonium fraction for developing bias and bias uncertainty terms. 

The trending analyses were performed on the HTC LCEs and the IHECSBE as listed in 

Section 5 (excluding the LEU-MISC-THERM-005 cases) for a total of 462 experiments. The 

proprietary FP critical benchmark data were excluded because the majority of applicants will not 

have access to this data set and, as discussed in Section 6.4.2, traditional techniques do not 

appear adequate for applying individual FP biases and bias uncertainties to BUC applications. 

Section 7.4.2 provides an evaluation using the SCALE S/U analysis tools for selecting critical 

benchmarks applicable to the various applications, consistent with the information in 

Section 6.2. All 609 experiments listed in Section 5 were evaluated for similarity. The S/U 

analysis tools enable a more robust methodology for determining critical benchmark applicability 

compared with traditional techniques, which are based on engineering judgment. 

Section 7.4.3 evaluates the application model parameter differences for the SNF nuclides when 

applicable LCE data are not available. The impacts on keff uncertainties generated based on the 

44-group cross-section covariance matrices using TSUNAMI-IP, as described in Section 6.3, 

are provided. 

7.4.1 Conventional Bias and Bias Uncertainty Assessment Impacts 

The keff results were examined for trends as a function of enrichment, plutonium content, and 

EALF. Single-parameter trending analyses were performed using the USLSTATS computer 

code distributed with SCALE. 

Table 7.3 to Table 7.5 show the bias and bias uncertainty calculated for each application model 

variant. The bias value is the difference between the best-estimate linear fit (BELF) of the critical 

experiment data as a function of the independent variable at the value from the application 

model and keff = 1 (bias = kBELF  1). The bias uncertainty in the tables is the total uncertainty 

including the variance of the population and a tolerance factor used to create the 95% 

probability/95% confidence interval based on sample population. The bias uncertainty is the 

same for a given trending parameter for the different cases (with the exception of the different 

cross-section library sensitivity cases) because the experimental data used in the trending 

analysis are the same. The bias uncertainty varies slightly for the different trending parameters 

and among experiment sets because the linear fit to the data varies. 
89

Table 7.3 Bias and uncertainty as a function of EALF 

Description Change from base 

Bias/bias uncertainty (k) 

Final burnup (GWd/MTU) 

10 25 40 57 

PWR SFP model 

Base case -- -1.57E-03 / 1.46E-02 -1.50E-03 / 1.46E-02 -1.44E-03 / 1.46E-02 -1.38E-03 / 1.46E-02Assembly design B&W 15×15 -1.46E-03 / 1.46E-02 -1.35E-03 / 1.46E-02 -1.26E-03 / 1.46E-02 -1.17E-03 / 1.46E-02

W 17×17 no BAs -1.58E-03 / 1.46E-02 -1.51E-03 / 1.46E-02 -1.46E-03 / 1.46E-02 -1.41E-03 / 1.46E-02

Rack design Unpoisoned panels -1.63E-03 / 1.46E-02 -1.59E-03 / 1.46E-02 -1.56E-03 / 1.46E-02 -1.54E-03 / 1.46E-02

Cell pitch increased 0.5 in. -1.60E-03 / 1.46E-02 -1.54E-03 / 1.46E-02 -1.49E-03 / 1.46E-02 -1.45E-03 / 1.46E-02

Poison panel B10 +10% -1.57E-03 / 1.46E-02 -1.49E-03 / 1.46E-02 -1.43E-03 / 1.46E-02 -1.38E-03 / 1.46E-02

Poison panel B10 10% -1.57E-03 / 1.46E-02 -1.50E-03 / 1.46E-02 -1.44E-03 / 1.46E-02 -1.39E-03 / 1.46E-02

Decay time 0 d -1.57E-03 / 1.46E-02 -1.50E-03 / 1.46E-02 -1.45E-03 / 1.46E-02 -1.39E-03 / 1.46E-02

1 year -1.57E-03 / 1.46E-02 -1.49E-03 / 1.46E-02 -1.43E-03 / 1.46E-02 -1.38E-03 / 1.46E-025 year -1.57E-03 / 1.46E-02 -1.49E-03 / 1.46E-02 -1.42E-03 / 1.46E-02 -1.37E-03 / 1.46E-02

20 year -1.57E-03 / 1.46E-02 -1.48E-03 / 1.46E-02 -1.40E-03 / 1.46E-02 -1.36E-03 / 1.46E-0240 year -1.57E-03 / 1.46E-02 -1.48E-03 / 1.46E-02 -1.39E-03 / 1.46E-02 -1.36E-03 / 1.46E-02

Soluble boron 1000 ppma -1.44E-03 / 1.46E-02 -1.35E-03 / 1.46E-02 -1.29E-03 / 1.46E-02 -1.22E-03 / 1.46E-02

ppm for keff = 0.94 -1.53E-03 / 1.46E-02 -1.45E-03 / 1.46E-02 -1.38E-03 / 1.46E-02 -1.32E-03 / 1.46E-02

Cross-section library ENDF-B/V -3.16E-03 / 1.54E-02 -- -4.14E-03 / 1.54E-02 --

ENDF-B/VI -3.04E-03 / 1.53E-02 -- -3.96E-03 / 1.53E-02 --

Axial burnup 1 node -1.55E-03 / 1.46E-02 -1.47E-03 / 1.46E-02 -1.41E-03 / 1.46E-02 -1.37E-03 / 1.46E-02

aParts per million boron by mass.
90

Table 7.4 Bias and uncertainty as a function of final uranium enrichment 

Description Change from base 

Bias/bias uncertainty (k) 

Final burnup (GWd/MTU) 

10 25 40 57 

PWR SFP model 

Base case -- -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02Assembly design B&W 15×15 -1.70E-03 / 1.47E-02 -1.69E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

W 17×17 no BAs -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.66E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

Rack design Unpoisoned panels -1.75E-03 / 1.47E-02 -1.75E-03 / 1.47E-02 -1.75E-03 / 1.47E-02 -1.75E-03 / 1.47E-02

Cell pitch increased 0.5 in. -1.68E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

Poison panel B10 +10% -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

Poison panel B10 -10% -1.69E-03 / 1.47E-02 -1.69E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.66E-03 / 1.47E-02

Decay time 0 d -1.69E-03 / 1.47E-02 -1.69E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.66E-03 / 1.47E-02

1 year -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.66E-03 / 1.47E-02 -1.65E-03 / 1.47E-025 year -1.69E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02 -1.64E-03 / 1.47E-02

20 year -1.68E-03 / 1.47E-02 -1.66E-03 / 1.47E-02 -1.63E-03 / 1.47E-02 -1.64E-03 / 1.47E-0240 year -1.68E-03 / 1.47E-02 -1.65E-03 / 1.47E-02 -1.62E-03 / 1.47E-02 -1.64E-03 / 1.47E-02

Soluble boron 1000 ppma -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

ppm for keff = 0.94 -1.69E-03 / 1.47E-02 -1.68E-03 / 1.47E-02 -1.67E-03 / 1.47E-02 -1.65E-03 / 1.47E-02

Cross-section library ENDF-B/V -2.82E-03 / 1.57E-02 -- -2.80E-03 / 1.57E-02 --

ENDF-B/VI -2.82E-03 / 1.55E-02 -- -2.80E-03 / 1.55E-02 --

Axial burnup 1 node -1.70E-03 / 1.47E-02 -1.70E-03 / 1.47E-02 -1.69E-03 / 1.47E-02 -1.70E-03 / 1.47E-02

aParts per million boron by mass.
91

Table 7.5 Bias and uncertainty as a function of final plutonium content 

Description Change from base 

Bias/bias uncertainty (k) 

Final burnup (GWd/MTU) 

10 25 40 57 

PWR SFP model 

Base case -- -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02Assembly design B&W 15×15 -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

W 17×17 no BAs -2.26E-03 / 1.43E-02 -2.22E-03 / 1.43E-02 -2.19E-03 / 1.43E-02 -2.17E-03 / 1.43E-02

Rack design Unpoisoned panels -2.24E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

Cell pitch increased 0.5 in. -2.25E-03 / 1.43E-02 -2.21E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

Poison panel B10 +10% -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

Poison panel B10 -10% -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

Decay time 0 d -2.25E-03 / 1.43E-02 -2.21E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

1 year -2.25E-03 / 1.43E-02 -2.21E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-025 year -2.25E-03 / 1.43E-02 -2.21E-03 / 1.43E-02 -2.18E-03 / 1.43E-02 -2.16E-03 / 1.43E-02

20 year -2.25E-03 / 1.43E-02 -2.22E-03 / 1.43E-02 -2.19E-03 / 1.43E-02 -2.17E-03 / 1.43E-0240 year -2.26E-03 / 1.43E-02 -2.22E-03 / 1.43E-02 -2.19E-03 / 1.43E-02 -2.17E-03 / 1.43E-02

Soluble boron 1000 ppma -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

ppm for keff = 0.94 -2.25E-03 / 1.43E-02 -2.20E-03 / 1.43E-02 -2.17E-03 / 1.43E-02 -2.15E-03 / 1.43E-02

Cross-section library ENDF-B/V -2.51E-03 / 1.50E-02 -- -2.51E-03 / 1.50E-02 --

ENDF-B/VI -2.51E-03 / 1.50E-02 -- -2.51E-03 / 1.50E-02 --

Axial burnup 1 node -2.23E-03 / 1.43E-02 -2.19E-03 / 1.43E-02 -2.15E-03 / 1.43E-02 -2.11E-03 / 1.43E-02

aParts per million boron by mass.
92 

As can be seen, using conventional trending analysis techniques, the bias and bias uncertainty 

as a function of the respective trending parameters produce similar values for the different 

parametric evaluations, with the largest differences coming from use of different cross-section 

libraries. The biases generated based on the final plutonium fraction trending parameter provide 

the most conservative bias and bias uncertainty values for all cases except the different crosssection libraries. The impacts of SNF system parameter changes on the burnup-dependent 

base case biases, calculated in terms of percent difference using the final plutonium fraction 

trending parameter, are illustrated in Figure 7.1 to Figure 7.4. Note that the base case bias 

uncertainty is a factor of ~7 greater than the base case bias and hence subsumes the changes 

in the base case bias due to the system parameter changes. 

Figure 7.1 Percentage change in bias as a function of decay time. 

The results in Figure 7.1 illustrate the effects on the bias of nuclide decay and buildup over a 

40-year decay time for different burnups. The changes are greater at the higher burnups where 

the discharge plutonium fractions are higher. These results demonstrate that different decay 

times can have about a 1.2% effect on the calculated bias at high burnup. This effect is very 

small compared with the bias uncertainty values. 

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

0 10 20 30 40 50 60

 Bias (%)

Assembly Average Burnup (GWd/MTU)

0 yr decay

1 yr decay

5 yr decay

20 yr decay

40 yr decay
93 

Figure 7.2 Percentage change in bias from rack design variations. 

The results in Figure 7.2 illustrate the effects of variations in storage rack design and 

configuration. As can be seen, a rack design that does not rely on interstitial neutron absorbers 

for criticality control has increased reliance on BUC. Note the substantially lower initial 

enrichments in Table 7.2 needed to yield a target keff of 0.99. The changes are greater at the 

lower burnups in which the discharge SNF isotopic compositions have the greatest variation 

from the base case. As burnup increases, the ratio of net plutonium conversion/consumption 

decreases; therefore, the impact on the bias becomes less pronounced. Overall, these results 

indicate that variations in rack design have a small effect on the bias and that the impacts of the 

changes are very small compared with the base case bias uncertainty. 

-5.00E-01

-4.00E-01

-3.00E-01

-2.00E-01

-1.00E-01

0.00E+00

1.00E-01

2.00E-01

0 10 20 30 40 50 60

 Bias (%)

Assembly Average Burnup (GWd/MTU)

B-10 (+10%)

B-10 (-10%)

unpoisoned

pitch increase
94 

Figure 7.3 Percentage change in bias for different soluble boron concentrations. 

The results in Figure 7.3 illustrate the effects of different soluble boron concentrations on the 

bias and bias uncertainty. As can be seen, the impact is negligible (<0.1%) and should actually 

be 0 because the boron concentration affects the neutron spectrum and would only have 

impacts on trending parameters that vary with neutron energy. The negligible differences 

observed are due to the minor variations in isotopic compositions introduced from the use of 

different ORIGEN-ARP libraries as indicated in Section 7.3. 

-6.00E-02

-4.00E-02

-2.00E-02

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

0 10 20 30 40 50 60

 Bias (%)

Assembly Average Burnup (GWd/MTU)

1000 ppm

k=0.94
95 

Figure 7.4 Percentage change in bias for assembly and cross-section library parameter 

variations. 

The results in Figure 7.4 illustrate the effects on the bias of assembly design variations and 

cross-section library differences. As can be seen, the impact is small (~1%) for different 

assembly designs and slightly lower when a 1-node burnup profile is used but are ~11% to 

~16% when different cross-section libraries are used. The change in bias is even greater for the 

different cross-section libraries when the EALF trending parameter is used. Historically, 

ENDF/B-V and -VI plutonium cross sections had a tendency to overpredict keff (slight positive 

bias), and U cross sections underpredicted keff (slight negative bias). Therefore, as the final 

plutonium fraction increases, the percentage change from the ENDF/B-VII cross-section 

libraries will increase. 

-4.00E+00

-2.00E+00

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

1.60E+01

1.80E+01

0 10 20 30 40 50 60

 Bias (%)

Assembly Average Burnup (GWd/MTU)

BW 15x15 assembly

ENDF/B-5

ENDF/B-6

Assembly w/no_BAs

1_node
96 

7.4.2 Sensitivity and Uncertainty Based Benchmark Selection Bias 

and Bias Uncertainty Impacts 

A weakness associated with single-parameter trending analysis is that the method assumes that 

the analyst has identified the most important trending parameter and that nothing is changing 

other than the parameter. In reality, the true bias varies as a function of many variables, some of 

which are not independent. As discussed in Section 3.2.4, the TSUNAMI-IP program was used 

to generate the ck benchmark similarity metric. The similarity assessment results and bias and 

bias uncertainty based on ck, EALF, final plutonium content, and final uranium content trending 

parameters for the PWR SFP parametric application models are presented in Table 7.6 to 

Table 7.9. Note that in the tables some cells are shaded. These particular application model 

variations were not within the range of applicability of the critical benchmark experiments and 

required extrapolation to calculate a bias and bias uncertainty. Typically, extrapolation is not 

recommended unless the source of the trend is thoroughly understood. Hence, these values are 

presented for comparative purposes only and would need to be evaluated more thoroughly as 

suggested in Appendix C of Ref. 3. 

For the various parametric models, the number of similar experiments was fairly constant with 

the base case application model, with the exception at low burnup (i.e., 10 GWd/MTU) of the 

B&W 15×15 assembly design, the W 17×17 with no burnable absorbers (BAs) inserted during 

the depletion, and the 1000 ppm soluble boron concentration cases. These differences 

gradually became smaller as burnup increased. The most likely reason for this is variation in the 

discharge isotopic compositions for the B&W 15×15 and W 17×17 with no BAs. These 

assemblies experience very different spectral characteristics from the base case during the 

initial burnup. As the assemblies are burned for a longer time period, the differences in spectral 

characteristics become more smoothed out because the fuel isotopic composition has a 

stronger influence than the other reactor components (e.g., burnable poison rods are burned 

out). The differences between the 1000 ppm boron case and the base case are most likely 

attributable to the difference in keff (0.99 versus 0.84), causing the 1000 ppm case to have a 

much lower overall sensitivity to nuclear data uncertainty. Overall, the minimum number of at 

least marginally similar experiments for any application model was 69, compared with 134 for 

the base case model. 
97

Table 7.6 Bias and uncertainty based on ck trending 

Description Change from base 

Bias/bias uncertainty (k) / No. of experiments with ck > 0.8 

Final burnup (GWd/MTU) 

10 25 40 57 

PWR SFP model 

Base case -- NC b 1.89E-03 / 9.19E-03 / 198 3.62E-03 / 1.27E-02 / 259 4.20E-03 / 1.49E-02 / 281Assembly design B&W 15×15 NC -1.54E-03 /7.06E-03 / 168 4.50E-03 / 1.36E-02 / 232 4.13E-03 / 1.32E-02 / 237

W 17×17 no BAs NC -1.33E-03 /6.97E-03 / 165 1.47E-03 / 8.67E-03 / 200 2.95E-03 / 1.20E-02 / 268

Rack design Unpoisoned panels NC 7.39E-03 / 1.82E-02 / 252 5.46E-03 / 1.73E-02 / 285 5.11E-03 / 1.69E-02 / 286

Cell pitch increased 0.5 in. NC 1.45E-03 / 8.65E-03 / 198 2.86E-03 / 1.19E-02 / 272 3.01E-03 / 1.38E-02 / 284

Poison panel B10 +10% NC 1.89E-03 / 9.09E-03 / 198 3.16E-03 / 1.22E-02 / 250 4.19E-03 / 1.49E-02 / 281

Poison panel B10 -10% NC 2.13E-03 / 9.53E-03 / 199 3.72E-03 / 1.28E-02 / 264 4.25E-03 / 1.50E-02 / 281

Decay time 0 d NC 1.89E-03 / 9.09E-03 / 198 2.85E-03 / 1.18E-02 / 247 4.13E-03 / 1.48E-02 / 281

1 year NC 1.84E-03 / 9.04E-03 / 198 2.84E-03 / 1.17E-02 / 241 3.97E-03 / 1.47E-02 / 2815 year NC -1.52E-03 / 6.98E-03 / 171 3.00E-03 / 1.18E-02 / 235 3.79E-03 / 1.45E-02 / 281

20 year NC -1.71E-03 / 6.89E-03 / 167 1.79E-03 / 8.99E-03 / 198 4.13E-03 / 1.48E-02 / 28140 year NC 1.36E-03 /6.94E-03 / 166 1.82E-03 / 9.02E-03 / 197 2.96E-03 / 1.21E-02 / 274

Soluble boron 1000 ppma NC -1.33E-03 / 7.17E-03 / 169 4.25E-03 / 1.33E-02 / 235 6.29E-03 / 1.66E-02 / 264

ppm for keff = 0.94 NC 2.01E-03 / 9.31E-03 / 198 3.31E-03 / 1.23E-02 / 241 5.27E-03 / 1.55E-02 / 279

Cross-section library ENDF-B/V N/Ac N/A N/A N/A

ENDF-B/VI N/A N/A N/A N/A

Axial burnup 1 node NC NC NC NC

a Parts per million boron by mass. b NC = not calculated, insufficient number of experiments with ck > 0.9 for bias calculation. c N/A = not available, only benchmark experiment SDFs using ENDF/B-VII are available. 
98

Table 7.7 Bias and uncertainty based on EALF trending 

Description Change from base 

Bias/bias uncertainty (k) / No. of experiments with ck > 0.8 

Final burnup (GWd/MTU)

10 25 40 57

PWR SFP model

Base case -- -1.47E-03 / 7.12E-03 / 134 -1.71E-03 / 8.30E-03 / 198 -2.04E-03 / 1.09E-02 / 259 -2.04E-03 / 1.29E-02 / 281Assembly design B&W 15×15 -1.84E-03 / 7.53E-03 / 91 -1.36E-03 / 7.73E-03 / 168 -7.33E-04 / 1.05E-02 / 232 -5.83E-04 / 1.04E-02 / 237

W 17×17 no BAs -1.47E-03 / 7.79E-03 / 69 -1.52E-03 / 7.24E-03 / 165 -1.67E-03 / 8.30E-03 / 200 -1.99E-03 / 1.10E-02 / 268

Rack design Unpoisoned panels -1.10E-03 / 7.88E-03 / 142 -2.80E-03 / 1.22E-02 / 252 -3.04E-03 / 1.29E-02 / 285 -2.99E-03 / 1.31E-02 / 286

Cell pitch increased 0.5 in. -1.31E-03 / 6.93E-03 / 147 -1.72E-03 / 8.30E-03 / 198 -2.42E-03 / 1.10E-02 / 272 -2.55E-03 / 1.30E-02 / 284

Poison panel B10 +10% -1.48E-03 / 7.12E-03 / 134 -1.71E-03 / 8.30E-03 / 198 -1.88E-03 / 1.06E-02 / 250 -2.02E-03 / 1.29E-02 / 281

Poison panel B10 -10% -1.47E-03 / 7.10E-03 / 137 -1.74E-03 / 8.50E-03 / 199 -2.11E-03 / 1.10E-02 / 264 -2.08E-03 / 1.29E-02 / 281

Decay time 0 d -1.46E-03 / 7.83E-03 / 129 -1.71E-03 / 9.03E-03 / 198 -1.79E-03 / 1.06E-02 / 247 -2.10E-03 / 1.30E-02 / 281

1 year -1.48E-03 / 7.21E-03 / 129 -1.71E-03 / 8.30E-03 / 198 -1.67E-03 / 1.04E-02 / 241 -2.01E-03 / 1.29E-02 / 2815 year -1.50E-03 / 7.22E-03 / 128 -1.22E-03 / 7.69E-03 / 171 -1.58E-03 / 1.04E-02 / 235 -1.96E-03 / 1.29E-02 / 281

20 year -1.51E-03 / 7.28E-03 / 124 -1.32E-03 / 7.57E-03 / 167 -1.69E-03 / 8.30E-03 / 198 -1.91E-03 / 1.29E-02 / 28140 year -1.51E-03 / 7.28E-03 / 124 -1.37E-03 / 7.58E-03 / 166 -1.71E-03 / 8.29E-03 / 197 -1.71E-03 / 1.10E-02 / 274

Soluble boron 1000 ppma -1.99E-03 / 7.48E-03 / 74 -1.41E-03 / 7.75E-03 / 169 -1.03E-03 / 1.04E-02 / 235 -1.11E-03 / 1.25E-02 / 264

ppm for keff = 0.94 -1.62E-03 / 7.30E-03 / 123 -1.70E-03 / 8.30E-03 / 198 -1.48E-03 / 1.04E-02 / 241 -1.74E-03 / 1.25E-02 / 279

Cross-section libraryb, c

ENDF-B/V -1.84E-03 / 7.34E-03 / 125 N/A -2.95E-03 / 1.04E-02 / 226 N/A

ENDF-B/VI -5.67E-03 / 1.08E-02 / 133 N/A -6.77E-03 / 1.08E-02 / 234 N/A

Axial burnup 1 node -1.43E-03 / 7.83E-03 / 138 -1.66E-03 / 9.03E-03 / 181 -1.56E-03 / 1.06E-02 / 205 -1.61E-03 / 1.30E-02 / 213

aParts per million boron by mass. bN/A = not available, only benchmark experiment SDFs using ENDF/B-VII are available. cck comparison with benchmark experiment SDFs using ENDF/B-VII, but trending analysis based on ENDF/B-V and ENDF/B-VI. 
99

Table 7.8 Bias and uncertainty based on final plutonium content trending 

Description Change from base 

Bias/bias uncertainty (k) / No. of experiments with ck > 0.8 

Final burnup (GWd/MTU)

10 25 40d 57

PWR SFP model

Base case -- 5.72E-02 / 7.13E-03 / 134 3.09E-05 / 7.05E-03 / 198 -2.11E-03 / 9.84E-03 / 259 -2.67E-03 / 1.10E-02 / 281Assembly design B&W 15×15 6.05E-02 / 7.23E-03 / 91 -1.21E-03 / 7.14E-03 / 168 -1.80E-03 / 9.58E-03 / 232 -2.44E-03 / 9.53E-03 / 237

W 17×17 no BAs 7.03E-02 / 7.20E-03 / 69 -1.37E-04 / 8.80E-03 / 165 -5.98E-04 / 7.08E-03 / 200 -2.21E-03 / 9.90E-03 / 268

Rack design Unpoisoned panels -2.26E-03 / 7.71E-03 / 142 -7.77E-04 / 9.81E-03 / 252 -3.52E-03 / 1.40E-02 / 285 -3.52E-03 / 1.40E-02 / 286

Cell pitch increased 0.5 in. 5.77E-02 / 6.99E-03 / 147 7.16E-05 / 7.05E-03 / 198 -2.13E-03 / 9.89E-03 / 272 -2.58E-03 / 1.13E-02 / 284

Poison panel B10 +10% 5.74E-02 / 7.13E-03 / 134 3.43E-05 / 7.05E-03 / 198 -1.93E-03 / 9.60E-03 / 250 -2.67E-03 / 1.10E-02 / 281

Poison panel B10 -10% 5.66E-02 / 7.12E-03 / 137 -6.72E-05 / 7.22E-03 / 199 -2.09E-03 / 9.88E-03 / 264 -2.67E-03 / 1.10E-02 / 281

Decay time 0 d 5.79E-02 / 7.19E-03 / 129 5.92E-05 / 7.05E-03 / 198 -1.81E-03 / 9.49E-03 / 247 -2.62E-03 / 1.10E-02 / 281

1 year 5.84E-02 / 7.19E-03 / 129 9.88E-05 / 7.05E-03 / 198 -1.77E-03 / 9.47E-03 / 241 -2.59E-03 / 1.10E-02 / 2815 year 5.97E-02 / 7.20E-03 / 128 -1.25E-03 / 7.10E-03 / 171 -1.48E-03 / 9.56E-03 / 235 -2.44E-03 / 1.10E-02 / 281

20 year 6.23E-02 / 7.24E-03 / 124 -1.43E-03 / 7.50E-03 / 167 -5.52E-04 / 7.05E-03 / 198 -2.14E-03 / 1.10E-02 / 28140 year 6.33E-02 / 7.24E-03 / 124 -8.76E-04 / 7.88E-03 / 166 -4.47E-04 / 7.03E-03 / 197 -2.22E-03 / 9.95E-03 / 274

Soluble boron 1000 ppma 6.03E-02 / 7.11E-03 / 74 -1.16E-03 / 7.11E-03 / 169 -1.67E-03 / 9.56E-03 / 235 -2.57E-03 / 1.01E-02 / 264

ppm for keff = 0.94 5.78E-02 / 7.25E-03 / 123 3.49E-05 / 7.05E-03 / 198 -1.80E-03 / 9.47E-03 / 241 -2.69E-03 / 1.03E-02 / 279

Cross-section libraryb, c

ENDF-B/V 4.32E-02 / 7.54E-03 / 125 N/A -1.32E-03 / 9.45E-03 / 226 N/A

ENDF-B/VI 3.86E-02 / 7.38E-03 / 133 N/A -5.61E-03 / 9.62E-03 / 234 N/A

Axial burnup 1 node 2.50E-03 / 9.48E-03 / 138 -1.26E-03 / 8.46E-03 / 181 -2.38E-03 / 9.68E-03 / 205 -3.52E-03 / 1.02E-02 / 213

aParts per million boron by mass. bN/A = not available, only benchmark experiment SDFs using ENDF/B-VII are available. 

cck comparison with benchmark experiment SDFs using ENDF/B-VII, but trending analysis based on ENDF/B-V and ENDF/B-VI. dShaded cells for comparative purposes only but are extrapolations outside range of applicability. 
100

Table 7.9 Bias and uncertainty based on final uranium enrichment trending 

Description Change from base 

Bias uncertainty (k) / No. of experiments with ck > 0.8 

Final burnup (GWd/MTU)

10 25 40d 57

PWR SFP model

Base case -- 9.15E-02 / 6.90E-03 / 134 4.26E-04 / 7.26E-03 / 198 2.35E-03 / 9.04E-03 / 259 5.71E-03 / 1.04E-02 / 281Assembly design B&W 15×15 -5.47E-01 / 7.14E-03 / 91 -1.12E-04 / 7.56E-03 / 168 -9.29E-03 / 8.78E-03 / 232 -8.98E-03 / 8.79E-03 / 237

W 17×17 no BAs 1.21E-01 / 7.23E-03 / 69 -1.04E-03 / 8.59E-03 / 165 1.54E-03 / 7.27E-03 / 200 4.01E-03 / 9.09E-03 / 268

Rack design Unpoisoned panels 1.16E-04 / 8.21E-03 / 142 -6.14E-03 / 9.75E-03 / 252 -5.93E-03 / 1.06E-02 / 285 -5.14E-03 / 1.06E-02 / 286

Cell pitch increased 0.5 in. 1.47E-01 / 6.75E-03 / 147 1.47E-03 / 7.26E-03 / 198 4.39E-03 / 9.08E-03 / 272 5.72E-03 / 1.05E-02 / 284

Poison panel B10 +10% 1.03E-01 / 6.90E-03 / 134 5.77E-04 / 7.26E-03 / 198 2.27E-03 / 8.89E-03 / 250 5.71E-03 / 1.04E-02 / 281

Poison panel B10 -10% 8.02E-02 / 6.89E-03 / 137 3.92E-04 / 7.33E-03 / 199 2.02E-03 / 9.08E-03 / 264 5.27E-03 / 1.04E-02 / 281

Decay time 0 d 8.10E-02 / 6.95E-03 / 129 2.80E-04 / 7.26E-03 / 198 1.67E-03 / 8.81E-03 / 247 5.28E-03 / 1.04E-02 / 281

1 year 9.48E-02 / 6.96E-03 / 129 7.70E-04 / 7.26E-03 / 198 2.38E-03 / 8.78E-03 / 241 6.16E-03 / 1.04E-02 / 2815 year 1.19E-01 / 6.98E-03 / 128 -1.51E-03 / 7.53E-03 / 171 3.79E-03 / 8.79E-03 / 235 6.64E-03 / 1.04E-02 / 281

20 year 1.45E-01 / 7.02E-03 / 124 -2.01E-03 / 7.95E-03 / 167 4.09E-03 / 7.26E-03 / 198 7.44E-03 / 1.04E-02 / 28140 year 1.56E-01 / 7.02E-03 / 124 -1.40E-03 / 8.21E-03 / 166 4.83E-03 / 7.25E-03 / 197 5.70E-03 / 9.12E-03 / 274

Soluble boron 1000 ppma 7.55E-02 / 7.11E-03 / 74 -1.27E-03 / 7.52E-03 / 169 1.95E-03 / 8.79E-03 / 235 5.75E-03 / 9.81E-03 / 264

ppm for keff = 0.94 8.80E-02 / 7.04E-03 / 123 3.53E-04 / 7.26E-03 / 198 1.75E-03 / 8.78E-03 / 241 5.76E-03 / 9.84E-03 / 279

Cross-section libraryb, c

ENDF-B/V 1.46E-01 / 7.20E-03 / 125 N/A 4.26E-03 / 8.65E-03 / 226 N/A

ENDF-B/VI 1.19E-01 / 7.04E-03 / 133 N/A 5.80E-04 / 8.89E-03 / 234 N/A

Axial burnup 1 node -1.23E-03 / 9.73E-03 / 138 -4.03E-04 / 7.69E-03 / 181 5.91E-04 / 8.82E-03 / 205 -4.63E-04 / 1.02E-02 / 213

aParts per million boron by mass. bN/A = not available, only benchmark experiment SDFs using ENDF/B-VII are available. cck comparison with benchmark experiment SDFs using ENDF/B-VII, but trending analysis based on ENDF/B-V and ENDF/B-VI. d Shaded cells for comparative purposes only but are extrapolations outside range of applicability.
101 

7.4.3 Nonapplicable LCE Nuclide Validation Assessment 

A principal challenge for crediting FPs in a BUC safety evaluation is the limited availability of 

relevant FP critical experiments for bias and bias uncertainty determination, and the issue of 

how to apply the individual FP biases calculated from the experiments to those of the 

application model. This is the same challenge as for crediting minor actinides such as 236U, 

243Am, and 237Np. Neutron energy spectrum shifts, as well as the presence of other materials, 

may significantly affect the bias associated with any individual isotope of interest. The 

uncertainties in the computed keff values due to uncertainties in the cross-section data were 

computed, as described in Sections 3.2.5 and 6.3, by combining the sensitivity of keff to the 

cross-section data with the cross-section covariance data. The TSUNAMI-IP module was used 

to propagate the poorly validated nuclide (FPs and minor actinide) cross-section uncertainties to 

keff uncertainties for each of the parametric models. Table 7.10 provides the results of the crosssection uncertainty analysis for the parametric PWR SFP application models using BUC with 

actinides and 16 FPs as listed in Section 4. Table 7.11 provides the results of the cross-section 

uncertainty analysis, in terms of nuclide uncertainty-to-worth ratios, for the base case PWR SFP 

application model as a function of burnup using all actinides and FPs supported by SCALE. 

Table 7.12 provides the results of the cross-section uncertainty analysis, in terms of nuclide 

uncertainty-to-worth ratios, for the cask application model at burnups of 10 and 40 GWd/MTU 

using all isotopes supported by SCALE, and for the SNF isotopes consisting of actinides and 16 

FPs. 
102

Table 7.10 Summary of one sigma uncertainty results for PWR SFP parametric application models 

Description Change from base Burnup (GWd/MTU) Parameter Total uncertainty (k) UVa uncertainty (k) UV worth (k) UV uncert/worth (%) 

Base case -- 10 0.0048 0.0003 -0.0274 1.10

25 0.0050 0.0006 -0.0483 1.2040 0.0051 0.0008 -0.0639 1.2857 0.0050 0.0010 -0.0743 1.37

Assembly design B&W 15×15 10 0.0050 0.0003 -0.0290 1.13

25 0.0052 0.0006 -0.0503 1.2640 0.0052 0.0009 -0.0656 1.3757 0.0051 0.0011 -0.0755 1.47

W 17×17 10 0.0046 0.0003 -0.0257 1.12

(No BAs) 25 0.0048 0.0006 -0.0461 1.21

40 0.0048 0.0008 -0.0617 1.3157 0.0048 0.0010 -0.0722 1.38

Rack design Unpoisoned panels 10 0.0066 0.0003 -0.0338 1.01

25 0.0067 0.0006 -0.0574 1.0540 0.0067 0.0008 -0.0759 1.1057 0.0065 0.0010 -0.0874 1.15

Cell pitch increased 10 0.0046 0.0003 -0.0278 1.10

0.25 in. 25 0.0048 0.0006 -0.0480 1.18

40 0.0049 0.0008 -0.0630 1.2857 0.0049 0.0010 -0.0720 1.34

Poison panel B10 

+10% 10 0.0048 0.0003 -0.0277 1.11

25 0.0050 0.0006 -0.0480 1.2040 0.0050 0.0008 -0.0637 1.2957 0.0050 0.0010 -0.0737 1.37
103

Description Change from base Burnup (GWd/MTU) Parameter Total uncertainty (k) UVa uncertainty (k) UV worth (k) UV uncert/worth (%) 

Poison panel B10 -

10% 10 0.0048 0.0003 -0.0278 1.10

25 0.0050 0.0006 -0.0484 1.1940 0.0051 0.0008 -0.0643 1.2857 0.0050 0.0010 -0.0744 1.36

Decay time 0 d 10 0.0048 0.0003 -0.0249 1.13

25 0.0050 0.0006 -0.0457 1.2340 0.0051 0.0008 -0.0611 1.3257 0.0050 0.0010 -0.0714 1.40

1 year 10 0.0048 0.0003 -0.0310 1.07

25 0.0049 0.0006 -0.0516 1.1640 0.0050 0.0008 -0.0665 1.2557 0.0050 0.0010 -0.0759 1.33

5 year 10 0.0047 0.0003 -0.0316 1.03

25 0.0049 0.0006 -0.0526 1.1140 0.0049 0.0008 -0.0685 1.2057 0.0048 0.0010 -0.0754 1.27

20 year 10 0.0047 0.0003 -0.0315 0.99

25 0.0048 0.0006 -0.0518 1.0840 0.0048 0.0008 -0.0676 1.1857 0.0047 0.0009 -0.0755 1.21

40 year 10 0.0047 0.0003 -0.0311 0.99

25 0.0047 0.0005 -0.0510 1.0840 0.0048 0.0008 -0.0666 1.1857 0.0051 0.0010 -0.0792 1.21

Table 7.10 Summary of one sigma uncertainty results for PWR SFP parametric application models (continued) 
104

Description Change from base Burnup (GWd/MTU) Parameter Total uncertainty (k) UVa uncertainty (k) UV worth (k) UV uncert/worth (%) 

Soluble boron 1000 ppm 10 0.0041 0.0002 -0.0209 1.18

25 0.0044 0.0005 -0.0377 1.2940 0.0045 0.0007 -0.0516 1.3957 0.0045 0.0009 -0.0608 1.48

Search for keff = 0.94 10 0.0045 0.0003 -0.0254 1.12

25 0.0047 0.0005 -0.0443 1.2240 0.0048 0.0008 -0.0587 1.3257 0.0048 0.0010 -0.0678 1.41

Cross-section ENDF-B/V 10 0.0048 0.0003 -0.0278 1.12library 25 -- -- -- --

40 0.0050 0.0008 -0.0632 1.3157 -- -- -- --

ENDF-B/VI 10 0.0048 0.0003 -0.0282 1.11

25 -- -- -- --40 0.0051 0.0008 -0.0648 1.2957 -- -- -- --

Axial burnup 1 node 10 0.0052 0.0004 -0.0366 1.12

25 0.0055 0.0008 -0.0624 1.2140 0.0055 0.0011 -0.0810 1.3157 0.0057 0.0013 -0.0981 1.36

aUV = unvalidated nuclides represented by the 16 FPs and 3 minor actinides (i.e., 243Am, 237Np, and 236U) identified in Section 7.2. 

Table 7.10 Summary of one sigma uncertainty results for PWR SFP parametric application models (continued) 
105

Table 7.11 Unvalidated nuclide uncertainty-to-worth ratios (k) results for PWR SFP application model using all isotopes 

BUC 

Burnup (GWd/MTU) 5 10 18 30 40 50 60 70 

Minor actinides (3) (%) 3.52 3.52 3.59 3.69 3.80 3.90 3.87 3.82FP (16) (%) 0.94 0.91 0.92 0.96 0.99 1.02 1.02 1.03Other actinides (%) 10.43 11.06 13.14 16.59 27.38 28.71 62.92 62.57Other FP (%) 2.10 1.69 1.68 1.66 1.50 1.69 1.69 1.70Total UV nuclides in fuel (%)a 1.47 1.32 1.35 1.41 1.42 1.50 1.51 1.53

a Structural materials need to be accounted for on an application model specific basis. 

Table 7.12 Unvalidated nuclide uncertainty to worth ratios (k) results for GBC32 application models 

BUC isotope set All nuclides 28 actinides and FPs Burnup (GWd/MTU) 10 40 10 40 Minor actinides (3) (%) 3.45 3.74 3.42 3.62FP (16) (%) 0.85 0.90 0.85 0.89Other actinides (%) 10.87 11.23 N/A N/AOther FP (%) 2.11 2.08 N/A N/ATotal UV nuclides in fuel (%)a 1.15 1.35 1.02 1.18a Structural materials need to be accounted for on an application model specific basis. 
106 

7.5 SENSITIVITY ANALYSIS SUMMARY 

The bias and bias uncertainty for the various parametric cases were calculated and compared in 

Section 7.4.1 without the proprietary FP data set. They are presented in Table 7.3 to Table 7.5 

based on traditional trending methods as identified in NUREG/CR-6698. When traditional 

trending parameters are used (i.e., parameters other than ck), the final plutonium fraction 

trending parameter provides the most conservative bias and bias uncertainty values for all 

cases except the different cross-section libraries. PWR SFP calculated bias values ranged from 

1.17103

 to 4.14103 with uncertainties ranging from 1.43102 to 1.57102. The impacts of 

SNF system parameter changes on the burnup-dependent base case biases show that the base 

case bias uncertainty is a factor of ~7 greater than the base case bias and hence subsumes the 

changes in bias due to the system parameter changes. 

The more rigorous, physics-based S/U analysis techniques for critical benchmark selection was 

utilized in the work reported in Section 7.4.2. As can be seen, the individual application model 

specific bias and bias uncertainty values are sometimes more limiting than the base case 

values. This shows that using a more concise set of critical benchmark experiments that exhibit 

similar sensitivities to nuclear data uncertainty as the application model, yields a more accurate 

estimate of the application model specific bias and bias uncertainty than the results presented in 

Section 7.4.1. In Section 7.4.1, the large number of critical experiments obscures application 

model specific effects because of the inclusion of critical experiments that are not really 

applicable. 

Section 7.4.3 evaluates the parametric variation effects directly on the nuclides (i.e., FPs and 

minor actinides 243Am, 237Np, and 236U) for which applicable LCE data are not available. 

TSUNAMI-IP was used to assess the FP and minor actinide uncertainty in keff based on using 

the SCALE 44-group cross-section covariance libraries as a bounding method for addressing 

bias and bias uncertainty for FPs and minor actinides. The TSUNAMI-IP–calculated combined 

minor actinide and FP uncertainty at a 1 level based on the cross-section covariance data is 

presented in Table 7.10. The minor actinide and FP cross-section uncertainty ranges from 

approximately 1% of the worth at lower burnups (i.e., 10 GWd/MTU) to ~1.5% of the worth at 

higher burnups (i.e., 57 GWd/MTU). Note that these values are for the BUC isotope set 

consisting of actinides and 16 FPs. An upper value of 1.5% of the worth is also applicable for 

SNF isotopic compositions consisting of all nuclides in the SFP configuration, as well as the 

cask configuration as depicted in Table 7.11 and Table 7.12. 
107 

8. CONCLUSIONS AND RECOMMENDATIONS 

This report presented a validation approach for BUC criticality safety analyses of commercial 

SNF storage systems that include credit for fission products. Generic safety application models 

representative of PWR and BWR fuel storage racks and PWR fuel in a high-capacity drystorage/transportation cask were used for the demonstration. Models of 609 critical experiment 

configurations, which are listed in Appendix A, were used to perform this BUC validation study. 

Included in the validation set were 124 LEU configurations and 194 mixed uranium–plutonium 

systems described in the IHECSBE (Ref. 9). The validation set also included 156 critical 

configurations from the French HTC critical experiment series (Refs. 10–13), which used fuel 

rods with uranium and plutonium compositions designed to be similar to SNF, and 135 critical 

configurations from the French FP Programme critical experiment series (Refs. 20–24). 

As part of the validation study, the critical configurations were used to determine computational 

bias and bias uncertainty for each of the applications. The impact of application model variations 

on bias and bias uncertainty was explored, and the results were presented in Section 7. 

Based on the analyses performed for this report, it is affirmed that criticality analysts should 

continue to validate BUC criticality safety evaluations to the extent possible, with the best 

available critical experiment data. MOX configurations from the IHECSBE and the HTC 

experiment configurations, collectively, provide sufficient data for validation of BUC analyses 

with major actinides and hence should be used for validation. LEU critical configurations should 

not be used in a conventional validation analysis to validate burned fuel systems because they 

do not include any bias contribution from the plutonium present in burned fuel. The validation 

statistical analysis should include bias trending analysis as a function of plutonium content, 

using a trending variable such as plutonium fraction (i.e., gram of Pu per gram of Pu + U). 

Critical experiments with uranium, plutonium, and FPs in the correct proportion to support 

conventional validation of FP BUC are not publicly available. Work was presented in 

Sections 6.3 and 6.4 that used the available FP critical experiments to estimate bias and bias 

uncertainty associated with the FPs. Because of the small number of critical experiments, the 

uncertainty on these FP bias estimates was determined to be significant. 

An approach based on calculated sensitivities and nuclear data uncertainties was demonstrated 

for generating conservative estimates of bias for actinide and FP nuclides for which adequate 

experimental data are not available. The uncertainty analysis technique yields an applicationspecific value for the uncertainty in keff due to the uncertainty in the nuclear data. Other 

comparisons (Section 3.2.5 and Appendix C) for cases in which adequate critical experiment 

data are available have demonstrated the validity and conservatism of the approach. 

Based on the analyses in this report, a set of recommendations has been developed for 

validation of SNF BUC criticality calculations: 

1. For the primary actinides (i.e., 234U, 235U, 238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, and 241Am), 

sufficient critical experiment data exist to adequately validate keff calculations via 

conventional validation approaches. Therefore, the bias in keff calculations due to the 

primary actinide compositions can be determined based on applicable critical experiments, 

such as the HTC critical experiment data and other MOX critical experiments. Some 

recommended candidates for mixed uranium-plutonium systems from the IHECSBE are 

provided in Section 5.2. Note that not all IHECSBE mixed uranium-plutonium systems were 
108 

evaluated, and use of other uranium-plutonium LCEs may be appropriate. Use of the HTC 

and recommended IHECSBE mixed uranium-plutonium systems should provide adequate 

validation for the primary actinides. Similarity index results for all critical experiments used in 

this report are provided in Appendix B. It is recommended that critical experiments with ck

values above 0.8 be considered candidates for use in computational method validation. 

2. A conservative estimate for the bias associated with minor actinide and FP nuclides of 1.5% 

of their worth may be used for kx. The range of applicability of this method is limited to lowenriched (<5.0 wt % 235U) LWR UOx SNF with the ENDF/B-V, -VI, or -VII cross-section 

libraries and a maximum burnup of 70 GWd/MTU, and a total minor actinide and FP nuclide 

worth not to exceed 0.1 k. Where methods and data similar to those used in this report are 

applied to models similar to those described in Section 4, uncertainty information from 

Section 6.3 may be used to cover actinide and fission product nuclides that are not validated 

via conventional approaches. 

3. The bias value determined for the primary actinides, per recommendation #1, and the bias 

value determined for the remaining actinide and FP nuclides, per recommendation #2, 

should be combined in an appropriate manner [e.g., using Eq.(3.1)]. 

4. Structural materials and integral fuel BAs (e.g., steel, aluminum, residual gadolinium in 

gadolinium fuel rods, other non-fuel materials) need to be accounted for in the criticality 

safety assessment and validation study. For systems that are similar to the application 

models in this report, the keff uncertainties due to nuclear data uncertainties, presented in 

Section 6.3, can be combined in quadrature and applied to the kp term as illustrated in 

Section 3. 
109 

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APPENDIX A 

SPENT NUCLEAR FUEL ASSEMBLY BENCHMARK DATA SUMMARY 

OF EXPERIMENTAL AND CALCULATED RESULTS 

A-1

Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results 

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) keff, exp σkeff,exp keff, calc σkeff,calc

LEU-COMP-THERM-001-001 9.61E-02 2.35 0 0 0.9998 0.0031 0.99879 0.00044 LEU-COMP-THERM-001-002 9.54E-02 2.35 0 0 0.9998 0.0031 0.99819 0.00042 LEU-COMP-THERM-001-003 9.45E-02 2.35 0 0 0.9998 0.0031 0.996 0.00048 LEU-COMP-THERM-001-004 9.51E-02 2.35 0 0 0.9998 0.0031 0.99754 0.00048 LEU-COMP-THERM-001-005 9.39E-02 2.35 0 0 0.9998 0.0031 0.99465 0.00043 LEU-COMP-THERM-001-006 9.47E-02 2.35 0 0 0.9998 0.0031 0.99715 0.00048 LEU-COMP-THERM-001-007 9.30E-02 2.35 0 0 0.9998 0.0031 0.9973 0.00046 LEU-COMP-THERM-001-008 9.42E-02 2.35 0 0 0.9998 0.0031 0.99523 0.00045 LEU-COMP-THERM-002-001 1.13E-01 4.31 0 0 0.9997 0.0020 0.99756 0.00012 LEU-COMP-THERM-002-002 1.13E-01 4.31 0 0 0.9997 0.0020 0.99891 0.0001 LEU-COMP-THERM-002-003 1.13E-01 4.31 0 0 0.9997 0.0020 0.99839 0.00011 LEU-COMP-THERM-002-004 1.12E-01 4.31 0 0 0.9997 0.0020 0.9979 0.00011 LEU-COMP-THERM-002-005 1.10E-01 4.31 0 0 0.9997 0.0020 0.99641 0.00012 LEU-COMP-THERM-010-005 3.56E-01 4.31 0 0 1.0000 0.0021 1.000103 0.000095 LEU-COMP-THERM-010-016 2.85E-01 4.31 0 0 1.0000 0.0028 1.002348 0.000099 LEU-COMP-THERM-010-017 2.79E-01 4.31 0 0 1.0000 0.0028 1.001632 0.000097 LEU-COMP-THERM-010-018 2.74E-01 4.31 0 0 1.0000 0.0028 1.001527 0.000099 LEU-COMP-THERM-010-019 2.68E-01 4.31 0 0 1.0000 0.0028 1.001189 0.000098 LEU-COMP-THERM-017-003 9.47E-02 2.35 0 0 1.0000 0.0031 0.998371 0.000099 LEU-COMP-THERM-017-004 2.03E-01 2.35 0 0 1.0000 0.0031 0.997441 0.000098 LEU-COMP-THERM-017-005 1.79E-01 2.35 0 0 1.0000 0.0031 0.998949 0.000099 LEU-COMP-THERM-017-006 1.69E-01 2.35 0 0 1.0000 0.0031 0.999169 0.000095 LEU-COMP-THERM-017-007 1.60E-01 2.35 0 0 1.0000 0.0031 0.999037 0.000096 LEU-COMP-THERM-017-008 1.34E-01 2.35 0 0 1.0000 0.0031 0.996872 0.000099 LEU-COMP-THERM-017-009 1.10E-01 2.35 0 0 1.0000 0.0031 0.996225 0.000094 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-2

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

LEU-COMP-THERM-017-010 9.98E-02 2.35 0 0 1.0000 0.0031 0.997803 0.000096 LEU-COMP-THERM-017-011 9.80E-02 2.35 0 0 1.0000 0.0031 0.997685 0.000097 LEU-COMP-THERM-017-012 9.67E-02 2.35 0 0 1.0000 0.0031 0.99777 0.000074 LEU-COMP-THERM-017-013 9.53E-02 2.35 0 0 1.0000 0.0031 0.997854 0.000098 LEU-COMP-THERM-017-014 9.46E-02 2.35 0 0 1.0000 0.0031 0.99815 0.000095 LEU-COMP-THERM-017-015 1.78E-01 2.35 0 0 1.0000 0.0028 0.996779 0.000078 LEU-COMP-THERM-017-016 1.71E-01 2.35 0 0 1.0000 0.0028 0.997713 0.000082 LEU-COMP-THERM-017-017 1.66E-01 2.35 0 0 1.0000 0.0028 0.998876 0.000081 LEU-COMP-THERM-017-019 1.62E-01 2.35 0 0 1.0000 0.0028 0.998011 0.000072 LEU-COMP-THERM-017-020 1.61E-01 2.35 0 0 1.0000 0.0028 0.996572 0.000062 LEU-COMP-THERM-017-021 1.59E-01 2.35 0 0 1.0000 0.0028 0.996875 0.000079 LEU-COMP-THERM-017-022 1.58E-01 2.35 0 0 1.0000 0.0028 0.99572 0.000077 LEU-COMP-THERM-017-023 1.69E-01 2.35 0 0 1.0000 0.0028 0.99759 0.000087 LEU-COMP-THERM-017-024 1.64E-01 2.35 0 0 1.0000 0.0028 0.998278 0.000091 LEU-COMP-THERM-017-025 1.57E-01 2.35 0 0 1.0000 0.0028 0.996378 0.000085 LEU-COMP-THERM-017-028 2.81E-01 2.35 0 0 1.0000 0.0028 0.997606 0.000077 LEU-COMP-THERM-017-029 2.52E-01 2.35 0 0 1.0000 0.0028 0.997695 0.000086 LEU-COMP-THERM-022-001 6.69E-01 9.83 0 0 1.0000 0.0046 1.000598 0.000095 LEU-COMP-THERM-022-002 2.83E-01 9.83 0 0 1.0000 0.0046 1.005049 0.000098 LEU-COMP-THERM-022-003 1.24E-01 9.83 0 0 1.0000 0.0036 1.005889 0.000097 LEU-COMP-THERM-022-004 8.25E-02 9.83 0 0 1.0000 0.0037 1.006811 0.000099 LEU-COMP-THERM-022-005 6.86E-02 9.83 0 0 1.0000 0.0038 1.002592 0.000099 LEU-COMP-THERM-022-006 5.45E-02 9.83 0 0 1.0000 0.0046 1.001045 0.000099 LEU-COMP-THERM-022-007 5.40E-02 9.83 0 0 1.0000 0.0046 1.003828 0.000094 LEU-COMP-THERM-023-001 8.21E-02 9.83 0 0 1.0000 0.0044 0.994209 0.000099 LEU-COMP-THERM-023-002 7.62E-02 9.83 0 0 1.0000 0.0044 0.997167 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-3

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

LEU-COMP-THERM-023-003 7.44E-02 9.83 0 0 1.0000 0.0044 0.998395 0.000099 LEU-COMP-THERM-023-004 7.26E-02 9.83 0 0 1.0000 0.0044 1.000376 0.000099 LEU-COMP-THERM-023-005 7.11E-02 9.83 0 0 1.0000 0.0044 1.00118 0.000099 LEU-COMP-THERM-023-006 6.97E-02 9.83 0 0 1.0000 0.0044 1.001677 0.000099 LEU-COMP-THERM-024-001 1.00E+00 9.83 0 0 1.0000 0.0054 0.999404 0.000098 LEU-COMP-THERM-024-002 1.40E-01 9.83 0 0 1.0000 0.0040 1.012075 0.000092 LEU-COMP-THERM-026-003 9.69E-01 4.92 0 0 1.0018 0.0062 1.003422 0.000099 LEU-COMP-THERM-042-001 1.69E-01 2.35 0 0 1.0000 0.0016 0.996729 0.000095 LEU-COMP-THERM-042-002 1.75E-01 2.35 0 0 1.0000 0.0016 0.996887 0.000093 LEU-COMP-THERM-042-003 1.82E-01 2.35 0 0 1.0000 0.0016 0.997765 0.000089 LEU-COMP-THERM-042-004 1.80E-01 2.35 0 0 1.0000 0.0017 0.99861 0.000093 LEU-COMP-THERM-042-005 1.77E-01 2.35 0 0 1.0000 0.0033 0.998294 0.000097 LEU-COMP-THERM-042-006 1.69E-01 2.35 0 0 1.0000 0.0016 0.998138 0.000086 LEU-COMP-THERM-042-007 1.74E-01 2.35 0 0 1.0000 0.0018 0.996322 0.000097 LEU-COMP-THERM-050-001 1.99E-01 4.74 0 0 1.0004 0.0010 0.99735 0.000099 LEU-COMP-THERM-050-002 1.90E-01 4.74 0 0 1.0004 0.0010 0.997352 0.000096 LEU-COMP-THERM-050-003 2.07E-01 4.74 0 822 1.0004 0.0010 0.99787 0.000099 LEU-COMP-THERM-050-004 1.97E-01 4.74 0 822 1.0004 0.0010 0.997357 0.000099 LEU-COMP-THERM-050-005 2.22E-01 4.74 0 5030 1.0004 0.0010 0.998855 0.000099 LEU-COMP-THERM-050-006 2.13E-01 4.74 0 5030 1.0004 0.0010 0.998444 0.0001 LEU-COMP-THERM-050-007 2.09E-01 4.74 0 5030 1.0004 0.0010 0.99875 0.000099 LEU-COMP-THERM-050-008 2.07E-01 4.74 0 0 1.0004 0.0010 0.995679 0.000099 LEU-COMP-THERM-050-009 1.96E-01 4.74 0 0 1.0004 0.0010 0.996095 0.000098 LEU-COMP-THERM-050-010 1.94E-01 4.74 0 0 1.0004 0.0010 0.995822 0.0001 LEU-COMP-THERM-050-011 2.15E-01 4.74 0 0 1.0004 0.0010 0.996621 0.000099 LEU-COMP-THERM-050-012 2.02E-01 4.74 0 0 1.0004 0.0010 0.997669 0.0001 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-4

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

LEU-COMP-THERM-050-013 1.99E-01 4.74 0 0 1.0004 0.0010 0.997671 0.000099 LEU-COMP-THERM-050-014 2.09E-01 4.74 0 0 1.0004 0.0010 0.9972 0.000099 LEU-COMP-THERM-050-015 2.07E-01 4.74 0 0 1.0004 0.0010 0.997948 0.000096 LEU-COMP-THERM-050-016 2.11E-01 4.74 0 0 1.0004 0.0010 0.999065 0.000099 LEU-COMP-THERM-050-017 2.10E-01 4.74 0 0 1.0004 0.0010 0.998805 0.0001 LEU-COMP-THERM-050-018 2.09E-01 4.74 0 0 1.0004 0.0010 0.998664 0.000099 LEU-COMP-THERM-079-001 2.96E-01 4.31 0 0 0.9999 0.0016 0.997516 0.000099 LEU-COMP-THERM-079-002 2.96E-01 4.31 0 0 1.0002 0.0016 0.99805 0.000099 LEU-COMP-THERM-079-003 3.01E-01 4.31 0 0 1.0005 0.0016 0.998475 0.000099 LEU-COMP-THERM-079-004 3.04E-01 4.31 0 0 1.0004 0.0016 0.998773 0.000099 LEU-COMP-THERM-079-005 3.09E-01 4.31 0 0 1.0004 0.0016 0.998973 0.000099 LEU-COMP-THERM-079-006 1.08E-01 4.31 0 0 0.9994 0.0008 0.998495 0.000099 LEU-COMP-THERM-079-007 1.08E-01 4.31 0 0 1.0003 0.0008 0.999274 0.000099 LEU-COMP-THERM-079-008 1.09E-01 4.31 0 0 1.0008 0.0008 1.000116 0.000099 LEU-COMP-THERM-079-009 1.10E-01 4.31 0 0 1.0003 0.0008 0.999749 0.000099 LEU-COMP-THERM-079-010 1.11E-01 4.31 0 0 1.0009 0.0008 1.000526 0.0001 LEU-MISC-THERM-005-001 1.15E-01 6.00 0 0 1.0000 0.0007 1.002596 0.0001 LEU-MISC-THERM-005-002 1.17E-01 6.00 0 0 1.0001 0.0007 1.002947 0.000099 LEU-MISC-THERM-005-003 1.19E-01 6.00 0 0 0.9999 0.0007 1.003035 0.000099 LEU-MISC-THERM-005-004 1.19E-01 6.00 0 0 1.0000 0.0007 1.002881 0.000099 LEU-MISC-THERM-005-005 1.19E-01 6.00 0 0 1.0000 0.0007 1.003026 0.000099 LEU-MISC-THERM-005-006 1.19E-01 6.00 0 0 1.0000 0.0007 1.003598 0.000099 LEU-MISC-THERM-005-007 1.19E-01 6.00 0 0 0.9999 0.0007 1.003058 0.000099 LEU-MISC-THERM-005-008 1.19E-01 6.00 0 0 0.9999 0.0007 1.002492 0.000099 LEU-MISC-THERM-005-009 1.19E-01 6.00 0 0 0.9999 0.0007 1.003133 0.000099 LEU-MISC-THERM-005-010 1.20E-01 6.00 0 0 0.9998 0.0007 1.002479 0.000099 LEU-MISC-THERM-005-011 1.20E-01 6.00 0 0 0.9999 0.0007 1.002549 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-5

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

LEU-MISC-THERM-005-012 1.20E-01 6.00 0 0 0.9999 0.0007 1.002305 0.000098 LEU-SOL-THERM-002-001 3.75E-02 4.89 0 0 1.0038 0.0040 1.000262 0.000099 LEU-SOL-THERM-002-002 3.93E-02 4.89 0 0 1.0024 0.0037 0.996015 0.000099 LEU-SOL-THERM-002-003 3.85E-02 4.89 0 0 1.0024 0.0044 1.001281 0.000099 LEU-SOL-THERM-003-001 4.02E-02 10.19 0 0 0.9997 0.0039 0.996464 0.000095 LEU-SOL-THERM-003-002 3.84E-02 10.19 0 0 0.9993 0.0042 0.995342 0.000099 LEU-SOL-THERM-003-003 3.81E-02 10.19 0 0 0.9995 0.0042 0.999539 0.000099 LEU-SOL-THERM-003-004 3.80E-02 10.19 0 0 0.9995 0.0042 0.993066 0.000099 LEU-SOL-THERM-003-005 3.54E-02 10.19 0 0 0.9997 0.0048 0.997705 0.000092 LEU-SOL-THERM-003-006 3.51E-02 10.19 0 0 0.9999 0.0049 0.998171 0.000099 LEU-SOL-THERM-003-007 3.49E-02 10.19 0 0 0.9994 0.0049 0.996629 0.000099 LEU-SOL-THERM-003-008 3.39E-02 10.19 0 0 0.9993 0.0052 0.999996 0.000095 LEU-SOL-THERM-003-009 3.38E-02 10.19 0 0 0.9996 0.0052 0.997637 0.000097 LEU-SOL-THERM-004-001 4.08E-02 9.97 0 0 0.9994 0.0008 1.00028 0.00048 LEU-SOL-THERM-004-002 3.98E-02 9.97 0 0 0.9999 0.0009 1.00119 0.00049 LEU-SOL-THERM-004-003 3.86E-02 9.97 0 0 0.9999 0.0009 0.99914 0.00047 LEU-SOL-THERM-004-004 3.78E-02 9.97 0 0 0.9999 0.0010 1.00182 0.00048 LEU-SOL-THERM-004-005 3.73E-02 9.97 0 0 0.9999 0.0010 1.00126 0.00046 LEU-SOL-THERM-004-006 3.68E-02 9.97 0 0 0.9994 0.0011 1.00059 0.00046 LEU-SOL-THERM-004-007 3.65E-02 9.97 0 0 0.9996 0.0011 1.00045 0.00041 MIX-COMP-THERM-001-001 9.48E-01 0.71 2.24E-01 0 1.0000 0.0025 1.000159 0.000099 MIX-COMP-THERM-001-002 2.68E-01 0.71 2.24E-01 0 1.0000 0.0026 0.999358 0.000099 MIX-COMP-THERM-001-003 1.62E-01 0.71 2.24E-01 0 1.0000 0.0032 0.997994 0.000099 MIX-COMP-THERM-001-004 1.13E-01 0.71 2.24E-01 0 1.0000 0.0039 1.000355 0.000099 MIX-COMP-THERM-002-001S 5.29E-01 0.71 2.04E-02 2 1.0024 0.0060 1.000817 0.000099 MIX-COMP-THERM-002-002S 7.01E-01 0.71 2.04E-02 688 1.0009 0.0047 1.001113 0.000099 MIX-COMP-THERM-002-003S 1.85E-01 0.71 2.04E-02 1 1.0042 0.0031 1.002517 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-6

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-002-004S 2.69E-01 0.71 2.04E-02 1090 1.0024 0.0024 1.005391 0.000099 MIX-COMP-THERM-002-005S 1.33E-01 0.71 2.04E-02 2 1.0038 0.0025 1.004704 0.000099 MIX-COMP-THERM-002-006S 1.76E-01 0.71 2.04E-02 767 1.0029 0.0027 1.005547 0.000099 MIX-COMP-THERM-003-001 8.50E-01 0.71 6.59E-02 0 1.0000 0.0072 1.000332 0.000069 MIX-COMP-THERM-003-002 5.17E-01 0.71 6.59E-02 0 1.0000 0.0059 1.001006 0.000069 MIX-COMP-THERM-003-003 6.13E-01 0.71 6.59E-02 337 1.0000 0.0054 1.000343 0.000069 MIX-COMP-THERM-003-004 1.81E-01 0.71 6.59E-02 0 1.0000 0.0031 1.001825 0.000069 MIX-COMP-THERM-003-005 1.50E-01 0.71 6.59E-02 0 1.0000 0.0027 1.001288 0.000069 MIX-COMP-THERM-003-006 9.83E-02 0.71 6.59E-02 0 1.0000 0.0023 1.002059 0.000069 MIX-COMP-THERM-004-001 1.39E-01 0.71 3.00E-02 0 1.0000 0.0046 0.995528 0.000099 MIX-COMP-THERM-004-002 1.38E-01 0.71 2.99E-02 0 1.0000 0.0046 0.996398 0.000099 MIX-COMP-THERM-004-003 1.38E-01 0.71 2.98E-02 0 1.0000 0.0046 0.996654 0.000099 MIX-COMP-THERM-004-004 1.15E-01 0.71 3.00E-02 0 1.0000 0.0039 0.996191 0.000099 MIX-COMP-THERM-004-005 1.14E-01 0.71 2.99E-02 0 1.0000 0.0039 0.997207 0.000099 MIX-COMP-THERM-004-006 1.13E-01 0.71 2.98E-02 0 1.0000 0.0039 0.997597 0.000096 MIX-COMP-THERM-004-007 8.98E-02 0.71 3.00E-02 0 1.0000 0.0040 0.997248 0.000099 MIX-COMP-THERM-004-008 8.95E-02 0.71 2.99E-02 0 1.0000 0.0040 0.997929 0.000099 MIX-COMP-THERM-004-009 8.91E-02 0.71 2.98E-02 0 1.0000 0.0040 0.998696 0.000099 MIX-COMP-THERM-004-010 7.76E-02 0.71 3.00E-02 0 1.0000 0.0051 0.998083 0.000099 MIX-COMP-THERM-004-011 7.73E-02 0.71 2.99E-02 0 1.0000 0.0051 0.99853 0.000099 MIX-COMP-THERM-005-001 3.73E-01 0.71 3.99E-02 0 1.0008 0.0022 1.001774 0.000099 MIX-COMP-THERM-005-002 2.48E-01 0.71 3.99E-02 0 1.0011 0.0026 0.999535 0.000097 MIX-COMP-THERM-005-003 1.71E-01 0.71 3.99E-02 0 1.0016 0.0029 1.006808 0.000098 MIX-COMP-THERM-005-004 1.41E-01 0.71 3.99E-02 0 1.0021 0.0028 1.029384 0.000099 MIX-COMP-THERM-005-005 1.06E-01 0.71 3.99E-02 0 1.0026 0.0036 1.005849 0.000099 MIX-COMP-THERM-005-006 9.17E-02 0.71 3.99E-02 0 1.0033 0.0042 1.005577 0.000095 MIX-COMP-THERM-005-007 8.75E-02 0.71 3.99E-02 0 1.0035 0.0042 1.007526 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-7

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-006-001 3.57E-01 0.71 2.04E-02 0 1.0016 0.0051 0.996918 0.000099 MIX-COMP-THERM-006-002 1.88E-01 0.71 2.04E-02 0 1.0017 0.0036 1.000826 0.000098 MIX-COMP-THERM-006-003 1.37E-01 0.71 2.04E-02 0 1.0026 0.0036 0.99683 0.000087 MIX-COMP-THERM-006-004 1.17E-01 0.71 2.04E-02 0 1.0051 0.0044 1.002949 0.000098 MIX-COMP-THERM-006-005 9.56E-02 0.71 2.04E-02 0 1.0040 0.0054 1.003484 0.000099 MIX-COMP-THERM-006-006 9.06E-02 0.71 2.04E-02 0 1.0055 0.0051 1.00127 0.000098 MIX-COMP-THERM-006-007 1.36E-01 0.71 2.04E-02 0 1.0024 0.0045 0.994319 0.000099 MIX-COMP-THERM-006-008 1.37E-01 0.71 2.04E-02 0 1.0035 0.0044 0.99387 0.000098 MIX-COMP-THERM-006-009 1.37E-01 0.71 2.04E-02 0 1.0035 0.0044 0.993377 0.000097 MIX-COMP-THERM-006-010 1.37E-01 0.71 2.04E-02 0 1.0021 0.0044 0.991588 0.000099 MIX-COMP-THERM-006-011 1.37E-01 0.71 2.04E-02 0 1.0032 0.0044 0.99167 0.000095 MIX-COMP-THERM-006-012 1.38E-01 0.71 2.04E-02 0 1.0032 0.0044 0.991285 0.000099 MIX-COMP-THERM-006-013 1.37E-01 0.71 2.04E-02 0 1.0021 0.0044 0.99269 0.000099 MIX-COMP-THERM-006-014 1.37E-01 0.71 2.04E-02 0 1.0026 0.0044 0.992422 0.000099 MIX-COMP-THERM-006-015 1.37E-01 0.71 2.04E-02 0 1.0033 0.0044 0.992061 0.000098 MIX-COMP-THERM-006-016 1.37E-01 0.71 2.04E-02 0 1.0035 0.0045 0.993068 0.000098 MIX-COMP-THERM-006-017 1.38E-01 0.71 2.04E-02 0 1.0026 0.0046 0.990815 0.000099 MIX-COMP-THERM-006-018 1.38E-01 0.71 2.04E-02 0 1.0023 0.0045 0.989968 0.000098 MIX-COMP-THERM-006-019 1.38E-01 0.71 2.04E-02 0 1.0032 0.0045 0.990804 0.000099 MIX-COMP-THERM-006-020 1.38E-01 0.71 2.04E-02 0 1.0033 0.0045 0.990674 0.000099 MIX-COMP-THERM-006-021 1.38E-01 0.71 2.04E-02 0 1.0030 0.0045 0.989963 0.000099 MIX-COMP-THERM-006-022 1.38E-01 0.71 2.04E-02 0 1.0024 0.0045 0.989822 0.000099 MIX-COMP-THERM-006-023 1.38E-01 0.71 2.04E-02 0 1.0030 0.0045 0.990511 0.000099 MIX-COMP-THERM-006-024 1.38E-01 0.71 2.04E-02 0 1.0030 0.0045 0.990545 0.000097 MIX-COMP-THERM-006-025 1.38E-01 0.71 2.04E-02 0 1.0024 0.0045 0.990283 0.000097 MIX-COMP-THERM-006-026 1.38E-01 0.71 2.04E-02 0 1.0021 0.0045 0.990283 0.000097 MIX-COMP-THERM-006-027 1.38E-01 0.71 2.04E-02 0 1.0033 0.0045 0.990749 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-8

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-006-028 1.38E-01 0.71 2.04E-02 0 1.0033 0.0046 0.990997 0.000099 MIX-COMP-THERM-006-029 9.53E-02 0.71 2.04E-02 0 1.0040 0.0087 0.9986 0.000099 MIX-COMP-THERM-006-030 9.54E-02 0.71 2.04E-02 0 1.0043 0.0087 0.997537 0.000099 MIX-COMP-THERM-006-031 9.55E-02 0.71 2.04E-02 0 1.0045 0.0087 0.996976 0.000099 MIX-COMP-THERM-006-032 9.56E-02 0.71 2.04E-02 0 1.0037 0.0087 0.995413 0.000099 MIX-COMP-THERM-006-033 9.57E-02 0.71 2.04E-02 0 1.0043 0.0087 0.995252 0.000099 MIX-COMP-THERM-006-034 9.58E-02 0.71 2.04E-02 0 1.0037 0.0087 0.994231 0.000099 MIX-COMP-THERM-006-035 9.55E-02 0.71 2.04E-02 0 1.0044 0.0087 0.997611 0.000099 MIX-COMP-THERM-006-036 9.56E-02 0.71 2.04E-02 0 1.0036 0.0087 0.995737 0.000098 MIX-COMP-THERM-006-037 9.58E-02 0.71 2.04E-02 0 1.0041 0.0087 0.995159 0.000098 MIX-COMP-THERM-006-038 9.57E-02 0.71 2.04E-02 0 1.0044 0.0087 0.995777 0.000098 MIX-COMP-THERM-006-039 9.60E-02 0.71 2.04E-02 0 1.0042 0.0088 0.993265 0.000097 MIX-COMP-THERM-006-040 9.60E-02 0.71 2.04E-02 0 1.0038 0.0087 0.992624 0.000099 MIX-COMP-THERM-006-041 9.60E-02 0.71 2.04E-02 0 1.0038 0.0087 0.992568 0.000099 MIX-COMP-THERM-006-042 9.60E-02 0.71 2.04E-02 0 1.0036 0.0087 0.992334 0.000097 MIX-COMP-THERM-006-043 9.59E-02 0.71 2.04E-02 0 1.0044 0.0087 0.993355 0.000092 MIX-COMP-THERM-006-044 9.60E-02 0.71 2.04E-02 0 1.0044 0.0087 0.992866 0.000098 MIX-COMP-THERM-006-045 9.60E-02 0.71 2.04E-02 0 1.0040 0.0087 0.992938 0.000099 MIX-COMP-THERM-006-046 9.60E-02 0.71 2.04E-02 0 1.0040 0.0087 0.992937 0.000099 MIX-COMP-THERM-006-047 9.60E-02 0.71 2.04E-02 0 1.0040 0.0087 0.992773 0.000099 MIX-COMP-THERM-006-048 9.60E-02 0.71 2.04E-02 0 1.0038 0.0087 0.992773 0.000099 MIX-COMP-THERM-006-049 9.60E-02 0.71 2.04E-02 0 1.0039 0.0087 0.992862 0.000096 MIX-COMP-THERM-006-050 9.60E-02 0.71 2.04E-02 0 1.0044 0.0087 0.99344 0.000097 MIX-COMP-THERM-007-001 1.89E-01 0.71 1.99E-02 0 1.0023 0.0035 1.00338 0.000099 MIX-COMP-THERM-007-002 1.38E-01 0.71 1.99E-02 0 1.0024 0.0039 0.998968 0.000099 MIX-COMP-THERM-007-003 1.16E-01 0.71 1.99E-02 0 1.0036 0.0046 1.001016 0.000099 MIX-COMP-THERM-007-004 9.58E-02 0.71 1.99E-02 0 1.0037 0.0057 1.000812 0.000094 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-9

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-007-005 9.08E-02 0.71 1.99E-02 0 1.0044 0.0061 0.998979 0.000099 MIX-COMP-THERM-008-001 3.79E-01 0.71 2.00E-02 0 0.9997 0.0032 0.997268 0.000095 MIX-COMP-THERM-008-002 1.93E-01 0.71 2.00E-02 0 1.0008 0.0030 0.998639 0.000099 MIX-COMP-THERM-008-003 1.39E-01 0.71 2.00E-02 0 1.0023 0.0038 0.998631 0.000099 MIX-COMP-THERM-008-003_Al 1.38E-01 0.71 2.00E-02 0 1.0023 0.0039 0.996786 0.000095 MIX-COMP-THERM-008-003_B1 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.994897 0.000099 MIX-COMP-THERM-008-003_B2 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.995821 0.000091 MIX-COMP-THERM-008-003_B3 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.9961 0.000099 MIX-COMP-THERM-008-003_B4 1.38E-01 0.71 2.00E-02 0 1.0023 0.0039 0.996278 0.000097 MIX-COMP-THERM-008-003_CdAir 1.39E-01 0.71 2.00E-02 0 1.0023 0.0040 0.995047 0.000093 MIX-COMP-THERM-008-003_CdAl 1.39E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995691 0.000099 MIX-COMP-THERM-008-003_CdB1 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.994727 0.000099 MIX-COMP-THERM-008-003_CdB2 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995156 0.00009 MIX-COMP-THERM-008-003_CdB3 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995418 0.000099 MIX-COMP-THERM-008-003_CdB4 1.39E-01 0.71 2.00E-02 0 1.0023 0.0041 0.994738 0.000099 MIX-COMP-THERM-008-003_CdH1 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995504 0.000095 MIX-COMP-THERM-008-003_CdH2 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.99496 0.000097 MIX-COMP-THERM-008-003_CdH3 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995141 0.000099 MIX-COMP-THERM-008-003_CdH4 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.995274 0.000099 MIX-COMP-THERM-008-003_CdH5 1.40E-01 0.71 2.00E-02 0 1.0023 0.0041 0.994902 0.000099 MIX-COMP-THERM-008-003_CdWater 1.40E-01 0.71 2.00E-02 0 1.0023 0.0040 0.994952 0.000095 MIX-COMP-THERM-008-003_H1 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.995021 0.000097 MIX-COMP-THERM-008-003_H2 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.995538 0.000097 MIX-COMP-THERM-008-003_H3 1.39E-01 0.71 2.00E-02 0 1.0023 0.0039 0.996075 0.000097 MIX-COMP-THERM-008-003_H4 1.38E-01 0.71 2.00E-02 0 1.0023 0.0039 0.996986 0.000097 MIX-COMP-THERM-008-003_H5 1.38E-01 0.71 2.00E-02 0 1.0023 0.0039 0.997032 0.000097 MIX-COMP-THERM-008-004 1.17E-01 0.71 2.00E-02 0 1.0015 0.0047 1.001757 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-10

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-008-005 9.58E-02 0.71 2.00E-02 0 1.0022 0.0056 1.002015 0.000099 MIX-COMP-THERM-008-006 9.08E-02 0.71 2.00E-02 0 1.0028 0.0065 1.001537 0.000096 MIX-COMP-THERM-009-001 5.17E-01 0.16 1.50E-02 0 1.0003 0.0054 0.999726 0.000092 MIX-COMP-THERM-009-002 3.09E-01 0.16 1.50E-02 0 1.0020 0.0049 0.993582 0.000097 MIX-COMP-THERM-009-003 1.57E-01 0.16 1.50E-02 0 1.0035 0.0050 0.997231 0.000092 MIX-COMP-THERM-009-004 1.18E-01 0.16 1.50E-02 0 1.0046 0.0062 0.99804 0.000086 MIX-COMP-THERM-009-005 9.61E-02 0.16 1.50E-02 0 1.0059 0.0074 1.00071 0.000094 MIX-COMP-THERM-009-006 9.07E-02 0.16 1.50E-02 0 1.0067 0.0080 0.992724 0.000092 MIX-COMP-THERM-011-001 5.46E-01 59.70 2.56E-01 0 1.0000 0.0024 1.002152 0.000099 MIX-COMP-THERM-011-002 5.39E-01 59.70 2.56E-01 0 1.0000 0.0024 1.003254 0.000099 MIX-COMP-THERM-011-003 5.18E-01 59.70 2.56E-01 0 1.0000 0.0025 1.002025 0.000099 MIX-COMP-THERM-011-004 2.46E-01 59.70 2.56E-01 0 1.0000 0.0018 0.999383 0.000098 MIX-COMP-THERM-011-005 2.52E-01 59.70 2.56E-01 0 1.0000 0.0016 0.999688 0.000099 MIX-COMP-THERM-011-006 2.59E-01 59.70 2.56E-01 0 1.0000 0.0016 0.999501 0.000099 MIX-COMP-THERM-012-001 1.33E-01 0.15 7.58E-02 0 1.0052 0.0067 0.97879 0.000099 MIX-COMP-THERM-012-002 1.33E-01 0.15 7.58E-02 0 1.0052 0.0067 0.979883 0.000097 MIX-COMP-THERM-012-003 1.33E-01 0.15 7.58E-02 0 1.0052 0.0067 0.977197 0.000099 MIX-COMP-THERM-012-004 1.34E-01 0.15 7.58E-02 0 1.0052 0.0067 0.981166 0.000099 MIX-COMP-THERM-012-005 1.33E-01 0.15 7.58E-02 0 1.0052 0.0067 0.979784 0.000099 MIX-COMP-THERM-012-006 1.34E-01 0.15 7.58E-02 0 1.0052 0.0075 0.983882 0.000099 MIX-COMP-THERM-012-007 6.44E-02 0.15 7.88E-02 0 1.0053 0.0134 1.033937 0.000099 MIX-COMP-THERM-012-008 6.43E-02 0.15 7.88E-02 0 1.0053 0.0055 1.029094 0.000098 MIX-COMP-THERM-012-009 6.41E-02 0.15 7.88E-02 0 1.0053 0.0055 1.026901 0.000099 MIX-COMP-THERM-012-010 6.41E-02 0.15 7.88E-02 0 1.0053 0.0055 1.026621 0.000099 MIX-COMP-THERM-012-011 6.41E-02 0.15 7.88E-02 0 1.0053 0.0055 1.025248 0.000099 MIX-COMP-THERM-012-012 6.42E-02 0.15 7.88E-02 0 1.0053 0.0055 1.027569 0.000099 MIX-COMP-THERM-012-013 6.45E-02 0.15 7.88E-02 0 1.0053 0.0158 1.036086 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-11

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-COMP-THERM-012-014 1.38E-01 0.15 1.46E-01 0 1.0012 0.0086 1.025491 0.000098 MIX-COMP-THERM-012-015 1.37E-01 0.15 1.46E-01 0 1.0012 0.0086 1.024827 0.000099 MIX-COMP-THERM-012-016 1.36E-01 0.15 1.46E-01 0 1.0012 0.0086 1.022106 0.000099 MIX-COMP-THERM-012-017 1.35E-01 0.15 1.46E-01 0 1.0012 0.0086 1.021574 0.000099 MIX-COMP-THERM-012-018 1.35E-01 0.15 1.46E-01 0 1.0012 0.0086 1.020982 0.000093 MIX-COMP-THERM-012-019 1.34E-01 0.15 1.46E-01 0 1.0012 0.0086 1.020518 0.000099 MIX-COMP-THERM-012-020 1.89E-01 0.15 1.46E-01 0 1.0014 0.0120 1.019034 0.000098 MIX-COMP-THERM-012-021 1.89E-01 0.15 1.46E-01 0 1.0014 0.0152 1.017898 0.000099 MIX-COMP-THERM-012-022 2.02E-01 0.15 1.46E-01 0 1.0014 0.0086 1.012976 0.000099 MIX-COMP-THERM-012-023 1.58E-01 0.15 3.00E-01 0 1.0007 0.0114 1.015748 0.000099 MIX-COMP-THERM-012-024 1.58E-01 0.15 3.00E-01 0 1.0007 0.0114 1.016363 0.000099 MIX-COMP-THERM-012-025 1.57E-01 0.15 3.00E-01 0 1.0007 0.0114 1.015311 0.000099 MIX-COMP-THERM-012-026 1.54E-01 0.15 3.00E-01 0 1.0007 0.0114 1.013192 0.000099 MIX-COMP-THERM-012-027 1.53E-01 0.15 3.00E-01 0 1.0007 0.0114 1.014137 0.000099 MIX-COMP-THERM-012-028 1.52E-01 0.15 3.00E-01 0 1.0007 0.0114 1.016432 0.000099 MIX-COMP-THERM-012-029 1.51E-01 0.15 3.00E-01 0 1.0007 0.0114 1.015605 0.000099 MIX-COMP-THERM-012-030 1.54E-01 0.15 3.00E-01 0 1.0007 0.0114 1.01417 0.0001 MIX-COMP-THERM-012-031 2.36E-01 0.15 3.00E-01 0 1.0017 0.0151 1.000971 0.000099 MIX-COMP-THERM-012-032 2.36E-01 0.15 3.00E-01 0 1.0017 0.0151 1.001484 0.000099 MIX-COMP-THERM-012-033 2.36E-01 0.15 3.00E-01 0 1.0017 0.0151 0.998008 0.000099 MIX-SOL-THERM-001-001 1.54E-01 0.70 2.19E-01 3 1.0000 0.0016 0.997637 0.000099 MIX-SOL-THERM-001-002 1.55E-01 0.70 2.20E-01 3 1.0000 0.0016 0.997643 0.000099 MIX-SOL-THERM-001-003 1.51E-01 0.70 2.21E-01 3 1.0000 0.0016 0.992688 0.000099 MIX-SOL-THERM-001-004 1.64E-01 0.70 2.22E-01 3 1.0000 0.0016 0.99689 0.000099 MIX-SOL-THERM-001-005 1.68E-01 0.70 2.21E-01 3 1.0000 0.0016 1.001138 0.000098 MIX-SOL-THERM-001-006 1.62E-01 0.70 2.22E-01 3 1.0000 0.0016 1.000883 0.000096 MIX-SOL-THERM-001-007 2.71E-01 2.29 9.68E-01 3 1.0000 0.0016 1.002787 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-12

Experiment ID EALF (eV) Enrich (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

MIX-SOL-THERM-001-008 1.43E-01 2.29 9.67E-01 2 1.0000 0.0016 1.001542 0.000099 MIX-SOL-THERM-001-009 8.95E-02 2.29 9.62E-01 1 1.0000 0.0016 1.000502 0.000099 MIX-SOL-THERM-001-010 1.11E-01 0.70 2.27E-01 2 1.0000 0.0016 1.0018 0.000099 MIX-SOL-THERM-001-011 1.08E-01 0.70 2.27E-01 2 1.0000 0.0050 1.007492 0.000099 MIX-SOL-THERM-001-012 1.05E-01 0.70 2.28E-01 2 1.0000 0.0050 1.008659 0.000098 MIX-SOL-THERM-001-013 8.16E-02 0.70 2.25E-01 2 1.0000 0.0016 0.997657 0.000096 MIX-SOL-THERM-002-001 4.18E-02 0.71 5.18E-01 1 1.0000 0.0024 1.003318 0.000097 MIX-SOL-THERM-002-002 4.17E-02 0.71 5.21E-01 1 1.0000 0.0024 1.003638 0.000092 MIX-SOL-THERM-002-003 4.27E-02 0.44 2.29E-01 1 1.0000 0.0024 1.003091 0.000097 MIX-SOL-THERM-004-001 6.95E-02 0.56 3.97E-01 2 1.0000 0.0033 0.996676 0.000099 MIX-SOL-THERM-004-002 6.55E-02 0.56 3.97E-01 2 1.0000 0.0033 0.996823 0.000099 MIX-SOL-THERM-004-003 6.81E-02 0.56 3.97E-01 2 1.0000 0.0068 0.998696 0.000099 MIX-SOL-THERM-004-004 1.69E-01 0.56 4.06E-01 4 1.0000 0.0078 1.001814 0.0001 MIX-SOL-THERM-004-005 1.54E-01 0.56 4.05E-01 4 1.0000 0.0029 0.997132 0.000099 MIX-SOL-THERM-004-006 1.85E-01 0.56 4.05E-01 4 1.0000 0.0029 0.996693 0.000099 MIX-SOL-THERM-004-007 3.36E-01 0.56 3.96E-01 5 1.0000 0.0026 0.998081 0.000099 MIX-SOL-THERM-004-008 2.55E-01 0.56 3.97E-01 5 1.0000 0.0026 0.998146 0.000099 MIX-SOL-THERM-004-009 2.95E-01 0.56 3.97E-01 5 1.0000 0.0077 0.998954 0.0001 MIX-SOL-THERM-005-001 6.93E-02 0.56 3.95E-01 2 1.0000 0.0037 0.992799 0.000097 MIX-SOL-THERM-005-002 6.50E-02 0.56 3.98E-01 2 1.0000 0.0037 1.000418 0.000098 MIX-SOL-THERM-005-003 1.49E-01 0.56 4.07E-01 4 1.0000 0.0037 1.002735 0.000098 MIX-SOL-THERM-005-004 1.46E-01 0.56 4.07E-01 4 1.0000 0.0037 1.000902 0.000096 MIX-SOL-THERM-005-005 1.86E-01 0.56 4.06E-01 4 1.0000 0.0037 0.988772 0.000096 MIX-SOL-THERM-005-006 3.39E-01 0.56 3.97E-01 5 1.0000 0.0037 0.989047 0.000097 MIX-SOL-THERM-005-007 2.43E-01 0.56 3.96E-01 5 1.0000 0.0037 0.999568 0.000077 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-13

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC1_01 7.06E-02 1.57 0.01104 0 PI* PI 1.00031 0.000094 HTC1_02 6.76E-02 1.57 0.01104 0 PI PI 1.000355 0.0001 HTC1_03 6.74E-02 1.57 0.01104 0 PI PI 1.000437 0.000099 HTC1_04 8.62E-02 1.57 0.01104 0 PI PI 1.000128 0.000099 HTC1_05 8.41E-02 1.57 0.01104 0 PI PI 1.000018 0.000099 HTC1_06 8.33E-02 1.57 0.01104 0 PI PI 0.999757 0.000099 HTC1_07 1.04E-01 1.57 0.01104 0 PI PI 0.999781 0.000099 HTC1_08 1.02E-01 1.57 0.01104 0 PI PI 0.999588 0.000099 HTC1_09 1.01E-01 1.57 0.01104 0 PI PI 0.999619 0.000099 HTC1_10 1.43E-01 1.57 0.01104 0 PI PI 0.999817 0.000099 HTC1_11 1.38E-01 1.57 0.01104 0 PI PI 0.99895 0.000099 HTC1_12 1.36E-01 1.57 0.01104 0 PI PI 0.998754 0.000092 HTC1_13 2.60E-01 1.57 0.01104 0 PI PI 0.997985 0.000099 HTC1_14 2.37E-01 1.57 0.01104 0 PI PI 0.997921 0.000099 HTC1_15 2.33E-01 1.57 0.01104 0 PI PI 0.998004 0.000099 HTC1_16 1.03E-01 1.57 0.01104 0 PI PI 0.999508 0.000099 HTC1_17 1.01E-01 1.57 0.01104 0 PI PI 0.99926 0.0001 HTC1_18 1.03E-01 1.57 0.01104 0 PI PI 0.997269 0.000099 HTC2B_01 2.50E-01 1.57 0.01104 100 PI PI 0.998582 0.000099 HTC2B_02 2.48E-01 1.57 0.01104 106 PI PI 0.997486 0.000099 HTC2B_03 2.58E-01 1.57 0.01104 205 PI PI 0.998025 0.000099 HTC2B_04 2.67E-01 1.57 0.01104 299 PI PI 0.998872 0.000099 HTC2B_05 2.78E-01 1.57 0.01104 400 PI PI 0.998393 0.000099 HTC2B_06 2.74E-01 1.57 0.01104 399 PI PI 0.998364 0.000099 HTC2B_07 2.83E-01 1.57 0.01104 486 PI PI 0.999737 0.000099 HTC2B_08 2.90E-01 1.57 0.01104 587 PI PI 0.998816 0.000099 HTC2B_09 1.68E-01 1.57 0.01104 595 PI PI 0.999772 0.000097 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-14

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC2B_10 1.63E-01 1.57 0.01104 499 PI PI 0.998417 0.000096 HTC2B_11 1.59E-01 1.57 0.01104 393 PI PI 1.000163 0.000099 HTC2B_12 1.52E-01 1.57 0.01104 295 PI PI 1.000327 0.000099 HTC2B_13 1.47E-01 1.57 0.01104 200 PI PI 0.99948 0.000099 HTC2B_14 1.42E-01 1.57 0.01104 89 PI PI 1.002154 0.000099 HTC2B_15 1.05E-01 1.57 0.01104 90 PI PI 1.003535 0.000097 HTC2B_16 1.09E-01 1.57 0.01104 194 PI PI 1.001781 0.000098 HTC2B_17 1.12E-01 1.57 0.01104 286 PI PI 1.003658 0.000099 HTC2B_18 1.17E-01 1.57 0.01104 415 PI PI 0.994315 0.000099 HTC2B_19 1.06E-01 1.57 0.01104 100 PI PI 1.000358 0.000099 HTC2B_20 9.09E-02 1.57 0.01104 220 PI PI 0.993473 0.000099 HTC2B_21 8.74E-02 1.57 0.01104 110 PI PI 0.99714 0.000099 HTC2G_01 2.56E-01 1.57 0.01104 0 PI PI 0.997596 0.000099 HTC2G_02 2.52E-01 1.57 0.01104 0 PI PI 0.997572 0.000098 HTC2G_03 2.74E-01 1.57 0.01104 0 PI PI 0.997364 0.000099 HTC2G_04 2.70E-01 1.57 0.01104 0 PI PI 0.997628 0.000099 HTC2G_05 2.67E-01 1.57 0.01104 0 PI PI 0.997547 0.000098 HTC2G_06 2.88E-01 1.57 0.01104 0 PI PI 0.996896 0.000099 HTC2G_07 2.81E-01 1.57 0.01104 0 PI PI 0.99678 0.000099 HTC2G_08 2.99E-01 1.57 0.01104 0 PI PI 0.996061 0.000099 HTC2G_09 2.95E-01 1.57 0.01104 0 PI PI 0.996248 0.0001 HTC2G_10 1.72E-01 1.57 0.01104 0 PI PI 0.997293 0.000097 HTC2G_11 1.64E-01 1.57 0.01104 0 PI PI 0.998279 0.000097 HTC2G_12 1.63E-01 1.57 0.01104 0 PI PI 0.998151 0.000099 HTC2G_13 1.56E-01 1.57 0.01104 0 PI PI 0.998612 0.0001 HTC2G_14 1.54E-01 1.57 0.01104 0 PI PI 0.998472 0.000099 HTC2G_15 1.49E-01 1.57 0.01104 0 PI PI 0.999848 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-15

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC2G_16 1.46E-01 1.57 0.01104 0 PI PI 0.999841 0.000098 HTC2G_17 1.08E-01 1.57 0.01104 0 PI PI 1.000852 0.000098 HTC2G_18 8.91E-02 1.57 0.01104 0 PI PI 1.00129 0.000099 HTC2G_19 1.15E-01 1.57 0.01104 0 PI PI 0.997328 0.000095 HTC2G_20 1.08E-01 1.57 0.01104 0 PI PI 1.00078 0.000099 HTC3_01 1.26E-01 1.57 0.01104 0 PI PI 0.997631 0.000099 HTC3_02 1.44E-01 1.57 0.01104 0 PI PI 0.999648 0.000099 HTC3_03 1.31E-01 1.57 0.01104 0 PI PI 0.997088 0.0001 HTC3_04 1.26E-01 1.57 0.01104 0 PI PI 0.99704 0.000099 HTC3_05 1.38E-01 1.57 0.01104 0 PI PI 0.996697 0.0001 HTC3_06 1.32E-01 1.57 0.01104 0 PI PI 0.99968 0.000097 HTC3_07 1.31E-01 1.57 0.01104 0 PI PI 0.995888 0.000099 HTC3_08 1.42E-01 1.57 0.01104 0 PI PI 1.003237 0.000099 HTC3_09 1.36E-01 1.57 0.01104 0 PI PI 0.995853 0.0001 HTC3_10 1.32E-01 1.57 0.01104 0 PI PI 0.996274 0.000099 HTC3_11 1.40E-01 1.57 0.01104 0 PI PI 0.995482 0.000099 HTC3_12 1.14E-01 1.57 0.01104 0 PI PI 0.999308 0.000099 HTC3_13 1.13E-01 1.57 0.01104 0 PI PI 0.999521 0.000099 HTC3_14 1.13E-01 1.57 0.01104 0 PI PI 0.999956 0.000099 HTC3_15 1.13E-01 1.57 0.01104 0 PI PI 0.999398 0.000099 HTC3_16 1.12E-01 1.57 0.01104 0 PI PI 1.000209 0.000099 HTC3_17 1.10E-01 1.57 0.01104 0 PI PI 1.00005 0.000099 HTC3_18 1.08E-01 1.57 0.01104 0 PI PI 1.000185 0.000099 HTC3_19 1.06E-01 1.57 0.01104 0 PI PI 1.000703 0.000099 HTC3_20 1.04E-01 1.57 0.01104 0 PI PI 1.000743 0.000099 HTC3_21 1.06E-01 1.57 0.01104 0 PI PI 0.999992 0.0001 HTC3_22 1.09E-01 1.57 0.01104 0 PI PI 1.000214 0.0001 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-16

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC3_23 1.17E-01 1.57 0.01104 0 PI PI 0.999049 0.000099 HTC3_24 1.53E-01 1.57 0.01104 0 PI PI 0.998679 0.0001 HTC3_25 1.29E-01 1.57 0.01104 0 PI PI 0.999733 0.0001 HTC3_26 1.17E-01 1.57 0.01104 0 PI PI 0.999273 0.0001 HTC4FE_01 1.55E-01 1.57 0.01104 0 PI PI 1.001338 0.000099 HTC4FE_02 1.52E-01 1.57 0.01104 0 PI PI 0.997921 0.000099 HTC4FE_03 1.49E-01 1.57 0.01104 0 PI PI 0.997465 0.000099 HTC4FE_04 1.45E-01 1.57 0.01104 0 PI PI 0.997726 0.000099 HTC4FE_05 1.42E-01 1.57 0.01104 0 PI PI 0.997696 0.000099 HTC4FE_06 1.41E-01 1.57 0.01104 0 PI PI 0.996808 0.000099 HTC4FE_07 1.39E-01 1.57 0.01104 0 PI PI 0.99634 0.000099 HTC4FE_08 1.38E-01 1.57 0.01104 0 PI PI 0.9962 0.000099 HTC4FE_09 1.37E-01 1.57 0.01104 0 PI PI 0.995904 0.000099 HTC4FE_10 1.37E-01 1.57 0.01104 0 PI PI 0.997785 0.000099 HTC4FE_11 1.34E-01 1.57 0.01104 0 PI PI 0.998095 0.000099 HTC4FE_12 1.37E-01 1.57 0.01104 0 PI PI 1.000659 0.000099 HTC4FE_13 1.36E-01 1.57 0.01104 0 PI PI 0.996201 0.000099 HTC4FE_14 1.52E-01 1.57 0.01104 0 PI PI 1.006066 0.000099 HTC4FE_15 1.46E-01 1.57 0.01104 0 PI PI 0.997497 0.000099 HTC4FE_16 1.39E-01 1.57 0.01104 0 PI PI 0.997434 0.000099 HTC4FE_17 1.38E-01 1.57 0.01104 0 PI PI 0.995483 0.000099 HTC4FE_18 1.36E-01 1.57 0.01104 0 PI PI 0.99503 0.000099 HTC4FE_19 1.35E-01 1.57 0.01104 0 PI PI 0.994927 0.000099 HTC4FE_20 1.34E-01 1.57 0.01104 0 PI PI 0.99455 0.0001 HTC4FE_21 1.36E-01 1.57 0.01104 0 PI PI 1.004835 0.000099 HTC4FE_22 1.77E-01 1.57 0.01104 0 PI PI 0.999606 0.000099 HTC4FE_23 1.68E-01 1.57 0.01104 0 PI PI 0.999983 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-17

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC4FE_24 1.60E-01 1.57 0.01104 0 PI PI 0.999222 0.000099 HTC4FE_25 1.59E-01 1.57 0.01104 0 PI PI 0.999086 0.000097 HTC4FE_26 1.57E-01 1.57 0.01104 0 PI PI 0.998842 0.000099 HTC4FE_27 1.56E-01 1.57 0.01104 0 PI PI 0.998697 0.000099 HTC4FE_28 1.55E-01 1.57 0.01104 0 PI PI 0.998726 0.000099 HTC4FE_29 1.46E-01 1.57 0.01104 0 PI PI 0.999267 0.000099 HTC4FE_30 1.36E-01 1.57 0.01104 0 PI PI 0.999734 0.000099 HTC4FE_31 1.30E-01 1.57 0.01104 0 PI PI 0.999448 0.000099 HTC4FE_32 1.26E-01 1.57 0.01104 0 PI PI 0.999482 0.000099 HTC4FE_33 1.24E-01 1.57 0.01104 0 PI PI 0.999645 0.000099 HTC4PB_01 1.55E-01 1.57 0.01104 0 PI PI 1.001169 0.000099 HTC4PB_02 1.51E-01 1.57 0.01104 0 PI PI 0.998384 0.000099 HTC4PB_03 1.47E-01 1.57 0.01104 0 PI PI 0.998223 0.0001 HTC4PB_04 1.44E-01 1.57 0.01104 0 PI PI 0.998542 0.000099 HTC4PB_05 1.41E-01 1.57 0.01104 0 PI PI 0.998287 0.000099 HTC4PB_06 1.36E-01 1.57 0.01104 0 PI PI 0.998541 0.000099 HTC4PB_07 1.34E-01 1.57 0.01104 0 PI PI 0.99892 0.000099 HTC4PB_08 1.40E-01 1.57 0.01104 0 PI PI 0.997751 0.000099 HTC4PB_09 1.39E-01 1.57 0.01104 0 PI PI 0.997326 0.000099 HTC4PB_10 1.38E-01 1.57 0.01104 0 PI PI 0.996814 0.000099 HTC4PB_11 1.37E-01 1.57 0.01104 0 PI PI 0.996884 0.000099 HTC4PB_12 1.37E-01 1.57 0.01104 0 PI PI 1.000861 0.000099 HTC4PB_13 1.37E-01 1.57 0.01104 0 PI PI 1.000935 0.000099 HTC4PB_14 1.36E-01 1.57 0.01104 0 PI PI 1.000094 0.000099 HTC4PB_15 1.32E-01 1.57 0.01104 0 PI PI 0.996566 0.000099 HTC4PB_16 1.35E-01 1.57 0.01104 0 PI PI 0.996709 0.000099 HTC4PB_17 1.51E-01 1.57 0.01104 0 PI PI 1.005001 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-18

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. Fraction pu/(pu+u) Sol. Boron (ppm) 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

HTC4PB_18 1.44E-01 1.57 0.01104 0 PI PI 0.998171 0.000099 HTC4PB_19 1.38E-01 1.57 0.01104 0 PI PI 0.998562 0.000099 HTC4PB_20 1.35E-01 1.57 0.01104 0 PI PI 0.999268 0.000099 HTC4PB_21 1.36E-01 1.57 0.01104 0 PI PI 0.997242 0.000096 HTC4PB_22 1.35E-01 1.57 0.01104 0 PI PI 0.996525 0.0001 HTC4PB_23 1.34E-01 1.57 0.01104 0 PI PI 0.9963 0.000099 HTC4PB_24 1.34E-01 1.57 0.01104 0 PI PI 0.995791 0.000099 HTC4PB_25 1.32E-01 1.57 0.01104 0 PI PI 0.998796 0.000099 HTC4PB_26 1.30E-01 1.57 0.01104 0 PI PI 0.99942 0.000099 HTC4PB_27 1.76E-01 1.57 0.01104 0 PI PI 0.998982 0.000099 HTC4PB_28 1.67E-01 1.57 0.01104 0 PI PI 0.999809 0.000099 HTC4PB_29 1.59E-01 1.57 0.01104 0 PI PI 0.99925 0.000099 HTC4PB_30 1.45E-01 1.57 0.01104 0 PI PI 0.999831 0.000099 HTC4PB_31 1.36E-01 1.57 0.01104 0 PI PI 1.000141 0.000099 HTC4PB_32 1.30E-01 1.57 0.01104 0 PI PI 1.000319 0.000099 HTC4PB_33 1.27E-01 1.57 0.01104 0 PI PI 1.00058 0.000099 HTC4PB_34 1.25E-01 1.57 0.01104 0 PI PI 1.000403 0.0001 HTC4PB_35 1.58E-01 1.57 0.01104 0 PI PI 0.999679 0.000099 HTC4PB_36 1.56E-01 1.57 0.01104 0 PI PI 0.999908 0.000099 HTC4PB_37 1.55E-01 1.57 0.01104 0 PI PI 0.999861 0.000099 HTC4PB_38 1.54E-01 1.57 0.01104 0 PI PI 0.999602 0.000099 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-19

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP1_173_01 2.05E-01 4.74 0 0 103Rh PI PI 1.000236 0.000099FP1_173_02 2.15E-01 4.74 0 0 103Rh PI PI 1.000398 0.000099FP1_173_03 2.15E-01 4.74 0 0 103Rh PI PI 0.999587 0.000099FP1_173_05 1.98E-01 4.74 0 0 103Rh PI PI 0.999666 0.000099FP1_173_06 2.07E-01 4.74 0 0 133Cs PI PI 0.999615 0.000099FP1_173_07 1.98E-01 4.74 0 0 133Cs PI PI 0.999313 0.000099FP1_173_08 2.15E-01 4.74 0 0 133Cs PI PI 0.999542 0.000099FP1_173_09 1.99E-01 4.74 0 0 133Cs PI PI 0.999228 0.000099FP1_173_10 1.97E-01 4.74 0 0 133Cs PI PI 0.999176 0.000099FP1_173_11 2.15E-01 4.74 0 0 133Cs PI PI 0.999242 0.000099FP1_173_12 2.07E-01 4.74 0 0 133Cs PI PI 0.999723 0.000099FP1_173_13 2.15E-01 4.74 0 0 133Cs PI PI 0.999589 0.000099FP1_173_14 2.16E-01 4.74 0 0 133Cs PI PI 0.999293 0.000099FP1_173_15 1.97E-01 4.74 0 0 133Cs PI PI 0.999559 0.000099FP1_173_16 2.16E-01 4.74 0 0 natNd PI PI 0.999607 0.000099FP1_173_17 1.98E-01 4.74 0 0 natNd PI PI 0.999663 0.000098FP1_173_18 2.14E-01 4.74 0 0 152Sm PI PI 0.999589 0.000099FP1_173_19 2.12E-01 4.74 0 0 152Sm PI PI 0.999196 0.000099FP1_173_20 2.10E-01 4.74 0 0 152Sm PI PI 0.999549 0.000099FP1_173_21 2.06E-01 4.74 0 0 152Sm PI PI 1.000071 0.000099FP1_173_22 2.04E-01 4.74 0 0 152Sm PI PI 0.999738 0.000099FP1_173_23 2.07E-01 4.74 0 0 155Gd PI PI 0.999457 0.000098FP1_173_24 2.04E-01 4.74 0 0 155Gd PI PI 0.998935 0.000099FP1_173_25 2.02E-01 4.74 0 0 155Gd PI PI 0.998953 0.000099
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-20

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP1_173_26 1.96E-01 4.74 0 0 155Gd PI PI 0.999467 0.000099FP1_173_27 1.98E-01 4.74 0 0 155Gd PI PI 0.999579 0.000099FP1_173_28 2.15E-01 4.74 0 0 Mixt. PI PI 0.999899 0.000099FP1_173_29 2.05E-01 4.74 0 0 Mixt. PI PI 1.000094 0.000099FP1_173_30 2.03E-01 4.74 0 0 Mixt. PI PI 0.999855 0.000099FP1_173_31 2.02E-01 4.74 0 0 149Sm PI PI 0.999498 0.00010 FP1_173_32 2.07E-01 4.74 0 0 149Sm PI PI 0.999878 0.000099FP1_173_34 2.07E-01 4.74 0 820.1 natB PI PI 1.000193 0.000099FP1_173_35 2.15E-01 4.74 0 0 HNO3 PI PI 0.998491 0.00010 FP1_173_36 1.91E-01 4.74 0 0 HNO3 PI PI 0.99814 0.000099FP1_173_37 2.15E-01 4.74 0 0 HNO3 PI PI 0.99903 0.000099FP1_173_38 2.07E-01 4.74 0 0 HNO3 PI PI 0.999412 0.000099FP1_173_39 1.99E-01 4.74 0 0 HNO3 PI PI 0.999646 0.000099FP1_173_40 1.98E-01 4.74 0 0 HNO3 PI PI 0.999741 0.000099FP1_173_41 2.13E-01 4.74 0 0 HNO3 PI PI 0.999031 0.000099FP1_173_42 2.12E-01 4.74 0 0 HNO3 PI PI 0.999045 0.00010 FP1_173_43 2.06E-01 4.74 0 0 HNO3 PI PI 0.999446 0.000099FP1_173_44 2.05E-01 4.74 0 0 HNO3 PI PI 0.999462 0.00010 FP1_173_45 2.04E-01 4.74 0 0 HNO3 PI PI 0.9994 0.000099FP1_173_46 1.99E-01 4.74 0 0 HNO3 PI PI 0.999826 0.000099FP1_173_47 2.04E-01 4.74 0 0 HNO3 PI PI 0.999773 0.000099FP3_176_01 2.93E-01 4.74 0 0 DUN PI PI 0.997286 0.000099FP3_176_02 2.82E-01 4.74 0 0 DUN PI PI 0.999111 0.00010 FP3_176_03 2.83E-01 4.74 0 0 DUN PI PI 0.998792 0.000099FP3_176_04 2.39E-01 4.74 0 0 DUN PI PI 0.998628 0.00010 FP3_176_05 2.39E-01 4.74 0 0 DUN PI PI 0.998734 0.000099
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-21

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP3_176_06 2.38E-01 4.74 0 0 DUN PI PI 0.998557 0.000099FP3_176_07 2.40E-01 4.74 0 0 DUN PI PI 0.998195 0.000099FP3_177_01 1.52E-01 1.57 1.05 0 DUN PI PI 1.003851 0.000099FP3_177_02 1.52E-01 1.57 1.05 0 DUN PI PI 1.003307 0.000099FP3_177_03 1.51E-01 1.57 1.05 0 DUN PI PI 1.003781 0.000099FP3_177_04 1.38E-01 1.57 1.05 0 DUN PI PI 1.003398 0.000099FP3_177_05 1.38E-01 1.57 1.05 0 DUN PI PI 1.003332 0.000099FP3_177_06 1.38E-01 1.57 1.05 0 DUN PI PI 1.00364 0.00010 FP3_177_07 1.38E-01 1.57 1.05 0 DUN PI PI 1.003592 0.000098FP2_174_HBC_01 2.34E-01 1.57 1.06 0 103Rh PI PI 0.998117 0.000099FP2_174_HBC_02 2.26E-01 1.57 1.06 0 103Rh PI PI 0.997367 0.000099FP2_174_HBC_03 2.33E-01 1.57 1.06 0 155Gd PI PI 1.000577 0.000099FP2_174_HBC_04 2.28E-01 1.57 1.06 0 155Gd PI PI 1.000232 0.00010 FP2_174_HBC_05 2.32E-01 1.57 1.06 0 149Sm PI PI 1.001045 0.000099FP2_174_HBC_06 2.27E-01 1.57 1.06 0 149Sm PI PI 1.001075 0.00010 FP2_174_HBC_07 2.26E-01 1.57 1.06 0 Mixt. PI PI 1.000533 0.000099FP2_174_HBC_08 2.35E-01 1.57 1.06 0 HNO3 PI PI 0.999143 0.00010 FP2_174_HBC_09 2.21E-01 1.57 1.06 0 HNO3 PI PI 0.999661 0.000099FP2_174_HBC_10 2.28E-01 1.57 1.06 0 HNO3 PI PI 0.999531 0.000099FP2_174_HBC_11 2.31E-01 1.57 1.06 0 HNO3 PI PI 0.999087 0.000099FP2_174_HBC_12 2.31E-01 1.57 1.06 0 HNO3 PI PI 0.99935 0.000099FP2_174_HBC_13 2.31E-01 1.57 1.06 0 HNO3 PI PI 0.999602 0.000099FP2_174_HBC_14 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.999353 0.00010 FP2_174_UO2_01 2.34E-01 1.57 1.06 0 133Cs PI PI 1.000927 0.000099FP2_174_UO2_02 2.33E-01 1.57 1.06 0 133Cs PI PI 1.000483 0.000099FP2_174_UO2_03 2.26E-01 1.57 1.06 0 133Cs PI PI 1.000571 0.000099
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-22

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP2_174_UO2_04 2.30E-01 1.57 1.06 0 133Cs PI PI 1.000531 0.000099FP2_174_UO2_05 2.29E-01 1.57 1.06 0 133Cs PI PI 1.000465 0.000099FP2_174_UO2_06 2.41E-01 1.57 1.06 0 103Rh PI PI 0.996885 0.000099FP2_174_UO2_07 2.41E-01 1.57 1.06 0 103Rh PI PI 0.996620 0.000099FP2_174_UO2_08 2.37E-01 1.57 1.06 0 103Rh PI PI 0.997042 0.000099FP2_174_UO2_09 2.31E-01 1.57 1.06 0 103Rh PI PI 0.997044 0.000099FP2_174_UO2_10 2.29E-01 1.57 1.06 0 103Rh PI PI 0.996799 0.000099FP2_174_UO2_11 2.29E-01 1.57 1.06 0 natNd PI PI 1.000237 0.000099FP2_174_UO2_12 2.29E-01 1.57 1.06 0 natNd PI PI 1.000076 0.000099FP2_174_UO2_13 2.38E-01 1.57 1.06 0 149Sm PI PI 1.001628 0.000100FP2_174_UO2_14 2.36E-01 1.57 1.06 0 149Sm PI PI 1.001914 0.000099FP2_174_UO2_15 2.33E-01 1.57 1.06 0 149Sm PI PI 1.000559 0.000099FP2_174_UO2_16 2.30E-01 1.57 1.06 0 149Sm PI PI 1.001505 0.000100FP2_174_UO2_17 2.25E-01 1.57 1.06 0 149Sm PI PI 1.000368 0.000100FP2_174_UO2_18 2.33E-01 1.57 1.06 0 152Sm PI PI 1.000790 0.000098FP2_174_UO2_19 2.28E-01 1.57 1.06 0 152Sm PI PI 1.000522 0.000099FP2_174_UO2_20 2.41E-01 1.57 1.06 0 155Gd PI PI 1.001308 0.000099FP2_174_UO2_21 2.33E-01 1.57 1.06 0 155Gd PI PI 0.999476 0.000099FP2_174_UO2_22 2.31E-01 1.57 1.06 0 155Gd PI PI 0.999607 0.000099FP2_174_UO2_23 2.34E-01 1.57 1.06 0 Mixt. PI PI 1.000041 0.000097FP2_174_UO2_24 2.29E-01 1.57 1.06 0 Mixt. PI PI 1.000291 0.000096FP2_174_UO2_25 2.47E-01 1.57 1.06 0 Mixt. PI PI 1.002539 0.000099FP2_174_UO2_26 2.41E-01 1.57 1.06 0 Mixt. PI PI 1.002514 0.000100FP2_174_UO2_27 2.50E-01 1.57 1.06 0 Mixt. PI PI 1.003020 0.000099FP2_174_UO2_28 2.47E-01 1.57 1.06 0 Mixt. PI PI 1.002835 0.000099FP2_174_UO2_29 2.57E-01 1.57 1.06 0 HNO3 PI PI 0.994993 0.000099FP2_174_UO2_30 2.57E-01 1.57 1.06 0 HNO3 PI PI 0.996099 0.000099FP2_174_UO2_31 2.43E-01 1.57 1.06 0 HNO3 PI PI 0.998027 0.000099
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-23

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP2_174_UO2_32 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.998988 0.000100FP2_174_UO2_33 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.998961 0.000099FP2_174_UO2_34 2.35E-01 1.57 1.06 0 HNO3 PI PI 0.997965 0.000099FP2_174_UO2_35 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.998289 0.000099FP2_174_UO2_36 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.998183 0.000099FP2_174_UO2_37 2.33E-01 1.57 1.06 0 HNO3 PI PI 0.998126 0.000099FP2_174_UO2_38 2.34E-01 1.57 1.06 0 HNO3 PI PI 0.997780 0.000099FP2_174_UO2_39 2.32E-01 1.57 1.06 0 HNO3 PI PI 0.997914 0.000099FP2_174_UO2_40 2.31E-01 1.57 1.06 0 HNO3 PI PI 0.998199 0.000100FP2_174_UO2_41 2.37E-01 1.57 1.06 0 HNO3 PI PI 0.997925 0.000099FP2_174_UO2_42 2.46E-01 1.57 1.06 0 HNO3 PI PI 0.996647 0.000099FP2_174_UO2_43 2.46E-01 1.57 1.06 0 HNO3 PI PI 0.997186 0.000100FP2_174_UO2_44 2.30E-01 1.57 1.06 0 HNO3 PI PI 0.998279 0.000098FP2_174_UO2_45 2.47E-01 1.57 1.06 0 HNO3 PI PI 0.996273 0.000099FP2_174_UO2_46 2.45E-01 1.57 1.06 0 HNO3 PI PI 0.997414 0.000099FP2_174_UO2_47 2.29E-01 1.57 1.06 0 HNO3 PI PI 0.997995 0.000099FP2_174_UO2_48 2.29E-01 1.57 1.06 0 HNO3 PI PI 0.998076 0.000099FP2_174_UO2_49 2.33E-01 1.57 1.06 0 HNO3 PI PI 0.998455 0.000099FP2_174_UO2_50 2.44E-01 1.57 1.06 0 HNO3 PI PI 0.997616 0.000099FP2_174_UO2_51 2.52E-01 1.57 1.06 0 HNO3 PI PI 0.995679 0.000099FP2_174_UO2_52 2.55E-01 1.57 1.06 0 HNO3 PI PI 0.996030 0.000099FP2_174_UO2_53 2.34E-01 1.57 1.06 0 HNO3 PI PI 0.997929 0.000099FP2_174_UO2_54 2.32E-01 1.57 1.06 0 HNO3 PI PI 0.998125 0.000099FP2_175_01 2.40E-01 1.57 1.06 0 HNO3 PI PI 0.997611 0.000099FP2_175_09 2.40E-01 1.57 1.06 0 DUN PI PI 1.000922 0.000097FP2_175_10 2.37E-01 1.57 1.06 0 DUN PI PI 1.000756 0.000099FP2_175_11 2.32E-01 1.57 1.06 0 DUN PI PI 1.000685 0.000099FP2_175_12 2.28E-01 1.57 1.06 0 DUN PI PI 1.0012 0.00010 
Table A.1 Critical experiments from IHECSBE and ENDF/B-VII 238 group library results (continued) 

A-24

Experiment ID EALF (eV) Enrich. (wt % 235U) Pu wt. fraction pu/(pu+u) Sol. boron (ppm) Fission product 

keff, exp

σkeff,exp

keff, calc

σkeff,calc

FP2_175_13 2.35E-01 1.57 1.06 0 DUN+149Sm PI PI 1.00201 0.000099FP2_175_14 2.33E-01 1.57 1.06 0 DUN+FP Mix PI PI 1.001594 0.000099FP2_175_15 2.28E-01 1.57 1.06 0 DUN+FP Mix PI PI 1.001308 0.000099

* PI = proprietary information 
APPENDIX B 

SIMILARITY ASSESSMENT RESULTS 

B-1 

Table B.1 Critical experiment similarity assessment ck values for applications 

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

1 LEU-COMP-THERM-001-001 0.554 0.459 0.611 0.521 0.450 

2 LEU-COMP-THERM-001-002 0.573 0.471 0.625 0.529 0.476 

3 LEU-COMP-THERM-001-003 0.585 0.478 0.634 0.534 0.493 

4 LEU-COMP-THERM-001-004 0.574 0.472 0.626 0.529 0.477 

5 LEU-COMP-THERM-001-005 0.592 0.482 0.638 0.536 0.503 

6 LEU-COMP-THERM-001-006 0.580 0.475 0.630 0.532 0.486 

7 LEU-COMP-THERM-001-007 0.594 0.483 0.640 0.536 0.507 

8 LEU-COMP-THERM-001-008 0.590 0.481 0.637 0.535 0.500 

9 LEU-COMP-THERM-002-001 0.420 0.373 0.495 0.451 0.298 

10 LEU-COMP-THERM-002-002 0.422 0.374 0.497 0.453 0.301 

11 LEU-COMP-THERM-002-003 0.428 0.378 0.502 0.455 0.309 

12 LEU-COMP-THERM-002-004 0.452 0.394 0.521 0.467 0.341 

13 LEU-COMP-THERM-002-005 0.464 0.402 0.531 0.473 0.357 

14 LEU-COMP-THERM-010-005 0.628 0.510 0.661 0.553 0.576 

15 LEU-COMP-THERM-010-016 0.496 0.432 0.568 0.507 0.393 

16 LEU-COMP-THERM-010-017 0.493 0.429 0.566 0.505 0.389 

17 LEU-COMP-THERM-010-018 0.493 0.429 0.565 0.504 0.388 

18 LEU-COMP-THERM-010-019 0.484 0.423 0.556 0.498 0.375 

19 LEU-COMP-THERM-017-003 0.603 0.489 0.647 0.541 0.520 

20 LEU-COMP-THERM-017-004 0.681 0.537 0.703 0.570 0.632 

21 LEU-COMP-THERM-017-005 0.660 0.524 0.689 0.563 0.599 

22 LEU-COMP-THERM-017-006 0.652 0.520 0.684 0.560 0.588 

23 LEU-COMP-THERM-017-007 0.648 0.517 0.680 0.558 0.582 

24 LEU-COMP-THERM-017-008 0.627 0.504 0.664 0.549 0.553 

25 LEU-COMP-THERM-017-009 0.599 0.487 0.644 0.539 0.514 

26 LEU-COMP-THERM-017-010 0.629 0.507 0.671 0.556 0.560 

27 LEU-COMP-THERM-017-011 0.623 0.502 0.666 0.553 0.549 

28 LEU-COMP-THERM-017-012 0.620 0.501 0.663 0.551 0.545 

29 LEU-COMP-THERM-017-013 0.616 0.498 0.659 0.548 0.539 

30 LEU-COMP-THERM-017-014 0.611 0.495 0.654 0.545 0.531 

31 LEU-COMP-THERM-017-015 0.646 0.521 0.688 0.571 0.578 

32 LEU-COMP-THERM-017-016 0.641 0.518 0.685 0.569 0.570 

33 LEU-COMP-THERM-017-017 0.640 0.517 0.683 0.568 0.567 

34 LEU-COMP-THERM-017-019 0.636 0.515 0.680 0.566 0.561 

35 LEU-COMP-THERM-017-020 0.631 0.512 0.676 0.563 0.553 

36 LEU-COMP-THERM-017-021 0.629 0.511 0.673 0.561 0.550 

37 LEU-COMP-THERM-017-022 0.612 0.499 0.659 0.553 0.524 

38 LEU-COMP-THERM-017-023 0.622 0.505 0.665 0.555 0.541 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-2

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

39 LEU-COMP-THERM-017-024 0.620 0.504 0.663 0.554 0.537 

40 LEU-COMP-THERM-017-025 0.626 0.507 0.668 0.557 0.544 

41 LEU-COMP-THERM-017-028 0.685 0.544 0.711 0.578 0.630 

42 LEU-COMP-THERM-017-029 0.675 0.537 0.704 0.575 0.615 

43 LEU-COMP-THERM-022-001 0.384 0.359 0.472 0.446 0.297 

44 LEU-COMP-THERM-022-002 0.358 0.336 0.447 0.425 0.261 

45 LEU-COMP-THERM-022-003 0.339 0.315 0.422 0.399 0.246 

46 LEU-COMP-THERM-022-004 0.342 0.313 0.417 0.390 0.261 

47 LEU-COMP-THERM-022-005 0.354 0.318 0.422 0.389 0.281 

48 LEU-COMP-THERM-022-006 0.418 0.356 0.468 0.412 0.379 

49 LEU-COMP-THERM-022-007 0.424 0.360 0.472 0.415 0.388 

50 LEU-COMP-THERM-023-001 0.352 0.318 0.424 0.392 0.278 

51 LEU-COMP-THERM-023-002 0.345 0.313 0.417 0.387 0.268 

52 LEU-COMP-THERM-023-003 0.344 0.312 0.416 0.386 0.267 

53 LEU-COMP-THERM-023-004 0.345 0.312 0.416 0.386 0.269 

54 LEU-COMP-THERM-023-005 0.347 0.314 0.418 0.387 0.271 

55 LEU-COMP-THERM-023-006 0.349 0.315 0.419 0.388 0.275 

56 LEU-COMP-THERM-024-001 0.403 0.372 0.486 0.456 0.327 

57 LEU-COMP-THERM-024-002 0.365 0.334 0.445 0.415 0.283 

58 LEU-COMP-THERM-026-003 0.520 0.453 0.582 0.519 0.441 

59 LEU-COMP-THERM-042-001 0.643 0.520 0.688 0.571 0.575 

60 LEU-COMP-THERM-042-002 0.658 0.529 0.697 0.575 0.597 

61 LEU-COMP-THERM-042-003 0.666 0.534 0.703 0.578 0.610 

62 LEU-COMP-THERM-042-004 0.667 0.534 0.703 0.578 0.610 

63 LEU-COMP-THERM-042-005 0.665 0.533 0.701 0.577 0.607 

64 LEU-COMP-THERM-042-006 0.647 0.522 0.689 0.570 0.580 

65 LEU-COMP-THERM-042-007 0.657 0.528 0.696 0.574 0.595 

66 LEU-COMP-THERM-050-001 0.416 0.376 0.498 0.460 0.288 

67 LEU-COMP-THERM-050-002 0.418 0.377 0.499 0.460 0.291 

68 LEU-COMP-THERM-050-003 0.432 0.387 0.511 0.469 0.309 

69 LEU-COMP-THERM-050-004 0.438 0.391 0.516 0.472 0.318 

70 LEU-COMP-THERM-050-005 0.450 0.400 0.526 0.479 0.334 

71 LEU-COMP-THERM-050-006 0.456 0.404 0.531 0.482 0.342 

72 LEU-COMP-THERM-050-007 0.459 0.406 0.533 0.483 0.347 

73 LEU-COMP-THERM-050-008 0.429 0.386 0.509 0.468 0.305 

74 LEU-COMP-THERM-050-009 0.435 0.389 0.514 0.470 0.313 

75 LEU-COMP-THERM-050-010 0.437 0.391 0.515 0.471 0.316 

76 LEU-COMP-THERM-050-011 0.436 0.391 0.515 0.472 0.314 

77 LEU-COMP-THERM-050-012 0.447 0.398 0.523 0.477 0.329 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-3

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

78 LEU-COMP-THERM-050-013 0.447 0.398 0.524 0.477 0.330 

79 LEU-COMP-THERM-050-014 0.456 0.405 0.531 0.483 0.342 

80 LEU-COMP-THERM-050-015 0.461 0.407 0.535 0.485 0.348 

81 LEU-COMP-THERM-050-016 0.455 0.403 0.530 0.482 0.340 

82 LEU-COMP-THERM-050-017 0.458 0.406 0.533 0.484 0.344 

83 LEU-COMP-THERM-050-018 0.457 0.405 0.532 0.483 0.343 

84 LEU-COMP-THERM-079-001 0.408 0.373 0.496 0.461 0.271 

85 LEU-COMP-THERM-079-002 0.409 0.374 0.497 0.462 0.272 

86 LEU-COMP-THERM-079-003 0.418 0.380 0.504 0.467 0.284 

87 LEU-COMP-THERM-079-004 0.423 0.384 0.508 0.470 0.292 

88 LEU-COMP-THERM-079-005 0.430 0.390 0.514 0.475 0.302 

89 LEU-COMP-THERM-079-006 0.413 0.368 0.491 0.449 0.289 

90 LEU-COMP-THERM-079-007 0.411 0.367 0.489 0.448 0.286 

91 LEU-COMP-THERM-079-008 0.424 0.376 0.499 0.455 0.304 

92 LEU-COMP-THERM-079-009 0.427 0.379 0.503 0.458 0.309 

93 LEU-COMP-THERM-079-010 0.440 0.388 0.513 0.464 0.326 

94 LEU-MISC-THERM-005-001 0.466 0.410 0.538 0.486 0.360 

95 LEU-MISC-THERM-005-002 0.471 0.414 0.542 0.489 0.367 

96 LEU-MISC-THERM-005-003 0.479 0.420 0.549 0.493 0.378 

97 LEU-MISC-THERM-005-004 0.480 0.421 0.549 0.494 0.379 

98 LEU-MISC-THERM-005-005 0.481 0.422 0.551 0.495 0.381 

99 LEU-MISC-THERM-005-006 0.484 0.424 0.552 0.497 0.384 

100 LEU-MISC-THERM-005-007 0.486 0.426 0.554 0.498 0.387 

101 LEU-MISC-THERM-005-008 0.491 0.429 0.558 0.501 0.394 

102 LEU-MISC-THERM-005-009 0.489 0.429 0.557 0.501 0.393 

103 LEU-MISC-THERM-005-010 0.489 0.429 0.557 0.501 0.393 

104 LEU-MISC-THERM-005-011 0.488 0.428 0.556 0.500 0.390 

105 LEU-MISC-THERM-005-012 0.489 0.429 0.557 0.501 0.392 

106 LEU-SOL-THERM-002-001 0.538 0.435 0.563 0.470 0.503 

107 LEU-SOL-THERM-002-002 0.509 0.418 0.543 0.461 0.458 

108 LEU-SOL-THERM-002-003 0.521 0.425 0.551 0.465 0.476 

109 LEU-SOL-THERM-003-001 0.403 0.345 0.446 0.395 0.346 

110 LEU-SOL-THERM-003-002 0.423 0.357 0.460 0.404 0.375 

111 LEU-SOL-THERM-003-003 0.429 0.361 0.465 0.406 0.384 

112 LEU-SOL-THERM-003-004 0.432 0.363 0.468 0.408 0.389 

113 LEU-SOL-THERM-003-005 0.489 0.397 0.508 0.429 0.473 

114 LEU-SOL-THERM-003-006 0.498 0.403 0.514 0.432 0.487 

115 LEU-SOL-THERM-003-007 0.506 0.407 0.519 0.434 0.499 

116 LEU-SOL-THERM-003-008 0.542 0.426 0.541 0.441 0.559 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-4

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

117 LEU-SOL-THERM-003-009 0.544 0.427 0.542 0.441 0.564 

118 LEU-SOL-THERM-004-001 0.418 0.355 0.459 0.404 0.368 

119 LEU-SOL-THERM-004-002 0.429 0.362 0.467 0.408 0.385 

120 LEU-SOL-THERM-004-003 0.441 0.369 0.475 0.412 0.403 

121 LEU-SOL-THERM-004-004 0.454 0.377 0.484 0.417 0.423 

122 LEU-SOL-THERM-004-005 0.464 0.383 0.491 0.420 0.439 

123 LEU-SOL-THERM-004-006 0.473 0.388 0.497 0.423 0.453 

124 LEU-SOL-THERM-004-007 0.482 0.393 0.503 0.426 0.466 

125 MIX-COMP-THERM-001-001 0.538 0.719 0.609 0.763 0.296 

126 MIX-COMP-THERM-001-002 0.516 0.690 0.584 0.733 0.283 

127 MIX-COMP-THERM-001-003 0.515 0.686 0.580 0.726 0.286 

128 MIX-COMP-THERM-001-004 0.522 0.692 0.584 0.728 0.295 

129 MIX-COMP-THERM-002-001S 0.673 0.827 0.744 0.867 0.402 

130 MIX-COMP-THERM-002-002S 0.699 0.852 0.759 0.880 0.439 

131 MIX-COMP-THERM-002-003S 0.629 0.785 0.706 0.833 0.353 

132 MIX-COMP-THERM-002-004S 0.697 0.852 0.748 0.871 0.446 

133 MIX-COMP-THERM-002-005S 0.630 0.785 0.703 0.829 0.359 

134 MIX-COMP-THERM-002-006S 0.693 0.846 0.740 0.862 0.445 

135 MIX-COMP-THERM-003-001 0.585 0.762 0.662 0.809 0.317 

136 MIX-COMP-THERM-003-002 0.569 0.746 0.648 0.796 0.302 

137 MIX-COMP-THERM-003-003 0.576 0.755 0.654 0.802 0.310 

138 MIX-COMP-THERM-003-004 0.542 0.713 0.617 0.762 0.286 

139 MIX-COMP-THERM-003-005 0.542 0.712 0.616 0.759 0.289 

140 MIX-COMP-THERM-003-006 0.558 0.725 0.623 0.763 0.312 

141 MIX-COMP-THERM-004-001 0.625 0.789 0.698 0.832 0.357 

142 MIX-COMP-THERM-004-002 0.628 0.792 0.700 0.834 0.360 

143 MIX-COMP-THERM-004-003 0.629 0.793 0.701 0.835 0.362 

144 MIX-COMP-THERM-004-004 0.625 0.787 0.695 0.828 0.360 

145 MIX-COMP-THERM-004-005 0.626 0.788 0.696 0.829 0.361 

146 MIX-COMP-THERM-004-006 0.629 0.791 0.698 0.831 0.365 

147 MIX-COMP-THERM-004-007 0.629 0.789 0.694 0.825 0.370 

148 MIX-COMP-THERM-004-008 0.631 0.791 0.695 0.826 0.372 

149 MIX-COMP-THERM-004-009 0.632 0.792 0.696 0.827 0.374 

150 MIX-COMP-THERM-004-010 0.640 0.798 0.699 0.828 0.386 

151 MIX-COMP-THERM-004-011 0.642 0.800 0.700 0.828 0.388 

152 MIX-COMP-THERM-005-001 0.613 0.785 0.690 0.831 0.340 

153 MIX-COMP-THERM-005-002 0.599 0.770 0.676 0.818 0.327 

154 MIX-COMP-THERM-005-003 0.594 0.764 0.669 0.810 0.327 

155 MIX-COMP-THERM-005-004 0.602 0.771 0.673 0.812 0.338 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-5

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

156 MIX-COMP-THERM-005-005 0.612 0.778 0.675 0.812 0.356 

157 MIX-COMP-THERM-005-006 0.635 0.798 0.687 0.819 0.387 

158 MIX-COMP-THERM-005-007 0.647 0.807 0.693 0.822 0.404 

159 MIX-COMP-THERM-006-001 0.649 0.805 0.726 0.851 0.372 

160 MIX-COMP-THERM-006-002 0.628 0.785 0.706 0.833 0.352 

161 MIX-COMP-THERM-006-003 0.626 0.781 0.700 0.826 0.354 

162 MIX-COMP-THERM-006-004 0.633 0.787 0.703 0.828 0.365 

163 MIX-COMP-THERM-006-005 0.650 0.800 0.711 0.832 0.390 

164 MIX-COMP-THERM-006-006 0.657 0.806 0.714 0.834 0.401 

165 MIX-COMP-THERM-006-007 0.626 0.781 0.700 0.826 0.355 

166 MIX-COMP-THERM-006-008 0.627 0.782 0.701 0.827 0.356 

167 MIX-COMP-THERM-006-009 0.628 0.783 0.702 0.828 0.357 

168 MIX-COMP-THERM-006-010 0.628 0.783 0.702 0.828 0.357 

169 MIX-COMP-THERM-006-011 0.629 0.784 0.703 0.829 0.358 

170 MIX-COMP-THERM-006-012 0.630 0.785 0.703 0.829 0.359 

171 MIX-COMP-THERM-006-013 0.627 0.781 0.701 0.827 0.355 

172 MIX-COMP-THERM-006-014 0.628 0.783 0.702 0.828 0.357 

173 MIX-COMP-THERM-006-015 0.629 0.784 0.703 0.829 0.358 

174 MIX-COMP-THERM-006-016 0.629 0.784 0.703 0.829 0.358 

175 MIX-COMP-THERM-006-017 0.630 0.785 0.704 0.830 0.359 

176 MIX-COMP-THERM-006-018 0.631 0.786 0.704 0.830 0.360 

177 MIX-COMP-THERM-006-019 0.631 0.786 0.704 0.830 0.360 

178 MIX-COMP-THERM-006-020 0.631 0.786 0.704 0.830 0.360 

179 MIX-COMP-THERM-006-021 0.632 0.787 0.704 0.830 0.361 

180 MIX-COMP-THERM-006-022 0.631 0.786 0.704 0.830 0.360 

181 MIX-COMP-THERM-006-023 0.631 0.786 0.704 0.830 0.360 

182 MIX-COMP-THERM-006-024 0.631 0.786 0.704 0.830 0.360 

183 MIX-COMP-THERM-006-025 0.631 0.786 0.704 0.830 0.360 

184 MIX-COMP-THERM-006-026 0.631 0.786 0.704 0.830 0.360 

185 MIX-COMP-THERM-006-027 0.631 0.786 0.704 0.830 0.360 

186 MIX-COMP-THERM-006-028 0.632 0.787 0.704 0.830 0.361 

187 MIX-COMP-THERM-006-029 0.650 0.801 0.711 0.832 0.390 

188 MIX-COMP-THERM-006-030 0.651 0.801 0.711 0.833 0.391 

189 MIX-COMP-THERM-006-031 0.651 0.802 0.712 0.833 0.392 

190 MIX-COMP-THERM-006-032 0.651 0.802 0.712 0.833 0.392 

191 MIX-COMP-THERM-006-033 0.652 0.802 0.712 0.833 0.393 

192 MIX-COMP-THERM-006-034 0.652 0.802 0.712 0.834 0.393 

193 MIX-COMP-THERM-006-035 0.651 0.801 0.711 0.833 0.391 

194 MIX-COMP-THERM-006-036 0.651 0.802 0.712 0.833 0.392 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-6

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

195 MIX-COMP-THERM-006-037 0.652 0.802 0.712 0.833 0.393 

196 MIX-COMP-THERM-006-038 0.652 0.802 0.712 0.834 0.393 

197 MIX-COMP-THERM-006-039 0.652 0.803 0.712 0.834 0.393 

198 MIX-COMP-THERM-006-040 0.653 0.803 0.713 0.834 0.394 

199 MIX-COMP-THERM-006-041 0.653 0.803 0.713 0.834 0.394 

200 MIX-COMP-THERM-006-042 0.653 0.803 0.713 0.834 0.394 

201 MIX-COMP-THERM-006-043 0.653 0.804 0.713 0.834 0.394 

202 MIX-COMP-THERM-006-044 0.653 0.804 0.713 0.834 0.394 

203 MIX-COMP-THERM-006-045 0.653 0.803 0.713 0.834 0.394 

204 MIX-COMP-THERM-006-046 0.653 0.803 0.713 0.834 0.394 

205 MIX-COMP-THERM-006-047 0.653 0.803 0.713 0.834 0.393 

206 MIX-COMP-THERM-006-048 0.653 0.803 0.713 0.834 0.393 

207 MIX-COMP-THERM-006-049 0.653 0.803 0.713 0.834 0.394 

208 MIX-COMP-THERM-006-050 0.653 0.804 0.713 0.834 0.394 

209 MIX-COMP-THERM-007-001 0.655 0.809 0.729 0.853 0.380 

210 MIX-COMP-THERM-007-002 0.651 0.804 0.723 0.846 0.380 

211 MIX-COMP-THERM-007-003 0.657 0.808 0.724 0.846 0.390 

212 MIX-COMP-THERM-007-004 0.674 0.821 0.730 0.849 0.416 

213 MIX-COMP-THERM-007-005 0.681 0.827 0.733 0.850 0.427 

214 MIX-COMP-THERM-008-001 0.700 0.851 0.766 0.885 0.432 

215 MIX-COMP-THERM-008-002 0.670 0.823 0.742 0.864 0.396 

216 MIX-COMP-THERM-008-003 0.669 0.821 0.737 0.859 0.398 

217 MIX-COMP-THERM-008-003_Al 0.669 0.821 0.737 0.859 0.399 

218 MIX-COMP-THERM-008-003_B1 0.672 0.824 0.739 0.861 0.403 

219 MIX-COMP-THERM-008-003_B2 0.672 0.824 0.739 0.861 0.403 

220 MIX-COMP-THERM-008-003_B3 0.670 0.822 0.738 0.860 0.401 

221 MIX-COMP-THERM-008-003_B4 0.669 0.821 0.737 0.859 0.399 

222 MIX-COMP-THERM-008-003_CdAir 0.673 0.825 0.740 0.862 0.404 

223 MIX-COMP-THERM-008-003_CdAl 0.673 0.825 0.740 0.862 0.404 

224 MIX-COMP-THERM-008-003_CdB1 0.673 0.824 0.740 0.861 0.403 

225 MIX-COMP-THERM-008-003_CdB2 0.673 0.825 0.740 0.862 0.404 

226 MIX-COMP-THERM-008-003_CdB3 0.673 0.825 0.740 0.862 0.404 

227 MIX-COMP-THERM-008-003_CdB4 0.673 0.824 0.740 0.861 0.404 

228 MIX-COMP-THERM-008-003_CdH1 0.673 0.825 0.740 0.862 0.404 

229 MIX-COMP-THERM-008-003_CdH2 0.673 0.825 0.740 0.862 0.405 

230 MIX-COMP-THERM-008-003_CdH3 0.674 0.826 0.740 0.862 0.405 

231 MIX-COMP-THERM-008-003_CdH4 0.673 0.825 0.740 0.862 0.405 

232 MIX-COMP-THERM-008-003_CdH5 0.673 0.825 0.740 0.862 0.404 

233 MIX-COMP-THERM-008-003_CdWater 0.673 0.825 0.740 0.862 0.404 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-7

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

234 MIX-COMP-THERM-008-003_H1 0.671 0.823 0.739 0.861 0.402 

235 MIX-COMP-THERM-008-003_H2 0.672 0.824 0.739 0.861 0.403 

236 MIX-COMP-THERM-008-003_H3 0.671 0.822 0.738 0.860 0.401 

237 MIX-COMP-THERM-008-003_H4 0.671 0.822 0.738 0.860 0.401 

238 MIX-COMP-THERM-008-003_H5 0.670 0.822 0.738 0.860 0.400 

239 MIX-COMP-THERM-008-004 0.675 0.825 0.739 0.859 0.409 

240 MIX-COMP-THERM-008-005 0.692 0.838 0.745 0.861 0.437 

241 MIX-COMP-THERM-008-006 0.699 0.843 0.747 0.860 0.449 

242 MIX-COMP-THERM-009-001 0.716 0.860 0.768 0.880 0.458 

243 MIX-COMP-THERM-009-002 0.660 0.807 0.720 0.835 0.400 

244 MIX-COMP-THERM-009-003 0.647 0.796 0.708 0.828 0.382 

245 MIX-COMP-THERM-009-004 0.647 0.797 0.706 0.826 0.385 

246 MIX-COMP-THERM-009-005 0.655 0.803 0.708 0.826 0.398 

247 MIX-COMP-THERM-009-006 0.657 0.804 0.708 0.825 0.401 

248 MIX-COMP-THERM-011-001 0.481 0.615 0.562 0.679 0.287 

249 MIX-COMP-THERM-011-002 0.481 0.615 0.562 0.679 0.287 

250 MIX-COMP-THERM-011-003 0.482 0.616 0.563 0.680 0.288 

251 MIX-COMP-THERM-011-004 0.517 0.648 0.593 0.707 0.319 

252 MIX-COMP-THERM-011-005 0.516 0.648 0.593 0.707 0.318 

253 MIX-COMP-THERM-011-006 0.516 0.647 0.593 0.707 0.319 

254 MIX-COMP-THERM-012-001 0.600 0.776 0.654 0.801 0.360 

255 MIX-COMP-THERM-012-002 0.600 0.776 0.654 0.801 0.360 

256 MIX-COMP-THERM-012-003 0.600 0.776 0.654 0.801 0.360 

257 MIX-COMP-THERM-012-004 0.599 0.776 0.654 0.801 0.359 

258 MIX-COMP-THERM-012-005 0.600 0.776 0.654 0.801 0.359 

259 MIX-COMP-THERM-012-006 0.599 0.776 0.654 0.801 0.359 

260 MIX-COMP-THERM-012-007 0.565 0.729 0.618 0.754 0.334 

261 MIX-COMP-THERM-012-008 0.565 0.729 0.618 0.755 0.335 

262 MIX-COMP-THERM-012-009 0.568 0.732 0.620 0.757 0.337 

263 MIX-COMP-THERM-012-010 0.568 0.732 0.620 0.757 0.338 

264 MIX-COMP-THERM-012-011 0.567 0.731 0.619 0.756 0.336 

265 MIX-COMP-THERM-012-012 0.567 0.731 0.619 0.756 0.336 

266 MIX-COMP-THERM-012-013 0.565 0.729 0.618 0.755 0.335 

267 MIX-COMP-THERM-012-014 0.543 0.712 0.599 0.742 0.318 

268 MIX-COMP-THERM-012-015 0.544 0.714 0.600 0.744 0.319 

269 MIX-COMP-THERM-012-016 0.545 0.715 0.601 0.745 0.320 

270 MIX-COMP-THERM-012-017 0.546 0.716 0.602 0.746 0.321 

271 MIX-COMP-THERM-012-018 0.548 0.718 0.603 0.747 0.322 

272 MIX-COMP-THERM-012-019 0.549 0.720 0.604 0.748 0.324 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-8

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

273 MIX-COMP-THERM-012-020 0.531 0.701 0.590 0.734 0.307 

274 MIX-COMP-THERM-012-021 0.531 0.700 0.590 0.734 0.307 

275 MIX-COMP-THERM-012-022 0.525 0.686 0.569 0.704 0.320 

276 MIX-COMP-THERM-012-023 0.518 0.687 0.573 0.717 0.304 

277 MIX-COMP-THERM-012-024 0.519 0.688 0.573 0.718 0.304 

278 MIX-COMP-THERM-012-025 0.521 0.690 0.575 0.719 0.306 

279 MIX-COMP-THERM-012-026 0.524 0.694 0.578 0.722 0.308 

280 MIX-COMP-THERM-012-027 0.527 0.697 0.580 0.725 0.311 

281 MIX-COMP-THERM-012-028 0.528 0.698 0.581 0.726 0.312 

282 MIX-COMP-THERM-012-029 0.530 0.700 0.583 0.728 0.313 

283 MIX-COMP-THERM-012-030 0.525 0.694 0.578 0.723 0.309 

284 MIX-COMP-THERM-012-031 0.502 0.670 0.559 0.703 0.291 

285 MIX-COMP-THERM-012-032 0.503 0.671 0.560 0.704 0.292 

286 MIX-COMP-THERM-012-033 0.502 0.670 0.559 0.703 0.292 

287 MIX-SOL-THERM-001-001 0.539 0.711 0.595 0.742 0.318 

288 MIX-SOL-THERM-001-002 0.539 0.711 0.595 0.741 0.318 

289 MIX-SOL-THERM-001-003 0.524 0.694 0.584 0.728 0.306 

290 MIX-SOL-THERM-001-004 0.539 0.712 0.596 0.742 0.318 

291 MIX-SOL-THERM-001-005 0.549 0.723 0.604 0.751 0.327 

292 MIX-SOL-THERM-001-006 0.523 0.693 0.583 0.728 0.304 

293 MIX-SOL-THERM-001-007 0.494 0.666 0.548 0.697 0.292 

294 MIX-SOL-THERM-001-008 0.495 0.665 0.550 0.696 0.289 

295 MIX-SOL-THERM-001-009 0.506 0.675 0.561 0.706 0.295 

296 MIX-SOL-THERM-001-010 0.539 0.711 0.595 0.740 0.319 

297 MIX-SOL-THERM-001-011 0.547 0.719 0.601 0.746 0.325 

298 MIX-SOL-THERM-001-012 0.539 0.710 0.594 0.739 0.319 

299 MIX-SOL-THERM-001-013 0.544 0.714 0.598 0.742 0.322 

300 MIX-SOL-THERM-002-001 0.568 0.734 0.612 0.749 0.340 

301 MIX-SOL-THERM-002-002 0.569 0.735 0.613 0.750 0.341 

302 MIX-SOL-THERM-002-003 0.576 0.741 0.619 0.755 0.347 

303 MIX-SOL-THERM-004-001 0.485 0.646 0.543 0.682 0.274 

304 MIX-SOL-THERM-004-002 0.496 0.658 0.554 0.693 0.284 

305 MIX-SOL-THERM-004-003 0.501 0.665 0.558 0.698 0.288 

306 MIX-SOL-THERM-004-004 0.494 0.661 0.552 0.696 0.286 

307 MIX-SOL-THERM-004-005 0.489 0.655 0.548 0.691 0.281 

308 MIX-SOL-THERM-004-006 0.476 0.641 0.536 0.679 0.270 

309 MIX-SOL-THERM-004-007 0.485 0.653 0.545 0.690 0.277 

310 MIX-SOL-THERM-004-008 0.496 0.665 0.555 0.701 0.286 

311 MIX-SOL-THERM-004-009 0.501 0.671 0.559 0.706 0.291 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-9

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

312 MIX-SOL-THERM-005-001 0.500 0.664 0.557 0.697 0.287 

313 MIX-SOL-THERM-005-002 0.523 0.689 0.579 0.720 0.307 

314 MIX-SOL-THERM-005-003 0.510 0.679 0.568 0.712 0.300 

315 MIX-SOL-THERM-005-004 0.515 0.684 0.572 0.717 0.304 

316 MIX-SOL-THERM-005-005 0.493 0.661 0.552 0.696 0.285 

317 MIX-SOL-THERM-005-006 0.500 0.671 0.559 0.706 0.291 

318 MIX-SOL-THERM-005-007 0.519 0.691 0.577 0.724 0.308 

319 HTC1_01 0.842 0.913 0.878 0.927 0.629 

320 HTC1_02 0.839 0.910 0.877 0.926 0.626 

321 HTC1_03 0.840 0.911 0.877 0.926 0.627 

322 HTC1_04 0.783 0.869 0.848 0.912 0.538 

323 HTC1_05 0.783 0.869 0.848 0.911 0.539 

324 HTC1_06 0.783 0.869 0.848 0.911 0.539 

325 HTC1_07 0.761 0.851 0.834 0.902 0.507 

326 HTC1_08 0.761 0.851 0.835 0.902 0.508 

327 HTC1_09 0.762 0.852 0.835 0.903 0.508 

328 HTC1_10 0.751 0.843 0.830 0.899 0.492 

329 HTC1_11 0.752 0.844 0.830 0.900 0.494 

330 HTC1_12 0.753 0.845 0.831 0.900 0.495 

331 HTC1_13 0.771 0.861 0.846 0.912 0.520 

332 HTC1_14 0.772 0.862 0.846 0.913 0.520 

333 HTC1_15 0.772 0.862 0.846 0.913 0.520 

334 HTC1_16 0.769 0.858 0.840 0.907 0.516 

335 HTC1_17 0.772 0.860 0.843 0.909 0.521 

336 HTC1_18 0.772 0.861 0.843 0.910 0.520 

337 HTC2B_01 0.788 0.877 0.858 0.924 0.540 

338 HTC2B_02 0.789 0.878 0.859 0.925 0.542 

339 HTC2B_03 0.801 0.889 0.868 0.932 0.557 

340 HTC2B_04 0.815 0.903 0.878 0.942 0.577 

341 HTC2B_05 0.828 0.914 0.886 0.949 0.594 

342 HTC2B_06 0.828 0.914 0.886 0.949 0.594 

343 HTC2B_07 0.841 0.926 0.895 0.956 0.612 

344 HTC2B_08 0.851 0.935 0.901 0.961 0.628 

345 HTC2B_09 0.861 0.945 0.906 0.966 0.640 

346 HTC2B_10 0.845 0.931 0.897 0.959 0.615 

347 HTC2B_11 0.828 0.916 0.887 0.951 0.591 

348 HTC2B_12 0.811 0.901 0.875 0.941 0.568 

349 HTC2B_13 0.793 0.884 0.862 0.929 0.544 

350 HTC2B_14 0.774 0.866 0.848 0.916 0.521 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-10

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

351 HTC2B_15 0.791 0.879 0.858 0.923 0.544 

352 HTC2B_16 0.813 0.900 0.873 0.937 0.573 

353 HTC2B_17 0.837 0.921 0.889 0.950 0.605 

354 HTC2B_18 0.857 0.939 0.900 0.959 0.635 

355 HTC2B_19 0.795 0.883 0.861 0.926 0.550 

356 HTC2B_20 0.846 0.926 0.891 0.948 0.623 

357 HTC2B_21 0.818 0.901 0.873 0.934 0.583 

358 HTC2G_01 0.795 0.884 0.863 0.929 0.550 

359 HTC2G_02 0.794 0.884 0.863 0.929 0.549 

360 HTC2G_03 0.813 0.901 0.876 0.940 0.574 

361 HTC2G_04 0.813 0.902 0.877 0.941 0.575 

362 HTC2G_05 0.813 0.902 0.877 0.941 0.574 

363 HTC2G_06 0.829 0.916 0.887 0.950 0.596 

364 HTC2G_07 0.831 0.918 0.888 0.951 0.599 

365 HTC2G_08 0.846 0.932 0.898 0.959 0.621 

366 HTC2G_09 0.846 0.932 0.898 0.959 0.622 

367 HTC2G_10 0.862 0.946 0.906 0.966 0.642 

368 HTC2G_11 0.837 0.925 0.892 0.956 0.604 

369 HTC2G_12 0.838 0.926 0.892 0.956 0.605 

370 HTC2G_13 0.812 0.902 0.875 0.941 0.569 

371 HTC2G_14 0.813 0.903 0.876 0.942 0.570 

372 HTC2G_15 0.783 0.875 0.854 0.923 0.532 

373 HTC2G_16 0.785 0.876 0.856 0.924 0.534 

374 HTC2G_17 0.804 0.892 0.867 0.932 0.561 

375 HTC2G_18 0.836 0.917 0.884 0.943 0.608 

376 HTC2G_19 0.840 0.925 0.891 0.953 0.611 

377 HTC2G_20 0.808 0.896 0.870 0.934 0.566 

378 HTC3_01 0.817 0.903 0.878 0.941 0.575 

379 HTC3_02 0.821 0.907 0.882 0.945 0.580 

380 HTC3_03 0.824 0.910 0.883 0.946 0.584 

381 HTC3_04 0.823 0.908 0.882 0.945 0.582 

382 HTC3_05 0.824 0.910 0.884 0.946 0.584 

383 HTC3_06 0.832 0.916 0.889 0.949 0.595 

384 HTC3_07 0.821 0.907 0.882 0.944 0.580 

385 HTC3_08 0.826 0.912 0.886 0.948 0.587 

386 HTC3_09 0.826 0.911 0.885 0.947 0.587 

387 HTC3_10 0.826 0.911 0.885 0.947 0.587 

388 HTC3_11 0.824 0.910 0.884 0.946 0.584 

389 HTC3_12 0.771 0.861 0.844 0.911 0.517 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-11

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

390 HTC3_13 0.780 0.869 0.851 0.917 0.528 

391 HTC3_14 0.792 0.879 0.860 0.924 0.543 

392 HTC3_15 0.797 0.883 0.863 0.927 0.549 

393 HTC3_16 0.803 0.889 0.868 0.930 0.557 

394 HTC3_17 0.811 0.895 0.873 0.934 0.567 

395 HTC3_18 0.821 0.903 0.879 0.939 0.581 

396 HTC3_19 0.816 0.899 0.875 0.935 0.576 

397 HTC3_20 0.818 0.900 0.876 0.936 0.579 

398 HTC3_21 0.784 0.871 0.852 0.917 0.535 

399 HTC3_22 0.770 0.859 0.842 0.909 0.517 

400 HTC3_23 0.761 0.852 0.836 0.905 0.506 

401 HTC3_24 0.776 0.866 0.850 0.917 0.523 

402 HTC3_25 0.804 0.890 0.869 0.931 0.558 

403 HTC3_26 0.793 0.880 0.860 0.925 0.543 

404 HTC4FE_01 0.836 0.920 0.893 0.953 0.602 

405 HTC4FE_02 0.836 0.920 0.893 0.953 0.602 

406 HTC4FE_03 0.837 0.920 0.893 0.953 0.602 

407 HTC4FE_04 0.837 0.920 0.893 0.953 0.602 

408 HTC4FE_05 0.836 0.919 0.892 0.953 0.601 

409 HTC4FE_06 0.834 0.918 0.891 0.952 0.599 

410 HTC4FE_07 0.835 0.919 0.891 0.952 0.599 

411 HTC4FE_08 0.833 0.918 0.890 0.951 0.597 

412 HTC4FE_09 0.832 0.916 0.889 0.950 0.594 

413 HTC4FE_10 0.833 0.917 0.890 0.951 0.596 

414 HTC4FE_11 0.830 0.914 0.889 0.949 0.593 

415 HTC4FE_12 0.844 0.926 0.897 0.955 0.612 

416 HTC4FE_13 0.840 0.922 0.894 0.953 0.606 

417 HTC4FE_14 0.842 0.925 0.897 0.956 0.609 

418 HTC4FE_15 0.838 0.921 0.894 0.954 0.603 

419 HTC4FE_16 0.834 0.918 0.891 0.952 0.598 

420 HTC4FE_17 0.833 0.917 0.891 0.951 0.597 

421 HTC4FE_18 0.833 0.917 0.890 0.951 0.595 

422 HTC4FE_19 0.832 0.916 0.889 0.950 0.594 

423 HTC4FE_20 0.830 0.914 0.888 0.949 0.591 

424 HTC4FE_21 0.839 0.922 0.895 0.954 0.605 

425 HTC4FE_22 0.801 0.888 0.870 0.933 0.556 

426 HTC4FE_23 0.804 0.891 0.872 0.935 0.560 

427 HTC4FE_24 0.811 0.896 0.876 0.938 0.569 

428 HTC4FE_25 0.810 0.896 0.876 0.938 0.567 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-12

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

429 HTC4FE_26 0.810 0.895 0.875 0.937 0.567 

430 HTC4FE_27 0.808 0.894 0.874 0.936 0.565 

431 HTC4FE_28 0.809 0.894 0.874 0.936 0.565 

432 HTC4FE_29 0.822 0.905 0.883 0.943 0.583 

433 HTC4FE_30 0.825 0.908 0.885 0.945 0.586 

434 HTC4FE_31 0.820 0.904 0.882 0.943 0.579 

435 HTC4FE_32 0.812 0.897 0.877 0.939 0.568 

436 HTC4FE_33 0.807 0.893 0.873 0.936 0.562 

437 HTC4PB_01 0.831 0.916 0.889 0.950 0.595 

438 HTC4PB_02 0.831 0.916 0.889 0.950 0.594 

439 HTC4PB_03 0.832 0.917 0.889 0.950 0.595 

440 HTC4PB_04 0.833 0.917 0.889 0.950 0.596 

441 HTC4PB_05 0.831 0.916 0.888 0.949 0.594 

442 HTC4PB_06 0.828 0.913 0.886 0.948 0.590 

443 HTC4PB_07 0.827 0.912 0.885 0.947 0.587 

444 HTC4PB_08 0.832 0.916 0.888 0.950 0.594 

445 HTC4PB_09 0.830 0.915 0.888 0.949 0.592 

446 HTC4PB_10 0.832 0.916 0.889 0.950 0.594 

447 HTC4PB_11 0.829 0.914 0.887 0.948 0.591 

448 HTC4PB_12 0.841 0.923 0.895 0.953 0.607 

449 HTC4PB_13 0.841 0.923 0.895 0.954 0.608 

450 HTC4PB_14 0.841 0.923 0.894 0.953 0.606 

451 HTC4PB_15 0.836 0.919 0.891 0.951 0.600 

452 HTC4PB_16 0.837 0.920 0.892 0.951 0.602 

453 HTC4PB_17 0.835 0.919 0.892 0.952 0.600 

454 HTC4PB_18 0.833 0.917 0.890 0.951 0.597 

455 HTC4PB_19 0.830 0.915 0.888 0.949 0.592 

456 HTC4PB_20 0.829 0.914 0.887 0.948 0.591 

457 HTC4PB_21 0.831 0.916 0.889 0.950 0.593 

458 HTC4PB_22 0.831 0.915 0.888 0.949 0.593 

459 HTC4PB_23 0.830 0.915 0.888 0.949 0.592 

460 HTC4PB_24 0.829 0.914 0.887 0.949 0.590 

461 HTC4PB_25 0.827 0.912 0.886 0.947 0.588 

462 HTC4PB_26 0.825 0.910 0.885 0.946 0.585 

463 HTC4PB_27 0.795 0.883 0.864 0.929 0.547 

464 HTC4PB_28 0.798 0.885 0.866 0.930 0.550 

465 HTC4PB_29 0.804 0.891 0.870 0.933 0.559 

466 HTC4PB_30 0.817 0.901 0.878 0.939 0.575 

467 HTC4PB_31 0.819 0.902 0.879 0.940 0.577 
Table B.1 Critical experiment similarity assessment ck values for applications 

(continued) 

B-13

No. Experiment ID 

PWR SFP 

10 

GWd/MTU 

PWR SFP 

40 

GWd/MTU 

GBC-32 

10 

GWd/MTU 

GBC-32 

40 

GWd/MTU 

BWR SFP 

11 

GWd/MTU 

468 HTC4PB_32 0.812 0.897 0.874 0.936 0.568 

469 HTC4PB_33 0.805 0.891 0.869 0.932 0.558 

470 HTC4PB_34 0.799 0.886 0.865 0.929 0.551 

471 HTC4PB_35 0.805 0.891 0.870 0.934 0.560 

472 HTC4PB_36 0.804 0.890 0.870 0.933 0.559 

473 HTC4PB_37 0.804 0.890 0.870 0.933 0.559 

474 HTC4PB_38 0.804 0.890 0.870 0.933 0.559 

APPENDIX C 

BIAS AND BIAS UNCERTAINTY USING GLLSM 

C-1 

C.1 GENERALIZED LINEAR LEAST-SQUARES METHOD (GLLSM) 

BIAS ESTIMATES 

A new capability for SCALE allows the prediction of computational biases and bias uncertainties 

with the SCALE TSURFER program (Ref. 14, Section M21), which applies a generalized linear 

least-squares method (GLLSM) (Ref. 25) technique using the keff sensitivity data, calculated keff

values, expected keff values, experimental uncertainty information, and cross-section covariance 

data to generate cross-section adjustments that minimize the overall chi-square (χ2

) statistic for 

the system of critical experiments. Cross-section covariance data are used as a restraint on 

cross-section adjustments. Benchmark-model keff uncertainty values and user-specified 

correlation data for benchmark model keff values are used as restraints on benchmark-model keff

adjustments. The cross-section adjustments are then combined with the keff sensitivity data for 

the safety analysis model(s) to produce bias estimates. If similar experiments are available to 

validate the use of a particular nuclide in the application, the uncertainty of the bias for this 

nuclide is reduced through the GLLSM procedure. In TSURFER, experiments that are dissimilar 

from the application can still provide useful information for bias assessment if at least one 

material demonstrates similar sensitivities to those of the experiments that are similar to the 

application. If similar experiments are not available to validate a particular nuclide, the 

uncertainty in the bias for the given nuclide is determined using the unadjusted SCALE crosssection covariance data (or for nuclides and reactions not present in the covariance file, userspecified values may be used). A recent detailed derivation of the GLLSM formalism is given in 

Ref. 25. The general formalism allows cross correlations between the initial integral experiment 

measurements and the original nuclear data, such as would be present if the calculations used 

a previously “adjusted” library of nuclear data. 

The TSURFER procedure for bias and bias uncertainty assessment is quite different from those 

traditionally used in criticality-safety evaluations based on interpolation or extrapolation of a 

trend line with a confidence band treating uncertainties in the data as well as uncertainties in the 

trend line itself. Instead of trending the data, TSURFER assimilates individual data components, 

rejecting inconsistent components based on user input criteria. Historically, the validity of a 

calculation performed for some application has been established by considering how well the 

same calculational methods and nuclear data perform for a set of representative benchmark 

experiments. While a simple comparison of the computed and experimental results is very 

informative, it does not fully take advantage of the valuable information provided by the 

measured integral responses. If the original sets of calculated and experimental responses are 

consolidated in a consistent manner (i.e., correctly accounting for uncertainties), then the 

“adjusted” results should be a better estimate of the true responses because the revised 

response values are based upon more information than was available in either the original 

calculations or measurements alone. This is essentially a statement of the Bayes Theorem from 

probability theory, which indicates how prior information (calculated responses) can be evolved 

by incorporating additional information (integral measurements) into more reliable posterior 

results (the adjusted responses). The equations used for the GLLSM are provided in Broadhead 

et al. (Ref. 25). 

TSURFER performs an assessment of sources of the computational bias by multiplying the 

individual sensitivities of the application by the cross-section adjustments that are performed 

within its implementation. Hence, TSURFER can predict individual biases in application keff

values associated with individual reactions, such as (n,) absorptions by FP nuclides. In addition 

to generating cross-section adjustments, TSURFER calculates the reduction in the nuclear data 

uncertainty that results from application of the GLLSM, generating a set of revised cross-section 

covariance data. As a result of application of the chi-squared minimization technique, the 
C-2 

revised covariance data include many more correlations between neutron energy groups, 

reactions, and nuclides than were present in the unmodified covariance data. The revised 

covariance data can be applied to the keff sensitivity data of the safety analysis model(s) to 

quantify the residual uncertainty in keff due to the post-adjustment uncertainty in the nuclear 

data. One of the challenges yet to be resolved prior to TSURFER’s being recommended for 

criticality safety assessments is that it is not presently clear how the residual uncertainty in keff

should be modified or used to support compliance with the 10 CFR 50.68 requirements for use 

of a 95% probability with a 95% confidence bias and uncertainty. Another limitation is the lack of 

experimental correlation data. Uncertainties in benchmark experiments are rigorously quantified 

and documented in the IHECSBE and other experiment documents. Where experiments use the 

same materials or same measurement devices, uncertainties quantified for different 

experiments will be correlated. Of the approximately 4000 experiments in IHECSBE, only about 

60 have experimental correlations quantified. Hence, TSURFER can currently be used only to 

confirm bias and bias uncertainty results obtained using other methods. 

C.2 GENERALIZED LINEAR LEAST-SQUARES METHODS 

The analysis is conducted with a suite of benchmark experiments for which the benchmark keff

values and their uncertainties, as well as correlations in uncertainties between benchmarks, are 

quantified. The unbiased or adjusted keff for the application is computed through sensitivity 

coefficients, not through a criticality calculation using adjusted nuclear data. Thus, with a 

complete set of experiments to validate important components in the application, a precise bias 

with a small uncertainty can be predicted. Where the experimental coverage is lacking, a bias 

can be predicted with an appropriately large uncertainty. 

The TSURFER method is much more suitable than traditional bias estimation techniques, given 

the limited number of directly comparable experiments (with and without FPs) and the 

unresolved nature of some observed trends or differences in the FP data. Also, TSURFER is 

better suited to use experiments involving mixtures of FPs than are conventional techniques. 

A significant benefit of the TSURFER technique is that it provides a means to use information 

from experiments that have low (<0.8) TSUNAMI-IP–determined similarity coefficients (i.e., ck

values) with respect to a given application model. Traditional validation techniques necessitate 

high similarity in order to develop appropriate biases. 

C.3 GLLSM RESULTS 

Bias and bias uncertainty results of the TSURFER analyses are provided in Table C.1 for the 

PWR SFP BUC application models using actinides plus 16 FPs. From Table C.1, note that with 

the exception of 103Rh, the FP biases are positive and that the overall bias for the seven FPs 

evaluated is positive. 

 
C-3 

Table C.1 TSURFER results using actinide + 16 FP isotopes 

Configuration PWR 

SFP 

PWR 

SFP 

PWR 

SFP 

PWR 

SFP 

Fuel burnup (GWd/MTU) 10 25 40 57 

Initial application keff 0.99039 0.98991 0.98997 0.99006

Initial uncertainty (k) for application keff 0.00480 0.00506 0.00506 0.00501

Total bias (k) in initial keff 0.00189 0.00156 0.00172 0.00188

Adjusted application keff 0.98852 0.98834 0.98824 0.98816

Uncertainty for adjusted keff (k) 0.00074 0.00065 0.00067 0.00072

 

Bias (k) in initial keff by FP nuclide 103Rh 0.00013 0.00037 0.00054 0.00066

133Cs 0.00009 0.00022 0.00032 0.00039

143Nd 0.00019 0.00045 0.00063 0.00076

145Nd 0.00005 0.00013 0.00020 0.00025

149Sm 0.00042 0.00048 0.00054 0.00054

152Sm 0.00004 0.00010 0.00014 0.00017

155Gd 0.00000 0.00000 0.00000 0.00000

Total FP bias (k) in initial keff 0.00066 0.00101 0.00129 0.00145

 

Residual uncertainty (k) for adjusted keff by FP 

nuclidea

 

 

103Rh 7.3×106 2.1×105 3.1×105 3.8×105

133Cs 8.1×106 2.0×105 2.9×105 3.6×105

143Nd 5.7×105 1.3×104 1.8×104 2.1×104

145Nd 4.2×105 1.0×104 1.6×104 2.0×104

149Sm 4.0×105 4.5×105 5.0×105 5.1×105

152Sm 8.7×106 2.1×105 2.9×105 3.4×105

155Gd -- -- -- --

Residual uncertainty (k) in adjusted keff for 7 FP 

nuclides 8.3×105 1.7×104 2.5×104 3.0×104

a

Bias uncertainty data are 1-σ and are based on (n,γ) reactions only.

The TSURFER calculated total bias and residual nuclear data uncertainty for the various 

parametric application models are provided in Table C.2. The impacts of the parametric 

variations on the FP biases are presented in Table C.3 with residual FP nuclear data uncertainty 

values provided in Table C.4. Only the six FPs that are present in the critical benchmark 

experiment suite are listed. The 0 decay time cases were not evaluated with TSURFER. 

Because the FP experiment data are proprietary and most applicants will not have access to 

them, and other publicly available FP experiments are limited in quantity, the TSUNAMI-IP 

results in Table C.5 were compared with the TSURFER results. These results are presented in 

Figure C.1, showing that the base case FP uncertainty based on the cross-section covariance 

data at a 1 confidence level is bounding of the true FP bias and bias uncertainty based on 

experimental data, as calculated using GLLSM techniques. 
C-4

Table C.2 TSURFER total bias and bias uncertainty (1) 

Description Change from base 

Bias / residual nuclear data uncertainty (∆k) 

Final BU (GWd/MTU) 

10 25 40 57 

PWR SFP model 

Assembly design B&W 15×15 1.99E-03 / 7.99E-04 1.76E-03 / 6.96E-04 2.03E-03 / 7.36E-04 2.30E-03/7.92E-04

W 17×17 no BAs 2.01E-03 / 7.49E-04 1.73E-03 / 6.30E-04 1.88E-03 / 6.52E-04 1.92E-03/6.88E-04

Rack design Unpoisoned panels 5.48E-04 / 1.36E-03 1.29E-04 / 1.21E-03 4.01E-04 / 1.17E-03 6.18E-04/1.16E-03

Cell pitch increased 0.5 in. 1.54E-03 / 6.88E-04 1.36E-03 / 5.96E-04 1.55E-03 / 6.38E-04 1.58E-03/6.73E-04

Poison panel B10 +10% 1.82E-03 / 7.44E-04 1.59E-03 / 6.40E-04 1.77E-03 / 6.75E-04 1.94E-03/7.25E-04

Poison panel B10 -10% 1.80E-03 / 7.40E-04 1.54E-03 / 6.31E-04 1.77E-03 / 6.68E-04 1.94E-03/7.20E-04

Decay time 1 yr 1.89E-03 / 7.34E-04 1.69E-03 / 6.28E-04 1.91E-03 / 6.60E-04 2.06E-03/7.04E-04

5 yr 1.98E-03 / 7.29E-04 2.02E-03 / 6.19E-04 2.40E-03 / 6.49E-04 2.50E-03/6.79E-04

20 yr 2.16E-03 / 7.27E-04 2.57E-03 / 6.27E-04 3.28E-03 / 6.85E-04 3.44E-03/7.04E-0440 yr 2.24E-03 / 7.25E-04 2.81E-03 / 6.41E-04 3.68E-03 / 7.21E-04 3.89E-03/7.53E-04

Soluble boron 1000 ppma 1.75E-03 / 6.91E-04 1.41E-03 / 6.15E-04 1.56E-03 / 6.55E-04 1.67E-03/7.02E-04

ppm for keff = 0.94 1.79E-03 / 7.02E-04 1.52E-03 / 6.12E-04 1.67E-03 / 6.53E-04 1.80E-03/7.03E-04

Axial burnup 1 node 1.94E-03 / 7.51E-04 2.09E-03 / 7.20E-04 2.45E-03 / 8.25E-04 2.56E-03/9.66E-04

aParts per million boron by mass. 
C-5

Table C.3 TSURFER FP isotope bias 

Description Change from base Burnup (GWd/MTU) FP isotope bias (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Base case -- 10 0.00013 0.00009 0.00019 0.00005 0.00042 0.00004 0.00000 0.00066

25 0.00037 0.00022 0.00045 0.00013 0.00048 0.00010 0.00000 0.0010140 0.00054 0.00032 0.00063 0.00020 0.00054 0.00014 0.00000 0.0012957 0.00066 0.00039 0.00076 0.00025 0.00054 0.00017 0.00000 0.00145

Assembly design B&W 15×15 10 0.00013 0.00008 0.00009 0.00003 0.00036 0.00002 0.00000 0.00045

25 0.00032 0.00017 0.00019 0.00008 0.00041 0.00004 0.00000 0.0005840 0.00045 0.00025 0.00027 0.00012 0.00043 0.00006 0.00000 0.0006857 0.00053 0.00030 0.00032 0.00015 0.00044 0.00007 0.00000 0.00076

W 17×17 10 0.00008 0.00006 0.00007 0.00003 0.00037 0.00002 0.00000 0.00046

(No BAs) 25 0.00024 0.00015 0.00017 0.00007 0.00044 0.00004 0.00000 0.00062

40 0.00037 0.00022 0.00024 0.00010 0.00048 0.00005 0.00000 0.0007357 0.00045 0.00026 0.00030 0.00013 0.00048 0.00006 0.00000 0.00078

Rack design Unpoisoned panels 10 0.00010 0.00006 0.00009 0.00003 0.00047 0.00002 0.00000 0.00057

25 0.00027 0.00014 0.00018 0.00007 0.00052 0.00004 0.00000 0.0006840 0.00039 0.00021 0.00025 0.00010 0.00056 0.00006 0.00000 0.0008057 0.00046 0.00026 0.00031 0.00012 0.00056 0.00006 0.00000 0.00085

Cell pitch increased 10 0.00009 0.00006 0.00007 0.00003 0.00041 0.00002 0.00000 0.00050

0.25 in. 25 0.00024 0.00014 0.00016 0.00006 0.00050 0.00004 0.00000 0.00066

40 0.00036 0.00021 0.00023 0.00010 0.00053 0.00005 0.00000 0.0007657 0.00043 0.00024 0.00028 0.00012 0.00053 0.00006 0.00000 0.00080

Poison panel B10 +10% 10 0.00009 0.00006 0.00007 0.00003 0.00041 0.00002 0.00000 0.00050

25 0.00026 0.00015 0.00017 0.00007 0.00046 0.00004 0.00000 0.0006340 0.00038 0.00022 0.00024 0.00010 0.00051 0.00005 0.00000 0.0007657 0.00046 0.00027 0.00029 0.00013 0.00052 0.00006 0.00000 0.00082
C-6

Description Change from base Burnup (GWd/MTU) FP isotope bias (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Poison panel B10 -10% 10 0.00009 0.00006 0.00007 0.00003 0.00041 0.00002 0.00000 0.00050

25 0.00026 0.00015 0.00017 0.00007 0.00046 0.00004 0.00000 0.0006340 0.00038 0.00022 0.00024 0.00010 0.00052 0.00005 0.00000 0.0007657 0.00046 0.00027 0.00030 0.00013 0.00052 0.00006 0.00000 0.00082

Decay time 1 year 10 0.00013 0.00006 0.00008 0.00003 0.00048 0.00002 0.00000 0.00053

25 0.00030 0.00015 0.00017 0.00007 0.00054 0.00004 0.00001 0.0006840 0.00042 0.00022 0.00024 0.00010 0.00057 0.00005 0.00001 0.0007857 0.00049 0.00027 0.00029 0.00013 0.00057 0.00006 0.00002 0.00084

5 year 10 0.00013 0.00006 0.00008 0.00003 0.00047 0.00002 0.00001 0.00053

25 0.00029 0.00015 0.00017 0.00007 0.00053 0.00004 0.00003 0.0006940 0.00041 0.00022 0.00024 0.00010 0.00056 0.00005 0.00004 0.0008057 0.00047 0.00026 0.00028 0.00012 0.00055 0.00006 0.00006 0.00086

20 year 10 0.00012 0.00006 0.00007 0.00003 0.00046 0.00002 0.00002 0.00053

25 0.00027 0.00014 0.00016 0.00006 0.00052 0.00004 0.00004 0.0006840 0.00038 0.00021 0.00023 0.00010 0.00055 0.00005 0.00007 0.0008257 0.00043 0.00024 0.00026 0.00011 0.00053 0.00006 0.00009 0.00086

40 year 10 0.00012 0.00006 0.00007 0.00003 0.00046 0.00001 0.00002 0.00053

25 0.00026 0.00014 0.00015 0.00006 0.00052 0.00003 0.00004 0.0006840 0.00038 0.00021 0.00022 0.00010 0.00055 0.00005 0.00007 0.0008157 0.00041 0.00023 0.00026 0.00011 0.00052 0.00005 0.00009 0.00085

Soluble boron 1000 ppm 10 0.00008 0.00006 0.00006 0.00002 0.00030 0.00001 0.00000 0.00037

25 0.00022 0.00013 0.00013 0.00006 0.00036 0.00003 0.00000 0.0005040 0.00033 0.00020 0.00020 0.00009 0.00040 0.00005 0.00000 0.0006057 0.00041 0.00024 0.00025 0.00011 0.00041 0.00006 0.00000 0.00066

Table C.3 TSURFER FP isotope bias (continued) 
C-7

Description Change from base Burnup (GWd/MTU) FP isotope bias (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Search for keff = 0.94 10 0.00009 0.00006 0.00007 0.00003 0.00037 0.00002 0.00000 0.00046

25 0.00024 0.00014 0.00015 0.00006 0.00043 0.00004 0.00000 0.0005940 0.00036 0.00021 0.00022 0.00010 0.00046 0.00005 0.00000 0.0006957 0.00044 0.00026 0.00027 0.00012 0.00047 0.00006 0.00000 0.00075

Cross-section ENDF-B/V 10 N/Ab N/A N/A N/A N/A N/A N/A N/Alibrary 25 N/A N/A N/A N/A N/A N/A N/A N/A

40 N/A N/A N/A N/A N/A N/A N/A N/A57 N/A N/A N/A N/A N/A N/A N/A N/A

ENDF-B/VI 10 N/A N/A N/A N/A N/A N/A N/A N/A

25 N/A N/A N/A N/A N/A N/A N/A N/A40 N/A N/A N/A N/A N/A N/A N/A N/A57 N/A N/A N/A N/A N/A N/A N/A N/A

Axial burnup 1 node 10 0.00013 0.00009 0.00010 0.00004 0.00050 0.00003 0.00000 0.00063

25 0.00034 0.00020 0.00022 0.00009 0.00057 0.00005 0.00000 0.0007940 0.00048 0.00028 0.00031 0.00014 0.00059 0.00007 0.00000 0.0009157 0.00057 0.00033 0.00039 0.00017 0.00059 0.00008 0.00000 0.00100

aBias data based on (n, ) reactions only. bN/A = not available because sensitivity data files have been generated only for ENDF/B-VII cross-section library. 

Table C.3 TSURFER FP isotope bias (continued) 
C-8

Table C.4 TSURFER FP residual uncertainty (1) 

Description Change from base Burnup (GWd/MTU) FP isotope residual uncertainty (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Base case -- 10 7.3E-06 8.1E-06 5.7E-05 4.2E-05 4.0E-05 8.7E-06 -- 8.3E-05

25 2.1E-05 2.0E-05 1.3E-04 1.0E-04 4.5E-05 2.1E-05 -- 1.7E-0440 3.1E-05 2.9E-05 1.8E-04 1.6E-04 5.0E-05 2.9E-05 -- 2.5E-0457 3.8E-05 3.6E-05 2.1E-04 2.0E-04 5.1E-05 3.4E-05 -- 3.0E-04

Assembly design B&W 15×15 10 2.5E-05 2.4E-05 1.0E-04 5.5E-05 5.9E-05 1.9E-05 -- 1.4E-04

25 5.9E-05 5.4E-05 2.1E-04 1.3E-04 6.8E-05 4.1E-05 -- 2.7E-0440 8.3E-05 7.7E-05 2.9E-04 1.9E-04 7.1E-05 5.4E-05 1.5E-06 3.8E-0457 9.7E-05 9.3E-05 3.4E-04 2.4E-04 7.1E-05 6.2E-05 2.5E-06 4.5E-04

W 17×17 10 1.6E-05 1.9E-05 8.8E-05 4.4E-05 6.1E-05 1.5E-05 -- 1.2E-04

(No BAs) 25 4.5E-05 4.5E-05 1.9E-04 1.1E-04 7.3E-05 3.5E-05 -- 2.5E-04

40 6.8E-05 6.7E-05 2.7E-04 1.7E-04 7.8E-05 4.9E-05 -- 3.5E-0457 8.3E-05 8.2E-05 3.3E-04 2.1E-04 7.9E-05 5.7E-05 1.1E-06 4.2E-04

Rack design Unpoisoned panels 10 1.9E-05 2.1E-05 1.2E-04 4.8E-05 7.7E-05 1.9E-05 -- 1.5E-04

25 5.2E-05 4.6E-05 2.4E-04 1.1E-04 8.5E-05 4.1E-05 -- 2.9E-0440 7.4E-05 6.7E-05 3.2E-04 1.6E-04 9.2E-05 5.3E-05 -- 3.9E-0457 8.7E-05 8.1E-05 3.8E-04 2.0E-04 9.2E-05 6.1E-05 1.3E-06 4.6E-04

Cell pitch increased 10 1.7E-05 2.0E-05 8.9E-05 4.6E-05 6.7E-05 1.6E-05 -- 1.2E-04

0.25 in. 25 4.5E-05 4.4E-05 1.9E-04 1.0E-04 8.2E-05 3.3E-05 -- 2.4E-04

40 6.7E-05 6.4E-05 2.7E-04 1.6E-04 8.7E-05 4.6E-05 -- 3.4E-0457 8.0E-05 7.6E-05 3.2E-04 1.9E-04 8.6E-05 5.2E-05 1.3E-06 4.0E-04

Poison panel B10 +10% 10 1.7E-05 2.0E-05 8.9E-05 4.6E-05 6.7E-05 1.6E-05 -- 1.2E-04

25 4.8E-05 4.7E-05 2.0E-04 1.1E-04 7.5E-05 3.6E-05 -- 2.5E-0440 7.0E-05 6.8E-05 2.7E-04 1.7E-04 8.4E-05 4.9E-05 -- 3.5E-0457 8.5E-05 8.3E-05 3.2E-04 2.1E-04 8.5E-05 5.7E-05 1.3E-06 4.2E-04
C-9

Description Change from base Burnup (GWd/MTU) FP isotope residual uncertainty (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Poison panel B10 -10% 10 1.7E-05 2.0E-05 9.0E-05 4.5E-05 6.7E-05 1.6E-05 -- 1.2E-04

25 4.8E-05 4.7E-05 2.0E-04 1.1E-04 7.5E-05 3.6E-05 -- 2.5E-0440 7.0E-05 6.8E-05 2.7E-04 1.7E-04 8.4E-05 4.9E-05 -- 3.5E-0457 8.6E-05 8.3E-05 3.3E-04 2.1E-04 8.5E-05 5.7E-05 1.3E-06 4.2E-04

Decay time 1 year 10 2.5E-05 2.0E-05 9.8E-05 4.5E-05 7.8E-05 1.5E-05 2.1E-06 1.4E-04

25 5.6E-05 4.7E-05 2.0E-04 1.1E-04 8.9E-05 3.5E-05 5.4E-06 2.6E-0440 7.7E-05 6.8E-05 2.7E-04 1.6E-04 9.3E-05 4.8E-05 9.1E-06 3.5E-0457 9.1E-05 8.3E-05 3.2E-04 2.1E-04 9.2E-05 5.6E-05 1.2E-05 4.2E-04

5 year 10 2.4E-05 2.0E-05 9.5E-05 4.4E-05 7.7E-05 1.5E-05 7.4E-06 1.3E-04

25 5.4E-05 4.6E-05 1.9E-04 1.1E-04 8.7E-05 3.4E-05 1.9E-05 2.5E-0440 7.6E-05 6.7E-05 2.7E-04 1.6E-04 9.2E-05 4.7E-05 3.1E-05 3.4E-0457 8.7E-05 8.0E-05 3.1E-04 2.0E-04 9.0E-05 5.4E-05 4.2E-05 4.0E-04

20 year 10 2.3E-05 1.9E-05 9.1E-05 4.2E-05 7.5E-05 1.4E-05 1.3E-05 1.3E-04

25 5.0E-05 4.4E-05 1.8E-04 1.0E-04 8.5E-05 3.2E-05 3.0E-05 2.4E-0440 7.1E-05 6.5E-05 2.5E-04 1.6E-04 9.0E-05 4.5E-05 4.9E-05 3.3E-0457 8.0E-05 7.4E-05 2.9E-04 1.9E-04 8.6E-05 5.1E-05 6.7E-05 3.8E-04

40 year 10 2.2E-05 1.9E-05 8.9E-05 4.1E-05 7.5E-05 1.4E-05 1.3E-05 1.3E-04

25 4.9E-05 4.3E-05 1.8E-04 9.9E-05 8.4E-05 3.1E-05 3.0E-05 2.3E-0440 7.0E-05 6.4E-05 2.4E-04 1.5E-04 9.0E-05 4.4E-05 4.9E-05 3.2E-0457 7.7E-05 7.2E-05 2.8E-04 1.8E-04 8.4E-05 4.9E-05 6.9E-05 3.7E-04

Soluble boron 1000 ppm 10 1.5E-05 1.7E-05 6.8E-05 3.9E-05 4.9E-05 1.4E-05 -- 9.6E-05

25 4.1E-05 4.1E-05 1.5E-04 9.4E-05 5.9E-05 3.1E-05 -- 2.0E-0440 6.2E-05 6.1E-05 2.2E-04 1.5E-04 6.5E-05 4.3E-05 -- 2.9E-0457 7.6E-05 7.5E-05 2.7E-04 1.9E-04 6.7E-05 5.1E-05 9.7E-07 3.5E-04

Table C.4 TSURFER FP residual uncertainty (1) (continued) 
C-10

Description Change from base Burnup (GWd/MTU) FP isotope residual uncertainty (k)a 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Search for keff = 0.94 10 1.6E-05 1.9E-05 8.2E-05 4.4E-05 6.1E-05 1.5E-05 -- 1.1E-04

25 4.5E-05 4.5E-05 1.8E-04 1.0E-04 7.1E-05 3.4E-05 -- 2.3E-0440 6.7E-05 6.5E-05 2.5E-04 1.6E-04 7.6E-05 4.7E-05 -- 3.2E-0457 8.1E-05 7.9E-05 3.0E-04 2.0E-04 7.7E-05 5.4E-05 1.1E-06 3.9E-04

Cross-section ENDF-B/V 10 N/A N/A N/A N/A N/A N/A N/A N/Alibrary 25 N/A N/A N/A N/A N/A N/A N/A N/A

40 N/A N/A N/A N/A N/A N/A N/A N/A57 N/A N/A N/A N/A N/A N/A N/A N/A

ENDF-B/VI 10 N/A N/A N/A N/A N/A N/A N/A N/A

25 N/A N/A N/A N/A N/A N/A N/A N/A40 N/A N/A N/A N/A N/A N/A N/A N/A57 N/A N/A N/A N/A N/A N/A N/A N/A

Axial burnup 1 node 10 2.5E-05 2.9E-05 1.3E-04 6.8E-05 8.1E-05 2.4E-05 -- 1.7E-04

25 6.3E-05 6.3E-05 2.6E-04 1.5E-04 9.3E-05 4.8E-05 -- 3.3E-0440 8.9E-05 8.7E-05 3.5E-04 2.2E-04 9.7E-05 6.1E-05 -- 4.5E-0457 1.1E-04 1.0E-04 4.3E-04 2.8E-04 9.7E-05 7.1E-05 1.6E-06 5.5E-04

aBias uncertainty data based on (n, ) reactions only. bN/A = not available because sensitivity data files have been generated only for ENDF/B-VII cross-section library. 

Table C.4 TSURFER FP residual uncertainty (1) (continued) 
C-11

Table C.5 TSUNAMI-IP seven FP bounding uncertainty in keff at 1 confidence 

Description Change from base Burnup (GWd/MTU) FP isotope nuclear data uncertainty (k) 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Base case -- 10 4.6E-05 5.0E-05 1.1E-04 4.7E-05 1.5E-04 2.0E-05 1.3E-07 2.1E-04

25 1.3E-04 1.2E-04 2.5E-04 1.2E-04 1.7E-04 4.7E-05 4.3E-07 3.8E-0440 1.9E-04 1.7E-04 3.5E-04 1.7E-04 1.9E-04 6.4E-05 9.0E-07 5.1E-0457 2.3E-04 2.1E-04 4.2E-04 2.2E-04 1.9E-04 7.4E-05 1.6E-06 6.0E-04

Assembly design B&W 15×15 10 6.8E-05 6.1E-05 1.3E-04 5.8E-05 1.4E-04 2.5E-05 2.5E-07 2.2E-04

25 1.6E-04 1.4E-04 2.7E-04 1.4E-04 1.5E-04 5.2E-05 8.7E-07 4.0E-0440 2.3E-04 1.9E-04 3.8E-04 2.0E-04 1.6E-04 7.0E-05 1.8E-06 5.5E-0457 2.7E-04 2.3E-04 4.5E-04 2.5E-04 1.6E-04 7.9E-05 3.1E-06 6.5E-04

W 17×17 10 4.3E-05 4.9E-05 1.1E-04 4.6E-05 1.4E-04 2.0E-05 1.1E-07 2.0E-04

(No BAs) 25 1.3E-04 1.2E-04 2.5E-04 1.1E-04 1.7E-04 4.6E-05 3.6E-07 3.7E-04

40 1.9E-04 1.7E-04 3.6E-04 1.7E-04 1.8E-04 6.4E-05 7.6E-07 5.1E-0457 2.3E-04 2.1E-04 4.4E-04 2.2E-04 1.8E-04 7.4E-05 1.3E-06 6.1E-04

Rack design Unpoisoned panels 10 5.8E-05 6.0E-05 1.6E-04 5.2E-05 1.8E-04 2.8E-05 1.4E-07 2.6E-04

25 1.5E-04 1.3E-04 3.1E-04 1.1E-04 1.9E-04 5.4E-05 4.7E-07 4.3E-0440 2.1E-04 1.8E-04 4.2E-04 1.7E-04 2.1E-04 7.1E-05 9.5E-07 5.7E-0457 2.5E-04 2.2E-04 4.9E-04 2.1E-04 2.1E-04 8.0E-05 1.6E-06 6.7E-04

Cell pitch increased 10 4.4E-05 4.8E-05 1.1E-04 4.5E-05 1.6E-04 1.9E-05 1.4E-07 2.1E-04

0.25 in. 25 1.3E-04 1.1E-04 2.5E-04 1.1E-04 1.9E-04 4.3E-05 4.5E-07 3.7E-04

40 1.9E-04 1.6E-04 3.5E-04 1.7E-04 2.0E-04 5.9E-05 9.5E-07 5.0E-0457 2.2E-04 1.9E-04 4.2E-04 2.0E-04 2.0E-04 6.7E-05 1.6E-06 5.9E-04

Poison panel B10 +10% 10 4.7E-05 5.1E-05 1.1E-04 4.8E-05 1.5E-04 2.1E-05 1.3E-07 2.1E-04

25 1.3E-04 1.2E-04 2.5E-04 1.2E-04 1.7E-04 4.7E-05 4.3E-07 3.8E-0440 1.9E-04 1.7E-04 3.6E-04 1.7E-04 1.9E-04 6.3E-05 9.0E-07 5.1E-0457 2.3E-04 2.1E-04 4.3E-04 2.2E-04 1.9E-04 7.3E-05 1.6E-06 6.1E-04
C-12

Description Change from base Burnup (GWd/MTU) FP isotope nuclear data uncertainty (k) 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Poison panel B10 -10% 10 4.7E-05 5.1E-05 1.2E-04 4.7E-05 1.5E-04 2.1E-05 1.3E-07 2.1E-04

25 1.3E-04 1.2E-04 2.6E-04 1.2E-04 1.7E-04 4.7E-05 4.3E-07 3.8E-0440 1.9E-04 1.7E-04 3.6E-04 1.7E-04 1.9E-04 6.4E-05 9.0E-07 5.2E-0457 2.4E-04 2.1E-04 4.3E-04 2.2E-04 1.9E-04 7.4E-05 1.6E-06 6.1E-04

Decay time 1 year 10 6.9E-05 5.2E-05 1.3E-04 4.6E-05 1.8E-04 2.0E-05 2.5E-06 2.4E-04

25 1.5E-04 1.2E-04 2.6E-04 1.1E-04 2.0E-04 4.5E-05 6.7E-06 4.0E-0440 2.1E-04 1.7E-04 3.6E-04 1.7E-04 2.1E-04 6.2E-05 1.1E-05 5.3E-0457 2.5E-04 2.1E-04 4.3E-04 2.2E-04 2.1E-04 7.2E-05 1.5E-05 6.2E-04

5 year 10 6.7E-05 5.1E-05 1.2E-04 4.5E-05 1.8E-04 1.9E-05 9.1E-06 2.4E-04

25 1.5E-04 1.2E-04 2.5E-04 1.1E-04 2.0E-04 4.4E-05 2.3E-05 3.9E-0440 2.1E-04 1.7E-04 3.5E-04 1.7E-04 2.1E-04 6.1E-05 3.8E-05 5.2E-0457 2.4E-04 2.0E-04 4.1E-04 2.1E-04 2.0E-04 6.9E-05 5.1E-05 6.0E-04

20 year 10 6.3E-05 4.8E-05 1.2E-04 4.3E-05 1.7E-04 1.8E-05 1.6E-05 2.3E-04

25 1.4E-04 1.1E-04 2.3E-04 1.0E-04 1.9E-04 4.1E-05 3.7E-05 3.7E-0440 2.0E-04 1.6E-04 3.3E-04 1.6E-04 2.1E-04 5.8E-05 6.1E-05 5.0E-0457 2.2E-04 1.8E-04 3.8E-04 1.9E-04 2.0E-04 6.5E-05 8.3E-05 5.6E-04

40 year 10 6.2E-05 4.8E-05 1.2E-04 4.3E-05 1.7E-04 1.8E-05 1.6E-05 2.3E-04

25 1.4E-04 1.1E-04 2.3E-04 1.0E-04 1.9E-04 4.0E-05 3.7E-05 3.6E-0440 1.9E-04 1.6E-04 3.2E-04 1.6E-04 2.0E-04 5.7E-05 6.1E-05 4.9E-0457 2.1E-04 1.8E-04 3.7E-04 1.9E-04 1.9E-04 6.3E-05 8.6E-05 5.5E-04

Soluble boron 1000 ppm 10 4.0E-05 4.4E-05 8.7E-05 4.1E-05 1.1E-04 1.8E-05 9.4E-08 1.6E-04

25 1.1E-04 1.0E-04 2.0E-04 9.8E-05 1.3E-04 4.0E-05 3.2E-07 3.0E-0440 1.7E-04 1.5E-04 2.8E-04 1.5E-04 1.5E-04 5.5E-05 6.9E-07 4.3E-0457 2.1E-04 1.8E-04 3.5E-04 1.9E-04 1.5E-04 6.4E-05 1.2E-06 5.1E-04

Table C.5 TSUNAMI-IP seven FP bounding uncertainty in keff at 1 confidence (continued) 
C-13

Description Change from base Burnup (GWd/MTU) FP isotope nuclear data uncertainty (k) 103Rh 133Cs 143Nd 145Nd 149Sm 152Sm 155Gd Total 

Search for keff = 0.94 10 4.5E-05 4.9E-05 1.1E-04 4.5E-05 1.4E-04 2.0E-05 1.2E-07 1.9E-04

25 1.2E-04 1.1E-04 2.3E-04 1.1E-04 1.6E-04 4.4E-05 3.8E-07 3.5E-0440 1.8E-04 1.6E-04 3.2E-04 1.7E-04 1.7E-04 6.0E-05 8.0E-07 4.8E-0457 2.2E-04 2.0E-04 3.9E-04 2.1E-04 1.8E-04 6.9E-05 1.4E-06 5.6E-04

Cross-section ENDF-B/V 10 4.5E-05 4.3E-05 1.1E-04 4.4E-05 1.5E-04 1.9E-05 1.4E-07 2.0E-04library 25 -- -- -- -- -- -- -- --

40 1.9E-04 1.4E-04 3.3E-04 1.6E-04 1.9E-04 5.9E-05 9.3E-07 4.8E-0457 -- -- -- -- -- -- -- --

ENDF-B/VI 10 4.4E-05 4.8E-05 1.1E-04 4.5E-05 1.5E-04 1.9E-05 1.3E-07 2.0E-04

25 -- -- -- -- -- -- -- --40 1.9E-04 1.7E-04 3.3E-04 1.7E-04 1.9E-04 6.1E-05 8.8E-07 4.9E-0457 -- -- -- -- -- -- -- --

Axial burnup 1 node 10 6.9E-05 7.5E-05 1.6E-04 7.1E-05 1.8E-04 3.2E-05 1.4E-07 2.8E-04

25 1.8E-04 1.6E-04 3.4E-04 1.6E-04 2.1E-04 6.2E-05 5.2E-07 4.9E-0440 2.5E-04 2.2E-04 4.6E-04 2.3E-04 2.2E-04 7.9E-05 1.1E-06 6.6E-0457 2.9E-04 2.7E-04 5.7E-04 2.9E-04 2.2E-04 9.2E-05 2.0E-06 7.9E-04

Table C.5 TSUNAMI-IP seven FP bounding uncertainty in keff at 1 confidence (continued) 
C-14 

The TSURFER results for the application models show the combined FP bias values ranging 

from 3.7×10-4 to 1.45×10-3. The TSURFER FP bias values are essentially equal to or less than 

the 3 sigma error band of the cross-section covariance uncertainty. The results indicate that the 

FP cross sections consistently overpredict keff when combined, hence confirming the validity of 

using the cross-section covariance data to bound the bias because no credit for positive bias is 

taken. 

Figure C.1 Net FP bias and bias uncertainty compared against bounding FP covariance 

uncertainty. 

-2.E-03

-2.E-03

-1.E-03

-5.E-04

0.E+00

5.E-04

1.E-03

2.E-03

2.E-03

3.E-03

0 10 20 30 40 50 60

Bounding keff Adjustment Due to FPs (

k)

Assembly Average Burnup (GWd/MTU)

Base

bw15

pitch

unpoisoned

B-10 (+10%)

B-10 (-10%

1yr decay

5yr decay

20yr decay

40yr decay

1000ppm

keff=0.94 ppmB

No BAs

1 node BU

FP Covariance Unc, 1s

FP Covariance Unc, 2s

FP Covariance Unc, 3s
APPENDIX D 

EXAMPLE TRITON DEPLETION CODE INPUT 

D-1 

PWR Assembly

=t-depl parm=(centrm,addnux=3) 

PWR Westinghouse OFA 17x17 with WABA, 1/4 assembly model, 4.0 wt% enriched 

v7-238 

read comp 

' 

'fuel 1.0 wt% 

 uo2 1 den=10.5216 1 1100 92235 4.0 

 92238 96.0 end 

'clad 

 zirc4 2 1 620 end 

'water moderator with 1000 ppm soluble boron 

 h2o 3 den=0.63 1 610 end 

 arbmb 0.63 1 1 0 0 5000 100 3 1000e-06 610 end 

'gap 

 n 4 den=0.00125 1 620 end 

'guide tube 

 zirc4 5 1 610 end 

' 

'WABA inner water moderator with 1000 ppm soluble boron 

 h2o 10 den=0.63 1 610 end 

 arbmb 0.63 1 1 0 0 5000 100 10 1000e-06 610 end 

'WABA inner cladding 

 zirc4 11 1 610 end 

'WABA inner gap 

 n 12 den=0.00125 1 610 end 

'WABA Al2O3-B4C 

 b-10 13 0 3.0697E-3 610.0 end 

 b-11 13 0 1.2753E-2 610.0 end 

 c 13 0 3.9521E-3 610.0 end 

 al 13 0 2.6344E-2 610.0 end 

 o 13 0 3.9506E-2 610.0 end 

'WABA Al2O3-B4C 

 b-10 14 0 3.0697E-3 610.0 end 

 b-11 14 0 1.2753E-2 610.0 end 

 c 14 0 3.9521E-3 610.0 end 

 al 14 0 2.6344E-2 610.0 end 

 o 14 0 3.9506E-2 610.0 end 

'WABA Al2O3-B4C 

 b-10 15 0 3.0697E-3 610.0 end 

 b-11 15 0 1.2753E-2 610.0 end 

 c 15 0 3.9521E-3 610.0 end 

 al 15 0 2.6344E-2 610.0 end 

 o 15 0 3.9506E-2 610.0 end 

'WABA Al2O3-B4C 

 b-10 16 0 3.0697E-3 610.0 end 

 b-11 16 0 1.2753E-2 610.0 end 

 c 16 0 3.9521E-3 610.0 end 

 al 16 0 2.6344E-2 610.0 end 

 o 16 0 3.9506E-2 610.0 end 

'WABA Al2O3-B4C 

 b-10 17 0 3.0697E-3 610.0 end 

 b-11 17 0 1.2753E-2 610.0 end 

 c 17 0 3.9521E-3 610.0 end 

 al 17 0 2.6344E-2 610.0 end 
D-2 

 o 17 0 3.9506E-2 610.0 end 

'WABA outer gap 

 n 18 den=0.00125 1 610 end 

'WABA outer cladding 

 zirc4 19 1 610 end 

'WABA outer water moderator with 1000 ppm soluble boron 

 h2o 20 den=0.63 1 610 end 

 arbmb 0.63 1 1 0 0 5000 100 20 1000e-06 610 end 

'WABA guide tube 

 zirc4 21 1 610 end 

'WABA pitch water moderator with 1000 ppm soluble boron 

 h2o 22 den=0.63 1 610 end 

 arbmb 0.63 1 1 0 0 5000 100 22 1000e-06 610 end 

'ring around WABA for centrm 4.0 wt% 

 uo2 23 den=10.5216 1 1100 92235 4.0 

 92238 96.0 end 

' 

end comp 

' ---------------------------------------------------------------- 

' Cell data 

' ---------------------------------------------------------------- 

read celldata 

 latticecell squarepitch pitch=1.2598 3 

 fueld=0.7844 1 

 gapd=0.8001 4 

 cladd=0.9144 2 end 

 multiregion cylindrical right_bdy=white end 

 10 0.28575 11 0.33910 12 0.35305 13 0.35767 

 14 0.36690 15 0.38999 16 0.39923 17 0.40385 

 18 0.41785 19 0.48387 20 0.56135 21 0.60200 

 22 0.71077 23 0.80 end zone 

end celldata 

' ---------------------------------------------------------------- 

' Depletion data 

' ---------------------------------------------------------------- 

read depletion 

 1 flux 13 14 15 16 17 

end depletion 

' ---------------------------------------------------------------- 

' Burn data 

' ---------------------------------------------------------------- 

read burndata 

 power=60.0 burn=1500 down=0 nlib=30 end 

end burndata 

' ---------------------------------------------------------------- 

' NEWT model data 

' ---------------------------------------------------------------- 

read model 

Westinghouse OFA 17x17, 4.0 wt% uo2 

read parm 

 run=yes 

end parm 

read materials 

 1 1 ! fuel ! end 

 2 1 ! clad ! end 

 3 2 ! water ! end 

 4 0 ! gap ! end 
D-3 

 5 1 ! guide tube ! end 

 10 2 ! WABA inner water ! end 

 11 1 ! WABA clad ! end 

 12 0 ! WABA inner gap ! end 

 13 2 ! WABA poison rod ! end 

 14 2 ! WABA poison rod ! end 

 15 2 ! WABA poison rod ! end 

 16 2 ! WABA poison rod ! end 

 17 2 ! WABA poison rod ! end 

 18 0 ! WABA gap ! end 

 19 1 ! WABA outer clad ! end 

 20 2 ! WABA outer water ! end 

 21 1 ! WABA guide tube ! end 

 22 2 ! WABA pitch water ! end 

end materials 

read geom 

unit 1 

com='fuel rod' 

 cylinder 10 .3922 

 cylinder 20 .40005 

 cylinder 30 .4572 

 cuboid 40 4p0.6299 

 media 1 1 10 

 media 4 1 20 -10 

 media 2 1 30 -20 

 media 3 1 40 -30 

 boundary 40 4 4 

unit 5 

com='guide tube' 

 cylinder 10 .28575 

 cylinder 20 .33910 

 cylinder 30 .35305 

 cylinder 40 .35767 

 cylinder 50 .36690 

 cylinder 60 .38999 

 cylinder 70 .39923 

 cylinder 80 .40385 

 cylinder 90 .41785 

 cylinder 100 .48387 

 cylinder 110 .56135 

 cylinder 120 .602 

 cuboid 130 4p0.6299 

 media 10 1 10 

 media 11 1 20 -10 

 media 12 1 30 -20 

 media 13 1 40 -30 

 media 14 1 50 -40 

 media 15 1 60 -50 

 media 16 1 70 -60 

 media 17 1 80 -70 

 media 18 1 90 -80 

 media 19 1 100 -90 

 media 20 1 110 -100 

 media 21 1 120 -110 

 media 22 1 130 -120 

 boundary 130 4 4 

unit 11 
D-4 

com='right half of fuel rod' 

 cylinder 10 .3922 chord +x=0 

 cylinder 20 .40005 chord +x=0 

 cylinder 30 .4572 chord +x=0 

 cuboid 40 0.6299 0.0 2p0.6299 

 media 1 1 10 

 media 4 1 20 -10 

 media 2 1 30 -20 

 media 3 1 40 -30 

 boundary 40 2 4 

unit 12 

com='top half of fuel rod' 

 cylinder 10 .3922 chord +y=0 

 cylinder 20 .40005 chord +y=0 

 cylinder 30 .4572 chord +y=0 

 cuboid 40 2p0.6299 0.6299 0.0 

 media 1 1 10 

 media 4 1 20 -10 

 media 2 1 30 -20 

 media 3 1 40 -30 

 boundary 40 4 2 

unit 51 

com='right half of guide tube' 

 cylinder 10 .28575 chord +x=0.0 

 cylinder 20 .33910 chord +x=0.0 

 cylinder 30 .35305 chord +x=0.0 

 cylinder 40 .35767 chord +x=0.0 

 cylinder 50 .36690 chord +x=0.0 

 cylinder 60 .38999 chord +x=0.0 

 cylinder 70 .39923 chord +x=0.0 

 cylinder 80 .40385 chord +x=0.0 

 cylinder 90 .41785 chord +x=0.0 

 cylinder 100 .48387 chord +x=0.0 

 cylinder 110 .56135 chord +x=0.0 

 cylinder 120 .602 chord +x=0.0 

 cuboid 130 0.6299 0.0 2p0.6299 

 media 10 1 10 

 media 11 1 20 -10 

 media 12 1 30 -20 

 media 13 1 40 -30 

 media 14 1 50 -40 

 media 15 1 60 -50 

 media 16 1 70 -60 

 media 17 1 80 -70 

 media 18 1 90 -80 

 media 19 1 100 -90 

 media 20 1 110 -100 

 media 21 1 120 -110 

 media 22 1 130 -120 

 boundary 130 2 4 

unit 52 

com='top half of guide tube' 

 cylinder 10 .28575 chord +y=0.0 

 cylinder 20 .33910 chord +y=0.0 

 cylinder 30 .35305 chord +y=0.0 

 cylinder 40 .35767 chord +y=0.0 

 cylinder 50 .36690 chord +y=0.0 
D-5 

 cylinder 60 .38999 chord +y=0.0 

 cylinder 70 .39923 chord +y=0.0 

 cylinder 80 .40385 chord +y=0.0 

 cylinder 90 .41785 chord +y=0.0 

 cylinder 100 .48387 chord +y=0.0 

 cylinder 110 .56135 chord +y=0.0 

 cylinder 120 .602 chord +y=0.0 

 cuboid 130 2p0.6299 0.6299 0.0 

 media 10 1 10 

 media 11 1 20 -10 

 media 12 1 30 -20 

 media 13 1 40 -30 

 media 14 1 50 -40 

 media 15 1 60 -50 

 media 16 1 70 -60 

 media 17 1 80 -70 

 media 18 1 90 -80 

 media 19 1 100 -90 

 media 20 1 110 -100 

 media 21 1 120 -110 

 media 22 1 130 -120 

 boundary 130 4 2 

unit 53 

com='1/4 instrument tube' 

 cylinder 10 .56135 chord +x=0 chord +y=0 

 cylinder 20 .602 chord +x=0 chord +y=0 

 cuboid 40 0.6299 0.0 0.6299 0.0 

 media 3 1 10 

 media 5 1 20 -10 

 media 3 1 40 -20 

 boundary 40 2 2 

global unit 10 

 cuboid 10 10.7083 0.0 10.7083 0.0 

 array 1 10 place 1 1 0 0 

 media 3 1 10 

 boundary 10 34 34 

end geom 

read array 

 ara=1 nux=9 nuy=9 typ=cuboidal 

 fill 

 53 12 12 52 12 12 52 12 12 

 11 1 1 1 1 1 1 1 1 

 11 1 1 1 1 1 1 1 1 

 51 1 1 5 1 1 5 1 1 

 11 1 1 1 1 1 1 1 1 

 11 1 1 1 1 5 1 1 1 

 51 1 1 5 1 1 1 1 1 

 11 1 1 1 1 1 1 1 1 

 11 1 1 1 1 1 1 1 1 

 end fill 

end array 

read bounds 

 all=refl 

end bounds 

end model 

end 

=shell 
D-6 

 cp ft33f001.cmbined $RTNDIR/origenlib-4.0 

end

 
D-7 

BWR Assembly

=t-depl parm=(centrm, addnux=3, weight) 

BWR GE 10×10 fuel assembly - averaged assembly, uo2-gd pin - 5 

v7-238 

' generic ge10x120-8, 3wt% Gd rods, fuel assembly 

read comp 

' water channel clad 

zirc2 1 1.0 567 end 

' water Channel coolant 

h2o 2 den=0.776 1.0 512 end 

' Coolant between assemblies 

h2o 3 den=0.776 1.0 512 end 

' Assembly channel 

zirc2 4 1.0 512 end 

' fuel, no-Gd 

uo2 10 den=10.41 1.00 840 92235 5 92238 95 end 

' fuel, with Gd 

uo2 20 den=10.41 0.97 840 92235 5 92238 95 end 

gd2o3 20 den=10.41 0.03 840 end 

uo2 21 den=10.41 0.97 840 92235 5 92238 95 end 

gd2o3 21 den=10.41 0.03 840 end 

uo2 22 den=10.41 0.97 840 92235 5 92238 95 end 

gd2o3 22 den=10.41 0.03 840 end 

uo2 23 den=10.41 0.97 840 92235 5 92238 95 end 

gd2o3 23 den=10.41 0.03 840 end 

uo2 24 den=10.41 0.97 840 92235 5 92238 95 end 

gd2o3 24 den=10.41 0.03 840 end 

' cladding & moderator 

zirc2 5 1.0 567 end 

h2o 6 den=0.776 1.0 512 end 

zirc2 7 1.0 567 end 

h2o 8 den=0.776 1.0 512 end 

end comp 

' ---------------------------------------------------------------- 

' Cell data 

' ---------------------------------------------------------------- 

read celldata 

latticecell squarepitch pitch=1.295 6 

 fueld=0.876 10 

 gapd=0.894 0 

 cladd=1.026 5 end 

 centrmdata alump=0.3 pmc_omit=1 nmf6=-1 end centrmdata 

multiregion cylindrical left_bdy=reflected right_bdy=white end 

 20 0.19588 

 21 0.27702 

 22 0.33927 

 23 0.39176 

 24 0.438 

 0 0.447 

 7 0.513 

 8 0.73062 end zone 

 centrmdata alump=0.3 pmc_omit=1 nmf6=-1 end centrmdata 

end celldata 

' ---------------------------------------------------------------- 
D-8 

' Depletion data 

' ---------------------------------------------------------------- 

read depletion 

 10 flux 20 21 22 23 24 end 

end depletion 

' ---------------------------------------------------------------- 

' Burn data 

' ---------------------------------------------------------------- 

read burndata 

 power=26.44 burn=2 nlib=1 down=0 end 

 power=26.44 burn=200 nlib=10 down=0 end 

 power=26.44 burn=200 nlib=10 down=3 end 

end burndata 

read opus 

 title= Masses of Fuel Nuclides 

 units=grams 

 time=days 

 typarms=nucl 

 libtype=all 

 symnuc= 

 u-234 u-235 u-236 u-238 

 np-237 

 pu-238 pu-239 pu-240 pu-241 pu-242 

 am-241 am-243 

 mo-95 tc-99 ag-109 ru-101 rh-103 cs-133 

 nd-143 nd-145 eu-151 eu-153 

 gd-154 gd-155 gd-156 gd-157 gd-158 gd-160 

 sm-147 sm-148 sm-149 sm-150 sm-151 sm-152 end 

end opus 

' ---------------------------------------------------------------- 

' NEWT model data 

' ---------------------------------------------------------------- 

read model 

BWR GE 10×10 fuel assembly - averaged assembly, uo2-gd pin - 5 

read parm 

 run=yes 

 cmfd=1 

 xycmfd=2 

 drawit=yes 

 epsilon=1e-5 

 converg=mix 

 inners=6 

 therm=yes 

 therms=1 

 outers=9999 

end parm 

read materials 

 1 1 ! WC-Zr ! end 

 2 3 ! WC-W ! end 

 3 3 ! As-W ! end 

 4 1 ! As-Zr ! end 

 10 1 ! fuel ! end 

 20 1 ! fuel-gd ! end 

 21 1 ! fuel-gd ! end 

 22 1 ! fuel-gd ! end 

 23 1 ! fuel-gd ! end 

 24 1 ! fuel-gd ! end 
D-9 

 5 1 ! clad ! end 

 6 3 ! mod ! end 

 7 1 ! clad ! end 

 8 3 ! mod ! end 

end materials 

read geom 

unit 1 

com='UO2 fuel pin' 

 cylinder 10 0.438 

 cylinder 20 0.447 

 cylinder 30 0.513 

 cuboid 40 4p0.6475 

 media 10 1 10 

 media 0 1 20 -10 

 media 5 1 30 -20 

 media 6 1 40 -30 

 boundary 40 4 4 

unit 2 

com='gd-UO2 fuel pin' 

 cylinder 6 0.19588 

 cylinder 7 0.27702 

 cylinder 8 0.33927 

 cylinder 9 0.39176 

 cylinder 10 0.438 

 cylinder 20 0.447 

 cylinder 30 0.513 

 cuboid 40 4p0.6475 

 media 20 1 6 

 media 21 1 7 -6 

 media 22 1 8 -7 

 media 23 1 9 -8 

 media 24 1 10 -9 

 media 0 1 20 -10 

 media 7 1 30 -20 

 media 8 1 40 -30 

 boundary 40 4 4 

unit 3 

com='water filled position' 

 cuboid 10 4p0.6475 

 media 2 1 10 

 boundary 10 4 4 

unit 4 

com='water rod' 

 cylinder 10 1.161 

 cylinder 20 1.261 

 media 2 1 10 

 media 1 1 20 -10 

 boundary 20 8 8 

global unit 10 

com='assembly' 

 cuboid 10 4p6.475 

 cuboid 20 4p6.675 

 cuboid 30 4p7.62 

 array 1 10 place 1 1 -5.8275 -5.8275 

 hole 4 origin x=1.295 y=1.295 

 hole 4 origin x=-1.295 y=-1.295 

 media 4 1 20 -10 
D-10 

 media 3 1 30 -20 

 boundary 30 12 12 

end geom 

read array 

 ara=1 nux=10 nuy=10 

 fill 

 1 1 1 1 1 1 1 1 1 1 

 1 1 1 1 1 2 1 1 1 1 

 1 1 1 1 1 1 2 1 1 1 

 1 1 2 3 3 1 1 2 1 1 

 1 1 1 3 3 1 1 1 2 1 

 1 1 2 1 1 3 3 1 1 1 

 1 1 1 1 1 3 3 1 1 1 

 1 1 1 1 2 1 2 1 1 1 

 1 1 1 1 1 1 1 1 1 1 

 1 1 1 1 1 1 1 1 1 1 end fill 

end array 

read bounds 

 all=refl 

end bounds 

end data 

end 

' ---------------------------------------------------------------- 

=shell 

 mkdir $RTNDIR/${CASE_NAME}_compositions 

 cp StdCmpMix* $RTNDIR/${CASE_NAME}_compositions/ 

end 



UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/CR-7109 An Approach for Validating Actinide and Fission Product Burnup Credit 

Criticality Safety Analyses—Criticality (Keff) Predictions