Technical Basis for Peak 

Reactivity Burnup Credit for 

BWR Spent Nuclear Fuel in 

Storage and Transportation 

Systems

Office of Nuclear Regulatory Research

NUREG/CR-7194

ORNL/TM-2014/240
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Technical Basis for Peak 

Reactivity Burnup Credit for 

BWR Spent Nuclear Fuel in 

Storage and Transportation 

Systems

Manuscript Completed: December 2014

Date Published: April 2015

Prepared by: 

William (B.J.) Marshall

Brian J. Ade

Stephen M. Bowman

Ian C. Gauld

Germina Ilas

Ugur Mertyurek

Georgeta Radulescu

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6170

M. Aissa, NRC Project Manager

NRC Job Code V6452

Office of Nuclear Regulatory Research

NUREG/CR-7194

ORNL/TM-2014/240

iii

ABSTRACT

Criticality safety analyses of pressurized-water-reactor (PWR) spent nuclear fuel (SNF) 

assemblies in storage and transportation casks frequently take credit for reactivity reduction 

during depletion. This credit is commonly referred to as “burnup credit” (BUC) as outlined in 

U.S. Nuclear Regulatory Commission (NRC) Interim Staff Guidance (ISG) 8, Revision 3, 

“Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transportation and 

Storage Casks.” However, such credit for boiling-water reactor (BWR) SNF is not addressed in 

ISG 8. The focus of this report is to document studies performed to provide a technical basis for 

the application of BUC in storage and transportation casks using BWR peak reactivity methods. 

Most BWR fuel assemblies contain gadolinium oxide (Gd2O3, or gadolinium) burnable absorber 

in some fuel rods. The gadolinium absorber depletes more rapidly than the fuel during the initial 

part of its irradiation, which causes the fuel assembly reactivity to increase and reach a maximum 

value at an assembly average burnup typically less than 20 gigawatt days per metric ton of 

uranium (GWd/MTU). Then the reactivity decreases for the remainder of fuel assembly 

irradiation. Criticality analyses of BWR spent fuel pools (SFPs) typically employ what are 

known as peak reactivity methods to account for this behavior in the SNF. Some peak reactivity 

methods correlate the peak reactivity value in storage to the infinite multiplication factor (kinf) in 

the standard cold core geometry (SCCG). The SCCG is an infinite planar array of fuel 

assemblies in reactor geometry, typically a 6-inch pitch, flooded with full density water at 20°C. 

The peak reactivity methods are also sometimes referred to as “gadolinium credit.”

This report reviews the most commonly used peak reactivity methods in SFP analyses for BWR 

SNF to provide technical background for potential application to storage and transportation 

casks, including (1) an examination of the fuel assembly lattice design and operating parameters 

that affect the burnup and reactivity of the peak reactivity in storage and transportation 

configurations, (2) validation of these reactivity calculations, and (3) validation of the depleted 

isotopic inventories in BWR SNF at burnups associated with peak reactivity. Each of these three 

areas is investigated in detail in this report. This report is focused on peak reactivity, so it applies 

to fuel assemblies with average burnups of approximately 20 GWd/MTU or less. Burnup credit 

for BWR fuel assemblies with typical discharge burnups will be addressed in future reports 

planned over the next few years.

The following parameters have been studied, and their impact on the reactivity of BWR SNF has 

been quantified for determining potentially limiting conditions: initial fuel composition, number 

and loading of gadolinium pins, control blade insertion (referred to as “rodded” vs. “unrodded” 

conditions), moderator void fraction (unrodded and rodded), fuel temperature, specific power, 

and operating history. The depletion parameters used and the nuclides credited in an analysis will 

depend on the methodology developed and implemented by the applicant.

A suitable number of critical experiments has been identified to support validation of peak 

reactivity analysis of BWR SNF. All experiments identified in this report are low-enriched

uranium (LEU), water-moderated pin array experiments. Penalty factors have been developed for 

the unvalidated transuranic, gadolinium, and fission product nuclides included in generic BUC 

cask (GBC)-68 models used in this report. The sum of these three factors is less than 0.5% Δk.
iv

The physics of BWR fuel depletion are well understood, reliable, and predictable in their effects 

on discharged fuel reactivity near peak reactivity. This study confirms that a conservative set of 

analysis conditions can be identified and implemented to allow criticality safety analysis of 

BWR SNF for peak reactivity BUC in storage and transportation casks.
v

CONTENTS

Page

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

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

LIST OF TABLES .................................................................................................................................xi

LIST OF ACRONYMS AND UNITS...................................................................................................xiii

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

2 CURRENT PEAK REACTIVITY METHODS .................................................................................3

2.1 GENERAL CONSIDERATIONS FOR PEAK REACTIVITY ANALYSES ............................3

2.2 SCCG LIMIT WITH GADOLINIUM CREDIT.......................................................................7

2.3 SCCG LIMIT WITHOUT GADOLINIUM CREDIT ............................................................. 10

2.4 OTHER METHODS.............................................................................................................. 15

3 FACTORS AFFECTING PEAK REACTIVITY IN STORAGE AND TRANSPORTATION 

CASKS...........................................................................................................................................17

3.1 SENSITIVITY STUDY METHODOLOGY .......................................................................... 17

3.2 CALCULATIONAL METHODS, MODELS, AND CODES ................................................. 18

3.2.1 Triton........................................................................................................................ 19

3.2.2 CSAS/KENO ............................................................................................................ 19

3.2.3 Cask Application Model............................................................................................ 22

3.3 FUEL DESIGN TYPES......................................................................................................... 23

3.4 RESULTS .............................................................................................................................25

3.4.1 Isotopic Modeling during Depletion .......................................................................... 25

3.4.2 Gadolinium Loading.................................................................................................. 31

3.4.3 Gadolinium Pattern.................................................................................................... 43

3.4.4 Void Fraction ............................................................................................................ 48

3.4.5 Control Blade Insertion ............................................................................................. 52

3.4.6 Operating Parameters ................................................................................................ 60

3.4.7 Three-Dimensional Modeling .................................................................................... 71

3.5 SUMMARY OF FACTORS AFFECTING PEAK REACTIVITY.......................................... 74

3.5.1 Summary of Sensitivity Studies................................................................................. 74

3.5.2 Recommended Minimum Analyses ........................................................................... 78

3.5.3 Areas for Further Study ............................................................................................. 78

4 VALIDATION OF CASK REACTIVITY CALCULATIONS ........................................................ 81

4.1 CODES AND METHODS..................................................................................................... 81

4.2 METHODOLOGY FOR VALIDATION STUDIES............................................................... 82

4.3 SDF SOURCES..................................................................................................................... 83

4.4 POTENTIALLY APPLICABLE EXPERIMENTS................................................................. 84

4.4.1 Vanished Lattice with Actinide-Only Modeling ......................................................... 84

4.4.2 Vanished Lattice with Actinide and Fission Product Modeling................................... 86

4.4.3 Full Lattice with Actinide and Fission Product Modeling........................................... 90

4.5 BIAS AND UNCERTAINTY DETERMINATION ............................................................... 92

4.5.1 Bias and Uncertainty without Trending Analysis ....................................................... 94

4.5.2 Traditional Trending Analysis ................................................................................... 94

4.5.3 ck Trending................................................................................................................ 96
vi

4.6 PENALTIES FOR UNVALIDATED NUCLIDES................................................................. 97

4.6.1 Plutonium.................................................................................................................. 98

4.6.2 Residual Gadolinium................................................................................................. 99

4.6.3 Fission Products and Minor Actinides...................................................................... 100

4.7 SUMMARY OF VALIDATION OF CASK REACTIVITY CALCULATIONS................... 101

5 VALIDATION OF SPENT FUEL NUCLIDE COMPOSITIONS.................................................. 103

5.1 APPLICATION MODEL .................................................................................................... 103

5.2 NUCLIDE IMPORTANCE TO REACTIVITY.................................................................... 105

5.3 CODES AND METHODS................................................................................................... 107

5.4 APPLICABLE EXPERIMENTAL DATA ........................................................................... 108

5.5 OECD/NEA BWR BENCHMARK...................................................................................... 111

5.6 BIAS AND UNCERTAINTY DETERMINATION ............................................................. 112

5.6.1 Nuclide Uncertainty Analysis.................................................................................. 112

5.6.2 keffBias and Uncertainty Analysis ............................................................................ 114

5.6.3 keff Bias and Uncertainty Results.............................................................................. 115

5.7 CONCLUSIONS AND RECOMMENDATIONS ................................................................ 116

6 SUMMARY AND CONCLUSIONS............................................................................................. 119

6.1 CURRENT PEAK REACTIVITY METHODS FOR SPENT FUEL POOLS ....................... 119

6.2 PEAK REACTIVITY ANALYSIS SUMMARY.................................................................. 120

6.3 VALIDATION OF CASK REACTIVITY CALCULATIONS SUMMARY......................... 121

6.4 ISOTOPIC VALIDATION SUMMARY ............................................................................. 121

6.5 CONCLUSIONS ................................................................................................................. 122

7 REFERENCES ............................................................................................................................. 125

APPENDIX A. TRITON DEPLETION MODELING DETAILS.........................................................A-1

APPENDIX B. GADOLINIUM PATTERNS ......................................................................................B-1

APPENDIX C. EXPERIMENTS CONSIDERED................................................................................C-1

APPENDIX D. CRITICAL EXPERIMENTS WITH CK VALUES NO LESS THAN 0.8.....................D-1

APPENDIX E. VALIDATION DATA ................................................................................................ E-1

APPENDIX F. ISOTOPIC VALIDATION DATA ...............................................................................F-1
vii

LIST OF FIGURES

Page

Figure 2.1. Example BWR fuel assembly containing seven lattices [5]. ................................................5

Figure 2.2. Reactivity trajectories for a BWR fuel assembly with different gadolinium loadings...........6

Figure 2.3. Sample correlation of krack and SCCG kinf [3]. (used by permission) ....................................8

Figure 2.4. Correlations of krack vs. SCCG kinf for a range of fuel design types [7]. .............................. 11

Figure 2.5. Variation in kinf (SCCG) with burnup without gadolinium for 4.90% fuel [8]. ................... 12

Figure 2.6. krack vs. burnup for a range of gadolinium loadings [4]...................................................... 13

Figure 2.7. Interpolation of minimum gadolinium loading requirement [4]. ........................................ 14

Figure 3.1. SCALE sequences, modules, and codes used for calculations. .......................................... 18

Figure 3.2. Example of GBC-68 half cask model................................................................................ 22

Figure 3.3. Detailed representation of a single storage cell in the GBC-68 cask model........................ 22

Figure 3.4. GE14 full and vanished lattices in reactor geometry.......................................................... 24

Figure 3.5. Full and vanished lattice layouts for the GE14 assembly [5]. ............................................ 25

Figure 3.6. 2D Cask kinf as a function of burnup for fuel with no initial gadolinium loading and 

three nuclide sets, AEAI modeling strategy. ..................................................................... 27

Figure 3.7. 2D Cask kinf as a function of burnup for fuel initially containing six pins with 2 

wt% gadolinium and four nuclide sets, AEAI modeling strategy....................................... 29

Figure 3.8. Gadolinium-free lattice layout for the full and vanished lattices. ....................................... 32

Figure 3.9. Two gadolinium pin layout for the full and vanished lattices............................................. 33

Figure 3.10. Four gadolinium pin layout for the full and vanished lattices. ........................................... 33

Figure 3.11. Six gadolinium pin layout for the full and vanished lattices............................................... 34

Figure 3.12. Eight gadolinium pin layout for the full and vanished lattices. .......................................... 34

Figure 3.13. TRITON eigenvalue trajectories for the PEPI isotopic strategy varying the 

gadolinium content and number of gadolinium pins.......................................................... 36

Figure 3.14. Dominating cross sections in gadolinium-bearing fuel pins............................................... 37

Figure 3.15. (a) Percentage of 155Gd remaining as a function of radial location in the fuel pin for 

the 6×2Gd, 6×4Gd, 6×6Gd, 6×8Gd, and 6×10Gd cases at 10 GWd/MTU and 

(b) eigenvalue trajectories for the 6-gadolinium pin cases. ................................................ 38

Figure 3.16. Cask kinf as a function of burnup for 2 wt% gadolinium in a range of pins, 

AO nuclides. .................................................................................................................... 39

Figure 3.17. Cask kinf as a function of burnup for 2 wt% gadolinium in a range of pins, 

AFP nuclides.................................................................................................................... 40

Figure 3.18. Cask kinf as a function of burnup for gadolinium pins with a range of initial 

gadolinium loadings, AO nuclides.................................................................................... 41

Figure 3.19. Cask kinf as a function of burnup for six gadolinium pins with a range of initial 

gadolinium loadings, AFP nuclides. ................................................................................. 42

Figure 3.20. Cask kinf as a function of burnup for all 15 patterns, AO nuclide set. ................................. 44

Figure 3.21. Cask kinf as a function of burnup for all 15 patterns, AFP nuclide set................................. 45

Figure 3.22. Gadolinium patterns 2 (P2)............................................................................................... 46

Figure 3.23. Gadolinium patterns 3 (P3)............................................................................................... 47

Figure 3.24. Gadolinium patterns 9 (P9)............................................................................................... 47

Figure 3.25. Gadolinium patterns 5 (P5)............................................................................................... 48

Figure 3.26. Cask kinf as a function of burnup for several depletion moderator void fractions, 

AO nuclide set. ................................................................................................................ 49

Figure 3.27. 239Pu atom density as a function of burnup for several depletion moderator 

void fractions. .................................................................................................................. 50
viii

Figure 3.28. Cask kinf as a function of burnup for several depletion moderator void fractions, 

AFP nuclide set................................................................................................................ 51

Figure 3.29. 155Gd atom density as a function of burnup for several depletion moderator 

void fractions. .................................................................................................................. 52

Figure 3.30. Cask kinf as a function of burnup for several depletion moderator void fractions and 

rodded depletion, AO nuclide set...................................................................................... 53

Figure 3.31. 239Pu atom density as a function of burnup for several depletion moderator void 

fractions, rodded depletion. .............................................................................................. 54

Figure 3.32. Cask kinf as a function of burnup for several depletion moderator void fractions, 

rodded depletion, AFP nuclide set. ................................................................................... 55

Figure 3.33. Cask kinf as a function of burnup for several depletion moderator void fractions and 

the AFP nuclide set, comparing rodded and unrodded depletion........................................ 56

Figure 3.34. 235U concentration difference (in percent) between rodded and unrodded cases. ................ 57

Figure 3.35. 155Gd concentration difference (in percent) between rodded and unrodded cases. .............. 57

Figure 3.36. 155Gd atom density as a function of burnup for several depletion moderator void 

fractions and rodded depletion.......................................................................................... 58

Figure 3.37. 155Gd atom density over a range of burnup for rodded and unrodded depletion with 

0% and 80% void. ............................................................................................................ 59

Figure 3.38. Cask kinf as a function of burnup at 25 W/g for different fuel temperatures, AO 

nuclide set........................................................................................................................ 61

Figure 3.39. Cask kinf as a function of burnup at 25 W/g for different fuel temperatures, AFP 

nuclide set........................................................................................................................ 63

Figure 3.40. Cask kinf as a function of burnup for different specific powers with 950 K fuel 

temperature, AO nuclide set. ............................................................................................ 65

Figure 3.41. Cask kinf as a function of burnup for different specific powers with 950 K fuel 

temperature, AFP nuclide set............................................................................................ 67

Figure 3.42. Cask kinf as a function of burnup for four different operating histories, AO 

nuclide set........................................................................................................................ 70

Figure 3.43. Cask kinf as a function of burnup for four different operating histories, AFP 

nuclide set........................................................................................................................ 71

Figure 3.44. Cask reactivity as a function of burnup, unrodded depletion with 40% void fraction, 

all nuclide sets.................................................................................................................. 72

Figure 3.45. Cask reactivity as a function of burnup, rodded depletion with 0% void fraction, all 

nuclide sets. ..................................................................................................................... 73

Figure 4.1. ck values for critical experiments compared to GBC-68 with vanished lattice and 

AO nuclides. .................................................................................................................... 85

Figure 4.2. ck values greater than or equal to 0.8 with vanished lattice and AO nuclides. .................... 86

Figure 4.3. ck values for critical experiments compared to GBC-68 with vanished lattice and 

AFP nuclides.................................................................................................................... 87

Figure 4.4. ck values greater than or equal to 0.8 with vanished lattice and AFP nuclides.................... 88

Figure 4.5. Sensitivity profile comparison for 155Gd between GBC-68 with vanished lattice and 

LEU-COMP-THERM-005-010. ....................................................................................... 89

Figure 4.6. Values for critical experiments compared to GBC-68 with full lattice and 

AFP nuclides.................................................................................................................... 90

Figure 4.7. ck values greater than or equal to 0.8 with full lattice and AFP nuclides. ........................... 91

Figure 4.8. Changes in ck values between vanished lattice and full lattice. .......................................... 92

Figure 4.9. C/E trend and limits as a function of enrichment............................................................... 95

Figure 4.10. C/E trend and limits as a function of EALF. ..................................................................... 96

Figure 4.11. C/E trend and limits as a function of ck. ............................................................................ 97

Figure 5.1. Illustration of the BWR fuel assembly in application model and fuel rod 

mixture locations............................................................................................................ 105
ix

Figure 5.2. Relative neutron absorption fractions in typical UO2 fuel with gadolinium. [38] ............. 106

Figure 5.3. keff relative sensitivity coefficients (absolute) for the BWR application model at 

peak reactivity for actinides, fission products, and residual 155Gd.................................... 107

Figure A.1. Lattice layout highlighting the three different sets of Dancoff factors used in this 

SCALE/TRITON analysis..............................................................................................A-1

Figure A.2. PEPI lattice layout (left) and SCALE/TRITON representation (right). ............................A-2

Figure A.3. AEPI lattice layout (left) and SCALE/TRITON representation (right).............................A-3

Figure A.4. Visual depiction of the grouping of depletion mixtures based on Dancoff factor for 

4.40 wt% fuel.................................................................................................................A-3

Figure A.5. PEAI lattice layout (left) and SCALE/TRITON representation (right).............................A-4

Figure A.6. AEAI lattice layout (left) and SCALE/TRITON representation (right)............................A-4

Figure B.1. Gadolinium patterns 0 (same as used in the Gd-loading study, P0)..................................B-1

Figure B.2. Gadolinium patterns 1 (P1).............................................................................................B-1

Figure B.3. Gadolinium patterns 2 (P2).............................................................................................B-2

Figure B.4. Gadolinium patterns 3 (P3).............................................................................................B-2

Figure B.5. Gadolinium patterns 4 (P4).............................................................................................B-3

Figure B.6. Gadolinium patterns 5 (P5).............................................................................................B-3

Figure B.7. Gadolinium patterns 6 (P6).............................................................................................B-4

Figure B.8. Gadolinium patterns 7 (P7).............................................................................................B-4

Figure B.9. Gadolinium patterns 8 (P8).............................................................................................B-5

Figure B.10. Gadolinium patterns 9 (P9).............................................................................................B-5

Figure B.11. Gadolinium patterns 10 (P10).........................................................................................B-6

Figure B.12. Gadolinium patterns 11 (P11).........................................................................................B-6

Figure B.13. Gadolinium patterns 12 (P12).........................................................................................B-7

Figure B.14. Gadolinium patterns 13 (P13).........................................................................................B-7

Figure B.15. Gadolinium patterns 14 (P14).........................................................................................B-8

Figure F.1. Burnup vs. enrichment for available BWR RCA data.......................................................F-2

Figure F.2. Effect of void fraction change (-10%) on isotopic content for 5 GWd/MTU BWR 

fuel. ................................................................................................................................F-3

Figure F.3. JPDR core map [F1]........................................................................................................F-6

Figure F.4. JPDR samples axial locations [F1]...................................................................................F-7

Figure F.5. Illustration of SCALE/TRITON model for JPDR assembly. ............................................F-8

Figure F.6. Diagram of assembly C16 enrichment profile [F1]...........................................................F-9

Figure F.7. Illustration of SCALE/TRITON model for Gundremmingen sample C16-B3.................F-11

Figure F.8. Radial loading diagram of assembly 2F2DN23..............................................................F-13

Figure F.9. Measurement positions for rod SF99. ............................................................................F-13

Figure F.10. Illustration of SCALE/TRITON model for Fukushima Daini-2 SF99 samples................F-15

Figure F.11. Illustration of SCALE/TRITON model for Ohi-2 assembly. ..........................................F-18

Figure F.12. Variation with burnup of (C/M-1) for 235U and 239Pu......................................................F-20

xi

LIST OF TABLES

Page

Table 3.1. Nuclides included in the three sets of BUC isotopes considered........................................ 20

Table 3.2. All TRITON default nuclides included in depletion calculations (ALL) (94 total 

nuclides, TRITON “addnux=2” nuclides) [11].................................................................. 20

Table 3.3. Uncertainty in keff due to uncertainty in nuclear data for BUC application models ............ 21

Table 3.4. Change in cask kinf, AEAI-AEPI, zero initial gadolinium .................................................. 27

Table 3.5. Change in cask kinf, AEAI-PEAI, zero initial gadolinium .................................................. 28

Table 3.6. Change in cask kinf, AEAI-PEPI, zero initial gadolinium................................................... 28

Table 3.7. Change in cask kinf, AEAI-AEPI, six rods with 2 wt% initial gadolinium .......................... 30

Table 3.8. Change in cask kinf, AEAI-PEAI, six rods with 2 wt% initial gadolinium .......................... 30

Table 3.9. Change in cask kinf, AEAI-PEPI, six rods with 2 wt% initial gadolinium........................... 30

Table 3.10. Number of pins and gadolinium content per pin................................................................ 32

Table 3.11. Cask kinf values for various patterns with the AO nuclide set............................................. 44

Table 3.12. Cask kinf values for various patterns with the AFP nuclide set ........................................... 46

Table 3.13. Fuel temperatures, specific powers, and operating histories .............................................. 60

Table 3.14. Cask Δkinf values for 25 W/g depletion case, 950 K base case, AO nuclide set .................. 62

Table 3.15. Cask Δkinf values for 35 W/g depletion case, 950 K base case, AO nuclide set .................. 62

Table 3.16. Cask Δkinf values for 45 W/g depletion case, 950 K base case, AO nuclide set .................. 62

Table 3.17. Cask Δkinf values for 25 W/g case, 1100 K ̶ 850 K, AO nuclide set.................................. 62

Table 3.18. Cask Δkinf values for 25 W/g depletion case, 950 K base case, AFP nuclide set................. 64

Table 3.19. Cask Δkinf values for 35 W/g depletion case, 950 K base case, AFP nuclide set................. 64

Table 3.20. Cask Δkinf values for 45 W/g depletion case, 950 K base case, AFP nuclide set................. 64

Table 3.21. Cask Δkinf values for 25 W/g case, 1100 K ̶ 850 K, AFP nuclide set .................................. 64

Table 3.22. Cask Δkinf values for 35 W/g and 45 W/g, 850 K fuel temperature, AO nuclide set............ 66

Table 3.23. Cask Δkinf values for 35 W/g and 45 W/g 950 K fuel temperature, AO nuclide set ............ 66

Table 3.24. Cask Δkinf values for 35 W/g and 45 W/g 1100 K fuel temperature, AO nuclide set........... 66

Table 3.25. 235U and 239Pu number densities for different specific powers and 950 K fuel 

temperature ...................................................................................................................... 67

Table 3.26. Cask Δkinf values for 35 W/g and 45 W/g, 850 K fuel temperature, AFP nuclide set .......... 68

Table 3.27. Cask Δkinf values for 35 W/g and 45 W/g, 950 K fuel temperature, AFP nuclide set .......... 68

Table 3.28. Cask Δkinf values for 35 W/g and 45 W/g, 1100 K fuel temperature, AFP nuclide set ........ 68

Table 3.29. 149Sm number densities at a range of specific powers and 950 K fuel temperature............. 69

Table 3.30. Difference between 2D cask kinf and 3D cask keff, unrodded depletion with 40% 

void fraction..................................................................................................................... 73

Table 3.31. Difference between 2D cask kinf and 3D cask keff, rodded depletion with 0% void 

fraction ............................................................................................................................74

Table 3.32. Summary of parameters affecting discharged reactivity for BWR peak reactivity 

analysis considering the AO nuclide set............................................................................ 75

Table 3.33. Summary of parameters affecting discharged reactivity for BWR peak reactivity 

analysis considering the AFP nuclide set .......................................................................... 76

Table 4.1. Bias and bias uncertainty values....................................................................................... 94

Table 4.2. Uncertainty contributions from major transuranic nuclides ............................................... 99

Table 4.3. Uncertainty contribution from 155Gd............................................................................... 100

Table 4.4. Uncertainty contribution from major fission products and minor actinides...................... 101

Table 5.1. Evaluated experimental spent fuel nuclide data............................................................... 110
xii

Table 5.2. Isotopic bias and bias uncertainty values associated with calculated BWR isotopic 

concentrations................................................................................................................ 113

Table 5.3. keff results and margin for uncertainty for the GBC-68 cask model ................................. 116

Table C.1. Critical experiments considered for validation ................................................................C-1

Table D.1. Experiments with a ck no less than 0.8, vanished lattice – actinide only..........................D-1

Table D.2. Experiments with a ck no less than 0.8, vanished lattice – actinides and fission 

products.........................................................................................................................D-2

Table D.3. Experiments with a ck no less than 0.8, full lattice – actinides and fission products ........D-3

Table E.1. Validation data for vanished lattice with actinides and fission products........................... E-1

Table F.1. Sources of RCA data for BWR isotopic validation...........................................................F-1

Table F.2. Selected RCA isotopic validation data set........................................................................F-4

Table F.3. JPDR assembly design data [F1, F2] ...............................................................................F-6

Table F.4. JPDR samples data [F1, F2] ............................................................................................F-7

Table F.5. Comparison calculation-measurement for JPDR samples................................................F-8

Table F.6. Gundremmingen-A assembly design data ......................................................................F-10

Table F.7. Gundremmingen-A samples data...................................................................................F-10

Table F.8. Comparison calculation-measurement for Gundremmingen-A samples..........................F-11

Table F.9. Fukushima-Daini-2 assembly design data ......................................................................F-14

Table F.10. Fukushima-Daini-2 samples data...................................................................................F-14

Table F.11. Comparison calculation-measurement for Fukushima Daini-2 samples..........................F-15

Table F.12. Ohi-2 assembly design data [F8] ...................................................................................F-17

Table F.13. Ohi-2 samples data........................................................................................................F-17

Table F.14. Comparison calculation-measurement for Ohi-2 samples (actinides).............................F-19

Table F.15. Comparison calculation-measurement for Ohi-2 samples (Gd).......................................F-19

Table F.16. Statistical data for the BWR samples (BUC nuclides)...................................................F-20
xiii

LIST OF ACRONYMS AND UNITS

2D two-dimensional

3D three-dimensional

ADSNF assay data of spent nuclear fuel

AE average enrichment

AEAI average enrichment with average isotopics

AEPI average-enrichment with pin-wise isotopics

AFP actinides and fission products (includes minor actinides and major fission 

products)

AFPNG actinides and fission products with no gadolinium

AI average isotopics

ALL all nuclides in depletion calculations

ANS American Nuclear Society

ANSI American National Standards Institute

AO actinide-only

BOL beginning of life

BUC burnup credit

BWR boiling water reactor

C/E calculated-to-expected

CFR Code of Federal Regulations

COMP solid composition (fuel form)

CSN Consejo de Seguridad Nuclear [Spanish Nuclear Safety Council]

DICE Database for the International Criticality Safety Benchmark Evaluation Project

EALF energy of average lethargy of fission

EGBUC Expert Group on Burnup Credit Criticality Safety

FHP full power followed by half power

FP full power

FTHP full power followed by three-quarter power followed by half-power

GBC generic burnup credit cask

GWd gigawatt days

HFP hot full power

HP half power

HTC French Haut Taux de Combustion

IHECSBE International Handbook of Evaluated Criticality Safety Benchmark 

Experiments

ISG Interim Staff Guidance

JAEA Japanese Atomic Energy Agency

JAERI Japanese Atomic Energy Research Institute

JENDL Japanese Evaluated Nuclear Data Library

JPDR Japan Power Demonstration Reactor

LCT LEU-COMP-THERM

LEU low enriched uranium

MCT MIX-COMP-THERM

MIX mixed uranium/plutonium
xiv

MOX mixed oxide 

MST MIX-SOL-THERM

MTU metric ton of uranium

NEA Nuclear Energy Agency

NRA Nuclear Regulation Authority [Japan]

NRC U.S. Nuclear Regulatory Commission

NSC Nuclear Science Committee

OECD Organisation for Economic Co-operation and Development

ORNL Oak Ridge National Laboratory

PE pin-wise initial enrichment

PEAI pin-wise enrichment with average isotopics

PEPI pin-wise enrichment with pin-wise isotopics

PI pin-wise isotopics

PIE postirradiation examination

PLE plenum

PSZ power shaping zone

PWR pressurized water reactor

RCA radiochemical assay

REGAL Rod Extremity and Gadolinia AnaLysis

SAMS Sensitivity Analysis Module for SCALE

SCALE Standardized Computer Analyses for Licensing Evaluation

SCCG standard cold core geometry

SCK•CEN Studiecentrum voor Kernenergie 

SDF sensitivity data file

SFCOMPO Spent Fuel Isotopic Composition Database

SFP spent fuel pool

SNF spent nuclear fuel

S/U sensitivity/uncertainty

SWAT Step Wise Burnup Analysis Code System

TEPCO Tokyo Electric Power Company

THERM thermal (flux spectrum)

TRITON two-dimensional transport and depletion module for characterization of spent 

nuclear fuel

TSUNAMI Tools for Sensitivity and Uncertainty Analysis Methodology Implementation

TSUNAMI-IP TSUNAMI-Indices and Parameters

USL upper safety limit

USLSTATS Upper Safety Limit Statistics

VALID Verified, Archived Library of Inputs and Data (SCALE)

V vanished rod location

WPNCS Working Party of Nuclear Criticality Safety

WR water rod (location)
1

1 INTRODUCTION

Criticality safety analyses of fuel assemblies in spent nuclear fuel (SNF) storage and 

transportation systems are performed to demonstrate that these systems are adequately subcritical 

per the requirements of Title 10 of the Code of Federal Regulations (CFR) Parts 71 and 72 [1]. 

The U.S. Nuclear Regulatory Commission (NRC) staff reviews analyses of pressurized water 

reactor (PWR) SNF that credit the reduction in assembly reactivity caused by depletion of fissile 

nuclides and buildup of neutron absorbing nuclides during power operation using guidance in the 

Division of Spent Fuel Storage and Transportation Interim Staff Guidance (ISG) 8, 

Revision 3 [2]. This credit for reactivity reduction during depletion is commonly referred to as 

“burnup credit” (BUC). Such credit for boiling-water reactor (BWR) SNF is not addressed in 

ISG-8. The focus of this report is to document studies performed to provide a technical basis for 

the review of BWR peak reactivity methods in dry storage casks and transportation packages, 

hereafter referred to as “casks.”

The analysis of SNF in spent fuel pools (SFPs), as regulated by 10 CFR Part 50, allows a 

combination of BUC and credit for residual burnable absorber in BWR fuel. However, analysis 

of BWR SNF in casks currently assumes fresh fuel with no burnable absorber. Most BWR fuel 

assemblies contain gadolinium oxide (Gd2O3, or gadolinium) burnable absorber in some fuel 

rods, so reactivity increases early in assembly irradiation before reaching a peak and 

subsequently decreases until end of life. The early increase in reactivity results from the more 

rapid depletion of the burnable absorber than the fuel. A BWR BUC method that takes credit for 

gadolinium must consider this effect. This type of analysis is known as a peak reactivity method. 

Some peak reactivity methods correlate the peak reactivity value in storage to the infinite 

multiplication factor (kinf) in the standard cold core geometry (SCCG). These techniques are also 

referred to as using an SCCG approach. The SCCG is an infinite planar array of fuel assemblies 

in reactor geometry, typically a 6-inch pitch, flooded with full density water at 20°C. The peak 

reactivity methods are also sometimes called “gadolinium credit,” as some residual burnable 

absorber material is typically credited. The peak reactivity methods used most frequently in SFP 

analyses for BWR SNF are reviewed in Section 2 as a background for development of a 

technical basis for the application of peak reactivity methods to BWR SNF casks.

This report presents (1) an examination of the lattice design and operating parameters that affect 

the burnup and the effective multiplication factor (keff) value associated with the peak reactivity 

in storage and transportation configurations, (2) validation of these reactivity calculations, and 

(3) validation of the BWR SNF nuclide concentrations in terms of impact on keff. Each of these 

three areas is investigated in this report. The analysis of design and depletion parameters 

affecting peak reactivity is presented in Section 3, “Factors Affecting Peak Reactivity,” while the 

validations of reactivity determinations and isotopic inventories are presented in Section 4, 

“Validation of Cask Reactivity Calculations,” and Section 5, “Validation of BWR Isotopic 

Concentrations near Peak Reactivity.” A final summary is presented in Section 6, “Summary and 

Conclusions.”

3

2 CURRENT PEAK REACTIVITY METHODS

Although no BUC methods are currently applied to BWR SNF casks, a range of methods has 

been developed and implemented over the last 20 years for analysis of BWR fuel in SFPs at 

nuclear power plants. Two different methods have been used to qualify the vast majority of the 

current discharged inventory. The methods create a correlation between the neutron 

multiplication factor (kinf or keff) in the storage rack and the SCCG kinf [3, 4]. For simplicity, this 

report will refer to the storage rack kinf or keff as “krack.” This correlation is used to determine the 

maximum SCCG kinf that can be shown to meet the regulatory limits for the storage rack; thus, 

implementation is based on limiting the SCCG kinf. The primary advantages of this methodology 

are that a single limit exists that covers storage of fuel at any burnup and that the SCCG kinf is 

calculated by BWR fuel vendors as part of the reload analysis process. Because the maximum 

SCCG kinf over all burnups is shown to be lower than the limit, it can therefore be implemented 

as a constraint on bundle design to ensure that all assemblies can be stored at the plant. These 

two most common methods will be discussed in Sections 2.2 and 2.3.

For completeness, other peak reactivity methods are also noted. These methods are either under 

development or in limited use currently at BWR power plants.

2.1 GENERAL CONSIDERATIONS FOR PEAK REACTIVITY 

ANALYSES

All of the peak reactivity methods used in SFP analyses share common characteristics and 

approaches. These similarities are driven by the physics of the BWR fuel being analyzed and by 

the regulatory requirements that must be met.

BWR fuel assemblies consist of multiple axial zones. Each unique axial zone is identified by the 

number of fuel rods, the enrichment of the fuel in each lattice location, and the number and 

loading of gadolinium rods. Each unique axial zone within the same assembly is referred to as a 

“lattice.” Modern BWR designs include part-length fuel rods. Lower lattices contain fuel rods in 

all locations, but lattices at higher elevations have empty fuel rod locations. The top and bottom 

axial zones contain reduced or natural enrichment blankets that are typically about 6 inches long. 

The full lattices above the bottom blanket are usually referred to as “power-shaping zone” and 

“dominant” lattices. Lattices with empty fuel rod locations are referred to as “vanished” lattices; 

some fuel designs contain multiple vanished lattices with differing numbers of fuel rods. 

Additionally, plenum lattices exist in axial elevations in the plenum region of the part-length 

rods. An example of a fuel assembly layout with seven unique lattices is shown in Figure 2.1, 

adapted from Fensin, “Optimum BWR Fuel Design Strategies to Enhance Reactor Shutdown by 

the Standby Liquid Control System” [5].

The reactivity behavior of BWR fuel assemblies as a function of fuel burnup is the primary 

consideration in all analyses and is thus examined here in additional detail. As mentioned 

previously, nearly all BWR fuel contains gadolinium burnable absorber fuel rods. The 

gadolinium loading in each assembly is determined by selecting the number of rods containing 

gadolinium and the enrichment in weight percent of gadolinium loaded in each rod. The location 

of the gadolinium rods within the assembly lattice also affects the depletion of the absorber. For 
4

example, gadolinium loaded in areas of increased moderation, such as areas near water holes or 

bypass channels, depletes faster because of its large thermal absorption cross section. These 

differences impact the fuel assembly reactivity trajectory as a function of burnup. This reactivity 

trajectory is of utmost importance in peak reactivity methods because the reactivity of the fuel 

assembly at the peak is dependent upon the burnup where the peak occurs.
5

Figure 2.1. Example BWR fuel assembly containing seven lattices [5].
6

Peak reactivity typically occurs at burnups less than ~20 gigawatt days per metric ton of uranium 

(GWd/MTU) for modern fuel assembly designs. After equilibrium xenon is established, during 

the first ~100 hours at full power, the reactivity of fuel without gadolinium decreases nearly 

linearly. The addition of gadolinium to the fuel results in a lower initial reactivity that increases 

to a peak as the gadolinium depletes, then merges with a similar trajectory to that of fuel without 

gadolinium until the end of life. Examples of this behavior are shown in Figure 2.2, which 

compares depletion of fuel without gadolinium and with two different gadolinium loadings. The 

reactivity curves of the gadolinium-loaded assemblies are virtually the same as the gadoliniumfree assembly after peak reactivity. A comparison of light and heavy gadolinium loadings shows 

that the earlier peak for the light loading (less gadolinium rods with lower gadolinium 

enrichment) is significantly higher than the later peak experienced in the heavier loading (more 

gadolinium rods with higher gadolinium enrichment). The factors that affect gadolinium 

depletion are the most important parameters for peak reactivity analyses because they impact 

when the peak occurs and thus the magnitude of the peak reactivity. The design and depletion 

parameters affecting peak reactivity are explored in detail in Section 3. 

Figure 2.2 also illustrates the relative importance of credits for both fuel burnup and residual 

gadolinium. The credit for burnup is essentially the reactivity difference between fresh fuel 

conditions and the conditions at the assumed burnup of peak reactivity for the fuel without 

gadolinium. The credit for residual gadolinium is the difference in reactivity between the fuel 

with and without gadolinium at the burnup of peak reactivity. Although this figure shows the 

relative magnitudes of these credits for different core depletion conditions, the magnitudes of 

these credits in rack conditions are similar.

Figure 2.2. Reactivity trajectories for a BWR fuel assembly with different gadolinium loadings.

1.15

1.20

1.25

1.30

1.35

1.40

1.45

0 5 10 15 20

Hot Full Power kinf

Burnup (GWd/MTU)

No Gadolinium Light Gadolinium Heavy Gadolinium
7

Little information is available in the open literature on the nuclides credited in peak reactivity 

methods. Typical commercial lattice codes include TGBLA, CASMO, or PHOENIX. The 

nuclides included in the BWR SNF compositions depend on the depletion code and code version. 

More recently, BWR SFP analyses have implemented a generic depletion uncertainty of 5% of 

the reactivity difference between fresh fuel with no gadolinium and fuel at peak reactivity based 

on the Kopp Letter [6].

Each method includes reactivity allowances for biases and uncertainties. The biases typically 

come from the criticality code validation. The uncertainties are typically derived from 

manufacturing tolerances on the fuel assembly and on the storage rack, the uncertainty in the 

code bias, an allowance for eccentric positioning of assemblies in the storage cells, the use of 

different codes to calculate SCCG kinf and krack, and uncertainty in the Monte Carlo estimate of 

krack. The number of allowances used, the processes used to determine them, and their 

magnitudes vary among the various methods. The uncertainties are typically combined using the

square root of the sum of the squares of the independent uncertainty allowances. The calculated 

best estimate krack value is then combined with these allowances to demonstrate that the 

regulatory limit of 0.95 specified in 10 CFR 50.68 [1] is met. The evaluation of these biases and 

uncertainties is an essential part of the criticality analysis but is not described in detail in this 

section, as the same general techniques are used for all methods currently implemented in BWR 

SFP analyses.

The storage rack calculation is typically performed for a two-dimensional (2D) model of the 

storage rack and fuel assembly using the most reactive lattice with reflective boundary 

conditions, but some three-dimensional (3D) models have also been used. The resulting 

calculated krack values can therefore be either kinf (2D models) or keff (3D models). The 

conservatism of the 2D model compared to the 3D model is examined in Section 3.4.7.

There are two primary SCCG methods, and each uses a different approach. One method uses a 

range of operating conditions and different lattices as well as credit for residual gadolinium. The 

other method uses limiting operating conditions and does not credit gadolinium. These methods 

are described in the following two subsections.

2.2 SCCG LIMIT WITH GADOLINIUM CREDIT

The SCCG-limit-with-gadolinium-credit method gives credit for residual gadolinium and 

examines several different lattices including a range of enrichments, gadolinium loadings, and 

gadolinium patterns over multiple burnups. This method is described in a case study presented in 

“Uncertainty Contribution to Final In-Rack k(95/95) from the In-Core k∞ Criterion 

Methodology for Spent Fuel Storage Rack Criticality Safety Analyses” (Hannah et al) [3]. The 

krack calculations use a range of fuel lattice designs, enrichments, and gadolinium loadings. A 

range of depletion conditions is studied, including different lattice types, burnups, enrichments, 

gadolinium loadings, and void fractions. The SCCG kinf and the krack are calculated for each 

lattice at a range of burnups, and these data are used to create a single correlation between krack

and SCCG kinf. The correlation is intended to cover the full range of lattices, enrichment, and 

gadolinium loadings that could conceivably be used in the core, and therefore includes a variety 

of designs to cover each of these parameters. A limiting case is identified from the calculated 

results as a peak reactivity that is near but greater than the desired SCCG kinf limit. Finally, this 
8

case is demonstrated to meet regulatory requirements for fuel storage. Each of these steps is 

examined further, and then a summary of the method is presented.

This method uses a lattice average enrichment. The considered lattice average enrichments range 

from 2.8 to 4.9 wt% 235U [3]. Various gadolinium loadings are considered, including a case with 

no burnable absorber loading. The void fraction is the only depletion parameter that is explicitly 

varied.

The results from these calculations are used to generate a correlation between krack and SCCG 

kinf. The uncertainty in the correlation is determined to establish a 95% confidence, 95% 

probability (95/95) upper bound on the correlation [3]. Figure 2.3 [3] shows the best estimate 

correlation as a solid line and the 95%/95% upper bound as a dashed line. The nominal value for 

krack is determined through the nominal correlation, and the uncertainty is combined with the 

other applicable uncertainties in the analysis generated with the design basis lattice.

Figure 2.3. Sample correlation of krack and SCCG kinf [3]. (used by permission)

As described above, this design basis lattice is selected from points on the correlation that are 

near but greater than the proposed SCCG kinf limit. The consideration of only points that are 

above the proposed SCCG kinf limit ensures that a reactive lattice is used and adds conservatism 

to the analysis by explicitly demonstrating that an assembly that should not be placed in the rack 

can be stored safely. The lattice that generates the highest rack efficiency of the candidates near 

but over the limit is selected as the design basis lattice. The rack efficiency is calculated by 

dividing krack by the SCCG kinf, and it serves to normalize the krack values for differences in 

SCCG kinf. The rack efficiency changes from one lattice to another based on neutron spectrum 

and residual gadolinium content, which impact the worth of the neutron absorber panels in the 

rack and communication among assemblies. For example, two lattices with the same krack values 
9

might have different SCCG kinf values; the lattice with the lower SCCG kinf is of more concern 

and is properly identified because of its higher efficiency. The goal is to identify the lattice with 

the highest krack value that also has a SCCG kinf at or just above the proposed limit. This design 

basis lattice is used in the evaluation of manufacturing tolerances, biases, and uncertainties. 

The final step is to combine the biases and uncertainties calculated for the design basis assembly, 

the code predictions, and the correlation method to demonstrate that the design basis lattice 

meets regulatory requirements for fuel storage. The terms are combined as described in the 

following equation:

K(95/95) = KNominal + ∆KBias + ∆KTolerance + ∆KUncertainty (3)

The KNominal term is derived from the correlation, and the remaining terms ∆KTolerance, ∆KBias, and 

∆KUncertainty are determined by the tolerance calculations, the code prediction validation study, 

and the correlation uncertainty, respectively. If the resulting K(95%/95%) value does not meet 

the regulatory requirements, a new lower SCCG kinf limit is proposed, and the process is 

repeated.

This method has some benefits. First, it uses real lattice designs in the generation of the 

correlation curve. This is feasible as the method is used by a BWR fuel vendor, and thus the 

analysts have access to a large number of lattice designs. The method also explicitly considers a 

range of assembly design and operating conditions including gadolinium loadings, enrichment, 

and void fractions. The inclusion of the uncertainty of the fit in the assessment of K(95%/95%) is 

also a strength. The method also allows storage of fuel with comparison against one limit. Other 

methods in SFP analysis use a combination of two or three limits on enrichment, gadolinium 

loading, and/or SCCG kinf. The use of a single limit simplifies implementation and reduces the 

probability of mischaracterizing an assembly relative to the limit.

There are also potential areas of concern. The most significant area of concern is the use of 

potentially non-limiting depletion conditions in the generation of the correlation of krack to SCCG 

kinf. This concern applies to the use of multiple void fractions during depletion. A study such as 

the one documented in Section 3.4.4 could be performed to identify the limiting void fraction. 

Using only this single void fraction in the depletion calculations could provide additional 

confidence that the correlation is conservative. The use of potentially non-limiting points is of 

concern as these points would act to lower the correlation. Although these points may also 

increase the uncertainty in the fit, this is likely to be a small effect. A second area of concern is 

the use of points that are far from limiting reactivities. As shown in Figure 2.3, some points used 

in generating the correlation have krack values as low as about 0.4. It is highly desirable that the 

correlation be generated using only points that are near the limit, so that the correlation is based 

on points of direct relevance to the limit. There is significant scatter in the data for these points 

near the limit, although this may be a result of the limited number of lattices considered in the 

case study presented [Fig. 2 of Reference 3].

The SCCG-limit-with-gadolinium-credit methodology has been implemented in several SFPs 

over the last 20 years. The method requires a large number of lattice designs, but the use of real 

lattice designs provides a degree of accuracy in the analysis that is lacking in some of the other 

methods. However, the use of a sizeable number of real lattice designs may be problematic for 
10

implementation by a cask vendor without ready access to a reliable collection of such design 

information. The SCCG-limit-with-gadolinium-credit method attempts to balance some of the 

conservatisms of the peak reactivity methods, such as considering all assemblies to be identical 

and all at peak reactivity, with a less conservative depletion analysis including non-limiting 

depletion conditions and lattices. In summary, the SCCG kinf with gadolinium credit method 

provides a fairly straightforward approach to demonstrating safe storage of BWR fuel 

assemblies.

2.3 SCCG LIMIT WITHOUT GADOLINIUM CREDIT

The SCCG-limit-without-gadolinium credit method uses different limits in different 

implementations. In some cases [7], it includes a maximum enrichment limit, a minimum 

gadolinium requirement limit, and an SCCG kinf limit. In other cases [8], it uses only the 

minimum gadolinium requirement and SCCG limits. The development and application of each of 

these limits are discussed in this section of the report.

The SCCG-limit-without-gadolinium-credit method has historically included a bias of 1% Δk,

along with the other bias and uncertainty terms. This conservatism is primarily intended to cover 

potential discrepancies between SFP criticality vendor calculations of SCCG kinf and fuel vendor 

calculations of SCCG kinf using a different computational code and different gadolinium loadings 

and patterns [4].

The maximum enrichment limit is calculated using fresh fuel with no gadolinium. It is simply the 

highest fresh fuel enrichment with a reactivity that satisfies the regulatory requirement for 

storage. For lattices with average enrichments at or below this limit, no further comparisons are 

necessary to qualify the lattice for storage. The limit is determined by calculating krack over a 

range of enrichments in the storage configuration to determine the limiting enrichment. This 

method is essentially the same one used in licensing BWR storage and transportation casks 

currently under the fresh fuel assumption. 

The SCCG limit is generated in this method in a manner similar to the SCCG-limit-withgadolinium-credit method described in the previous section; however, there are some key 

differences in the methodology details. As with the other SCCG limit, correlations are 

constructed between krack and SCCG kinf. However, this method explicitly generates a separate 

correlation for each fuel design type. An example set of correlations is provided in Figure 2.4. 

Once again, an SCCG kinf limit is proposed and ultimately shown to meet storage requirements 

with krack and appropriate biases and uncertainties.
11

Figure 2.4. Correlations of krack vs. SCCG kinf for a range of fuel design types [7].

The correlation is developed by determining krack and the SCCG kinf for a range of different 

burnups for a uniform lattice of fuel rods without gadolinium using the maximum enrichment 

that occurs in that lattice. The points for this correlation exhibit much more linear behavior than 

that shown in Figure 2.3 because the points come from the depletion of fuel without burnable 

absorbers. Separate depletion calculations are performed for each assembly type of interest, as 

shown in Figure 2.4, and explicit calculations are performed to generate separate correlations for 

full and vanished lattices as necessary. Only the most reactive correlation is used in setting the 

storage limit. Another difference is that sensitivity studies are performed to determine the 

depletion conditions that create the most reactive correlation, and only these limiting depletion 

conditions are used. Because these depletion calculations are performed without gadolinium, the 

limiting conditions will be different from those where the fuel with burnable absorber is 

modeled.

For assemblies with enrichments greater than the maximum enrichment limit, a minimum 

gadolinium loading requirement is needed in the current SFP implementation for fuel with

burnups below the minimum burnup where fuel without burnable absorbers meets the SCCG kinf

limit (Fig. 2.5). For the analysis illustrated in this figure, the minimum burnup for which fuel 

could be stored solely with the SCCG kinf limit is 12.6 GWd/MTU.
12

Figure 2.5. Variation in kinf (SCCG) with burnup without gadolinium for 4.90% fuel [8].

Two different approaches have been used to determine the gadolinium loading requirement. 

Generally, a single combination of minimum rods and minimum gadolinium loading is 

determined, while in some instances, multiple combinations are used to meet regulatory 

requirements. The more common approach generates a limit by performing depletion 

calculations for various combinations of (1) the number of gadolinium-bearing rods and (2) the 

number of gadolinium loadings per rod, as illustrated in the example in Figure 2.6. 

The peak value of krack is plotted versus the gadolinium concentration for each unique number of 

gadolinium-bearing rods, and interpolation is performed to determine at what concentration krack

satisfies regulatory requirements. An example using the results from Figure 2.6 is provided in 

Figure 2.7. In this example from Criticality Safety Evaluation for the Nine Mile Point 2 Rack 

Installation Project, it was shown that six rods with 4.2 wt% gadolinium would meet the loading 

requirements [7]. The less common approach simply selects combinations that meet the loading 

limit. For example, if the limit on krack is 0.92, then Figure 2.6 would indicate that either six rods 

with 5 wt% gadolinium would be acceptable or eight rods with 4 wt% gadolinium would be 

acceptable. In both approaches, additional gadolinium rods and/or additional gadolinium loading 
13

increases the reactivity margin, so these gadolinium loading specifications are the minimum 

requirements.

Figure 2.6. krack vs. burnup for a range of gadolinium loadings [4].
14

Figure 2.7. Interpolation of minimum gadolinium loading requirement [4].

The SCCG-limit-without-gadolinium-credit method has some benefits. The method adds 

conservatism relative to the other peak reactivity methods beyond the minimum required burnup 

by not modeling gadolinium poison in the fuel. The margin added by neglecting the residual 

gadolinium poison is small, but this approach allows the use of a single lattice for each fuel 

design type. This simplifies the analysis by significantly reducing the number of depletion 

calculations needed to generate the correlation between krack and SCCG kinf. The use of only 

limiting depletion conditions is also conservative, and using a single set of depletion conditions 

eliminates scatter in the correlation of krack and SCCG kinf. Furthermore, using the correlation 

from the bounding assembly design type and lattice adds another layer of conservatism, and it 

also simplifies the analysis by eliminating interface conditions between different assembly 

design types in storage.

This method also presents areas of concern. It is a more complicated method for implementation 

as it requires multiple limits that apply in different burnup regimes. For this method to be 

executed properly, the depletion conditions used to determine the gadolinium loading 

requirements would be different from those without gadolinium that are used to determine the 

SCCG kinf correlation. Sensitivity studies would need to be performed and documented to 

demonstrate that both sets of depletion conditions are conservative in their respective areas of 

applicability. No basis has been presented for the magnitude of the 1% penalty for differences 

between calculated SCCG kinf values. A method that does not credit residual gadolinium in 
15

storage also presents an advantage since validation of the depleted gadolinium is not required 

because the material is not credited.

The primary drawback to this method is the complexity of multiple limits and the differing 

depletion conditions necessary in the analysis. The simplicity of performing depletion 

calculations only for fuel with no burnable absorbers is offset by the requirement to consider the 

presence of gadolinium at low burnup. The use of different sets of depletion parameters for 

different limits may increase the complexity of the necessary validation effort for depleted 

number density calculations because both sets of conditions must be validated.

The SCCG-limit-without-gadolinium-credit method is used to demonstrate the criticality safety 

of BWR fuel assemblies in SFPs. There are subtle but important differences between this method 

and the SCCG-limit-with-gadolinium-credit method described in the previous section. The 

primary difference is that in this method, the SCCG limit is based on a correlation created 

without credit for gadolinium. The storage of fresh and low burnup fuel requires that a separate 

gadolinium requirement be determined and met in the burnup range in which the reactivity of 

unpoisoned fuel is too high. The method has some advantages in terms of conservatism, and 

even with the additional limit, it is still simple to implement in power plant operations. This 

method has been widely used in the nuclear power industry for about the last 20 years.

2.4 OTHER METHODS

Other methods have been proposed or used in SFP analysis for BWR fuel, but limited 

information is available for some of these methods in the open literature. Additional methods are 

likely to be developed for storage and transportation cask applications. One recent example is 

provided in Gadolinium Credit Application for Transportation and Storage Casks loaded with 

BWR UO2 Assemblies [9].

17

3 FACTORS AFFECTING PEAK REACTIVITY IN STORAGE 

AND TRANSPORTATION CASKS

As discussed in Section 2.1, several different depletion and lattice design parameters can 

influence the burnup of peak reactivity, thus influencing the reactivity of the fuel lattice at the 

peak. This section describes sensitivity studies performed to identify the factors most important 

to conservative determinations of peak reactivity for various sets of nuclides modeled in the 

storage and transportation configuration. These studies are intended not only to determine the 

most important parameters affecting peak reactivity analysis, but also to determine the 

conservative direction for each of these parameters. All studies are performed within the generic 

BUC (GBC)-68 cask model [10]. The models used for the GBC-68 cask include reflective 

boundary conditions, and thus they effectively model an infinite array of casks. For this reason, 

all reactivity calculation results reported in this section are infinite multiplication factors and are 

referred to as cask kinf values.

This section provides an overview of the methodology used in the sensitivity studies, a review of 

the codes and methods used to perform the calculations, and a discussion of the BWR fuel design 

type used for this work. The detailed results for the studies are presented, and a summary is 

provided at the conclusion of the section.

3.1 SENSITIVITY STUDY METHODOLOGY

The methodology used in these studies is intended to identify the factors most important to 

conservative reactivity determinations for discharged BWR fuel. Some of these studies would 

likely need to be repeated as a part of any BWR peak reactivity analysis for a specific storage or 

transportation cask design. The sensitivity studies would need to be performed within the 

methodology used for the application and thus may generate differences in the magnitude of 

reactivity effects documented in this report. It is expected, however, that the primary parameters

controlling fuel assembly reactivity near its peak will be common among any methods used.

The first studies performed in this section relate to the modeling of the BWR fuel both during 

depletion and in the storage/transportation configuration. To establish a technical basis for peak 

reactivity BUC, these studies have been performed to identify an acceptable approach for 

modeling the complex initial and depleted distributions of fissile and absorbing nuclides within

the fuel assembly. Detailed, complicated models are constructed for baseline calculations to 

investigate the conservatism of simplified models that can be generated and executed more 

quickly. The results of these studies provide a basic modeling approach used for the remaining 

sensitivity studies.

The remaining studies are mainly focused on the impact of lattice design and operational 

parameters on fuel assembly reactivity. The effects of gadolinium loading are investigated by 

varying (1) the number of gadolinium-bearing rods and the gadolinium content of these rods, 

(2) the gadolinium rod pattern, (3) void fraction, (4) control blade insertion, and (5) core 

operating parameters. As described in Section 3.2, depletion calculations are performed with the 

same nuclide set for each set of conditions being modeled. The depleted isotopic number 

densities are then decayed for five years to represent an approximate minimum post-irradiation 
18

cooling time prior to cask loading which would represent the maximum reactivity. Various sets 

of nuclides are then modeled in the storage/transportation configuration as discussed in Section 

3.2. The reactivity effect of each parameter is thus established for actinide-only (AO) models, as 

well as for models including actinide and fission product (AFP) nuclides. The effect of including 

different nuclide sets in the criticality safety model is thus studied directly.

3.2 CALCULATIONAL METHODS, MODELS, AND CODES

This section presents the methods, codes, and models used in generating the results presented in 

Section 3.4. A description of the general approach to the sensitivity studies is presented, 

followed by a discussion of the SCALE sequences used for depletion and cask modeling. The 

models used for each step are also discussed in this section. The last portion of this section 

includes a discussion of the fuel assembly type considered in this work; the GE14 fuel assembly 

type is the base model considered, as it is the most common fuel assembly type used in domestic 

BWR plants today and includes features common to other advanced fuel design types.

Figure 3.1. SCALE sequences, modules, and codes used for calculations.

The calculations were performed with the publicly available version 6.1.2 of SCALE [11]. 

TRITON/NEWT was used to perform 2D lattice depletion calculations for various operating 

conditions. Isotopic concentrations corresponding to burnup points at or near the reactivity peak 

were then extracted from the TRITON output files. The nuclide concentrations were then 

decayed for five years using ORIGEN. The resulting nuclide concentration values (in the form of 

SCALE composition input) were passed to KENO in order to perform the cask criticality 
19

calculations. Figure 3.1 is a simplified flowchart showing how the calculations were performed 

with SCALE for these BWR BUC sensitivity studies. 

3.2.1 Triton

TRITON is a multipurpose SCALE control module for transport, depletion, and sensitivity and 

uncertainty analysis. TRITON can be used to provide automated, problem-dependent crosssection processing, followed by multigroup transport calculations for 1D, 2D, and 3D 

configurations. This functionality can be used in tandem with the ORIGEN depletion module to 

predict isotopic concentrations, source terms, and decay heat, as well as to generate few-group 

homogenized cross sections for nodal core calculations. In the context of this work, TRITON is 

used for automating resonance self-shielding (CENTRM/BONAMI), 2D neutron transport 

(NEWT), and fuel depletion calculations (ORIGEN), which constitute a single time step of the 

depletion calculations. Many of these steps are simulated in order to perform the full depletion 

calculations.

For this project, TRITON was used to perform 2D lattice depletion calculations over a range of 

varying conditions. A set of 94 nuclides was included in the transport model, corresponding to 

the “addnux=2” option (default in TRITON), while more than 2000 nuclides were tracked during 

the ORIGEN depletion and decay calculations. Seven equal-area radial rings were used in the 

gadolinium-bearing fuel pins to capture radial depletion of gadolinium. Seven equal-area rings 

provide the necessary solution accuracy in a reasonable computational time [12]. The ENDF/BVII.0 238-group cross-section library was used with the “parm=weight” option in TRITON to 

collapse the 238-group library to a 49-group working library. Details of the TRITON models are 

documented in Appendix A. After depletion calculations were complete, the output files 

generated during the TRITON depletion calculations were post-processed to generate depleted 

and decayed fuel composition files to be used in subsequent criticality calculations.

3.2.2 CSAS/KENO

The CSAS/KENO criticality sequence was used for reactivity calculations for the GBC-68. 

Although KENO is a 3D code, it will essentially perform 2D calculations by using reflective 

axial boundary conditions. The sequence provides automated, problem-dependent cross-section 

processing, followed by multi-group Monte Carlo transport to solve the keff eigenvalue problem. 

Most of the calculations performed to support this report used reflective axial boundary 

conditions to create a model that is effectively 2D, as the model is both infinite and uniform in 

axial extent, for simplicity and conservatism. All calculations were performed using the 238-

group neutron library based on ENDF/B-VII.0. 

Four different sets of nuclides are considered in the fuel modeling in the CSAS models: 

(1) major AO, (2) major and minor AFPs; (3) major and minor actinides with no credit for 

gadolinium (AFPNG); and (4) TRITON “addnux=2” set of 94 nuclides modeled in the transport 

portion of the depletion calculations (ALL). The nuclides used in the AO and AFP nuclide sets 

are taken from NUREG/CR-7109 [13] and are the same as those typically used in PWR BUC. 

The BUC nuclides considered in the AO, AFP, and AFPNG sets are provided in Table 3.1. The 

AFPNG set is included to study the possibility of AFP BUC without credit for residual 
20

gadolinium poison. The nuclides in the ALL set from TRITON, which approximates modeling 

all actinides and fission products that would impact keff, are provided in Table 3.2. 

Table 3.1. Nuclides included in the three sets of BUC isotopes considered

Actinide-only (AO) nuclides (10 nuclides)

234U 235U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 16O

Major and minor AFPs (29 total nuclides)

234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 243Am 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm 150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd 16O

Major and minor AFPNG (28 total nuclides)

234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 243Am 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm 150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 16O

Table 3.2. All TRITON default nuclides included in depletion calculations (ALL) 

(94 total nuclides, TRITON “addnux=2” nuclides) [11]

234U 235U 236U 238U 237Np 238Pu 239Pu 240Pu 241Pu 242Pu 241Am 242Am 243Am 242Cm 243Cm 244Cm 1

H 10B 11B 14N 16O 83Kr 93Nb 95Nb 91Zr 93Zr 94Zr 95Zr 96Zr 95Mo 97Mo 98Mo 99Mo 100Mo 99Tc 101Ru 102Ru 103Ru 104Ru 106Ru 103Rh 105Rh 105Pd 107Pd 108Pd 109Ag 113Cd 115In 126Sn 127I 129I 135I 131Xe 133Xe 135Xe 133Cs 134Cs 135Cs 137Cs 139La 140Ba 141Ce 142Ce 143Ce 144Ce 141Pr 143Pr 143Nd 144Nd 145Nd 146Nd 147Nd 148Nd 147Pm 148Pm 149Pm 147Sm 149Sm 150Sm 151Sm 152Sm 153Sm 151Eu 153Eu 154Eu 155Eu 156Eu 152Gd 154Gd 155Gd 156Gd 157Gd 158Gd 160Gd

Table 3.3 (Table 6.10 from Reference 13) provides the uncertainty in keff for several BUC models 

containing PWR or BWR SNF due to nuclide cross-section uncertainties. Differences in these 

values largely represent differences in the sensitivities of the system keff to the nuclides listed 

because the same cross-section covariance data are used for both types of fuel. The minor 

actinides and fission products for the BWR SFP model have similar sensitivities to the PWR SFP 

model, indicating that the inclusion of these same nuclides from PWR BUC is reasonable for this 

evaluation of BWR BUC at peak reactivity. 
21

Table 3.3. Uncertainty in keff due to uncertainty in nuclear data for 

BUC application models

BUC model keff uncertainty (∆k)

Model SFP GBC-32 BWR

Burnup (GWd/MTU) 10 10 11

All nuclides 0.00471 0.00468 0.00402

Major actinides (9) 0.00463 0.00455 0.00393

234U 0.00000 0.00000 0.00000

235U 0.00270 0.00246 0.00293

238U 0.00250 0.00246 0.00211

238Pu 0.00000 0.00000 0.00000

239Pu 0.00281 0.00292 0.00154

240Pu 0.00017 0.00018 0.00011

241Pu 0.00008 0.00007 0.00003

242Pu 0.00001 0.00001 0.00000

241Am 0.00000 0.00003 0.00000

Minor actinides (3) 0.00007 0.00007 0.00013

243Am 0.00000 0.00000 0.00000

237Np 0.00002 0.00002 0.00001

236U 0.00007 0.00007 0.00013

FP (16) 0.00022 0.00024 0.00023

95Mo 0.00001 0.00001 0.00002

99Tc 0.00002 0.00002 0.00003

101Ru 0.00002 0.00002 0.00003

103Rh 0.00004 0.00006 0.00008

109Ag 0.00000 0.00000 0.00000

133Cs 0.00005 0.00005 0.00008

147Sm 0.00000 0.00002 0.00000

149Sm 0.00015 0.00016 0.00010

150Sm 0.00001 0.00001 0.00002

151Sm 0.00008 0.00008 0.00006

152Sm 0.00002 0.00002 0.00003

143Nd 0.00011 0.00012 0.00014

145Nd 0.00004 0.00004 0.00008

151Eu 0.00000 0.00000 0.00000

153Eu 0.00001 0.00001 0.00002

155Gd 0.00000 0.00001 *

Other actinides 0.00003 0.00000 0.00000

Other FP 0.00015 0.00008 0.00014

Structural materials 0.00081 0.00106 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).
22

Fuel

Zircaloy-2

Stainless steel

Water

B4C/Al absorber

3.2.3 Cask Application Model

The cask model used in this work is the GBC-68 cask, which was developed as a computational 

benchmark for BWR BUC studies [10]. The cask models used in this study represent 2D slices 

of the cask loaded with SNF. The cask basket, absorber panels, and cask body are modeled 

explicitly, as shown in Figure 3.2, as well as the fuel, cladding, water tubes, and assembly 

channel. Figure 3.3 shows a detailed view of a single storage cell containing a GE14 fuel 

assembly model of the vanished lattice. A more complete description of the GE14 assembly and 

its full and vanished lattices is provided in Section 3.3.

Figure 3.2. Example of GBC-68 half cask model.

Figure 3.3. Detailed representation of a single storage cell in the GBC-68 cask model.

The fuel compositions are provided at specific burnups after extraction from the TRITONgenerated output files (“ft71f001” files, ORIGEN concentration files). The burnups at which 

compositions were extracted were chosen based on the location of the peak reactivity in the 2D 

assembly model with points ranging within ±5 GWd/MTU of the peak reactivity burnup. If no 

significant peak existed in the eigenvalue trajectory, then compositions were extracted for a 

default set of burnup values between 5–15 GWd/MTU. ORIGEN was used to extract the 

compositions from the ft71f001 files and decay the compositions for five years, which is a 

representative minimum cooling time in the SFP before transfer to a storage or transportation

cask. The fuel cladding, water tubes, and assembly channel are modeled as Zircaloy-2 using the 

default SCALE specification. All water in the model is assumed to be full density, and the cask 

Stainless steel

Water
23

is assumed to be fully flooded. Full density water is also modeled in the gap between the fuel 

pellet and the fuel cladding. These assumptions are typical of criticality safety analysis models 

and are not expected to have significant impacts on the sensitivity results presented in Section 

3.4. Additional discussion of the depleted fuel and gadolinium composition modeling is provided 

in Section 3.4.1.

The cask calculations were performed using multigroup KENO. All fuel rods without 

gadolinium are modeled using the LATTICECELL treatment for multigroup resonance selfshielding calculations. The gadolinium pins are modeled with the same seven rings used in the 

depletion calculations. A MULTIREGION cell is used to process the multigroup cross sections 

for these rods. The KENO calculations considered 10,000 particles per generation, skipping the 

first 100 generations. The desired uncertainty was set to be no more than 0.0001 Δk.

Calculations were performed for a range of burnups around the peak reactivity burnup 

determined in the depletion calculations. KENO calculations were performed for each of the four 

nuclide sets shown in Tables 3.1 and 3.2 at each burnup considered. With the removal of 

gadolinium in the AO and AFPNG sets, no reactivity peak occurs. The calculations are intended 

to provide an estimate of the conservatism due to the use of the AO, AFP, and AFPNG nuclide 

sets compared to the ALL set. Comparisons of the AFP and AFPNG results provide a direct 

measure of the residual gadolinium credit. This could be important when validation of depleted 

compositions, including the residual gadolinium, is considered.

3.3 FUEL DESIGN TYPES

The primary fuel assembly model used in this study was the GE14 fuel assembly. This assembly 

has a 10×10 array of fuel pins and contains two large central water rods. Each water rod

displaces four fuel rods. In addition, the assembly has a channel box with rounded corners that 

are slightly thicker than the sidewalls. Modeling data for the GE14 assembly, including fuel 

enrichment and gadolinium loading, were taken from Reference 5. The GE14 fuel assembly can 

contain many axial levels with varying fuel enrichment and gadolinium loading. Due to the 

presence of part-length fuel rods which terminate at approximately half the total height of the 

fuel assembly, the GE14 fuel assembly contains two primary axial zones (or levels). These two

axial regions are full and vanished zones. A 2D slice through one of these axial zones is referred 

to as a “lattice.” As the name implies, the full lattice has a fuel rod occupying every position in 

the fuel pin array, and the vanished lattices are located above the part-length rods, so these rods 

are vanished from the lattice. SCALE/TRITON representations of GE14 full and vanished

lattices with an eight-gadolinium-pin layout are illustrated in core geometry, with the control 

blade present, in Figure 3.4.

The GE14 fuel assembly was chosen as the main fuel assembly for the studies herein because

(1) it is a common fuel assembly in U.S. BWRs, (2) it contains advanced geometry features 

commonly seen in modern BWR fuel assemblies (water rods, rounded channel corners, partlength rods, etc.), (3) it is commonly loaded with relatively highly enriched fuel pins (near 5.0 

w/o 235U), and (4) it typically contains many gadolinium-bearing fuel pins. Studying various 

characteristics in a modern, highly heterogeneous fuel lattice such as the GE14 allows extension 

of the basic results to other highly heterogeneous fuel configurations. Previous studies [4, 14] 
24

have shown that the GE14 bundle design is more reactive than smaller GE lattices (7×7, 8×8, 

and 9×9) at burnups at which peak reactivity occurs.

The fuel assembly design in Reference 5 was used as a basis for further model modifications. 

Various studies, such as those investigating gadolinium fuel pin loading and gadolinium fuel pin 

patterns, were implemented by modification of the original lattice design to suit the needs of the 

sensitivity studies.

The fuel enrichment and gadolinium layouts for the full and vanished lattices are illustrated in 

Figure 3.5 [5]. A box with a single number signifies the fuel pin enrichment in wt% 235U, and a 

box with two numbers signifies the enrichment (top) and gadolinium content in wt% gadolinium 

(bottom). The large boxes labeled “WR” specify the large central water rod, and boxes with a 

“V” specify a vanished fuel pin.

Figure 3.4. GE14 full and vanished lattices in reactor geometry.

FULL VANISHED
25

Figure 3.5. Full and vanished lattice layouts for the GE14 assembly [5].

3.4 RESULTS

This section presents the results of the sensitivity studies, which in turn support the 

recommendations presented in Section 3.5. These studies are intended to determine general 

trends for the representative fuel lattices used. They are not intended to provide absolute results 

to be used in licensing actions. Some of the results indicate areas in which application-specific 

studies may be needed to demonstrate that conservative or appropriate modeling assumptions 

have been used in the criticality safety analysis. Each study is presented in a separate subsection; 

the first few studies—which are related to fuel modeling, gadolinium loading, and gadolinium 

rod patterns—are necessary to support the selection of base models used for the remaining 

studies on void fraction, control blade insertion, and operating parameters.

3.4.1 Isotopic Modeling during Depletion

When using a general-purpose lattice depletion tool such as TRITON, the user has a significant 

number of modeling choices to make, which could impact the isotopic content produced from 

simulation of the model. In other software specifically designed for lattice depletion and nodal 

data generation, such as CASMO [15] or fuel vendor software, the user might not have the 

multitude of options available for modeling choices. In the interest of covering all the options 

that a user might select for isotopic modeling, four isotopic modeling strategies were chosen and 

used throughout this work. The strategies were used consistently in the TRITON depletion and 

KENO reactivity calculations so that whichever strategy was used to generate a particular set of 

depleted fuel isotopics was also used in the cask model including those depleted compositions.

The four chosen options are (1) pin-wise enrichment with pin-wise isotopics (PEPI), (2) pin-wise 

enrichment with average isotopics (PEAI), (3) average-enrichment with pin-wise isotopics 

(AEPI), and (4) average-enrichment with average isotopics (AEAI). “Pin-wise enrichment” 

refers to explicitly modeling the actual fuel enrichment in each fuel pin location in the lattice, 

while “average enrichment” refers to using the average fuel enrichment over the lattice for every 

fuel pin location in the lattice. “Pin-wise isotopics” refers to explicitly modeling the fuel 

depletion in each individual fuel pin in the lattice, while “average isotopics” refers to modeling a 

FULL VANISHED
26

group of like-enrichment fuel pins as a single depletion material in the model. The average 

enrichment for the lattices modeled in this study is 4.305 wt% 235U.

PEPI is the most accurate method of modeling depletion in the fuel lattice, as the initial 

enrichment is modeled in each fuel pin and the isotopics are tracked separately in each fuel pin. 

PEAI is slightly less accurate: each fuel pin contains the correct initial fuel enrichment, but each 

like-enrichment group is tracked as a single mixture in the depletion calculation. In AEPI, the 

average enrichment for the lattice is calculated and used in each fuel pin, but the isotopics are 

individually tracked in each fuel pin. This method is feasible within TRITON, but it erases any 

impact that the differing initial loadings might have on these pin-wise depleted compositions. In 

AEAI, the average enrichment for the lattice is calculated and used in each fuel pin, and the 

isotopics are tracked as a single group. In both average enrichment scenarios, the gadolinium 

content is discrete (loaded only in certain fuel pins) rather than being averaged over the entire 

lattice. In both the average isotopics cases (AEAI and PEAI), one mixture is used for each radial 

ring in all gadolinium-bearing fuel pins. That is, in all gadolinium-bearing pins, the outer ring of 

a gadolinium-bearing pin contains identical isotopics to all the other gadolinium-bearing pins, 

but the isotopics in each radial ring are tracked separately. Conversely, in the pin-wise isotopics 

cases (PEPI and AEPI), every radial ring in every gadolinium-bearing pin is depleted as a 

separate mixture. 

The choice of the isotopic modeling strategies impacts the depleted isotopic concentrations and 

resulting reactivity calculations, so it is important to determine which of these strategies is most 

(and least) conservative from a reactivity standpoint.

The results for the vanished lattice containing no gadolinium rods are shown in Figure 3.6 for the 

AO, AFP, and ALL nuclide sets using the AEAI modeling strategy. 
27

Figure 3.6. 2D Cask kinf as a function of burnup for fuel with no initial gadolinium loading and 

three nuclide sets, AEAI modeling strategy.

The reactivity change is nearly linear over the burnup range of interest because no gadolinium 

was loaded in the fresh fuel. Calculations are performed for the same lattice at the same burnups, 

assuming AEPI, PEAI, and PEPI modeling. The difference in calculated cask kinf for each of the 

isotopic modeling strategies is provided in Tables 3.4–3.6. 

Table 3.4. Change in cask kinf, AEAI-AEPI, zero initial gadolinium

Burnup 

(GWd/MTU)

AO AFP ALL

Δkinf σ Δkinf σ Δkinf σ

5.04 -0.00017 0.00014 -0.00041 0.00014 0.00012 0.00014

6.96 -0.00015 0.00014 -0.00039 0.00014 -0.00043 0.00014

8.00 -0.00025 0.00014 -0.00070 0.00014 -0.00051 0.00014

9.01 -0.00014 0.00014 -0.00032 0.00014 -0.00069 0.00014

9.97 -0.00040 0.00014 -0.00108 0.00014 -0.00056 0.00014

11.02 -0.00017 0.00014 -0.00041 0.00014 0.00012 0.00014
28

Table 3.5. Change in cask kinf, AEAI-PEAI, zero initial gadolinium

Burnup 

(GWd/MTU)

AO AFP ALL

Δkinf σ Δkinf σ Δkinf σ

5.04 0.00305 0.00014 0.00302 0.00014 0.00335 0.00014

6.96 0.00300 0.00014 0.00278 0.00014 0.00304 0.00014

8.00 0.00279 0.00014 0.00271 0.00014 0.00278 0.00014

9.01 0.00286 0.00014 0.00291 0.00014 0.00272 0.00014

9.97 0.00280 0.00014 0.00268 0.00014 0.00263 0.00014

11.02 0.00305 0.00014 0.00302 0.00014 0.00335 0.00014

Table 3.6. Change in cask kinf, AEAI-PEPI, zero initial gadolinium

Burnup 

(GWd/MTU)

AO AFP ALL

Δkinf σ Δkinf σ Δkinf σ

5.04 0.00311 0.00014 0.00303 0.00014 0.00323 0.00014

6.96 0.00327 0.00014 0.00284 0.00014 0.00294 0.00014

8.00 0.00280 0.00014 0.00283 0.00014 0.00267 0.00014

9.01 0.00311 0.00014 0.00285 0.00014 0.00266 0.00014

9.97 0.00253 0.00014 0.00221 0.00014 0.00272 0.00014

11.02 0.00264 0.00014 0.00238 0.00013 0.00251 0.00014

Similar results for the vanished lattice containing six gadolinium rods with 2 wt% gadolinium in 

gadolinium fuel pins are shown in Figure 3.7 for the AO, AFP, AFPNG, and ALL nuclide sets

using the AEAI modeling strategy.
29

Figure 3.7. 2D Cask kinf as a function of burnup for fuel initially containing six pins 

with 2 wt% gadolinium and four nuclide sets, AEAI modeling strategy.

The AO and AFPNG nuclide sets show a nearly linear depletion because the residual gadolinium 

is not included in the model. The AFP and ALL sets include the gadolinium and therefore show a 

reactivity peak at approximately 7.5 GWd/MTU. At this burnup, the residual gadolinium is 

worth about 1.25% Δk. The minor actinides, residual 155Gd, and top 16 fission products are worth 

3.6% Δk. The remaining fission products are worth approximately 0.4% Δk. The difference in 

calculated cask kinf for each of the isotopic modeling strategies is provided in Tables 3.7–3.9.
30

Table 3.7. Change in cask kinf, AEAI-AEPI, six rods with 2 wt% initial gadolinium

Burnup 

(GWd/MTU)

AO AFP AFPNG ALL

Δkinf σ Δkinf σ Δkinf σ Δkinf σ

6.46 -0.00046 0.00014 -0.00021 0.00014 -0.00063 0.00014 -0.00002 0.00014

6.96 -0.00032 0.00014 0.00018 0.00014 -0.00064 0.00014 0.00009 0.00014

7.47 -0.00011 0.00014 -0.00002 0.00014 -0.00008 0.00014 0.00000 0.00014

8.00 -0.00030 0.00014 -0.00025 0.00014 -0.00048 0.00014 0.00017 0.00014

8.44 -0.00072 0.00014 0.00001 0.00014 -0.00057 0.00014 -0.00028 0.00014

9.01 -0.00045 0.00014 -0.00035 0.00014 -0.00061 0.00014 -0.00001 0.00014

Table 3.8. Change in cask kinf, AEAI-PEAI, six rods with 2 wt% initial gadolinium

Burnup 

(GWd/MTU)

AO AFP AFPNG ALL

Δkinf σ Δkinf σ Δkinf σ Δkinf σ

6.46 0.00324 0.00014 0.00403 0.00014 0.00301 0.00014 0.00413 0.00014

6.96 0.00308 0.00014 0.00435 0.00014 0.00285 0.00014 0.00420 0.00014

7.47 0.00319 0.00014 0.00401 0.00014 0.00311 0.00014 0.00391 0.00014

8.00 0.00297 0.00014 0.00373 0.00014 0.00296 0.00014 0.00392 0.00014

8.44 0.00291 0.00014 0.00384 0.00014 0.00283 0.00014 0.00371 0.00014

9.01 0.00306 0.00014 0.00346 0.00014 0.00279 0.00014 0.00354 0.00014

Table 3.9. Change in cask kinf, AEAI-PEPI, six rods with 2 wt% initial gadolinium

Burnup 

(GWd/MTU)

AO AFP AFPNG ALL

kinf σ kinf σ kinf σ kinf σ

6.46 0.00323 0.00014 0.00447 0.00014 0.00306 0.00014 0.00503 0.00014

6.96 0.00322 0.00014 0.00526 0.00014 0.00287 0.00014 0.00536 0.00014

7.47 0.00322 0.00014 0.00550 0.00014 0.00311 0.00014 0.00543 0.00014

8.00 0.00305 0.00014 0.00533 0.00014 0.00284 0.00014 0.00551 0.00014

8.44 0.00266 0.00014 0.00516 0.00014 0.00259 0.00014 0.00491 0.00014

9.01 0.00309 0.00014 0.00446 0.00014 0.00282 0.00014 0.00469 0.00014

For the cases both with and without gadolinium, the AEPI results are generally statistically 

equivalent to the AEAI results. The AEPI method requires many more depletion calculations 

than the AEAI method to calculate and track pin-wise isotopics. Because the two methods show 

nearly identical kinf results, use of the AEAI strategy is preferable because it requires less 

computational resources, and the strategy is self-consistent using assembly averages for both the 

initial enrichment loading and the tracking of isotopic depletion.

It is clear that the PEAI and PEPI pin-wise enrichment modeling approaches result in lower kinf

values that are similar to each other. These modeling approaches accurately represent the zoning 

designed into the lattice to help control power peaking near the periphery of the bundle. The 

PEAI and PEPI approaches are statistically equivalent in the AO and AFPNG cases, indicating 

that there is little impact of averaging the depleted fuel isotopics given a detailed depletion 

model. The PEAI results are more reactive than the PEPI results near peak reactivity for the 

6×2Gd AFP and ALL cases, indicating that the average gadolinium modeling results in a 

conservative reactivity determination. The significantly reduced reactivity estimates resulting 

from the pin-wise enrichment modeling compared to the average enrichment modeling indicate 

that the latter approach is not only simpler but is also more conservative. The AEAI modeling 
31

strategy is used for the remainder of the cask kinf results presented in this report unless noted 

otherwise. This strategy is adopted as it is simple and conservative.

This conclusion should be true for realistic BWR assembly designs because the driving 

consideration in assembly designs is the control of pin power peaking during power operations. 

A BWR assembly could be designed with higher enrichment near the periphery that would 

challenge the average enrichment assignment, but the design would result in unacceptable 

peaking near the gap between assemblies. This is especially true for most of the currently 

operating BWR plants that have larger gaps on the control blade side of the assembly than on the 

detector side. Some designs have symmetric gaps, which likely reduce the magnitude of 

enrichment zoning; this would act to lower the difference between average initial enrichment 

(AE) and pin-wise initial enrichment (PE) approaches but not reverse it.

3.4.2 Gadolinium Loading

The gadolinium loading in each assembly is controlled with two independent parameters: the 

number of pins containing gadolinium and the loading of the absorber in each of those pins. 

Assembly designs often contain different loadings in different gadolinium rods within the same 

lattice. For simplicity, all poisoned rods in a lattice contain the same gadolinium loading in this 

study. Lattices involving multiple gadolinium loadings should see similar effects, but the specific 

modeling used would need to be described and justified for each application. As discussed in 

Section 2.1, additional gadolinium tends to push the reactivity peak toward higher burnups and 

thus reduce the magnitude of the peak.

3.4.2.1 Depletion Studies

The gadolinium loading study consisted of running a number of cases based on the lattice in 

Figure 3.4, but varying the number of gadolinium-bearing pins and the concentration in those 

pins. This study is primarily intended to show the sensitivity of peak reactivity (absolute 

reactivity and location of the peak) as determined in the depletion calculations to the number of 

pins and the concentration of gadolinium. The number and content of gadolinium pins in the asdesigned lattice (an example is shown in Figure 3.4) result in a peak reactivity that is 

significantly lower (less limiting) than for lattices that contain fewer gadolinium pins with a 

lower gadolinium content. In the interest of generating results for more limiting cases, the 

number of pins and the gadolinium content in those pins were modified from the as-designed 

case by varying the number of gadolinium-bearing pins from 2 to 8 and the gadolinium content 

from 2 to 10 wt% gadolinium, as listed in Table 3.10. The locations of the gadolinium pins are a 

subset of the pin locations in the as-designed case. For each number of pins (2, 4, 6, and 8), five 

cases were run with each of the five different gadolinium loadings listed (2, 4, 6, 8, and 10), for a 

total of 20 cases considered for each lattice design. In addition, a gadolinium-free lattice was also 

simulated for comparison purposes. Throughout this document, the NxWGd format is used to 

specify various gadolinium-bearing lattices, where N is the number of pins and W is the weight 

percent of gadolinium in those pins.
32

Table 3.10. Number of pins and gadolinium content per pin

Number of Pins Gadolinium

wt%

2 2

4 4

6 6

8 8

10

The lattice layouts for the full and vanished lattices used in the gadolinium study can be found in 

Figures 3.8–3.12. In these figures, the numbers represent the fuel pin enrichment in that lattice 

location, and shaded boxes highlight gadolinium-bearing fuel pins. 

 

Figure 3.8. Gadolinium-free lattice layout for the full and vanished lattices.

FULL VANISHED
33

 

Figure 3.9. Two gadolinium pin layout for the full and vanished lattices.

 

Figure 3.10. Four gadolinium pin layout for the full and vanished lattices.

FULL VANISHED

FULL VANISHED
34

 

Figure 3.11. Six gadolinium pin layout for the full and vanished lattices.

 

Figure 3.12. Eight gadolinium pin layout for the full and vanished lattices.

As discussed in Section 3.3, “V” denotes the location of a vanished rod in the lattice, and “WR” 

shows the location of the two water rods. The location of the gadolinium pins remains constant, 

while the concentration is varied using the values shown in Table 3.9.

TRITON depletion calculations were performed for all cases (including all isotopic modeling 

strategies) using 40% void fraction (core average condition) in the moderator and representative 

FULL VANISHED

FULL VANISHED
35

fuel, clad, and moderator temperatures for BWRs. Eigenvalue trajectories (kinf vs. burnup) for the 

PEPI isotopic strategy (most precise modeling) and the vanished lattices (most reactive lattices) 

were extracted from the output files and plotted in Figure 3.13. Each subfigure (a–e) corresponds 

to a certain gadolinium concentration (2–10 wt% gadolinium, respectively) in the gadolinium 

pins, and each line corresponds to the number of gadolinium pins in the lattice. The black line in 

each of the figures is the eigenvalue trajectory for the gadolinium-free lattice. The results from 

the PEPI depletions are used in this figure because they are the most accurate. Results from the 

AEAI strategy were similar. Figure 3.13 shows that the lattice reactivity as a function of burnup 

is strongly correlated to the gadolinium concentration and number of gadolinium pins. 
36

 (a) 2 wt% Gd2O3 (b) 4 wt% Gd2O3

 (c) 6 wt% Gd2O3 (d) 8 wt% Gd2O3

 (e) 10 wt% Gd2O3

Figure 3.13. TRITON eigenvalue trajectories for the PEPI isotopic strategy varying the 

gadolinium content and number of gadolinium pins.

In all cases, after gadolinium has been depleted, the trajectories closely follow the gadoliniumfree trajectory. The number of gadolinium fuel pins has a significant impact on the initial 
37

reactivity of the lattice, but it has a relatively small impact on the location (burnup) and value 

(height) of peak reactivity. This is due to the spatial self-shielding in gadolinium fuel pins. 

Because gadolinium is a very strong neutron absorber (primarily 155Gd and 157Gd), very few 

thermal neutrons reach the interior of the gadolinium pins near beginning of life (BOL)—most 

neutrons are absorbed in the outermost radial region of the fuel pellet, meaning that more 

gadolinium fuel pins leads to a significant change in initial reactivity. Even when the gadolinium 

concentration is relatively low, the parasitic absorption by gadolinium is much more likely than 

fission in 235U as the gadolinium absorption cross sections are 2 to 3 orders of magnitude greater 

than 235U fission. This can be clearly observed in Figure 3.14, which plots the continuous energy 

cross sections for 155Gd, 157Gd, 238U (capture, n-gamma), and 235U (fission) (ENDF/B-VII.0, 

available in SCALE 6.1.2).

Figure 3.14. Dominating cross sections in gadolinium-bearing fuel pins.

Conversely, the gadolinium concentration has a relatively small impact on the initial reactivity, 

but it has a significant impact on the location (burnup) and value (height) of the reactivity peak. 

Because gadolinium is a very strong absorber, nearly all neutrons entering a gadolinium-bearing 

fuel pin will be absorbed by gadolinium, which explains the minimal impact on changing the 

initial gadolinium concentration. However, the concentration of gadolinium has a significant 

effect on the spatial depletion of gadolinium (the onion skin effect). Higher concentrations of 

gadolinium mean that gadolinium in the central portion of the pin will be shielded from neutrons 

by the outer region of the fuel pin for a longer period of time. This geometric self-shielding 

results in a slower overall depletion of gadolinium, which moves the reactivity peak to higher 

burnup, and thus, lower values further along the gadolinium-free trajectory. 
38

This effect is illustrated in Figure 3.15(a), which shows the percent of 155Gd remaining in the 

radial regions of gadolinium-bearing fuel pins for the 6-pin cases with concentrations ranging

from 2 wt% to 10 wt% gadolinium at a burnup of 10 GWd/MTU. Figure 3.15(b) plots the 

eigenvalue trajectories for the cases in Figure 3.15(a). Figure 3.15 shows that for higher 

gadolinium fractions, the depletion of the gadolinium occurs more slowly for the inner regions of 

the fuel pin – this is due to the larger spatial self-shielding for the higher concentrations cases as 

compared to the lower concentration cases. The impact is directly observed in Figure 3.15(b) –

initial kinf is similar for the five cases, but the burnup and magnitude of peak reactivity is 

significantly changed with increasing gadolinium concentration. 

 

 (a) (b)

Figure 3.15. (a) Percentage of 155Gd remaining as a function of radial location in the fuel pin 

for the 6×2Gd, 6×4Gd, 6×6Gd, 6×8Gd, and 6×10Gd cases at 10 GWd/MTU and 

(b) eigenvalue trajectories for the 6-gadolinium pin cases.

3.4.2.2 Cask Reactivity Studies

The depleted number densities for each of the twenty cases discussed in 3.4.2.1 are modeled in 

the cask using the AEAI strategy to investigate the effect of gadolinium loadings on discharged 

fuel reactivity. The results presented in the previous section document the effects of gadolinium 

loading on lattice reactivity during depletion, but the impact may vary in the 

storage/transportation cask. The results also depend on the nuclides included in the criticality 

safety model, and thus must be investigated.

The results for 2 wt% gadolinium per pin and a varying number of pins are shown for the AO 

nuclide set in Figure 3.16 and for the AFP nuclide set in Figure 3.17. Both figures also contain a 

line showing the reactivity of the assembly with no gadolinium initially loaded and the same 

nuclides included in the cask model. The results for the AO set, including only the nuclides listed 

for this set in Table 3.1, show that the number of pins has essentially no effect on the calculated 

cask kinf. These results indicate that the number of gadolinium pins has very little impact on cask 

reactivity for AO analysis in the burnup range at which peak reactivity occurs for these 

gadolinium loadings. The results for the AFP set show that as the gadolinium loading increases,

the reactivity peak is lower and it occurs at slightly higher burnups. The 2-pin and 4-pin loadings 

do not have sufficient gadolinium to create a peak, but instead they show a fairly uniform 
39

reactivity through about 7 GWd/MTU before reactivity falls. The results also show that at 

burnups beyond the peak, the reactivity curve is similar to the gadolinium-free lattice. These 

results are in good agreement with expectations, and they indicate that higher gadolinium 

loadings, given the same number of pins, cause the reactivity peak to occur at higher burnups 

with lower kinf values.

Figure 3.16. Cask kinf as a function of burnup for 2 wt% gadolinium in a range of pins, 

AO nuclides.
40

Figure 3.17. Cask kinf as a function of burnup for 2 wt% gadolinium in a range of pins, 

AFP nuclides.
41

The results for six gadolinium pins and a variable gadolinium loading per pin are shown in 

Figure 3.18 for the AO nuclides, along with the reactivity of the assembly with no initial 

gadolinium. 

Figure 3.18. Cask kinf as a function of burnup for gadolinium pins with a range of initial 

gadolinium loadings, AO nuclides.

The results for the AO nuclides show that for small gadolinium loadings, there is no effect; 

however, at higher loadings, the reactivity is slightly higher than for the assembly without initial 

gadolinium. This difference is caused by the spectral hardening effect of the gadolinium 

increasing the 239Pu production. At 21.4 GWd/MTU, the 6×10Gd fuel compositions have slightly 

less 235U, but they have 2% to 4% more plutonium than the compositions depleted without 

gadolinium. This high burnup is of interest because it is near peak reactivity of this relatively 

heavily loaded assembly; note that the cask kinf is below 0.88 at this point. The increase in 

plutonium production rate due to heavy gadolinium loadings may be an important phenomenon, 

depending upon the assembly enrichment and burnup. 

The results using the AFP nuclide set are shown in Figure 3.19, along with the reactivity of the 

assembly with no initial gadolinium. The results show that as the loading per pin increases, the 

reactivity peak comes at significantly higher burnups and much lower kinf values. This is in good 

agreement with expectations and the depletion studies. The heavier gadolinium loadings show a 
42

generally flat trajectory to burnups of greater than 20 GWd/MTU before reactivity starts to fall. 

As discussed in Section 2.1, the cause of this behavior is the additional burnup required to 

deplete the gadolinium and the lower remaining fuel reactivity at these higher burnups.

Figure 3.19. Cask kinf as a function of burnup for six gadolinium pins with a range of initial 

gadolinium loadings, AFP nuclides.

The results of the depletion studies presented in Section 3.4.2.1 and the cask studies presented in 

this section are consistent and support the same conclusions. It is clear that increasing the

gadolinium loading will cause the peak reactivity to be lower and to occur at a higher burnup.

Based on the results presented in this section, the 6×2Gd loading is selected for use in the 

remainder of the sensitivity studies. The 6×2Gd pattern was selected for use in remaining studies 

for four primary reasons: (a) it provides a definitive peak in reactivity; (b) the peak reactivity 

occurs at a burnup that is representative of those seen in SFP use of peak reactivity methods; (c) 

the peak is at low burnup resulting in a peak that has a large magnitude compared to other 

higher-gadolinium cases; and (d) six gadolinium pins provide a sufficient number of pins to 

enable a significant number of patterns for the gadolinium pattern study. 
43

3.4.3 Gadolinium Pattern

In order to study the impact of the gadolinium pin pattern on reactivity, the full and vanished 

lattice gadolinium patterns were modified from the original 6×2Gd pattern to 14 additional 

patterns, for a total of 15 patterns. To conserve masses of fuel and poison, only the 4.9 wt% 235U 

enriched fuel pins were used as gadolinium-bearing fuel pins, and the gadolinium concentration 

was held at 2 wt% for all cases. Vanished fuel pin lattice positions were not used for any 

gadolinium-pin locations so that the vanished and full lattices would have corresponding 

gadolinium patterns. Lattice and core design experience was used to determine potentially 

realistic fuel pin patterns; the 15 gadolinium patterns are shown in Appendix B.

The gadolinium patterns shown in Appendix B are fairly typical of BWR designs. In GE14 

lattices, there are typically a greater number of gadolinium-bearing pins in the northwest and 

southeast quadrants of the assemblies due to the orientation of the water rods. The orientation of 

the water rods cause power peaking in these regions of the assembly, so more poison is needed in 

these regions. Gadolinium rods are also used in both the northeast and southwest quadrants when 

a high number of gadolinium pins is required, but moving pins to these regions is unlikely to 

affect the results of this study. Modern BWR designs contain many gadolinium pins (10 to 18) 

ranging in gadolinium concentration from 2–9 wt% gadolinium. The cases studied here cover a 

realistic design space. However, if the gadolinium pattern varies significantly from normal, it 

could warrant further study. It is possible that credit could be taken for restrictions on gadolinium 

pin placement enforced by fuel vendors during lattice design, but these rules would likely need to 

be captured in the safety analysis report.

The cask kinf results for the 15 patterns with the AO nuclide set are shown in Figure 3.20. The 

sensitivity of the calculated cask kinf is low; the spread from maximum to minimum kinf is less 

than 0.1% Δk and is largely insensitive to burnup. The individual patterns are virtually 

indistinguishable because the kinf values are within 2 to 3 standard deviations of each other. 
44

Figure 3.20. Cask kinf as a function of burnup for all 15 patterns, AO nuclide set.

Table 3.11 provides the maximum cask kinf and the pattern from which it results for each burnup, 

along with the base case (Pattern 0) cask kinf. The base case pattern results in statistically 

equivalent reactivity with the maximum kinf pattern for most burnups considered, and that the 

impact of the gadolinium pattern on cask kinf with the AO nuclide set is negligible.

Table 3.11. Cask kinf values for various patterns with the AO nuclide set

Burnup

(GWd/MTU) Max kinf

Limiting 

Pattern Pattern 0 kinf

Uncertainty

(1 σ)

6.96 0.93879 12 0.93854 0.00010

7.47 0.93609 0 0.93609 0.00010

8.00 0.93331 9 0.93317 0.00010

8.44 0.93103 5 0.93058 0.00010

9.01 0.92804 9 0.92775 0.00010

The cask kinf results for all 15 patterns with the AFP nuclide set are shown in Figure 3.21. The 

calculated spread from maximum to minimum kinf is about 0.4% Δk near peak reactivity (near 7.5 

GWd/MTU) and decreases at higher burnups. At about 6.5 GWd/MTU, the full range is nearly 

0.7% Δk, but it drops to only about 0.2% Δk by 9 GWd/MTU. This behavior is plausible since 

the differences in gadolinium worth are diminishing as the gadolinium burns out in each pattern 

and the reactivity of all the lattices approaches the no-gadolinium fuel reactivity depletion 
45

trajectory. The peak reactivity occurs for most patterns at around 7.5 GWd/MTU, though for 

some it occurs at around 8 GWd/MTU. 

Patterns 2, 3, 9, and 12 show the highest reactivity peaks near 0.902. This is about 0.2% Δk

higher than the base case Pattern 0. These patterns have less residual gadolinium remaining and 

hence a higher kinf. The gadolinium in Pattern 2 is more depleted because the pins are more 

spread out than in the base case. Pattern 3 experiences more gadolinium depletion because of the 

separation of the pins and because two of the pins are near the water tubes with additional 

thermal flux nearby. Pattern 9 has more depleted gadolinium because five of the gadolinium pins 

are very near the central water tubes. Pattern 12 has four of the six gadolinium pins near the 

water tubes, which results in faster gadolinium depletion than the base case. 

Figure 3.21. Cask kinf as a function of burnup for all 15 patterns, AFP nuclide set.

Conversely, Pattern 10 has low reactivity because it has a large amount of residual gadolinium. 

Pattern 5 has the lowest peak kinf value, and also has a significantly higher residual gadolinium 

concentration. The large residual is caused by the relatively close grouping of the pins in the 

southeast quadrant; the proximity of the pins causes a supression in the thermal flux near this 

group of rods, leaving a higher residual gadolinium content. Table 3.12 provides kinf values for 

Patterns 0, 5, and 3 (representing nominal, low, and high reactivity cases, respectively) for 

several burnups in the range of interest.
46

Table 3.12. Cask kinf values for various patterns with the AFP nuclide set

Burnup

(GWd/MTU)

Pattern 0 Pattern 5 Burnup

(GWd/MTU)

Pattern 3

Cask kinf σ Cask kinf σ Cask kinf σ

6.46 0.89718 0.00010 0.89276 0.00010 6.26 0.89759 0.00010

6.96 0.89940 0.00010 0.89520 0.00010 6.76 0.90035 0.00010

7.47 0.90028 0.00010 0.89702 0.00010 7.26 0.90191 0.00010

8.00 0.90019 0.00010 0.89746 0.00010 7.79 0.90203 0.00010

8.44 0.89953 0.00010 0.89745 0.00010 8.22 0.90125 0.00010

9.01 0.89724 0.00010 0.89622 0.00010 8.78 0.89929 0.00010

The most reactive patterns—2, 3, and 9—are shown in Figures 3.22, 3.23, and 3.24, respectively. 

The least reactive Pattern 5 is shown in Figure 3.25. 

The results indicate that the reactivity of the base case pattern is near the middle of the field of 

cask reactivities resulting from a 6×2Gd loading, and it is used for the remaining studies in this 

report. The gadolinium pattern has a more significant effect on cask reactivity for the AFP 

nuclide set than it does for the AO set, but the magnitude of the effect is still small, at 

approximately ±0.25% Δk of Pattern 0 kinf value. This conclusion is limited to the number of pins 

and gadolinium loadings in this study.

Figure 3.22. Gadolinium patterns 2 (P2).
47

Figure 3.23. Gadolinium patterns 3 (P3).

Figure 3.24. Gadolinium patterns 9 (P9).
48

Figure 3.25. Gadolinium patterns 5 (P5).

3.4.4 Void Fraction

BWR cores contain a range of coolant void fractions, from near zero at the core inlet to nearly 

80% at the core exit in some cases. Higher exit void fractions may be experienced in some cores, 

but the range of void fractions studied here is broad enough to identify reactivity trends as a 

function of void fraction for this study. The range of void fractions would need to be studied by 

the license applicant to determine the impact it has on fuel reactivity, as the most reactive 2D 

slice must be considered in peak reactivity methods. An appropriate void fraction value would 

need to be selected and defended as part of the analysis. A series of depletion calculations was 

performed for five discrete void fractions using the base case 6×2Gd lattice ranging from 0 to 

80%, and the depleted compositions were used in the cask model with differing nuclide sets and 

the AEAI strategy. Note that the cask model is flooded with full density water in all cases; the 

effect being studied here is the moderator density during depletion. 

The results for the AO nuclide set at each of the five void fractions are shown in Figure 3.26 for 

a range of burnups. The burnups selected surround the peak reactivity in the cask model with the 

AFP nuclide set. It is clear from the figure that the reactivity of the cask is monotonically 

increasing with higher void fractions. This is a result of the hardening neutron spectrum at 

increasing void fractions. The harder spectrum causes additional 239Pu generation, which is a 

significant contributor to reactivity even at these relatively low burnups. 
49

Figure 3.26. Cask kinf as a function of burnup for several depletion moderator void fractions, 

AO nuclide set.

The 239Pu number densities for fuel rods in the central portion of the assembly for these 

calculations are shown in Figure 3.27, and they clearly demonstrate the results of the spectral 

hardening effect of higher void fractions. The overall reactivity change from 0% to 80% void is 

greater than 1% Δk at about 7.5 GWd/MTU; this is a significant impact that must be properly 

accounted for during depletion calculations for AO BUC.
50

Figure 3.27. 239Pu atom density as a function of burnup for several depletion moderator 

void fractions.

Results for the AFP nuclide set at each of the five void fractions are shown in Figure 3.28 for a 

range of burnups. The results are completely reversed in this case. The driving effect for the AFP 

nuclides is the amount of residual gadolinium, which is decreased by a more thermal spectrum 

because of the larger thermal absorption cross section for gadolinium (see Figure 3.14). The 

accelerated absorber depletion caused by the more thermal spectrum causes the assembly to 

reach peak reactivity at lower burnups, and thus at higher kinf values. As the void fraction 

increases, the gadolinium depletion is slower, causing a reduction in the reactivity peak and a 

shift to higher burnups. This is a key manifestation of the peak reactivity phenomenon. 
51

Figure 3.28. Cask kinf as a function of burnup for several depletion moderator void fractions, 

AFP nuclide set.

The volume-average 155Gd number density in the gadolinium pins is shown in Figure 3.29, 

demonstrating the impact of the void fraction on residual gadolinium concentration. The results 

also show that the residual gadolinium effect is stronger than the 239Pu effect, which is the 

primary driver for the AO nuclide set. The peak reactivity of the cask drops by about 0.4% Δk

from the 0% void fraction case to the 80% void fraction case. This is equivalent to about a ±0.2% 

Δk effect relative to the base case with a 40% void fraction. Clearly, the low void fraction case is 

bounding for the AFP nuclide set.
52

Figure 3.29. 155Gd atom density as a function of burnup for several depletion moderator 

void fractions.

3.4.5 Control Blade Insertion

BWR cores operate with some control blades, or rods, inserted (“rodded”) to control reactivity 

and power distributions. The control blades are inserted in the gaps between fuel assemblies; 

each assembly has two faces toward a blade and two faces away from a blade inserted between 

adjacent assemblies. The control blade can be seen in Figure 3.4, along the north and west faces 

of the assembly. The absorber in most BWR control blades is boron carbide (B4C), which has a 

strong thermal absorption cross section. Some control blades contain hafnium, which has similar 

control properties. Depletion under the rodded condition hardens the flux spectrum due to the 

absorption of thermal neutrons and induces radial burnup variation in both fuel and gadolinium 

pins that will likely influence discharged assembly reactivity. The presence of the control blade 

also hardens the neutron spectrum by displacing water in the control blade gap. A series of 

depletion calculations was performed with the control blade inserted for the full depletion for the 

same five discrete void fractions used in Section 3.4.4. The depleted compositions were used in 

the cask model with differing nuclide sets and the AEAI strategy. In all cases, the KENO model 

is flooded with full density water at room temperature (293 K). The effect being studied is the 

control blade insertion during depletion; this study will also determine if the impact of control 

blade insertion varies as a function of moderator void fraction in the depletion model.
53

The rodded depletion results for the AO nuclide set at each of the five void fractions are shown 

in Figure 3.30 for a range of burnups. The burnups selected surround the peak reactivity in the 

cask model with the AFP nuclide set. It is clear from the figure that the reactivity of the cask is 

monotonically increasing with higher void fractions. Comparison with the unrodded depletion 

results presented in Figure 3.26 shows that the presence of the control blade during depletion 

increases cask kinf up to 1% Δk. These results are driven by the hardening neutron spectrum at 

increasing void fractions and a significant spectral shift caused by the presence of the control 

blade during depletion. The harder spectrum causes additional 239Pu generation, which is a 

significant contributor to reactivity even at these relatively low burnups. The control blade effect 

on cask kinf is similar in magnitude to the reactivity increase caused by changing void fraction 

from 0% to 80% in the unrodded case. 

Figure 3.30. Cask kinf as a function of burnup for several depletion moderator void fractions and 

rodded depletion, AO nuclide set.

The 239Pu number densities for fuel rods in the central portion of the assembly for these 

calculations are shown in Figure 3.31, clearly demonstrating the results of the spectral hardening 

effect of higher void fractions and, by comparison with Figure 3.27, control blade insertion. 
54

Figure 3.31. 239Pu atom density as a function of burnup for several depletion moderator void 

fractions, rodded depletion.

As with the unrodded depletions, the sensitivity to void fraction increases with higher void 

fractions. The reactivity increase caused by control blade insertion is larger at higher void 

fractions. The results for the AFP nuclide set at each of the five void fractions are shown in 

Figure 3.32 for a range of burnups. 
55

Figure 3.32. Cask kinf as a function of burnup for several depletion moderator void fractions, 

rodded depletion, AFP nuclide set.

As with the unrodded results, the impact of void fraction is completely reversed compared to the 

AO nuclide set with highest reactivity for no void or low void (20%) cases. A comparison of the 

results for the unrodded and rodded cases, shown in Figure 3.33, indicates that control blade 

insertion results in a significant increase in cask kinf, by approximately 1% Δk. The reactivity 

peak occurs at lower burnups for smaller void fractions but at higher burnup for 80% void 

fraction. 
56

Figure 3.33. Cask kinf as a function of burnup for several depletion moderator void fractions and 

the AFP nuclide set, comparing rodded and unrodded depletion.

An important phenomenon in these cases is the impact of the control blade insertion on the 

depletion of the gadolinium rods. The gadolinium pattern used is shown in Figure 3.11 and 

contains four pins in the southeast quadrant of the assembly and two pins in the northwest 

quadrant. The presence of the control blade in the northwest corner of the lattice suppresses 

power on that half of the assembly, thus increasing the power and flux in the southeast half. The 

increased power and flux causes more depletion locally in the southeast quadrant. Figure 3.34

shows the percent change in the pin-wise 235U number densities in the depleted fuel (10.1 

GWd/MTU) from the rodded depletion to the unrodded depletion. In the 3D plot on the left, the 

height and color of the bar correspond to the percentage differences. The legend on the right 

applies to both the 3D and 2D plots. Positive values indicate larger number densities following 

rodded depletion.
57

Figure 3.34. 235U concentration difference (in percent) between rodded and unrodded cases. 

Figure 3.35 shows the same information for 155Gd; the large bars show the difference in residual 

gadolinium in the absorber rods and the fission product gadolinium in all fuel rods. The figure 

clearly illustrates the higher depletion of the gadolinium in the southeast quadrant of the 

assembly away from the control blade. The pin-wise isotopics were not used in the cask model, 

but are used to illustrate the radial burnup shift and its impact on average uranium and residual 

gadolinium concentrations. In the 3D plot on the left, the height and color of the bar correspond 

to the percent differences. The legend on the right applies to both the 3D and 2D plots. Positive 

values indicate larger number densities following rodded depletion.

Figure 3.35. 155Gd concentration difference (in percent) between rodded and unrodded cases. 

The volume averaged 155Gd concentration for the rodded cases is shown in Figure 3.36, and a 

comparison between the rodded and unrodded cases is shown for the 0% and 80% void fractions 

in Figure 3.37.
58

Figure 3.36. 155Gd atom density as a function of burnup for several depletion moderator void 

fractions and rodded depletion.
59

Figure 3.37. 155Gd atom density over a range of burnup for rodded and unrodded depletion with 

0% and 80% void.

These results indicate that the effect of control blade insertion is potentially dependent on the 

gadolinium pattern. If the majority of the gadolinium rods were on the rodded side of the 

assembly, the average residual gadolinium poison in the assembly would increase. Patterns that 

contain many gadolinium pins on the rodded side of the assembly are unlikely for assemblies 

designed for power operations since radial enrichment zoning is generally used to lower 

reactivity on the rodded side of the assembly and less gadolinium is therefore needed to control 

power peaking in these regions. Such patterns are certainly possible in criticality safety analysis, 

however, as the patterns developed by criticality safety analysts are not intended to meet power 

peaking limits, but rather are intended to maximize reactivity.

In summary, control blade insertion during depletion increases reactivity of discharged fuel for 

both the AO and the AFP nuclide sets with the gadolinium pattern used in this study. The AO 

rodded results increase with higher void fraction, while AFP rodded results increase with lower 

void fraction. It is conservative to model gadolinium pins on the opposite side of the assembly 

from the control blade, as this will deplete them faster. The maximum reactivity for discharged 

fuel occurs for AFP rodded depletion with zero and 20% void fractions during depletion. The 

presence of the control blade during depletion increases cask kinf by approximately 1% Δk for the 

AFP cases using the 6×2 gadolinium pattern.
60

3.4.6 Operating Parameters

The reactor operating parameters influence the depleted fuel compositions and thus the 

discharged fuel reactivity. This section presents sensitivity studies investigating the impact of 

fuel temperature, specific power, and operating history on cask kinf values. No studies are 

performed relating to moderator temperature as the core operates at the saturation temperature. 

Any change in power or coolant flow would result in void fraction changes, which were studied 

in Section 3.4.4.

The operating parameters were studied by performing a matrix of calculations as shown in Table 

3.13. All depletion calculations were performed unrodded with the 6×2 gadolinium pattern 

shown in Figure 3.11, and all cask calculations used the AEAI modeling strategy. Three fuel 

temperatures, three specific powers, and four operating histories were used. The following 

sections present results for each of the operating parameters investigated. Although all 36 

combinations of operating conditions were considered, not all of the results are presented, as the 

trends are similar across the range investigated.

Table 3.13. Fuel temperatures, specific powers, and operating histories

Fuel 

Temperatures 

(K)

Specific 

Powers 

(W/g)

Operating Histories

850 25 100% power

950 35 50% power

1100 45 100% power (5 GWd/MTU), 50% power (5 GWd/MTU), 

100% power

100% power (3 GWd/MTU), 75% power (3 GWd/MTU), 

50% power (4 GWd/MTU), 100% power
61

3.4.6.1 Fuel Temperature

The models used in all the studies presented in sections 3.4.1 through 3.4.5 of this report have 

assumed a fuel temperature of 950 K. This fuel temperature was used because it is typical of 

BWR fuel at hot full power (HFP) conditions; it was not chosen to be a bounding value. The 

sensitivity of cask kinf to fuel temperature was determined by performing unrodded depletion 

calculations at 850 K, 950 K, and 1100 K for each of the specific powers and operating histories 

shown in Table 3.13. The results for the AO nuclide set are shown for the three fuel temperatures 

and a specific power of 25 W/g in Figure 3.38. 

Figure 3.38. Cask kinf as a function of burnup at 25 W/g for different fuel temperatures, AO 

nuclide set.

The burnups selected surround the cask peak reactivity burnup with the AFP nuclide set. The 

change in cask kinf for the 850 K and 1100 K cases relative to the 950 K base case is shown for 

the 25 W/g, 35 W/g, and 45 W/g cases in Tables 3.14–3.16. The differences between the 1100 K 

and 850 K cases are shown in Table 3.17 for the 25 W/g case. 
62

Table 3.14. Cask Δkinf values for 25 W/g depletion case, 950 K base case, AO nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00001 0.09 0.00043 3.09

6.96 -0.00014 0.98 0.00056 4.01

7.47 -0.00033 2.38 0.00010 0.74

8.00 -0.00019 1.33 0.00050 3.59

8.44 0.00011 0.82 0.00055 3.93

9.01 -0.00004 0.32 0.00035 2.52

Table 3.15. Cask Δkinf values for 35 W/g depletion case, 950 K base case, AO nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00016 1.16 0.00019 1.37

6.96 -0.00046 3.31 0.00028 2.01

7.47 -0.00008 0.60 0.00052 3.68

8.00 0.00000 0.03 0.00048 3.44

8.44 -0.00023 1.67 0.00037 2.66

9.01 -0.00019 1.37 0.00021 1.52

Table 3.16. Cask Δkinf values for 45 W/g depletion case, 950 K base case, AO nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00020 1.39 0.00012 0.87

6.96 -0.00015 1.11 0.00014 1.03

7.47 -0.00031 2.18 0.00004 0.29

8.00 -0.00035 2.48 0.00025 1.76

8.44 -0.00026 1.87 0.00020 1.46

9.01 -0.00009 0.63 0.00050 3.56

Table 3.17. Cask Δkinf values for 25 W/g case, 1100 K ̶ 850 K, AO nuclide set

Burnup

(GWd/MTU)

Δkinf, 1100 K – 850 K

(Δk)

Δkinf, 1100 K – 850 K

(|Δk/σ|)

6.46 0.00044 3.18

6.96 0.00070 4.98

7.47 0.00044 3.12

8.00 0.00069 4.91

8.44 0.00043 3.10

9.01 0.00040 2.84

In each of the tables, the differences are shown both in actual kinf change, Δk, and in terms of the 

number of standard deviations, n=|Δk/σ|, that this difference represents. The comparison in terms 

of standard deviations helps provide context for the magnitude of the differences. Generally, 

differences that are less than 2σ are considered statistically equivalent. There is evidence of a 
63

weak trend of reactivity variation with increasing fuel temperatures at the lower two specific 

power levels. There is no clear indication of a trend as a function of burnup at any of the specific 

power levels. The comparison from maximum to minimum fuel temperatures presented in Table 

3.17 supports the conclusion that cask reactivity increases with increasing fuel temperatures 

during depletion, but it does not show any clear trends as a function of burnup. It can therefore 

be concluded that cask kinf increases slightly (~0.0020% Δk / 100 K) with increasing fuel 

temperature for the AO nuclide set in this study.

Figure 3.39 shows the results for the AFP nuclide set for the three fuel temperatures and a 

specific power of 25 W/g. 

Figure 3.39. Cask kinf as a function of burnup at 25 W/g for different fuel temperatures, AFP 

nuclide set.

Tables 3.18–3.20 show the change in cask kinf for the 850 K and 1100 K cases relative to the 950 

K base case for the 25 W/g, 35 W/g, and 45 W/g cases. The differences between the 1100 K and 

850 K cases are shown in Table 3.21 for the 25 W/g case. As with the results for the AO set, the 

differences are shown both in actual kinf change and in terms of the number of standard 

deviations this difference represents. No clear statistical trends are evident in the results, but it 
64

appears that kinf may increase slightly with increasing fuel temperature for the AFP nuclide set as 

well. This conclusion may change at the higher burnups considered for extended BUC.

Table 3.18. Cask Δkinf values for 25 W/g depletion case, 950 K base case, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00010 0.73 0.00000 0.01

6.96 -0.00004 0.26 0.00000 0.02

7.47 -0.00001 0.09 0.00014 1.00

8.00 0.00014 1.01 0.00035 2.49

8.44 -0.00005 0.35 0.00021 1.50

9.01 0.00011 0.80 0.00040 2.88

Table 3.19. Cask Δkinf values for 35 W/g depletion case, 950 K base case, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00015 1.11 0.00008 0.56

6.96 -0.00004 0.32 0.00025 1.78

7.47 0.00030 2.15 0.00031 2.22

8.00 -0.00007 0.52 0.00007 0.52

8.44 -0.00021 1.46 0.00010 0.74

9.01 0.00006 0.45 0.00053 3.87

Table 3.20. Cask Δkinf values for 45 W/g depletion case, 950 K base case, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf, 

850 K – 950 K

(Δk)

Δkinf, 

850 K – 950 K

(|Δk/σ|)

Δkinf, 

1100 K – 950 K

(Δk)

Δkinf, 

1100 K – 950 K

(|Δk/σ|)

6.46 -0.00008 0.55 -0.00015 1.07

6.96 -0.00017 1.21 0.00009 0.64

7.47 -0.00002 0.15 0.00021 1.46

8.00 -0.00009 0.66 0.00009 0.61

8.44 -0.00011 0.80 0.00014 1.00

9.01 -0.00009 0.67 0.00024 1.74

Table 3.21. Cask Δkinf values for 25 W/g case, 1100 K ̶ 850 K, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf, 1100 K – 850 K

(Δk)

Δkinf, 1100 K – 850 K

(|Δk/σ|)

6.46 0.00010 0.72

6.96 0.00003 0.24

7.47 0.00015 1.08

8.00 0.00021 1.49

8.44 0.00026 1.85

9.01 0.00028 2.06
65

3.4.6.2 Specific Power

The models used in all studies presented in sections 3.4.1–3.4.5 of this report assumed a specific 

power of 25 W/g. This specific power was used because it is typical of BWR fuel; it is not 

chosen to be a bounding value. The sensitivity of cask kinf to specific power was determined by 

performing unrodded depletion calculations at 25, 35, and 45 W/g for each of the fuel 

temperatures and operating histories shown in Table 3.13.

The results for the AO nuclide set are shown in Figure 3.40 for the three specific powers and at a 

fuel temperature of 950 K. The burnups selected surround the cask peak reactivity burnup with 

the AFP nuclide set. 

Figure 3.40. Cask kinf as a function of burnup for different specific powers with 950 K fuel 

temperature, AO nuclide set.

The change in cask kinf for the 35 W/g and 45 W/g cases relative to the 25 W/g base case is 

shown for the 850 K, 950 K, and 1100 K cases in Tables 3.22–3.24. In each of the tables, the 

differences are shown both in actual kinf change and in the number of standard deviations. 
66

Table 3.22. Cask Δkinf values for 35 W/g and 45 W/g, 850 K fuel temperature, AO nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 -0.00095 6.75 -0.00088 6.25

6.96 -0.00096 6.83 -0.00065 4.67

7.47 -0.00085 6.02 -0.00077 5.51

8.00 -0.00084 6.02 -0.00103 7.32

8.44 -0.00107 7.65 -0.00094 6.72

9.01 -0.00110 7.84 -0.00104 7.39

Table 3.23. Cask Δkinf values for 35 W/g and 45 W/g 950 K fuel temperature, AO nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 -0.00079 5.68 -0.00069 4.95

6.96 -0.00063 4.50 -0.00064 4.54

7.47 -0.00110 7.83 -0.00080 5.71

8.00 -0.00103 7.38 -0.00086 6.17

8.44 -0.00072 5.16 -0.00056 4.01

9.01 -0.00095 6.83 -0.00099 7.09

Table 3.24. Cask Δkinf values for 35 W/g and 45 W/g 1100 K fuel temperature, AO nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 -0.00104 7.39 -0.00100 7.13

6.96 -0.00091 6.48 -0.00106 7.50

7.47 -0.00069 4.89 -0.00086 6.20

8.00 -0.00105 7.53 -0.00112 8.00

8.44 -0.00089 6.46 -0.00090 6.51

9.01 -0.00109 7.81 -0.00085 6.04

Cask reactivity clearly drops slightly between 25 and 35 W/g at all three fuel temperatures. It 

appears that there is no statistically significant difference in cask reactivity between 35 and 45 

W/g, though reactivity may be slightly higher at 45 W/g. This may be evidence for a nonlinear 

relationship between specific power and reactivity, as noted for PWR BUC [16]. A review of 

depleted number densities shows that at higher specific powers, the 235U is slightly more 

depleted, but that slightly more 239Pu has been generated. The depleted number densities for nongadolinium fuel pins in the interior region of the fuel assembly are shown in Table 3.25. Note 

that the depleted 235U concentrations for the 35 and 45 W/g cases are nearly identical. Thus it 

appears that, at the burnups of interest for peak reactivity methods, the increase in 235U depletion 

is the primary cause of the reduction in cask reactivity between 25 and 35 W/g, and there is no 

significant change between 35 and 45 W/g. As with the fuel temperature sensitivity, it is possible 

that a different trend could manifest at the higher burnups associated with extended BWR BUC 

beyond peak reactivity.
67

Table 3.25. 235U and 239Pu number densities for different specific powers and 950 K fuel

temperature

Burnup

(GWd/MTU)

235U Number Density (a/b-cm) 239Pu Number Density (a/b-cm)

25 W/g 35 W/g 45 W/g 25 W/g 35 W/g 45 W/g

6.46 8.548E-04 8.504E-04 8.503E-04 4.727E-05 4.857E-05 4.874E-05

6.96 8.436E-04 8.391E-04 8.390E-04 4.996E-05 5.124E-05 5.143E-05

7.47 8.321E-04 8.275E-04 8.275E-04 5.261E-05 5.391E-05 5.410E-05

8.00 8.204E-04 8.156E-04 8.156E-04 5.525E-05 5.656E-05 5.676E-05

8.44 8.107E-04 8.058E-04 8.058E-04 5.735E-05 5.867E-05 5.888E-05

9.01 7.983E-04 7.933E-04 7.933E-04 5.999E-05 6.131E-05 6.153E-05

The results for the AFP nuclide set are shown for three specific powers and a fuel temperature of 

950 K in Figure 3.41. 

Figure 3.41. Cask kinf as a function of burnup for different specific powers with 950 K fuel 

temperature, AFP nuclide set.

The change in cask kinf for the 35 W/g and 45 W/g cases relative to the 25 W/g base case is 

shown for the 850 K, 950 K, and 1100 K cases in Tables 3.26–3.28. 
68

Table 3.26. Cask Δkinf values for 35 W/g and 45 W/g, 850 K fuel temperature, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 0.00023 1.66 -0.00015 1.04

6.96 -0.00021 1.53 -0.00096 6.85

7.47 -0.00032 2.27 -0.00105 7.48

8.00 -0.00099 7.10 -0.00163 11.64

8.44 -0.00139 9.91 -0.00214 15.48

9.01 -0.00188 13.41 -0.00241 17.21

Table 3.27. Cask Δkinf values for 35 W/g and 45 W/g, 950 K fuel temperature, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 0.00028 2.00 -0.00017 1.22

6.96 -0.00021 1.47 -0.00083 5.90

7.47 -0.00063 4.54 -0.00104 7.50

8.00 -0.00078 5.57 -0.00140 9.97

8.44 -0.00123 8.76 -0.00207 14.81

9.01 -0.00183 13.25 -0.00220 15.74

Table 3.28. Cask Δkinf values for 35 W/g and 45 W/g, 1100 K fuel temperature, AFP nuclide set

Burnup

(GWd/MTU)

Δkinf (Δk)

35 W/g – 25W/g

Δkinf (|Δk/σ|) 

35 W/g – 25W/g

Δkinf (Δk)

45 W/g – 25W/g

Δkinf (|Δk/σ|) 

45 W/g – 25W/g

6.46 -0.00032 2.29 -0.00032 2.29

6.96 -0.00073 5.24 -0.00073 5.24

7.47 -0.00098 6.99 -0.00098 6.99

8.00 -0.00166 11.80 -0.00166 11.80

8.44 -0.00215 15.24 -0.00215 15.24

9.01 -0.00236 17.16 -0.00236 17.16

Cask reactivity decreases with increased specific power. The differences among the specific 

powers are small at low burnups, but they grow noticeably with increasing burnup. The 239Pu 

number densities show a slight increase with increased specific power, and the 155Gd number 

densities show a slight decrease with increasing specific power. Both of these trends would 

indicate a small positive relationship between specific power and cask kinf. The number densities 

for the most important fission products—including 149Sm, 103Rh, and 143Nd [13]—are higher for 

higher specific powers. The 149Sm number densities shown in Table 3.29 indicate an increase of 

about 9% at 35 W/g compared to the 25 W/g base case and a total increase of about 18% at 45 

W/g. The effect of these increased absorbers overwhelms the slight differences in plutonium and 

gadolinium and creates a slight negative relationship that increases with burnup. 
69

Table 3.29. 149Sm number densities at a range of specific powers and 950 K fuel temperature

Burnup

(GWd/MTU)

149 Sm, 25 W/g

(a/b-cm)

149 Sm, 35 W/g

(a/b-cm)

Percent change

from 25 W/g

149 Sm, 45 W/g

(a/b-cm)

Percent 

change

from 25 W/g

6.46 1.08E-07 1.18E-07 8.95% 1.27E-07 17.34%

6.96 1.09E-07 1.18E-07 9.02% 1.28E-07 17.59%

7.47 1.09E-07 1.19E-07 9.10% 1.28E-07 17.83%

8.00 1.09E-07 1.19E-07 9.27% 1.29E-07 18.07%

8.44 1.09E-07 1.19E-07 9.44% 1.29E-07 18.33%

9.01 1.09E-07 1.20E-07 9.61% 1.30E-07 18.66%

The increasing fission product inventory at higher burnups also explains the burnup dependence 

of this effect, providing additional confidence that increased fission product generation at higher 

specific powers causes the cask reactivity to decrease. The effect is fairly small at peak reactivity 

(less than 0.1% Δk), but the effect increases to about 0.25% Δk by 9 GWd/MTU. This provides a 

clear indication that there is likely to be sensitivity to specific power for extended BWR BUC 

beyond peak reactivity. For peak reactivity methods, there is a small sensitivity indicating that 

lower specific powers lead to higher discharged reactivities as shown in Figure 3.41.

3.4.6.3 Operating History

The models used in all the studies presented in sections 3.4.1–3.4.5 of this report assumed a full 

power (FP) operating history. This assumption is typical for depletion calculations; the actual 

operating history of a fuel assembly, even if the reactor operates at FP for an entire cycle, is more 

complex. The sensitivity of cask kinf to other operating histories was determined by performing 

unrodded depletion calculations using each of the four power histories shown in Table 3.12 for 

each of the fuel temperatures and specific powers listed as well. In this section, the operating 

histories will be referred to as FP, half power (HP), full power followed by half power (FHP), 

and full power followed by three-quarter power followed by half power (FTHP).

The results for the AO nuclide set are shown for the four operating histories and a fuel 

temperature of 950 K in Figure 3.42. 
70

Figure 3.42. Cask kinf as a function of burnup for four different operating histories, AO nuclide set.

The burnups selected surround the cask peak reactivity burnup with the AFP isotope set. The 

results indicate that the FP operating history yields the highest discharge reactivity, while the 

other histories lead to lower cask kinf values that are statistically equivalent. The small magnitude 

of the changes among the different part-power histories for the AO set is consistent with the 

small magnitude of the sensitivity to specific power with the same nuclide set. The effect is 

reduced because the change among the histories is less dramatic than shifts of 10 W/g for the 

entire depletion. The FP operating history is limiting for cask kinf with the AO nuclide set.

The results for the AFP nuclide set are shown for the four operating histories and a fuel 

temperature of 950 K in Figure 3.43. 
71

Figure 3.43. Cask kinf as a function of burnup for four different operating histories, AFP 

nuclide set.

In this case, the FP history is the least reactive result. The HP history provides an upper bound on 

cask reactivity, and the FHP and FTHP histories yield results largely between the two. The peak 

reactivity burnup is largely unaffected by the power history, and the magnitude of the peak 

reactivity only shifts by about 0.2% Δk. The AFP operating history results are in good agreement 

with the AFP-specific power results presented in Section 3.4.6.2. The HP history is essentially 

equivalent to a specific power of 12.5 W/g, which would be expected to be more reactive than 

the 25 W/g FP history. A variable operating history is bounded by a constant history with an

appropriate low specific power for the AFP nuclide set.

3.4.7 Three-Dimensional Modeling

A final sensitivity study was performed to investigate the practice of using a 3D cask model 

containing a fuel assembly represented by a 2D lattice slice extruded to the full fuel assembly 

length. The axial features of the fuel assembly and cask are used as specified in the GBC-68 

definition [10]. Two sets of depleted fuel isotopics are modeled: the base case and the limiting 

case identified in the studies presented in this report for the AFP nuclide set. The base case is

unrodded depletion with 40% moderator void fraction and the 6×2Gd pattern shown in Figure 
72

3.11. The limiting case is rodded depletion with 0% void and the same 6×2Gd pattern. Both 

scenarios used 950 K fuel temperatures and a constant 25 W/g specific power depletion.

The results for the base case are shown in Figure 3.44 and for the limiting case in Figure 3.45. 

Both figures show all four nuclide sets for the 2D and 3D models. 

Figure 3.44. Cask reactivity as a function of burnup, unrodded depletion with 40% void fraction, 

all nuclide sets.
73

Figure 3.45. Cask reactivity as a function of burnup, rodded depletion with 0% void fraction, all 

nuclide sets.

The change in cask kinf values (Δk) is presented for the AO and AFP nuclide sets for the base 

case fuel model in Table 3.30 and for the rodded depletion in Table 3.31. The results show that 

the extruded lattice models result in slightly lower cask reactivities than the 2D models. The 

margin inherent in the 2D models compared to the 3D models is small. In these cases the 

difference in reactivity is about 0.2% Δk.

Table 3.30. Difference between 2D cask kinf and 3D cask keff, unrodded depletion with 40% void 

fraction

Burnup

(GWd/MTU

AO AFP AFPNG ALL

Δk σ Δk σ Δk σ Δk σ

6.46 0.00219 0.00014 0.00218 0.00014 0.00198 0.00014 0.00221 0.00014

6.96 0.00196 0.00014 0.00230 0.00014 0.00211 0.00014 0.00202 0.00014

7.47 0.00238 0.00014 0.00204 0.00014 0.00241 0.00014 0.00227 0.00014

8.00 0.00226 0.00014 0.00204 0.00014 0.00207 0.00014 0.00222 0.00014

8.44 0.00181 0.00014 0.00221 0.00014 0.00219 0.00014 0.00217 0.00014

9.01 0.00198 0.00014 0.00187 0.00014 0.00213 0.00014 0.00225 0.00014
74

Table 3.31. Difference between 2D cask kinf and 3D cask keff, rodded depletion 

with 0% void fraction

Burnup

(GWd/MTU)

AO AFP AFPNG ALL

Δk σ Δk σ Δk σ Δk σ

5.69 0.00193 0.00014 0.00197 0.00014 0.00243 0.00014 0.00208 0.00014

6.17 0.00215 0.00014 0.00186 0.00014 0.00226 0.00014 0.00224 0.00014

6.66 0.00219 0.00014 0.00192 0.00014 0.00221 0.00014 0.00213 0.00014

7.16 0.00233 0.00014 0.00213 0.00014 0.00206 0.00014 0.00194 0.00014

7.68 0.00230 0.00014 0.00178 0.00014 0.00213 0.00014 0.00224 0.00014

8.22 0.00215 0.00014 0.00228 0.00014 0.00223 0.00014 0.00214 0.00014

3.5 SUMMARY OF FACTORS AFFECTING PEAK REACTIVITY

The purpose of this section is to examine the impacts of important BWR design and operating 

parameters on reactivity, up to the peak reactivity. Sensitivity calculations have been performed 

over a range of parameters, including gadolinium loadings and assembly patterns, void fraction, 

control blade insertion, fuel temperature, specific power, and operating history. This section 

summarizes the sensitivity studies results, lists recommended analyses that should be presented 

as part of a criticality safety evaluation, and defines areas of future study. Conclusions for the 

report are presented in Section 6.

3.5.1 Summary of Sensitivity Studies

A range of parameters were studied to identify the important parameters for BWR peak reactivity 

and to quantify the potential sensitivity of calculated cask reactivity to these parameters. The 

primary fuel assembly model used in this study was the GE14 fuel assembly, which has a 10×10 

array of fuel pins and contains two large central water rods which each displace four fuel rods. 

Full and vanished lattices with no gadolinium-poisoned pins were used as the base case for AO 

BUC sensitivity studies. For the AFP BUC sensitivity studies, six gadolinium-poisoned fuel pins 

with 2.0 wt% gadolinium were used as the base case. The results of the sensitivity studies are 

summarized below and shown in Tables 3.32 and 3.33 for AO and AFP, respectively.
75

Table 3.32. Summary of parameters affecting discharged reactivity for BWR 

peak reactivity analysis considering the AO nuclide set

Parameter Range Studied Reactivity Impact

(%Δk)

Fuel composition modeling AEAI, PEAI, PEPI 0.3 

(AEAI)

Number of gadolinium pins 0 to 8 pins

(0 pins base case)

~0

(≤0.06 at 7 GWd/MTU)

Loading of gadolinium pins 0 to 10 wt% 0 to 0.5

(9 – 25 GWd/MTU)

Gadolinium pattern 15 patterns ~0

(±0.03 at 7 GWd/MTU)

Moderator void fraction, unrodded 0 to 80%

(40% base case)

-0.4 to +0.7

(0% void to 80% void)

Moderator void fraction, rodded 0 to 80%

(40% base case)

-0.6 to +1.1

(0% void to 80% void)

Control blade insertion unrodded vs. rodded 

(full depletion) ≤ 1 (rodded)

Fuel temperature 850 to 1100 K

(950 K base case) ~0.0020%Δk / 100 K

Specific power 25 to 45 W/g

(25 W/g base case)

0.1 

(35 and 45 W/g)

Operating history 4 histories

(FP base case) -0.1

Cask model dimension 2D, 3D

(2D base case) -0.2
76

Table 3.33. Summary of parameters affecting discharged reactivity for BWR 

peak reactivity analysis considering the AFP nuclide set

Parameter Range Studied Reactivity Impact

(%Δk)

Fuel composition modeling AEAI, PEAI, PEPI 0.5 

(AEAI)

Number of gadolinium pins 2 to 8 pins

(6 pins base case)

+1.3 to -0.2 

(2 to 8 pins)

Loading of gadolinium pins 2 to 10 wt%

(2 wt% base case)

-3 to -11

(4 wt% to 10 wt%)

Gadolinium pattern 15 patterns ±0.25 at peak reactivity

(~7.5 GWd/MTU)

Moderator void fraction, unrodded 0 to 80%

(40% base case)

+0.2 to -0.2

(0% void to 80% void)

Moderator void fraction, rodded 0 to 80%

(40% base case)

+0.1 to -0.2

(0% void to 80% void)

Control blade insertion unrodded vs. rodded 

(full depletion) ~1.0 (rodded)

Fuel temperature 850 to 1100 K

(950 K base case) 0

Specific power 25 to 45 W/g

(25 W/g base case)

-0.1

(peak reactivity)

Operating history 4 histories

(FP base case)

0.1

(HP case)

Cask model dimension 2D, 3D

(2D base case) -0.2

Most of the parameters studied affect reactivity through changes in the depleted fuel 

compositions. Two modeling approaches were examined for fuel compositions within the lattice: 

(1) the modeling of the initial enrichment zoning within a fuel assembly, and (2) the depletion 

and representation of the different depleted fuel mixtures in the cask. The initial enrichment 

zoning can be represented with PE or AE. The depleted compositions in the cask criticality 

model can use pin-wise isotopics (PI) or average isotopics (AI). The AE cases provide higher 

discharged reactivity than the PE cases by effectively moving fissile material to higher thermal 

flux regions around the periphery of the assembly and near the water tubes. There does not 

appear to be a strong dependence on the depleted fuel representation, but PI may lead to a 

slightly higher reactivity than AI. The AEPI approach is not recommended, however, because a 

significant contribution to the differences among the depleted fuel pins would be due to 

differences in initial concentrations that are not realistic. Therefore, the AEAI modeling strategy 

was chosen because of the moderate level of conservatism and the ease of modeling. The PE 

approaches would require additional effort to model the assembly more accurately.

The number and initial loading of gadolinium pins has negligible impact on AO BUC, because 

gadolinium is not included in the cask model. However, they impact both the magnitude of peak 

reactivity and the burnup at which it occurs for AFP BUC, as shown in Figures 3.17 and 3.19. 

The 6×2Gd pattern was selected for the AFP base case because it provides a definitive peak in 

reactivity, and the peak is at a relatively low burnup resulting in a peak that has a large 
77

magnitude compared to other higher gadolinium cases. A series of 15 gadolinium loading 

patterns (Appendix B) were examined to determine impacts on cask reactivity. The reactivity of 

the base case pattern was approximately average of the range of cask reactivities resulting from a 

6×2Gd loading, but the magnitude of the effect was small at approximately ±0.25% Δk at peak 

reactivity for AFP.

The impact of the void fraction on cask reactivity differs significantly between AO and AFP 

BUC cases. Cask reactivity increases with higher void fractions for the AO cases due to the 

hardening neutron spectrum at increasing void fractions. The overall reactivity change from 0% 

to 80% void is greater than 1% Δk at about 7.5 GWd/MTU for unrodded cases and greater than 

1.5% for rodded cases. This is a significant impact that must be properly accounted for during 

depletion calculations for AO BUC. The results for the AFP nuclide set are completely reversed: 

the low void fraction case is bounding. The driving effect for the AFP cases is the amount of 

residual gadolinium (the AO cases do not include residual gadolinium in the cask model), which 

is decreased by a more thermal spectrum because of the larger thermal absorption cross section 

for gadolinium. As the void fraction increases, the gadolinium depletion is slower, causing a 

reduction in the reactivity peak and a shift to higher burnups. The peak reactivity of the cask 

drops by about 0.4% Δk from 0% void fraction to 80% void fraction (±0.2% Δk relative to the 

40% void fraction base case) for unrodded cases, and slightly less for rodded cases. 

Depletion cases were run with control blades inserted for 0 to 80% void fraction cases to 

compare with the unrodded void fraction cases. The presence of the control blade during 

depletion increases cask kinf up to 1% Δk for AO cask reactivity cases. These results are driven 

by the hardening neutron spectrum at increasing void fractions and by a significant spectral shift 

caused by the presence of the control blade during depletion. The harder spectrum causes 

additional 239Pu generation, which is a significant contributor to reactivity, even at these 

relatively low burnups. For the AFP nuclide set, the maximum reactivity for discharged fuel 

occurs for rodded depletion with zero void fractions during depletion. The presence of the 

control blade during depletion increases cask kinf by approximately 1% Δk for AFP cases.

Fuel temperature effects were studied by performing depletion cases at 850 K and 1100 K in 

addition to the base case at 950 K. For AO cases, the cask reactivity increases slightly with 

increasing fuel temperatures during depletion. The cask kinf increases ~0.0020% Δk / 100 K with 

increasing fuel temperature for the AO cases. The AFP cases also appeared to show slightly 

higher cask kinf values with increasing fuel temperature during depletion, although there was no 

statistical trend.

The sensitivity of cask kinf to specific power was determined by performing unrodded depletion 

calculations at 25, 35, and 45 W/g for each of the three fuel temperatures and four operating 

histories, FP, HP, FHP, and FTHP. Cask reactivity drops slightly for the AO cases between 25 

and 35 W/g at all three fuel temperatures. It appears that there is no statistically significant 

difference in cask reactivity between 35 and 45 W/g. For AFP cases, cask reactivity decreases 

with increased specific power. The differences among the specific powers are small at low 

burnups, but grow with increasing burnup. The effect is fairly small at peak reactivity (~ 0.1% 

Δk) but increases to about 0.25% Δk by 9 GWd/MTU.
78

The FP operating history is limiting for cask kinf with the AO nuclide set. The part-power 

histories produce cask kinf values that are approximately 0.1% lower. The results for the AFP 

nuclide set are different in that the FP history is the least reactive result. The HP history provides 

an upper bound on cask reactivity (0.1% Δk), and the FHP and FTHP histories yield results 

largely between the two. It appears that an appropriately bounding low specific power is limiting 

for the AFP nuclide set.

Regarding 2D vs. 3D modeling, the 2D model represents all cask and fuel components with a 

uniform height and uses reflecting boundary conditions in the axial direction to mimic a 2D slice. 

The 3D model represents the cask and fuel assembly with the heights specified for the GBC-68 

computational benchmark model. The fuel is represented as a 2D slice extruded to the axial 

extent specified in the model definition. The results show that the 3D model is about 0.2% Δk

less reactive than the 2D model. The 3D model is a more accurate representation of the system, 

but the 2D model includes only a small margin of conservatism.

3.5.2 Recommended Minimum Analyses

A range of parameters has been investigated in this report, and one set of conclusions that can be 

drawn relates to which parameters are sufficiently variable or interdependent so that examination 

is recommended for each licensing analysis performed. The primary parameters of interest in this 

category are the gadolinium pattern used in the analysis and the way it interacts with control 

blade insertion. It is conceivable that some gadolinium patterns will be more reactive than others. 

More importantly, the power distribution shifts caused by control blade insertion drive the 

changes in residual gadolinium, and hence discharged fuel reactivity. These effects will be 

sensitive to the gadolinium pattern. Certain other key parameters do not need to be studied 

further to identify the direction of conservatism, but justification that the values used are 

appropriate should be provided as part of an application. The parameters that do not need further 

investigation for the GE14 design considered in this work include initial or depleted composition 

modeling, void fraction, fuel temperature, and operating history. 

3.5.3 Areas for Further Study

Several areas related to peak reactivity BUC could be further studied to provide additional 

confidence in the results generated in this report, clarify causes and relationships among 

parameters, or extend the area of applicability beyond the parameters, ranges, and fuel types 

studied here. One essential area that requires assessment is validation of reactivity calculations 

and depleted fuel isotopics. These validation assessments are provided in Sections 4 and 5, 

respectively. Other areas that could be studied further include the following:

• A wider range of lattice enrichment zoning patterns

• Additional gadolinium patterns, potentially including less constrained pattern 

development

• Expansion of the study of the interaction between gadolinium patterns and control blade 

effects
79

• Control blade programs, including both rodded and unrodded depletion during operation

• Additional fuel assembly design types

• 3D depletion calculations to investigate interactions between lattices

• Fuel assembly orientation within the cask

• Depletion effects of asymmetric gaps between assemblies in the core

• Parameter interdependencies and potential competing effects

81

4 VALIDATION OF CASK REACTIVITY CALCULATIONS

Consistent with industry standards [17] and regulatory guidance [2], criticality safety 

calculations must be validated against critical experiments to demonstrate the reliability of the 

computational methods and models and also to determine a bias and uncertainty applicable to the 

code and methods used. Validation of BUC is challenging due to the lack of critical experiments 

containing the appropriate AFP compositions [13]. The reactivity of typical BWR fuel lattices 

typically peak at less than ~20 GWD/MTU, which is significantly lower than the range of 

discharged assembly burnups. This provides unique challenges for validating BWR calculations

[13].

The French Haut Taux de Combustion (HTC) experiments [18] provide a highly representative 

set of actinide compositions for validation of PWR BUC. These experiments are designed to 

have actinide compositions similar to a PWR fuel assembly with an initial enrichment of 4.5 

wt% 235U and a discharged burnup of 37.5 GWd/MTU. This burnup is significantly higher than 

typical BWR peak reactivity values, resulting in higher plutonium fractions and a different 

distribution of plutonium nuclides than would be expected in the BWR design basis fuel 

composition. Nevertheless, the HTC experiments will be considered here for validation of BWR 

peak reactivity calculations, along with several other experiments drawn from the International 

Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE) [19].

This section provides an overview of studies performed to establish a basis for validating cask 

reactivity calculations for BWR peak reactivity methods implemented in a storage and 

transportation cask. Items in this section include (1) the methodology used, (2) a description of 

the codes and methods used, (3) a description of the three primary sources for sensitivity data 

files (SDFs) used to assess similarity between critical experiments and application models, (4) a

list of potentially applicable experiments identified in this work, (5) estimates for the bias and 

bias uncertainty using SCALE 6.1.2, (6) a discussion of potential penalties for unvalidated 

nuclides, and (7) a summary of the validation of cask reactivity calculations.

4.1 CODES AND METHODS

The majority of the work presented in this section is performed using tools from the SCALE 

code system’s Tools for Sensitivity and Uncertainty Analysis Methodology Implementation 

(TSUNAMI) suite. SDFs are generated using the TSUNAMI-3D sequence, which combines the 

KENO Monte Carlo code with the Sensitivity Analysis Module for SCALE (SAMS) code. 

Similarity assessments are performed with TSUNAMI - Indices and Parameters (TSUNAMI-IP).

The TSUNAMI-3D sequence is the control module for 3D cross-section sensitivity and 

uncertainty analysis. The sequence provides automated processing of material input and crosssection data, forward and adjoint neutron transport, calculation of sensitivity coefficients (i.e., 

sensitivity of keff to nuclear data variation), and determination of uncertainty in keff due to crosssection covariances. The SAMS module computes sensitivities based on the forward and adjoint 

fluxes calculated by KENO and generates an SDF containing the nuclide-, energy-, and reactiondependent keff sensitivity coefficients. These energy-dependent sensitivities are determined for 

each nuclide in the model using linear perturbation theory.
82

The three GBC-68 cask models used in these analyses are modeled in KENO V.a. Critical 

experiment models that were previously prepared using either KENO V.a or KENO-VI and are 

available from a variety of sources (as discussed below) are used in this work for convenience. The 

use of benchmark models from different criticality codes is not appropriate for application-specific 

validation since the validation must be performed with the same code as the licensing calculations. 

The geometry representation and tracking algorithms are different between the two KENO versions, 

so they implement different computational methods. The pooling of results from both codes is 

acceptable for this work because its primary purpose is to demonstrate validation feasibility.

TSUNAMI-IP is used to evaluate the similarity of critical experiments and application models 

and to determine uncertainties in cask reactivity due to cross-section covariance data. The 

similarity metric calculated in the ck value is a correlation coefficient and can therefore be 

determined by dividing the covariance between the experiment and application by the product of 

the uncertainties in the experiment and the application [11], as shown in Equation 1.

App Exp

2

AppExp

k c

σ σ

σ = (1)

Where: ck is the similarity between an application and an experiment

σ

2

AppExp is the covariance between the application and the experiment

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

σExp is the uncertainty in the experiment keff due to cross-section covariances

A ck value of 1 indicates that the keff values for two compared systems would be affected 

identically by nuclear data errors, which are the primary contributors to computational method 

bias. A ck value ≥ 0.8 is considered a high enough degree of similarity to be acceptable for use in 

validation studies [20] and is used as the cutoff for the acceptably similar experiments identified 

in Section 4.4.

4.2 METHODOLOGY FOR VALIDATION STUDIES

The goal of this criticality validation study is to identify applicable experiments for the validation 

of criticality calculations that incorporate BUC up to peak reactivity for BWR fuel in storage and 

transportation casks. 

Three GBC-68 cask models with full and vanished lattices were compared with a large number 

of critical experiment models using TSUNAMI-IP to determine how similar each experiment is 

to each application model. A significant advantage of this approach is that the cross-section 

uncertainties provide input to the similarity assessment; shared sensitivities with large 

uncertainties contribute more to ck than shared sensitivities with small uncertainties. A 

disadvantage is that an SDF must be generated for each experiment and each application for a 

comparison to be made. Fortunately, a large number of SDFs have been generated [21] by the 

Organisation for Economic Cooperation and Development/Nuclear Energy Agency 

(OECD/NEA) for use in scoping studies such as this one. The majority of the low–enriched, pinlattice critical experiments contained in the IHECSBE [19] have provided sensitivity data 

available in the public domain.
83

Once potentially applicable experiments have been identified, a brief validation study is 

presented using traditional trending methods and ck trending. While this validation study is not 

sufficiently rigorous to be considered as an example for any specific application, it is intended to 

demonstrate that a sufficient population of experiments has been identified. These studies 

include methods drawn from previous NUREG/CR reports on validation [22, 23].

The penalties developed for unvalidated nuclides (i.e., nuclides not well represented in the 

validation experiment set) are based on cross-section uncertainty values propagated with model 

sensitivity data to determine reactivity uncertainty due to cross-section uncertainties. The 

uncertainty in the storage/transportation configuration calculated reactivity is determined from 

TSUNAMI-IP and/or TSUNAMI-3D. This method is based on techniques similar to those used 

to determine the fission product penalty factor recommended for use in ISG-8 Revision 3 [2] as 

documented in NUREG/CR-7109 [13].

4.3 SDF SOURCES

The similarity assessment performed by TSUNAMI-IP requires a set of SDFs, which are typically 

generated using TSUNAMI-3D. The generation of SDFs can be time consuming, so identifying 

sources for SDFs to be used in this work is important. Three primary sources were considered: 

SDFs generated by the OECD/NEA, SDFs used in the preparation of NUREG/CR-7109, and SDFs 

in the SCALE validation library maintained at ORNL, known as the Verified, Archived Library of 

Inputs and Data (VALID) library [24]. Each of these sources is discussed briefly here. A complete 

list of the experiments considered in this validation work is provided in Appendix C. In total, over 

1100 low-enriched uranium (LEU) experiments were considered in this work, as well as more than 

575 mixed uranium/plutonium (MIX) experiments.

The generation of SDFs at the OECD/NEA is automated such that a large amount of sensitivity 

data is available in the public domain for use. These files are distributed in the IHECSBE. For 

the purposes of this report, sensitivity data from 1002 LEU-COMP-THERM (LCT) experiments 

data are used from this source, along with 200 MIX-COMP-THERM (MCT) and 26 MIX-SOLTHERM (MST) SDFs. This large collection of SDFs is a valuable resource for validation 

studies. The terms “COMP” and “SOL” indicate the fuel form (solid composition, e.g. UO2, and 

solution, respectively). The term “THERM” specifies the flux spectrum is thermal.

A number of SDFs available at ORNL were collected as part of the generation of 

NUREG/CR-7109 [13]. The inputs used to generate these SDFs are available for public 

download from the SCALE website [25]. This collection includes 124 LEU experiments and 194 

MIX experiments. The 156 HTC experiments were also considered in NUREG/CR-7109 and in 

this validation effort. The HTC data are proprietary and are therefore not freely distributed; the 

data necessary to build models of the HTC experiments can be acquired from ORNL at no cost 

after an appropriate non-disclosure agreement has been signed. Some of these cases were 

superseded by SDFs available in the VALID library.

The VALID library is maintained at ORNL to provide a source of high fidelity reviewed models 

and other data, including SDFs. Each file contained within VALID has been created and 

reviewed by qualified subject matter experts to provide confidence that the SDFs are correct and 
84

of high quality. A total of 123 LEU-COMP-THERM experiments from VALID are considered, 

along with 49 MIX-COMP-THERM cases.

Some experiments are included in multiple SDF sources. After elimination of duplicate 

experiments, a total of 1643 unique experiments are considered.

4.4 POTENTIALLY APPLICABLE EXPERIMENTS

TSUNAMI-3D models of the GBC-68 cask [10], loaded with full and vanished lattices, are used 

as applications for validation. Sensitivity data are generated for three GBC-68 cask models: the 

vanished lattice including AO and AFP compositions, and the full lattice with AFP

compositions. These were calculated with an initial enrichment of 4.305 wt% 235U, an 

approximately 7.5 GWd/MTU peak reactivity burnup, and a 5-year decay time. 

These SDFs are compared against the critical experiments described in the previous section to 

determine which experiments have sufficiently high similarity to be applicable for benchmarking 

BWR peak reactivity cask models. The results of these comparisons are provided for each of these 

cases, followed by a summary at the end of this section. In addition, the SDF for the BWR SFP 

rack application from NUREG/CR-7109 [13], which used a different lattice design, is used for 

comparison with the GBC-68 models to provide an indication of the possible range of validation 

results from different design basis BWR lattices. Peak reactivity for the SFP rack lattice was at a 

burnup of approximately 11 GWd/MTU, and the fuel was modeled with AFP compositions.

4.4.1 Vanished Lattice with Actinide-Only Modeling

The complete set of 1643 critical experiment SDFs is compared against the GBC-68 model with 

the vanished lattice with AO nuclide modeling for the BWR assembly. A plot of the resulting ck

values is shown in Figure 4.1. Each category of experiments is shown as a different data set, 

regardless of the source of the SDF. As evident from the figure, only a limited number of 

experiments is similar enough to the BWR peak reactivity model to have a ck value of 0.8 or 

greater. All of these suitably similar experiments are LEU-COMP-THERM cases. Seventy-six

cases are identified as being similar and applicable for validation. Three cases are excluded 

because of aberrant keff results likely resulting from poorly quantified compositions in the 

experiment, and two cases are excluded because the fissile material is UF6 instead of UO2. A list 

of the 71 remaining cases and their ck values is included in Appendix D. A plot of the ck values 

showing each evaluation as a different series is provided in Figure 4.2.

The highest ck values come from LEU-COMP-THERM-008, followed by LEU-COMP-THERM051 and then the LEU-COMP-THERM-011; the top 44 ck values come from these three 

evaluations. This is of potential concern because all three evaluations were performed at the 

same laboratory, the Babcock and Wilcox (B&W) Lynchburg Research Center, using the same 

fuel rods [19]. Ideally, a variety of experiments from different facilities involving different fuel, 

experimental facilities, and experimenters would provide a broader population of similar 

experiments to consider. The potential for correlation among the experiments may need to be 

considered when a large number of experiments are used incorporating many similar features, 

though the impact of this is as yet unclear and is under investigation [26, 27, 28]. At this time, 

the applicable ANSI/ANS standard [17] requires validation with experiments that are as similar 
85

as possible to the safety application, but the standard does not address the potential impact of 

experimental correlations. None of the experiments identified as being sufficiently similar to the 

GBC-68 cask contain plutonium, thus indicating that a penalty should be developed to cover the 

unvalidated nuclides. A discussion of this penalty factor is provided in Section 4.6.

Figure 4.1. ck values for critical experiments compared to GBC-68 with vanished lattice and 

AO nuclides.
86

Figure 4.2. ck values greater than or equal to 0.8 with vanished lattice and AO nuclides.

4.4.2 Vanished Lattice with Actinide and Fission Product Modeling

The complete set of 1643 critical experiment SDFs is also compared against the GBC-68 model 

with the vanished lattice with AFP nuclide modeling for the BWR assembly. A plot of the 

resulting ck values is shown in Figure 4.3. The cases with a ck value over 0.8 are nearly identical 

to those for the AO model. All suitably similar experiments are LEU-COMP-THERM cases.

Sixty-seven cases are identified as being similar and applicable for validation. Three cases are 

excluded because of aberrant keff results likely resulting from poorly quantified compositions in 

the experiment, and two cases are excluded because the fissile material is UF6 instead of UO2. A 

list of the 62 remaining cases and their ck values is included in Appendix D. A plot of the ck

values showing each evaluation as a different series is provided in Figure 4.4.
87

Figure 4.3. ck values for critical experiments compared to GBC-68 with vanished lattice and 

AFP nuclides.
88

Figure 4.4. ck values greater than or equal to 0.8 with vanished lattice and AFP nuclides.

The AFP validation cases contain the same potential weakness with regard to potential 

experiment correlations discussed in the previous section. Again, the top 44 cases come from the 

three evaluations based on the B&W experiments, though this makes up a larger fraction of the 

total population for this case than for the AO results discussed above.

There is a slight reduction in the number of experiments with acceptable similarity for use in 

validation compared to the AO case, and the cases that still exceed the 0.8 ck threshold generally 

have lower ck values. This is mostly a result of the addition of fission products to the model, 

most of which, as discussed further below, are not represented in the critical experiments. The 

effect is small, with ck values dropping by 0.01 or less in most cases. Some cases show higher 

similarity with the fuel, including actinides and fission products condition, though this difference 

is also typically small.

Only one case, LEU-COMP-THERM-005-010, contains gadolinium. The gadolinium in the 

experiment was dissolved in the moderator and was not present in absorber rods. Another 

difficulty is that the experiment contained natural gadolinium, consisting of a range of nuclides

including 14.8 atom% 155Gd and 15.65 atom% 157Gd [29]. Only 155Gd is included in the AFP 

nuclide set, as shown in Table 3.1. The majority of the residual gadolinium poison at peak 

reactivity is also 155Gd. Natural gadolinium does not have an appropriate isotopic mixture for 
89

validating residual or fission product gadolinium in BWR fuel at peak reactivity. An additional 

problem is that validation is not possible with only a single benchmark case.

A comparison of the total 155Gd sensitivity profiles for the GBC-68 model and LEU-COMPTHERM-005-010 are shown in Figure 4.5. 

Figure 4.5. Sensitivity profile comparison for 155Gd between GBC-68 with vanished lattice and 

LEU-COMP-THERM-005-010.

Approximately 93% of the 155Gd sensitivity comes from the mixtures used to model the 

gadolinium-bearing fuel rods, so the majority of the sensitivity is contributed by residual 

gadolinium and not fission product gadolinium. There is no method to separate the two 

gadolinium sources within the TSUNAMI codes. As shown in the figure, the energy-dependent 

behavior of the profiles is in good agreement, but the sensitivity in the critical experiment is 

more than twice the magnitude of that in the GBC-68 model. The integral sensitivity in the

critical experiment is approximately -0.025 as compared to -0.011 in the storage and 

transportation cask. A critical experiment with a lower gadolinium loading might show better 

agreement with the application sensitivity for 155Gd.

As noted previously, none of the experiments identified as candidates for validation contain 

plutonium, so a penalty for extended area of applicability may be necessary, as well as for 

residual gadolinium poison. None of the experiments contain any fission products other than 

gadolinium, necessitating an evaluation of a potential validation penalty for unvalidated nuclides. 

A discussion of these penalty factors is provided in Section 4.6.
90

4.4.3 Full Lattice with Actinide and Fission Product Modeling

The complete set of 1643 critical experiment SDFs is also compared against the GBC-68 model 

with the full lattice with AFP nuclide modeling for the BWR assembly. A plot of the resulting ck

values is shown in Figure 4.6. 

Figure 4.6. Values for critical experiments compared to GBC-68 with full lattice and 

AFP nuclides.

As in the two previous comparisons, only a limited number of experiments is similar enough to 

the BWR peak reactivity model to have a ck value over 0.8. All of these suitably similar 

experiments are LEU-COMP-THERM cases. Fifty-three cases are identified as being similar and 

applicable for validation. Two cases are excluded because of aberrant keff results likely resulting 

from poorly quantified compositions in the experiment. A list of the 51 remaining cases and their 

ck values is included in Appendix D. A plot of the ck values showing each evaluation as a 

different series is provided in Figure 4.7.
91

Figure 4.7. ck values greater than or equal to 0.8 with full lattice and AFP nuclides.

The AFP validation cases contain the same potential weakness with regard to potential 

experiment correlations discussed in the previous two sections. The top 18 cases, and 42 of the 

51 total cases, come from the three evaluations based on the B&W experiments. There is also a 

significant reduction in the number of evaluations that have at least one case with a ck value over 

0.8, potentially weakening the validation.

The number of experiments with an acceptable degree of similarity with the full lattice is lower 

than for the vanished lattice, even considering the same nuclide set. This change is largely driven 

by the differences in neutron spectrum between the vanished and full lattices. The full lattice has 

a significantly harder spectrum, with an energy-of-average-lethargy-of-fission (EALF) of 0.339 

eV, compared with the vanished lattice, which has an EALF of 0.222 eV. The replacement of 

fuel rods with water in the vanished lattice introduces significant moderation within the lattice, 

thus softening the neutron spectrum. Figure 4.8 shows the change in ck value for each of the 51 

candidate experiments for validation of the full lattice model as a function of EALF. 
92

Figure 4.8. Changes in ck values between vanished lattice and full lattice.

It is evident that experiments with an EALF around 0.25 eV have significant reductions in ck for 

the full lattice, while experiments with EALF values around 1 eV show little change in ck at all. 

This indicates that critical experiments with harder spectra could provide additional useful 

validation cases, if such cases can be identified.

As noted previously, none of the experiments identified as candidates for validation contain 

plutonium so a penalty for extended area of applicability may be necessary. None of the 

experiments contain any fission products, necessitating an evaluation of a potential validation 

penalty for unvalidated nuclides. A discussion of these penalty factors is provided in Section 4.6.

4.5 BIAS AND UNCERTAINTY DETERMINATION

One of the primary purposes of validation is to determine a bias and bias uncertainty associated 

with the computational method employed in a criticality safety analysis. The bias provides a 

measure of the difference between a computational result and the behavior of the real system. 

The bias is generally defined as shown in Equation 2 [22].
93

β = keff −1 (2)

Where: β is the bias

keff is the average calculated keff for the experiments in the 

benchmark suite

One result of this definition is that a negative bias indicates that the computational method under

predicts neutron multiplication, so this bias must be applied to the numerical results to ensure 

that a system predicted to be subcritical is in fact subcritical. Conversely, a positive bias 

indicates that the numerical simulation over predicts keff, though credit for this is generally not 

recommended [17].

This section provides a brief examination of the potential bias and bias uncertainty that could 

result from validation for a peak reactivity analysis of BWR fuel in a storage and transportation 

cask. The results presented here are not rigorous or complete and should not be used in lieu of 

performing an application-specific validation. Guidance on performing and documenting a 

complete validation can be found in References 22 and 23. Also, results are presented for only 

the vanished lattice with AFP modeling of the fuel composition; results for the AO model or the 

full lattice would be similar and thus are not presented. Results are presented for a non-trending 

method, a traditional trending analysis considering enrichment and EALF as trending 

parameters, and for a TSUNAMI-based validation based on ck trending.

For each of the 62 experiments used in this sample validation, the calculated-to-expected (C/E) 

ratio is determined based on SCALE calculations using KENO V.a or KENO-VI in SCALE 

6.1.2. As mentioned previously, multiple transport codes should not be pooled in a single 

validation because validation applies to a specific computational method. In this case, the 

practice is acceptable as a demonstration of methods and as an expediency to generate a large 

enough pool of acceptable candidates based on pre-existing models. Recent studies [30] have 

shown good agreement between KENO V.a and KENO-VI for identical models, so the pooling 

of results is not expected to have a significant effect on the results. The C/E ratio, enrichment, 

and EALF for each case considered in this sample validation are provided in Appendix D. The ck

values are provided in Appendix D.

The normality of the distribution of experiment set results was evaluated using 5- and 11-bin χ2

normality tests. These tests show that there is greater than 95% confidence that the results are not 

normally distributed. This deficiency is not addressed here because this demonstration is not 

intended as a full validation example. For simplicity, a sample validation is performed as if 

normality had been demonstrated. Consideration of other methods, including a non-parametric 

approach, may be needed for validation of criticality safety calculations with a validation suite 

that fails normality tests. Given the fact that more than 50 experiments with acceptable similarity 

have been identified, the non-parametric penalty is likely to be negligible. Therefore, the bias 

and bias uncertainty could be determined by a straightforward process of evaluating several of 

the calculated benchmark cases with the least conservative keff values.
94

4.5.1 Bias and Uncertainty without Trending Analysis

Prior to examining the data set for trends, a non-trending bias and bias uncertainty should be 

established [22]. This bias and bias uncertainty would be used if no trends are identified or 

accepted, or if the non-trending bias and bias uncertainty have a larger magnitude than those 

resulting from trending analyses. The non-trending method used is the simultaneous one-sided 

lower tolerance limit with inverse variance weighting of the data points [22]. For the data 

considered here, the resulting bias is -0.00354, and the 95%/95% bias uncertainty is 0.00526, 

making the combined bias and uncertainty -0.00879.

4.5.2 Traditional Trending Analysis

Trending analysis is recommended for validation analyses [22, 17] and can be useful in 

determining the most appropriate bias to apply for a particular safety application case or 

providing insight on potential causes of bias. In most validations, the assessment of the validity 

of trends has been judged by the coefficient of determination, R2

. This metric can be a poor 

measure of the validity of a trend in cases with significant scatter in the data set, as is typical for 

many validation sets. More robust statistical testing should be performed to determine the 

probability that a fit is better than random and to determine the probability that the slope is nonzero. These determinations can be made with an F-test and a Student’s T-test, respectively. Many 

different system parameters can be used as the independent parameter for trending, including 

enrichment, fuel pin pitch, spectral measures, poison content, and others. In this analysis, two 

common bias trending parameters, enrichment and EALF, are used to examine potential bias and 

bias uncertainty values resulting from the validation of BWR fuel at peak reactivity in a storage 

and transportation cask. The confidence band with administrative margin method, upper safety 

limit (USL)-1, as determined by the Upper Safety Limit Statistics (USLSTATS) module in 

SCALE [23], is used to determine the bias and bias uncertainty in the trending analyses.

The bias and bias uncertainty values for both trending parameters are shown in Table 4.1. 

Table 4.1. Bias and bias uncertainty values

Trend parameter Parameter value Bias 95%/95% bias 

uncertainty

Combined bias and 

uncertainty

Enrichment 3.51 wt% 235U -0.00136 0.00604 -0.00740

EALF 0.2217 eV -0.00396 0.00577 -0.00973

The enrichment trend, combined bias, and bias uncertainty from both trending and non-trending 

methods are shown in Figure 4.9; the EALF trend and limits are shown in Figure 4.10. The limits 

in the figures are shown relative to a keff limit of 1 to facilitate the comparison of the limits to the 

data. The limits as implemented in a specific application would instead be applied relative to the 

subcritical limit.

The combined bias and uncertainty for the non-trending and trending methods are generally in 

good agreement, ranging from -0.00740 to -0.00973. The bias varies significantly, especially 

between the enrichment trend and the EALF trend, but the uncertainty values are largely 

consistent. Figure 4.9 shows that as the enrichment trend passes above 1, USL-1 stops 

increasing. Beyond this point, the uncertainty of 0.00604 is applied with no credit for the positive 
95

bias. The trend relative to EALF does not get to a best estimate bias of 1, so there is no flat 

portion to USL-1 for that case. At the parameter values of interest, the bias and uncertainty 

resulting from the enrichment trend are smaller than the non-trending method, but the largest 

bias and largest combined bias and uncertainty result from the EALF trend. The overall results of 

all three methods show reasonable agreement in magnitude.

Figure 4.9. C/E trend and limits as a function of enrichment.
96

Figure 4.10. C/E trend and limits as a function of EALF.

4.5.3 ck Trending

One nontraditional trending approach that can be used with TSUNAMI-IP results is ck trending. 

This technique uses a linear least-squares fit of the C/E values as a function of ck and 

extrapolates to determine the bias at a ck value of 1.0. This ck value represents perfect similarity, 

which can essentially only be achieved by the application system itself. This approach can also 

be interpreted as massively multi-parameter interpolation; all possible differences are removed 

from the critical experiment as the ck approaches 1, whether they are caused by changes in 

enrichment, neutron energy spectrum, fissile materials or isotopic distributions, absorber 

materials, or any other causes. This method is described more fully in Section 9.1 of the 

TSUNAMI Primer [31].

There are potential disadvantages to ck trending, some of which are potentially important to this 

sample validation. The primary potential weakness of this method is that it can lead to inaccurate 

estimates of the bias for experiment sets that do not have ck values near 1. An example of this 

problem is provided in Reference 32. The bias for a sample validation system is calculated to be 

-0.0065 using experiments with ck values greater than 0.95, but the bias estimate from 

experiments with ck values between 0.8 and 0.9 is 0.0084. The change in the estimate of the 

system bias is more than 1% Δk; the former estimate is known to be more accurate because the 

application in this system was a measured critical configuration. Another difficulty with this 
97

technique is that the uncertainty band applied is non-linear, and it expands as the extrapolation 

grows. The uncertainty band can increase width quickly, and the resulting penalty can become 

significant.

The trend of C/E data as a function of ck is shown in Figure 4.11. The best estimate of the bias is 

calculated using the linear fit of the C/E values, shown as the blue solid line. USL-1 is shown in 

the red dashed line, and it incorporates the best estimate of the bias and the 95%/95% uncertainty 

in the prediction for the C/E value of the next sample from this distribution. The non-linear 

behavior of the uncertainty is evident as USL-1 is dropping for ck values higher than the known 

data points, despite the increasing bias trend. The estimate of the bias with a ck value of 1 is -

0.00275 with an uncertainty of 0.00695, which provides a combined bias and bias uncertainty of 

-0.00970. These results are in good agreement with the traditional trending and non-trending 

results presented previously.

Figure 4.11. C/E trend and limits as a function of ck.

4.6 PENALTIES FOR UNVALIDATED NUCLIDES

Any gaps in a validation must be identified and addressed [22, 23]. The sample validation results 

presented in the previous section all lack validation for several key nuclides, including 

plutonium, residual gadolinium, and fission products. A method for using TSUNAMI 

sensitivity/uncertainty (S/U) analysis to provide a quantitative estimate of such penalty factors is 

provided in NUREG/CR-7109 [13]. Similar techniques will be used in this section to illustrate 

the application of S/U tools for BWR fuel storage and transportation casks. The penalties will be 

estimated for the GBC-68 cask that has been used throughout this report, and the BWR SFP 

application case from NUREG/CR-7109 [13] will also be considered to provide an estimate of 

the potential range of the penalties. Penalties for plutonium, residual gadolinium, and fission 

products will be addressed separately in the following sections.
98

The S/U analysis approach is predicated on the assumptions that (1) the vast majority of the 

computational method-related biases will be captured by the validation study, (2) the primary 

cause of validation biases is nuclear data errors, and (3) these errors are bounded by the reported 

nuclear data uncertainties. The nuclear data uncertainty can then be multiplied by the sensitivity 

of the system keff to that nuclear data to translate the nuclear data uncertainty into a keff

uncertainty. For this application, TSUNAMI performs this assessment in an energy-dependent 

manner using the SCALE covariance library and the sensitivities calculated by TSUNAMI-3D. 

As discussed in NUREG/CR-7109 [13], the nuclear data uncertainties are 1-sigma values from

the covariance library, so the TSUNAMI-calculated results would need to be doubled to reach 

2-sigma and hence 95% confidence. Comparisons of the TSUNAMI estimates of keff uncertainty 

resulting from nuclear data indicate that the nuclear data uncertainties are significantly 

overestimated [13], so this additional penalty (i.e., 2-sigma versus 1-sigma) may not be 

necessary, but it expected to be conservative. The undercoverage penalty factors developed in 

this section are not generically applicable because only a limited number of lattices were 

considered. The factors should not be used directly in any licensing application.

4.6.1 Plutonium

All of the experiments identified as suitably similar for use in validation are LEU-COMPTHERM experiments and as such do not contain plutonium. Several options exist for addressing 

this validation gap, including adding experiments with plutonium to the validation suite despite 

low ck values or S/U analysis to assess the potential bias due to unvalidated plutonium nuclides. 

An S/U analysis is presented in this section to generate a conservative estimate for a penalty for 

lack of validation coverage for plutonium in the validation experiments used in this report.

The uncertainty in system multiplication can be estimated, as mentioned above, by multiplying 

the nuclear data uncertainty by the reactivity sensitivity of any nuclide or reaction of interest. In 

this case, the plutonium nuclides credited in the GBC-68 cask model are the nuclides of interest. 

The uncertainty due to plutonium was determined for the GBC-68 model with the vanished

lattice considering both AO and AFP compositions, the GBC-68 model with the full lattice and 

AFP compositions, and the BWR SFP application case from NUREG/CR-7109 [13] with AFP

compositions. These cases were selected to examine the sensitivity of the plutonium uncertainty 

to different nuclide sets, different lattices, and different peak reactivity burnups. Peak reactivity 

for the GBC-68 models with actinides and fission products is at approximately 7.5 GWd/MTU; 

peak reactivity for the BWR SFP model is 11 GWd/MTU [13].

The uncertainty in system reactivity is determined by TSUNAMI-IP for each reaction for each 

nuclide in the model. These individual reaction contributions can be combined to determine the 

total uncertainty contribution by nuclide. The total plutonium contribution to reactivity 

uncertainty can be determined by combining the individual nuclides in the same manner. 

The contributions for each of the plutonium nuclides and the total contribution for each of the 

models considered are shown in Table 4.2. The uncertainty contribution for 241Am is also shown, 

but 239Pu is the only relevant nuclide since the other transuranic nuclides have uncertainties at 

least two orders of magnitude lower.
99

Table 4.2. Uncertainty contributions from major transuranic nuclides

Nuclide

1-Sigma Uncertainty (% Δk)

GBC-68

SFP AFP

Vanished AO Vanished AFP Full AFP

238Pu 6.55E-05 6.27E-05 8.76E-05 1.24E-04 239Pu 1.38E-01 1.33E-01 1.53E-01 1.54E-01 240Pu 7.83E-03 7.34E-03 9.10E-03 1.13E-02 241Pu 1.67E-03 1.64E-03 1.99E-03 3.28E-03 242Pu 1.74E-04 1.65E-04 2.58E-04 4.96E-04 241Am 8.84E-04 8.27E-04 1.17E-03 1.07E-04

Total 0.138 0.134 0.153 0.155

The results indicate that the system uncertainty due to plutonium is dependent on lattice type, but 

the uncertainty is not strongly dependent on the presence of fission products. The two vanished

lattices have approximately 0.14% Δk uncertainty due to plutonium, while the two full lattices 

have slightly more uncertainty. The higher uncertainty in the full lattices is caused by larger 

plutonium sensitivities that result from larger plutonium number densities due to the harder 

neutron spectrum in the full lattice during depletion. The burnup of peak reactivity does not 

appear to have a strong effect on this result, as the difference in the full lattice uncertainties for 

GBC-68 vs. SFP is less than 0.005% Δk.

The uncertainties edited by TSUNAMI-IP represent 1-sigma confidence and thus should be 

doubled to represent 95% confidence of bounding the true bias for plutonium. Based on these 

results, a penalty of approximately 0.3% Δk should be sufficient to account for lack of plutonium 

validation in both full and vanished lattices. This penalty is applicable over most of the peak 

reactivity range for design basis lattices and would apply to AO or AFP analyses.

4.6.2 Residual Gadolinium

The AFP nuclide set contains 155Gd, which is a component in natural gadolinium as loaded into 

BWR fuel as a burnable absorber. In the gadolinium rods, it is impossible to separate the 

sensitivity of the residual burnable absorber gadolinium from the fission product gadolinium, but 

it is possible to compare the reactivity sensitivity of the 155Gd in the gadolinium rod mixtures to 

that of the SNF fission product 155Gd to generate an estimate for the relative importance of 

fission product gadolinium compared to residual gadolinium. 

From a comparison of 155Gd in SNF at peak reactivity burnup with and without gadolinium 

poison after a five-year cooling time, approximately 93% of the 155Gd sensitivity in the vanished

lattice GBC-68 models comes from the fuel mixtures initially loaded with gadolinium poison, so 

it is apparent that the majority of the 155Gd impact is due to residual burnable absorber. An S/U 

analysis can be used to generate a penalty factor for lack of coverage of the residual gadolinium 

in the validation suite based on the total 155Gd sensitivity in the model, so it will conservatively 

include both fission product and residual gadolinium.

The uncertainty in system reactivity due to 155Gd nuclear data uncertainties is shown in Table 4.3

for the GBC-68 model, with the vanished and full lattices with AFP representations of the fuel, 

and for the full lattice in the SFP application considered in NUREG/CR-7109 [13]. 
100

Table 4.3. Uncertainty contribution from 155Gd

Model Uncertainty (% Δk)

GBC-68 vanished 0.015

GBC-68 full 0.019

SFP full 0.024

The uncertainty contribution increases in the full lattice compared to the vanished lattice, and it 

is higher for the SFP model than for the GBC-68 model. However, these uncertainties are small 

for all three cases. In the GBC-68 models, this uncertainty represents about 1.25% of the 155Gd 

worth for the vanished lattice and about 1.37% for the full lattice.

A bounding estimate for the 1-sigma uncertainty in system reactivity due to 155Gd in the three 

models studied here is 0.025% Δk, which would result in a 2-sigma penalty of 0.05%. The 

penalty is relatively small, so added conservatism in this area will not significantly increase the 

conservatism of the analysis. Note that these uncertainties do not include the uncertainty in the 

calculation of residual gadolinium number densities. This depletion uncertainty is addressed in 

Section 5.

4.6.3 Fission Products and Minor Actinides

The worth of the major (i.e., top 16) fission products and minor actinides is approximately 3.6% 

Δk, as shown in Section 3.4.1. This section develops a penalty factor for major fission products 

and minor actinides for which no critical experiments are available. The penalty factor 

determined does not include consideration of 155Gd, as that nuclide was considered explicitly in 

the previous section.

The major fission products considered in the AFP nuclide set are provided in Table 3.1 in

Section 3.2.2. The minor actinides considered, 236U, 237Np, and 243Am, are also listed. The 

uncertainty contributions and totals for these 19 nuclides are provided in Table 4.4. The models 

considered are the GBC-68 with the vanished and full lattices and the BWR SFP application 

from NUREG/CR-7109 [13]. The main contributors to uncertainty are 149Sm, 143Nd, and 236U 

consistently across all three models. The uncertainties increase from vanished to full lattice and 

from the GBC-68 to the SFP. The higher uncertainties in the SFP model result from higher 

sensitivities caused by a higher burnup at peak reactivity. The uncertainty due to fission products 

and minor actinides ranges from 0.020% Δk for the GBC-68 model to 0.027% Δk for the SFP 

model.

A bounding estimate of the uncertainty due to minor actinides and major fission products based 

on the models examined here is 0.03% Δk, which would lead to a 2-sigma conservative estimate 

of 0.06% Δk. The 1-sigma uncertainty determined from fission products and minor actinides is 

equal to about 0.55% of their worth in the cask model. This would be bounded by the 

conservative bias estimate of 1.5% of the worth of the major fission products and minor actinides

from recommendation 2 in Section 8 of NUREG/CR-7109 [13]. The total worth was less than 

0.04 Δk, so the criterion that the total minor actinide and FP nuclide worth not exceed 0.1 Δk for 

application of recommendation 2 is also met. Implementation of this recommendation would add 
101

a small additional penalty, but this would allow common treatment of this validation penalty 

between BWR and PWR analyses.

Table 4.4. Uncertainty contribution from major fission products and minor actinides

Nuclide

1-Sigma Uncertainty (% Δk)

GBC-68 SFP full Vanished Full 95Mo 1.31E-03 1.62E-03 1.70E-03 99Tc 1.96E-03 2.14E-03 2.99E-03 101Ru 1.65E-03 2.05E-03 3.23E-03 103Rh 5.38E-03 6.75E-03 8.32E-03 109Ag 1.95E-04 2.65E-04 3.98E-04 133Cs 4.33E-03 5.25E-03 7.74E-03 147Sm 1.60E-03 1.90E-03 4.77E-04 149Sm 1.09E-02 1.13E-02 1.01E-02 150Sm 1.02E-03 1.14E-03 1.65E-03 151Sm 6.02E-03 5.97E-03 6.06E-03 152Sm 1.62E-03 1.95E-03 2.96E-03 143Nd 9.94E-03 1.04E-02 1.37E-02 145Nd 4.09E-03 5.10E-03 7.89E-03 151Eu 1.13E-04 1.23E-04 6.71E-06 153Eu 7.86E-04 1.00E-03 1.65E-03 236U 8.05E-03 9.79E-03 1.33E-02 237Np 1.00E-03 1.26E-03 1.46E-03 243Am 1.92E-06 3.58E-06 7.63E-06

Total 0.020 0.022 0.027

4.7 SUMMARY OF VALIDATION OF CASK REACTIVITY 

CALCULATIONS

A series of studies has been performed to investigate validation of cask keff calculations. This 

section presents the results of these studies and provides recommendations for BWR peak 

reactivity validations that are analogous to those provided in NUREG/CR-7109 [13] for PWR 

validations.

Several sources of SDFs have been used, as discussed in Section 4.3, providing a large number 

of candidate experiments. In total, over 1600 unique experiments were compared against cases 

ranging from application cases to experiment cases with ck values of 0.8 or higher.

A range of potentially useful experiments has been identified in Section 4.4 for use in AO or 

AFP analyses. GBC-68 applications with both the full and vanished lattices were considered. 

More than 50 experiments have been identified for each of these applications, allowing a 

sufficient population for validation. All experiments selected are LEU-COMP-THERM 

experiments and thus provide no validation of cross sections for transuranics, residual 

gadolinium, or for fission products.

A sample validation was presented in Section 4.5 using a non-trending method, a traditional 

trending method for enrichment and EALF, and a ck trending method. The resulting bias and bias 
102

uncertainty values were similar for each of the methods. The bias was approximately -0.00300

Δk, with an uncertainty of about 0.00600 Δk. The limiting combination of bias and bias

uncertainty is -0.00973 Δk and results from EALF trending.

Although the number of critical experiments with satisfactory similarity is sufficient for 

statistical analysis, the lack of several important nuclides in the validation suite is problematic. 

Penalty factors would therefore be required to extend the area of applicability to include these 

nuclides. A sensitivity/uncertainty analysis approach similar to that described in NUREG/CR7109 [13] was used to develop these factors in Section 4.6. The calculations showed that a

penalty factor of about 0.3% Δk for transuranics, plutonium, and americium was appropriate for 

the sample validation. The factor for residual gadolinium was calculated to be 0.05% Δk. The

factor for remaining fission products and minor actinides was calculated to be about 0.06% Δk. 

These penalty factors are fairly small, so it is unlikely that additional conservatism in them 

would have a noticeable impact on the overall conservatism of the analysis.

Validation calculations can be performed in compliance with the consensus ANSI/ANS standard 

[17] and with prior NUREG/CR recommendations [22, 23]. It has been demonstrated that 

penalty factors can be established that extend the validation area of applicability to account for 

some nuclides that cannot be validated with critical experiments at this time. Overall, the 

validation of cask reactivity calculations, including fuel at peak reactivity, does not present a 

technical barrier that would prevent implementation of peak reactivity methods for 

demonstrating the criticality safety of BWR SNF in storage and transportation casks.
103

5 VALIDATION OF SPENT FUEL NUCLIDE COMPOSITIONS

The approach for validating BWR BUC criticality safety analyses near peak reactivity 

investigated in this report consists of separately validating the cask reactivity calculations and the 

SNF compositions used in those calculations. These validation studies are based primarily on 

experimental data. Section 4 discusses the validation of cask reactivity calculations. This section 

provides a review of studies performed to establish a technical basis for validating the SNF

nuclide concentration in BWR SNF at peak reactivity, and the bias and uncertainty in the cask 

reactivity calculations associated with uncertainties in the SNF composition. 

Validation of calculated SNF compositions is performed by comparison of calculated nuclide 

contents against measured concentrations in SNF samples from BWR assemblies obtained by 

destructive radiochemical analysis. This approach to validating the SNF calculations for use in 

criticality analyses is broadly accepted and applied by the international nuclear criticality safety 

community [33, 34, 35, 36]. Validation of a depletion code using measured fuel sample 

compositions requires accurate local irradiation conditions at the location of the sample to avoid 

introducing significant modeling bias caused by uncertainties in the input data. Additional 

components of bias and uncertainty associated with this approach are introduced by uncertainties 

in the complex radiochemical analysis measurements themselves. The use of measured nuclide 

concentrations to validate burnup calculations is widely regarded as conservative because 

uncertainties in the measurements and in the reactor operating data cannot be eliminated or 

separated from other uncertainties in the calculations [36]. Recent comparisons of several 

different BUC validation approaches have corroborated that the uncertainties in criticality 

calculations using radiochemical assay (RCA) data as the basis for uncertainties were larger than 

alternate methods that did not rely on measured nuclide compositions [37].

This section provides an overview of an approach for validating SNF based on experimentally 

measured nuclide concentrations and the associated uncertainty in criticality calculations that 

apply these concentrations. Relevant characteristics of the application model are summarized in 

Section 5.1. The relative importance of actinide and fission product BUC nuclides, as well as the 

importance of residual 155Gd near peak reactivity for the application model, is presented in 

Section 5.2. The computational methods and data are described in Section 5.3. A summary of the 

available experimental data applicable to validation of SNF nuclide concentrations is provided in 

Section 5.4, and a more detailed review and vetting of all available data is provided in Appendix 

F. Section 5.5 summarizes the results from a recent OECDNEA BWR computational benchmark 

that includes code assessments in the burnup range near peak reactivity. The bias and uncertainty 

determination is covered in Section 5.6, which is organized by the analysis of the nuclide 

uncertainties, analysis of the keff uncertainties associated with the nuclide uncertainties, and a 

summary of the uncertainty results. Conclusions and recommendations related to depletion code 

validation are provided in Section 5.7.

5.1 APPLICATION MODEL

The application model in this study is the GBC-68 cask model described in Section 3.2.3. The 

fuel lattice used with this application model is the vanished fuel lattice with actinide-only 

modeling that is described in Section 4.41. It has been shown previously that vanished lattices 
104

result in the maximum peak reactivity value because the empty fuel rod locations provide more 

neutron moderation [4]. 

The fuel assembly nuclide concentrations in this application model were obtained using the 

depletion modeling approach described in Section 3.4.1. In this approach, the assembly-average

initial enrichment is used in each fuel rod. However, the spatial effects related to the fuel rod 

location in the assembly are treated explicitly, i.e., the neutronic influence of channel moderator 

of the edge and corner rods, and the proximity of fuel rods to internal water rods. The UO2 fuel 

rods are grouped into three different mixtures that deplete with the same compositions. Each 

group is assigned a unique mixture number to facilitate specification of different Dancoff factors 

[12] that account for the neutronic environment effect of adjacent fuel rods. The gadoliniumbearing Gd2O3-UO2 fuel rods were represented as a unique material. These rods were subdivided 

into seven rings with identical volumes, and each ring was assigned a unique mixture. 

Subdivision of the gadolinium rods is required for accurate representation of the gadolinium 

isotopes depletion during irradiation. 

The BWR fuel assembly model identifying the different fuel mixtures in the vanished lattice is 

illustrated in Figure 5.1. The fuel rods identified as 1–3 in this figure correspond to UO2 fuel 

mixtures 1-3 and rods identified as 4 represent the Gd2O3-UO2 fuel rods. Note that the Gd2O3

UO2 fuel rods actually contain 7 depletion mixtures (numbered 4–10 in the depletion model) in 

the subdivided rod; however, they are shown as a single mixture 4 in the figure for illustration 

purposes. 

The fuel compositions in the application model, which are identical to those in the model used in 

Section 4.4.1, correspond to an initial enrichment of 4.305 wt% 235U, an approximately 7.5-

GWd/MTU peak reactivity burnup, and a 5-year decay time.
105

1 2 2 2 2 2 2 2 2 1

2 3 3 3 3 2

2 3 3 3 4 2 2 3 3 2

2 3 3 2 2 2

2 3 4 2 2 3 2

2 3 2 2 3 4 2

2 2 2 3 3 2

2 3 3 2 2 3 3 3 4 2

2 3 3 4 4 2

1 2 2 2 2 2 2 2 2 1

UO2 fuel rod

Gadolinium-bearing UO2 rod

Water

Figure 5.1. Illustration of the BWR fuel assembly in application model and fuel rod 

mixture locations.

5.2 NUCLIDE IMPORTANCE TO REACTIVITY

The importance of the main actinides and gadolinium for BWR fuel as a function of burnup is 

shown in Figure 5.2 as the fractional neutron absorption in the fuel. This figure clearly shows 

that a relatively small number of actinides (235U, 238U, 239Pu, and 240Pu) and gadolinium are 

responsible for most of the neutron absorption at low burnup. Below approximately 15

GWd/MTU, these nuclides contribute more than 90% of the total neutron absorption from all 

nuclides in the fuel. 
106

Figure 5.2. Relative neutron absorption fractions in typical UO2 fuel with gadolinium. [38]

The importance of individual nuclides with respect to BWR fuel reactivity in the GBC-68 cask 

application model was determined using keff sensitivity coefficients calculated with TSUNAMI. 

The relative sensitivity coefficient Sn, defined as shown in Eq. 3 [11], is a relative measure of the 

first-order effect of changes in the nuclide concentration, Nn of nuclide n, on keff,

n n

eff eff

n N N

k k

S

δ

δ

= . (3)

The keff sensitivity coefficients for the application model with actinide, fission product, and 

residual 155Gd nuclides are illustrated in Figure 5.3. The keff sensitivity to the 155Gd concentration 

is observed to be larger than for any other single fission product isotope. 

As discussed in Section 4.6.2, the majority of the reactivity effect in the assembly due to 155Gd is 

from 155Gd in gadolinium-bearing fuel rods and not from fission product 155Gd in UO2 fuel rods. 

This is an indication of the importance to fuel reactivity of residual 155Gd in gadolinium-bearing 

fuel rods. For example, the reactivity worth of 155Gd is approximately 1.25% (see Section 3.4.1)

for the application model including 155Gd from both the residual 155Gd poison and fission product 

155Gd.

The presence of initial 157Gd in the gadolinium poison rods also results in significant neutron 

absorption at low burnup. This nuclide has previously not been considered in BUC (Table 3.1) 

because 157Gd is not an important fission product in BUC and is only significant when present as 

initial natural gadolinium poison. However, an analysis of gadolinium depletion indicates that 

157Gd depletes much more rapidly than 155Gd, and that in the range of peak reactivity, neutron 

absorption by 157Gd is significantly less than by 155Gd. Therefore, 157Gd has not been evaluated 

in the present study.
107

The sensitivity coefficients in Figure 5.3 show that the dominant actinides at low burnup include 

235U, 238U, 239Pu, and 240Pu. The most important fission products are 149Sm, 151Sm, 143Nd, and 

103Rh. The reactivity worth of minor actinides, residual 155Gd, and the top 16 fission products is 

approximately 3.6%. (See Section 3.4.1.)

Figure 5.3. keff relative sensitivity coefficients (absolute) for the BWR application model at peak 

reactivity for actinides, fission products, and residual 155Gd.

5.3 CODES AND METHODS

The computational analyses of the SNF nuclide compositions used in this work were performed 

using the SCALE 6.1.2 code system. The burnup calculations were performed using 2D 

assembly models developed for the NEWT deterministic multigroup neutron transport code, 

coupled with the ORIGEN code for isotope generation and depletion [39]. These calculations 

were performed using the TRITON (t-depl) depletion sequence (see Section 3.2.1). The 

ENDF/B-VII.0 238-group cross-section library [40] was used for all nuclide composition 

calculations. 

TRITON was used to calculate nuclide concentrations for the application model (see Sections

3.2.3 and 4.4.1) and to evaluate the experimental radiochemical assay data used to develop bias 

and uncertainty associated with the calculated nuclide concentrations. This code has the 

capability of simulating depletion of individual fuel rods in the fuel assembly model, and spatial 

subdivisions within a fuel rod. This capability allows an accurate representation of the local flux 

distribution for a specific fuel rod within the fuel assembly, which is required when validating 

the computer code predictions with measurements performed using small samples obtained from 

a single fuel rod.
108

The depletion models for the measured fuel samples and the application model were developed 

using a consistent approach to ensure that the nuclide bias and uncertainty estimated from the 

experimental data are directly applicable to the application model. For example, fuel rods 

containing gadolinium were subdivided into seven rings with equal volumes to provide an 

accurate and consistent representation of the gadolinium depletion. For models of the measured 

UO2 fuel samples, a burnup time step of 0.5 GWd/MTU was specified for burnups less than 15 

GWd/MTU and larger depletion steps (1–1.5 GWd/MTU) were used beyond 15 GWd/MTU. A 

burnup step of 0.5 GWD/MTU was used to model the depletion of gadolinium-bearing fuel 

samples.

Details of the fuel assembly models used for validation with experimental data are described in 

Appendix F.

5.4 APPLICABLE EXPERIMENTAL DATA

Validation of calculated SNF compositions for BWR fuel is challenging due to a limited number 

of measured samples that are publicly available for code benchmarking. Experimental data for 

burnups near peak reactivity are further limited since these burnups are generally lower than 

typical burnup values of measured BWR fuel samples from discharged fuel assemblies. In 

addition, much of the applicable validation data identified in this study are available from 

experimental programs performed in the 1970s and 1980s. These studies involved older 

assembly designs, and the measurements did not include many of the fission products currently 

considered in BUC. The availability of applicable experimental data for validation has a direct 

impact on the ability to validate the nuclides considered in a criticality safety analysis, and it also 

influences the BUC approach (e.g., AO, AFP, or a reduced set of nuclides).

The main characteristics of the SNF samples identified in this study as applicable to depletion 

code validation are summarized in Table 5.1. The burnup range of the 16 BWR fuel samples is

between 2.77 and 27.18 GWd/MTU, which encompasses the assembly peak reactivity burnup 

values (i.e., less than ~20 GWd/MTU) associated with different gadolinium concentrations and 

configurations analyzed in this report (see Figure 3.13). These data include samples with burnups 

exceeding the region of peak reactivity and were included to evaluate potential trends in the data 

in the low burnup regime. 

• Twelve samples were obtained from BWR 6×6 fuel assemblies operated in the Japan 

Power Demonstration Reactor (JPDR) [41] and the German Gundremmingen reactor 

[42]. These assemblies are older BWR fuel assembly designs that did not contain 

gadolinium burnable poison rods. 

• Four samples were obtained from a BWR 8×8-2 fuel assembly from the Japanese 

Fukushima-Daini-2 reactor [43]. This fuel contained gadolinium poison, though no 155Gd 

measurements were performed for the gadolinium-bearing samples. However, these 

samples provide information on the accuracy of burnup calculations for actinides in the 

presence of gadolinium poison.

• Three samples from the Japanese Ohi-2 reactor [43] were evaluated as these are the only 

publicly available data identified for gadolinium-bearing fuel rods (UO2–Gd2O3) that 

included gadolinium isotope measurements for the burnup range of interest. Ohi-2 is a 
109

PWR reactor that operates with 17×17 assemblies; therefore the data are not necessarily 

applicable to void conditions of BWRs.

A more detailed review and vetting of the available SNF experimental data for application to 

validating BWR fuel reactivity near peak reactivity is provided in Appendix F. Note that a 

number of available BWR samples were not considered in this study due to incomplete 

operational information, including the void concentrations at the location of the measured 

samples, and incomplete information on control absorber exposure. Also, several low burnup 

samples obtained from the extreme ends of the active fuel length were excluded due to bias 

caused by the fuel rod end region hardware; 3D neutron transport methods would be needed to 

accurately model these samples. In this study, 2D models were used to represent the fuel 

assemblies.

The 16 BWR fuel samples provide measurement data for the major actinide nuclides 235U, 238U, 

238Pu, 239Pu, 240Pu, 241Pu, and 242Pu. Measurements of 234U and 241Am is available for a subset of 

the 16 fuel samples. Review of the 241Am experimental data [34] indicates large analytical 

measurement uncertainties of ~20% that resulted in large deviations between calculations and 

measurements. The 241Am data were therefore not considered in this study due to their

measurement uncertainties that make a reliable validation of the calculated concentrations

impractical. 

The majority of the fission product nuclides generally considered in BUC (see Table 3.1) had no 

measurement data in the BWR experiments considered. Only two samples included 

measurements for the samarium nuclides — 149Sm and 151Sm — which represent the dominant 

fission products near peak reactivity (Figure 5.3). The limited fission product data derive from 

the fact that the early experimental programs were primarily motivated by actinide transmutation 

studies and radiological nuclides, and less by the stable and long-lived fission products important 

in BUC. 

The lack of adequate measurement data precludes the consideration of fission products in BWR 

BUC near peak reactivity using methods based on destructive radiochemical analysis data. 

Alternate uncertainty analysis methods such as Monte Carlo nuclear data uncertainty sampling 

[45] could be considered for unvalidated fission product nuclides. This approach is similar to that 

used in the validation of reactivity calculations (Section 4.6). However, application of these 

methods to estimate nuclide uncertainties from burnup calculations has not been extensively 

validated by this time.

The lack of adequate fission product data associated with BWR fuel near peak reactivity does not 

extend to higher burnup fuel where significantly more complete experimental data exist. Many of 

the more recent experimental programs for BWR fuel [46] have focused primarily on high 

burnup fuel and include measurements for most of the fission products considered in criticality 

calculations.

An additional consideration unique to BWR fuel near peak reactivity is the importance of the 

residual 155Gd in gadolinium-bearing fuel rods. The BWR experimental data considered do not 

include any fuel samples with measurements of 155Gd. To provide some assessment of the ability 

of computer codes and data to predict the depletion of 155Gd, surrogate measurement data for 
110

155Gd in gadolinium-bearing PWR fuel rods were considered in this validation study. Only three 

such measurements from the Ohi-2 reactor were available within the burnup range < 30 

GWd/MTU. The rationale for applying PWR surrogate 155Gd measurement data to the BWR 

isotopic validation is that the PWR fuel samples were irradiated in an environment similar to that 

of the bottom section of a BWR fuel assembly (i.e., the subcooled region of the assembly near 

the core coolant inlet). However, these 155Gd measurement data may be nonrepresentative of the 

middle and upper sections of a BWR fuel assembly containing void. 

The available measurement data for the actinide nuclides 234U, 235U, 238U, 238Pu, 239Pu, 240Pu, 

241Pu, and 242Pu in BWR fuel samples within the burnup range associated with peak reactivity 

provide the technical basis for the depletion code validation in terms of keff uncertainty presented 

in this report.

Table 5.1. Evaluated experimental spent fuel nuclide data

Reactor name

Reactor 

type

Lattice 

type

Measured 

fuel rod 

type

Number 

of 

samples

Enrichment 

(wt % 235U)

Burnup 

(GWd/MTU)

Gadolinium 

isotope 

measurements

Gundremmingen-A BWR 6×6 UO2 8 2.53

14.39 No

15.84 No

17.49 No

21.24 No

22.25 No

22.97 No

23.51 No

25.19 No

JPDR BWR 6×6 UO2 4 2.597

2.77 No

3.38 No

4.13 No

4.35 No

Fukushima-Daini-2 BWR 8×8-2 b

UO2–

Gd2O3

4 3.41

16.65 No

21.83 No

22.63 No

UO2 1 3.91 27.18 No

Ohi-2 a PWR 17×17 UO2–

Gd2O3

3 3.20

21.92 Yes

29.45 Yes

25.73 Yes

a PWR fuel samples analyzed to obtain data on residual 155Gd in gadolinium-bearing fuel rods. b An 8×8 lattice design with two water rods.
111

5.5 OECD/NEA BWR BENCHMARK

International computational benchmarks represent an important means for comparing the 

performance of nuclear analysis codes, models, and nuclear data, particularly when experimental 

data are limited or not available. These benchmarks provide opportunities to compare 

analysis/simulation codes, which use different methodologies, different nuclear data sets, and 

different modeling techniques. The Expert Group on Burnup Credit Criticality Safety (EGBUC) 

of the Working Party of Nuclear Criticality Safety (WPNCS) under the Nuclear Science 

Committee (NSC) of OECD/NEA is conducting the Phase III C benchmark on BWR fuel 

assembly burnup calculations to assess assembly peak reactivity [47]. The benchmark is being

coordinated by Japan and was primarily motivated by the requirement to assess computational 

methods for BUC in support of fuel handing activities at the damaged Fukushima reactors and 

spent fuel pools.

The benchmark model consists of an ATRIUM9, 9×9 BWR fuel assembly, with fuel rod 

enrichments in the assembly that vary from 2.1 to 4.9 wt% 235U. Twelve gadolinium rods contain 

5 wt% Gd2O3 with 3.4 wt% 235U enrichment. The assembly eigenvalue and isotopic 

concentrations were calculated for 40 nuclides as a function of burnup for 0%, 40% and 70% 

coolant void fractions. In addition, the participants calculated the eigenvalue at peak reactivity 

for each void fraction and the peak reactivity burnup. Benchmark results from more than 20

different computer codes and nuclear data libraries have been submitted.

A preliminary finding of the BWR benchmark is the variability in the predicted residual 155Gd 

concentration in the fuel. The uncertainty (2 sigma) in the 155Gd content for a burnup of 12 

GWd/MTU was observed to be between approximately 35% and 50% for the different void 

conditions, indicating that the results have a large dependence on the computer code, modeling, 

and/or the nuclear data used in the calculations. The large variability in the calculated results 

reinforces the need for additional code validation for residual 155Gd before it can be reliably used 

in BUC calculations.

Another important finding is the variability in the code predictions of peak reactivity and on the 

burnup associated with peak reactivity. The variability in the calculated peak k-infinity results (2 

sigma) was less than 1%, indicating relatively consistent agreement between codes. However, 

variability in the burnup value where peak reactivity occurs ranged from about 2.8% to 5.5% (2 

sigma) and was greatest for zero-void conditions. 

Although the OECD/NEA Phase III C BWR Benchmark is not based on experimental data, it 

will provide important information on the consistency of different code and nuclear data library 

performance in areas where validation data is lacking. These benchmarks also highlight areas 

where additional work is needed to assess code performance. 
112

5.6 BIAS AND UNCERTAINTY DETERMINATION

5.6.1 Nuclide Uncertainty Analysis

The bias and bias uncertainty values associated with BWR nuclide compositions within the 

burnup range characteristic to a BWR assembly reactivity peak are presented in this section. The 

nuclides with available validation data that are considered in this study include 234U, 235U, 238U, 

238Pu, 239Pu, 240Pu, 241Pu, 242Pu, and 155Gd (residual). The analysis does not include 241Am due to 

large measurement uncertainties. In addition, fission products are not included due to the lack of 

adequate measurement data. The bias and uncertainty in the calculated nuclide compositions are 

derived directly from comparisons of the calculated and measured nuclide concentrations. The 

nuclide bias, j Xi , is calculated with Eq. (4), 

j

i

j

i

j Xi = M /C , (4)

where

i = the index of a burnup-credit nuclide,

j = the index of a measured fuel sample in a set of NS samples,

j Mi = the measured concentration of nuclide i in fuel sample j,

j Ci = the calculated concentration of nuclide i in fuel sample j.

Provided that the j Xi values have a normal distribution, the probability frequency distributions 

of the j Xi values may be characterized by the sample mean Xi and standard deviation i s given by 

Eqs. (5) and (6), respectively.

S

N

j

j Xi Xi N S

/

1

∑=

= . (5)

1

( )

1

2

−

−

=

∑=

S

N

j

i

j

i

i N

X X

s

S

. (6)

Standard practice [48] in criticality safety evaluations does not credit biases that result in an 

overprediction of the effective neutron multiplication factor, keff. Hence, in this analysis, no 

credit is applied for the overprediction of fissile nuclides (i.e., 235U, 239Pu, and 241Pu) or the 

underprediction of neutron absorbing nuclides. With this approach, the mean for an isotope, or 

isotopic bias, ' Xi , is defined as shown in Eqs. (7) and (8) for fissile and neutron absorbing 

nuclides, respectively:







≤

> = 1,if 1,if 1 '

i

i i

i

X

X X

X , (7)







≥

< = 1,if 1

,if 1 '

i

i i

i

X

X X

X . (8)
113

Data normality of the j Xi values for each actinide isotope i and the NS fuel samples was assessed 

with the Shapiro-Wilk normality test at the 0.05 significance level [49]. The nuclide bias and 

uncertainty for the measured nuclides are summarized in Table 5.2. All the actinides pass the 

normality test except for 238U and 238Pu. The uncertainty associated with the calculated 238U 

concentration values is very small (e.g., standard deviation of the measured-to-calculated values 

was ~ 0.001) and has insignificant impact on keff uncertainty. For example, by applying the 238U 

bias uncertainty values of 0.001 and 0.002 (i.e., twice as much as the standard deviation value) to 

the calculated 238U concentration, the corresponding keff values differed by 13 pcm, a negligible 

impact. In this report, the effect on keff uncertainty of the normality assumption for the 238Pu 

results is considered to be negligible because keff has a very small sensitivity to the 238Pu content, 

as illustrated by the keff sensitivity coefficients in Figure 5.3. 

There are additional uncertainties in the estimation of the mean bias Xi and standard deviation 

i s due to the limited number of the measurements considered. As the number increases, there is 

increased confidence that the parameters Xi and i s are good estimates of the actual probability 

distribution. However, when the size is small, there is less confidence that the estimated 

parameters represent the population parameters, in a statistical sense, and the uncertainties in 

these estimates should be increased accordingly. In this study, statistical tolerance-limit factors 

were applied based on the number of measurements (fuel samples) available for each nuclide. 

Tolerance limits correspond to an interval, or range, within which a specified percentage of the 

population is expected to reside with a given confidence. In this report, the 95%/95% interval is 

defined such that 95% of the population is expected to reside within this range with 95% 

confidence. The development of the tolerance intervals is accomplished using tolerance-limit 

factors that are multipliers on the estimated standard deviation i s . In this work, the one-sided 

95%/95% tolerance limit factor (k1) is used to define the upper or lower limit of the population 

above which 95% of the population resides. 

Table 5.2. Isotopic bias and bias uncertainty values associated with calculated BWR isotopic 

concentrations

Isotope No. of 

samples

Burnup range 

(GWd/MTU)

Mean

Xi

Nuclide

bias

( ' Xi )

Standard

Deviation

( i s )

One-sided tolerance 

limit factor c

(k1)

234U 8 2.77–27.18 0.969 0.969 0.040 3.187 235U 16 2.77–27.18 0.985 1.000 0.023 2.524

238U 16 2.77–27.18 1.000 1.000 0.002 b 2.524

238Pu 16 2.77–27.18 1.039 1.000 0.098 2.524

239Pu 16 2.77–27.18 0.950 1.000 0.039 2.524

240Pu 16 2.77–27.18 0.967 0.967 0.048 2.524

241Pu 16 2.77–27.18 1.059 1.059 0.129 2.524

242Pu 16 2.77–27.18 1.012 1.000 0.121 2.524

155Gd a 3 21.47–29.45 2.440 1.000 1.719 7.656

a Surrogate isotopic validation data from gadolinium-bearing PWR UO2 fuel samples. b Standard deviation for 238U values was doubled to account for the non-normality of the distribution. c One-sided 95%/95% tolerance limit factors. 
114

Both the bias and the standard deviation associated with 155Gd concentration based on the three 

evaluated PWR fuel samples are very large. This is caused by erratic behavior in the 

measurement data, which may be due to very low isotopic abundances of 155Gd in the fuel, that

are challenging to measure with mass spectrometry. 

5.6.2 keffBias and Uncertainty Analysis

A number of methods for calculating keff uncertainty associated with uncertainties in calculated 

nuclide concentrations in SNF have previously been explored. The methods investigated in 

NUREG/CR-6811 [50] include both conservative bounding and best estimate approaches to 

uncertainty estimation. The bounding method applies bias and uncertainty associated with 

calculated isotopic concentrations in a way that maximizes the keff uncertainty value. This 

method increases the concentrations of the fissile nuclides based on their individual nuclide 

uncertainties estimated from validation studies, and it decreases the concentrations of the neutron 

absorbing nuclides. The best estimate methods previously applied to the analysis of uncertainty 

for PWR BUC [51] provide a more realistic representation of the uncertainties but are very 

computationally intensive. 

The bounding method for uncertainty determination was applied for BWR fuel near peak 

reactivity in this study. Specifically, the predicted concentrations of the fissile nuclides in Table 

5.2 (i.e., 235U, 239Pu, and 241Pu) are adjusted to their upper one-sided 95%/95% tolerance limit 

values [52] to account for the uncertainty in the calculations as determined from the experimental 

data. The concentrations of all neutron-absorbing nuclides (i.e., 234U, 238U, 238Pu, 240Pu, 242Pu, 

155Gd) are adjusted to their lower one-sided tolerance limit values. This conservative approach 

maximizes the reactivity in the application model. The nuclide concentrations adjusted for bias 

and uncertainty, '

i c are determined as:









× − ×

× + × = ( ), for neutron absorbing nuclides( ), for fissile nuclides

1

'

1

'

'

i i i

i i i

i

c X k s

c X k s

c (9)

where

i = the index of a BUC nuclide,

i c = calculated nuclide concentration,

' Xi = bias in the predicted fuel concentration for nuclide i [see Eqs. (5), (7), and (8)],

1 k = one-sided tolerance limit factor for 95% confidence and 95% of the population 

(Table 5.2),

i s = standard deviation in the predicted nuclide concentration as determined from the 

spent fuel sample data for nuclide i [see Eq. (5)].

This approach requires two criticality calculations to be performed for the application model. 

The first calculation applies the nuclide concentrations as calculated directly by the depletion 

code without any corrections. The second calculation applies nuclide concentrations that have 

been adjusted for estimated bias and uncertainty according to Eq. (9). The difference in the 

system eigenvalues between these calculations provides a direct and bounding estimate of the 

bias and uncertainty associated with the calculated nuclide compositions.
115

The large variability in the validation results for 155Gd and the statistical penalty associated with 

the small number of measurements, as defined by the tolerance limit factor (Table 5.2), results in 

a calculated 155Gd concentration after adjusting for bias and uncertainty ( '

i c ) that is negative. In 

effect, the uncertainty in the concentration is larger than the concentration value, eliminating 

155Gd from consideration in the BUC analysis based on the limited experimental data currently 

available.

The bounding method was used in this work to provide a conservative approach that maximizes 

the system reactivity and keff uncertainty for the following reasons:

1. The number of measured BWR fuel samples (see Section 5.2) in the burnup range of 

peak reactivity is limited. Only three different experimental programs were identified as 

sources of experimental data. While the tolerance limit factors statistically account for the 

low number of available measurements, there is reduced confidence in the nuclide 

experimental data, as there is an increased likelihood that any single set of measured data 

could potentially bias the results.

2. The BWR measurement data were limited to 6×6 and 8×8 assembly designs. No data 

were identified for modern assembly designs (e.g., 9×9 and 10×10) for low burnup fuel.

3. There is limited BWR data for fuel assemblies containing gadolinium-bearing fuel rods.

4. This method is easily applied to a heterogeneous fuel assembly in an application model 

that contains both UO2 and Gd2O3-UO2 fuel rods (i.e., described in Section 5.1). 

5.6.3 keff Bias and Uncertainty Results

The uncertainty in keff associated with nuclide biases and bias uncertainties was determined for 

the GBC-68 cask application model using the bounding method described in Section 5.6.2. The 

keff margin for uncertainty was calculated as the difference between the keff value using nuclide 

concentrations adjusted for bias and uncertainty (see Eq. 9) and the keff value using calculated 

nuclide concentrations (i.e., base case). The bias and uncertainty values used in Eq. 9 and the 

one-sided tolerance limit factors for 95% probability and 95% confidence level are listed in 

Table 5.2 [53]. The calculated keff values and uncertainty are presented in Table 5.3. The 

calculated keff margin for uncertainty due to the calculated nuclide concentrations is 0.0165 

(1.65% Δk).

The BWR SNF composition used in this study consisted of actinides only (see Table 3.1), 

excluding 241Am. The large measurement uncertainty of 241Am in the experiments considered 

precludes its reliable use for code validation.
116

Table 5.3. keff results and margin for uncertainty for the GBC-68 cask model

Description keff 

a

Calculated concentrations (AO base case) 0.9363

Adjusted concentrations as shown in Eq. (9) 0.9528

∆keff margin for nuclide uncertainty b 0.0165

(1.65% Δk) a Standard deviation from the Monte Carlo simulation = 0.0001. b 95% probability, 95% confidence level.

5.7 CONCLUSIONS AND RECOMMENDATIONS

A method for determining the uncertainty in keff calculations associated with the BWR SNF 

nuclide concentrations near peak reactivity has been demonstrated for the GBC-68 cask model 

described in Section 3.2.3 and the vanished lattice configuration (see Section 5.1 for details). 

This method is based on the direct application of measured BWR SNF composition data to 

estimate the uncertainties associated with the calculated nuclide composition used in BUC 

application models. 

The available experimental nuclide data for BWR fuel near peak reactivity currently limits BUC 

analyses to consider AO fuel compositions. Present radiochemical assay data lack sufficient 

fission product data that would enable validation for AFPs. Similarly, applicable data for residual 

155Gd are limited, and only three samples obtained from PWR fuel samples were evaluated in 

this work. However, the large variability in the validation results for 155Gd and the statistical 

penalty associated with the low number of measurements effectively eliminates any potential 

credit that can be obtained based on the existing measurement data.

The reactivity worth of 155Gd in the GBC-68 cask model at BWR fuel peak reactivity for the 

vanished assembly lattice was approximately 1.25% relative to crediting AO nuclides listed in 

Table 3.1. The margin for keff uncertainty in the calculated actinide compositions for the AO cask 

configuration is estimated to be 0.0165 with a 95% confidence level. The actinide compositions 

exclude 241Am due to large measurement uncertainties. Addition of fission product measurement 

data and improved 155Gd data in the range of peak reactivity could support credit for a substantial 

fraction of the reactivity worth from the omitted BUC nuclides, which represent approximately 

3.64% of the total reactivity worth. 

Although the analysis in this work was limited by the available validation data to consider AO 

compositions, the approach is applicable to fission products and residual 155Gd provided 

sufficient measurement data are obtained to support validation of the nuclide concentrations. The 

Belgian nuclear research center Studiecentrum voor Kernenergie (SCK•CEN) recently initiated a 

new research program called Rod Extremity and Gadolinia AnaLysis (REGAL) [54] to measure 

an extensive list of actinides and fission products in the burnup range of peak reactivity and also 

to measure residual gadolinium nuclides to validate gadolinium depletion. These commercial 

data could be acquired to increase the number of fuel samples in the burnup range of interest and 

dramatically expand the measured nuclides that could potentially be credited and reduce current 

levels of nuclide uncertainty. 
117

BUC programs in Japan are relatively advanced and have focused heavily on the acquisition of 

experimental data to support BWR BUC validation [43]. The Japan Nuclear Regulation 

Authority (NRA) also recently contributed new nuclide assay data to the OECD/NEA SNF assay 

database, the Spent Fuel Isotopic Composition Database (SFCOMPO) [55]. These new data 

should be reviewed and evaluated to assess possible applicability to the present studies. The 

Japanese Atomic Energy Agency (JAEA) and other research organizations have additional BWR 

validation data that could be acquired through international cooperation agreements. The Spanish 

Nuclear Safety Council, or Consejo de Seguridad Nuclear (CSN), has an active research 

program, has conducted several experimental studies [56, 57], and currently has a research 

initiative in the area of BWR fuel BUC. Collaboration with these international organizations

could be used to leverage limited experimental data, and cooperation on future research projects 

could further validate BWR BUC methodologies.

An emerging methodology for uncertainty analysis is the use of nuclear data uncertainty 

information (covariance matrices) to predict reactor physics parameters [58]. This method has 

recently been applied to the analysis of nuclide composition uncertainties [45]. This approach is 

based on Monte Carlo sampling of the underlying nuclear data uncertainties used in the calculation 

to estimate the uncertainties in calculated parameters. The methodology has been implemented in 

SCALE in the Sampler code, which performs stochastic sampling of the nuclear data. This 

approach is similar to that used by TSUNAMI, and in fact applies the same nuclear data covariance 

data files used by TSUNAMI as discussed in Section 4.1. Data uncertainty files have been recently 

expanded to include uncertainties in the nuclear decay data and fission product yields to provide a 

comprehensive uncertainty evaluation for spent fuel analyses. Preliminary studies [37] comparing 

this methodology with methods based on nuclide assay data and an independent approach 

proposed by industry show promising results. Such an approach may be valuable to support 

validation in situations of limited experimental data; however additional validation of these 

methods is needed before they can be used to support licensing analyses.

119

6 SUMMARY AND CONCLUSIONS

This report provides a technical basis for the use of peak reactivity methods to credit burnup in 

the criticality safety analysis of BWR storage casks and transportation systems. It presents an 

overview of current peak reactivity methods used in SNF pools as background for the evaluation 

of peak reactivity BUC in casks. Parameter studies were performed to identify the most 

important factors affecting peak reactivity analysis and the conservative direction for each of 

these parameters for various sets of nuclides modeled in the GBC-68 cask. Validation of 

criticality calculations for peak reactivity BWR fuel was performed with calculation of bias, 

uncertainties, and penalty factors. Validation is also presented for SNF isotopic inventories using 

RCA measurements of low burnup BWR fuel. A brief summary of each of these sections is 

presented here, followed by overall conclusions of this assessment of a technical basis for peak 

reactivity methods in storage and transportation casks.

6.1 CURRENT PEAK REACTIVITY METHODS FOR SPENT FUEL 

POOLS

The SCCG-limit-with-gadolinium-credit method gives credit for residual gadolinium and 

examines several different lattices including a range of enrichments, gadolinium loadings, and 

gadolinium patterns over multiple burnups. This method provides a fairly straightforward 

approach to demonstrating safe storage of BWR fuel assemblies. While this method requires a 

large number of lattice designs, the use of real lattice designs provides a degree of accuracy in 

the analysis that is lacking in some other methods.

The SCCG-limit-with-gadolinium-credit method has some potential shortcomings as well. The 

use of a sizeable number of real lattice designs may be problematic for implementation by a cask 

vendor without ready access to a reliable collection of such design information. The SCCG-limitwith-gadolinium-credit method attempts to balance some of the conservatisms of the peak 

reactivity methods, such as considering all assemblies to be identical and all at peak reactivity, 

with a less conservative depletion analysis including nonlimiting depletion conditions and 

lattices. Finally, the use of nonlimiting lattices and depletion conditions may also bias the 

correlation of krack and SCCG kinf in the low, potentially unconservative direction.

In comparison, the SCCG-limit-without-gadolinium-credit method has some advantages in terms 

of conservatism and is simple to implement in power plant operations. There are subtle but 

important differences between this method and the SCCG-limit-with-gadolinium-credit method. 

The primary difference is that in this method, the SCCG limit is based on a correlation created 

without credit for gadolinium.

The SCCG-limit-without-gadoliniumm-credit method also suffers from some potential areas of 

concern. The storage of fresh and low burnup fuel requires that a separate gadolinium 

requirement be determined and met in the burnup range in which the reactivity of unpoisoned 

fuel exceeds limits. This adds additional complexity, especially in the selection of fuel 

assemblies that are qualified for storage in a cask or package. The range of depletion conditions 

will also require more effort for validation of both criticality and composition calculations.
120

6.2 PEAK REACTIVITY ANALYSIS SUMMARY

A range of parameters was studied to identify the important parameters for BWR peak reactivity 

and to quantify the potential sensitivity of calculated cask reactivity to these parameters. A BWR 

BUC methodology would require a set of selected nuclides and the associated depletion 

conditions to ensure a conservative analysis. Those found to give the most reactive results are 

summarized in Tables 3.32 and 3.33 in Section 3.5.1. The most important operating conditions 

are void fraction and control blade insertion. For AO analyses, both high void fractions and 

control blade insertion increase reactivity. For AFP analyses, low void fractions increase 

reactivity at the peak; control blade insertion was also shown to be a positive reactivity effect in 

these studies, but is likely dependent on gadolinium rod pattern. Other parameters, including 

gadolinium pattern, fuel temperature, specific power, and operating history have smaller impacts 

on peak reactivity.

One set of conclusions that can be drawn from these studies relates to which parameters are 

sufficiently variable or interdependent so that examination is recommended for each licensing 

analysis performed. The primary parameters of interest in this category are the gadolinium 

pattern used in the analysis and the way it interacts with control blade insertion. It is conceivable 

that some gadolinium patterns will be more reactive than others. More importantly, the power 

distribution shifts caused by control blade insertion drive changes in residual gadolinium, and 

hence discharged fuel reactivity. These effects will be sensitive to the gadolinium pattern. 

Certain other key parameters do not need to be studied further to identify the direction of 

conservatism, but justification of the values used should be provided as part of an application. 

The parameters that do not need further investigation for the GE14 fuel assembly design 

considered in this work include initial or depleted composition modeling, void fraction, fuel 

temperature, and operating history. 

Several areas related to peak reactivity BUC could be further studied to provide additional 

confidence in the results generated in this report, clarify causes and relationships among 

parameters, or extend the area of applicability beyond the parameters, ranges, and fuel types 

studied here. Other areas that could be studied further include the following:

• A wider range of lattice enrichment zoning patterns

• Additional gadolinium patterns, potentially including less constrained pattern 

development

• Expansion of the study of the interaction between gadolinium patterns and control blade 

effects

• Control blade programs, including both rodded and unrodded depletion during operation

• Additional fuel assembly design types

• 3D depletion calculations to investigate interactions between lattices

• Fuel assembly orientation within the cask

• Depletion effects of symmetric gaps between assemblies in the core

• Parameter interdependencies and potential competing effects.
121

6.3 VALIDATION OF CASK REACTIVITY CALCULATIONS 

SUMMARY

Section 4 presents a series of studies that investigate validation of cask reactivity calculations. As 

discussed in Section 4.3, several sources of SDFs have been used, providing a large number of 

candidate experiments. In total, over 1600 unique experiments were compared against a range of 

application cases to experiment cases with ck values of 0.8 or higher.

A range of potentially useful experiments has been identified in Section 4.4 for use in AO or 

AFP analyses. More than 50 experiments have been identified for each application, allowing a 

sufficient population for validation. All experiments selected are LEU-COMP-THERM 

experiments and thus provide no validation of cross sections for plutonium or americium, 

residual gadolinium, or fission products. The experiments identified for use in validation are 

listed in Appendix C. A sample validation was presented in Section 4.5 using multiple methods; 

the results on which the validation is based are listed in Appendix D. The resulting bias and bias 

uncertainty values, of the single application model examined, were similar among each of the 

methods, and the limiting combination of bias and bias uncertainty was -0.00973 Δk .

Several important nuclides are not present in the validation suite used for the sample validation, 

as mentioned previously. A sensitivity/uncertainty analysis approach was used to develop these 

factors in Section 4.6. The calculations showed that a penalty factor of about 0.3% Δk for 

transuranics, plutonium, and americium was appropriate for the sample validation. The factor for 

residual gadolinium was calculated to be 0.05% Δk. The factor for remaining fission products 

and minor actinides was calculated to be about 0.06% Δk. These penalty factors are fairly small, 

so it is unlikely that additional conservatism in them would have a noticeable impact on the 

overall conservatism of the analysis.

Validation calculations can be performed in compliance with the consensus ANSI/ANS standard 

[17] and prior NUREG/CR recommendations [22, 23]. Modest penalty factors have been 

established that can extend the validation area of applicability to account for nuclides that cannot 

be validated with critical experiments at this time. Overall, the validation of cask reactivity 

calculations does not present a technical barrier that would prevent implementation of peak 

reactivity methods for demonstrating the criticality safety of BWR fuel in storage and 

transportation casks.

6.4 ISOTOPIC VALIDATION SUMMARY

A method for determining the uncertainty in keff calculations associated with the BWR SNF 

nuclide concentrations near peak reactivity has been demonstrated for the GBC-68 cask model 

and the vanished fuel assembly lattice configuration. This method is based on the direct 

application of measured BWR SNF composition data to estimate the uncertainties associated 

with the calculated nuclide composition used in BUC application models. 

The available experimental nuclide data for BWR fuel near peak reactivity currently limits BUC 

analyses to consider AO fuel compositions. Present radiochemical assay data lack sufficient 

fission product data that would enable validation for actinide and fission product compositions. 

Similarly, applicable data for residual 155Gd are limited, and only three samples obtained from 
122

PWR fuel samples were evaluated in this work. However, the large variability in the validation 

results for 155Gd and the statistical penalty associated with the low number of measurements 

effectively eliminates any credit that can be obtained based on the existing measurement data.

Addition of fission product measurement data and improved 155Gd data in the range of peak 

reactivity could support credit for a substantial fraction of the reactivity worth from the omitted 

BUC nuclides which represent approximately 4% of the total reactivity worth. 

Although the analysis in this work was limited by the available validation data to consider AO 

compositions, the approach is applicable to fission products and residual 155Gd provided 

sufficient measurement data are obtained to support validation of the nuclide concentrations. 

BUC programs in Belgium, Japan, and Spain currently have research initiatives in the area of 

BWR fuel BUC in which collaboration with international organizations could be used to 

leverage limited experimental data and cooperate on future research projects to validate BWR 

BUC methodologies.

6.5 CONCLUSIONS

The primary purpose of this report is to provide a technical basis for applying peak reactivity 

methods for BWR BUC in SNF storage and transportation casks. The results summarized above 

support several important conclusions.

• The physics of BWR fuel depletion are well understood, reliable, and predictable in their 

effects on discharged fuel reactivity near peak reactivity. A conservative set of analysis 

conditions can be identified and implemented to allow criticality safety analysis of BWR 

SNF at peak reactivity in storage and transportation casks.

• The conservative set of depletion parameters used in any analysis will be dependent on 

the methodology developed and implemented by an applicant, including the specific set 

of nuclides credited in the analysis.

• A suitable number of UO2 critical experiments can be identified to support validation of 

peak reactivity analysis of BWR SNF. All the experiments identified in this report are 

LEU, water-moderated pin array experiments.

• There is a need for critical experiment data with plutonium and/or gadolinium that have 

adequate similarity to low burnup BWR fuel. No such experiments were identified in this 

study.

• Penalty factors have been developed for the unvalidated transuranic, gadolinium, and 

fission product nuclides included in GBC-68 models used in this report. The sum of these 

three factors is less than 0.5% Δk.

• Isotopic validation for AO BUC near peak reactivity has been demonstrated with 

identified radiochemical assay data. A method for determining the uncertainty in keff

calculations associated with the BWR SNF nuclide concentrations near peak reactivity 

has been verified for the GBC-68 cask model and the vanished fuel assembly lattice 

configuration. 

• Additional radiochemical assay data are needed for modern design low burnup BWR fuel 

with gadolinium poison and fission product measurements. The addition of fission 

product measurement data and improved 155Gd data in the range of peak reactivity could 

support credit for a substantial fraction of the reactivity worth from the omitted BUC 
123

nuclides which represent approximately 4% of the total reactivity worth. Collaboration 

with international organizations could be used to leverage limited experimental data and 

to cooperate on future research projects to validate BWR BUC methodologies.

125

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APPENDIX A. TRITON DEPLETION MODELING DETAILS

A-1

A.1 TRITON DEPLETION MODELING DETAILS

Four different options were used for modeling the isotopic depletion of the fuel assemblies in TRITON in 

Section 3: (1) pin-wise enrichment with pin-wise isotopics (PEPI), (2) pin-wise enrichment with average 

isotopics (PEAI), (3) average-enrichment with pin-wise isotopics (AEPI), and (4) average-enrichment 

with average isotopics (AEAI). These four options were chosen in an effort to cover all options that an 

analyst might select for isotopic modeling. In the interest of clarity, these four options are further 

explained in this section. 

The four isotopic modeling options are a combination of two different sets of assumptions. The user can 

either assume that the fuel pins in a lattice contain their actual as-designed enrichment (pin-wise 

enrichment [PE]), or the user can assume that a single, lattice-average enrichment is used in each fuel pin 

(average enrichment [AE]). For either of these two assumptions, the user can then choose to either deplete 

a set of like-enrichment fuel pins as individual depletion regions (pin -wise isotopics, [PI]), or as a single 

average depletion region (average isotopics [AI]). The combinations of these different options provide the 

four options used throughout this work: PEPI, PEAI, AEPI, and AEAI. Although other modeling options 

exist, these four are likely to cover the range from least conservative to most conservative options. 

A further complication is the need to specify user-defined Dancoff factors for certain fuel pins in a boiling 

water reactor (BWR) fuel lattice when using SCALE [A1]. Accurate results for BWR lattices can be 

obtained by specifying user-defined Dancoff factors for fuel corner-, edge-, and water rod-adjacent fuel 

pins. The default Dancoff factor treatment in SCALE provides sufficient accuracy for all other fuel pins 

in the lattice. A plot illustrating the Dancoff factor treatment is shown in Figure A.1. The numbers 

indicate the 235U enrichment for each pin. Fuel pin locations that result in similar Dancoff factors have 

been shaded pink with single underlined numbers or blue with double underlined numbers. The unshaded 

boxes without underlined numbers signify a fuel pin location in which the SCALE default Dancoff factor 

treatment is used. 

Figure A.1. Lattice layout highlighting the three different sets of Dancoff factors used in this 

SCALE/TRITON analysis.
A-2

PEPI uses the as-designed fuel enrichment in each fuel pin location, and each fuel pin is depleted as a 

separate mixture. The Dancoff factors are applied as described in Figure A.1. Figure A.2 illustrates the 

PEPI lattice layout and SCALE/TRITON visualization of the lattice. (Double underlined numbers 

indicate special Dancoff factor treatment.) 

In the lattice layout, all fuel pin locations are unshaded, signifying that the fuel location uses a different 

depletion mixture than all other locations. This is also illustrated in the SCALE/TRITON representation 

in Figure A.2, which shows a different color for each fuel mixture in each diagonally symmetric location. 

 

Figure A.2. PEPI lattice layout (left) and SCALE/TRITON representation (right).

AEPI uses the lattice-average enrichment in all fuel locations; each fuel pin is depleted as a separate 

mixture. (Double underlining signifies special Dancoff factor treatment.) Figure A.3 shows the AEPI 

lattice layout and SCALE/TRITON visualization of the lattice can be found in Figure A.3. In the lattice 

layout, all fuel pin locations are unshaded, signifying that each fuel location uses a different depletion 

mixture than all other locations, assuming diagonal symmetry from upper left to lower right corner. This 

is also illustrated in the SCALE/TRITON representation in Figure A.3, which shows a different color for 

each fuel mixture in each diagonally symmetric location.
A-3

 

Figure A.3. AEPI lattice layout (left) and SCALE/TRITON representation (right).

Because separate Dancoff factors cannot be applied to a single fuel mixture, the 

AI option divides a set of like-enrichment fuel pins into three different depletion regions based on the 

Dancoff factor. The cross-section processing, and thus depletion, for these fuel pins must be separated by 

Dancoff factor grouping. For example, for the 4.40 wt% enriched set of fuel pins, three different fuel 

mixtures are required: as nine fuel pins receive the default Dancoff factor treatment, four receive a 

specialized Dancoff factor corresponding to the fuel pins along the assembly edge and near water rods, 

and one fuel pin receives a specialized Dancoff factor corresponding to the fuel location adjacent to both 

water rods. Figure A.4 presents a lattice layout highlighting this treatment using different shading for each 

set of depletion mixtures. In Figure A.4 a single depletion mixture is used for the green-shaded fuel 

locations (no underlined text), a second depletion mixture is used for the blue-shaded fuel locations 

(double underlined text), and a third depletion mixture is used for the orange-shaded fuel location (single 

underlined text). 

Figure A.4. Visual depiction of the grouping of depletion mixtures based on Dancoff factor for 

4.40 wt% fuel.

PEAI uses the as-designed fuel enrichment in each fuel pin location, and fuel is depleted in separate 

groups based on fuel enrichment and Dancoff factor. The lattice layout and SCALE/TRITON 

representation of the PEAI options are shown in Figure A.5. Similar to Figure A.4, the shading in the 

boxes of the lattice layout signify different depletion mixtures – the same color is used for each 
A-4

enrichment group, but the opacity is adjusted and the text is underlined in order to signify different groups 

of depletion mixtures that are required for separated Dancoff factor treatment. In the SCALE/TRITON 

layout of Figure A.5 (right), a large number of like-colored fuel pin locations are observed, indicating that 

the same mixture is used in each of those fuel pins. 

 

Figure A.5. PEAI lattice layout (left) and SCALE/TRITON representation (right).

AEAI uses the lattice-average enrichment in all fuel locations, and fuel is depleted by Dancoff factor 

groups. Figure A.6 shows the lattice layout and SCALE/TRITON representation of the AEAI option. 

As in Figure A.5, the shading in the boxes of the lattice layout signify different depletion mixtures—the 

same color is used for each enrichment group, but the opacity is adjusted and the numbers are underlined 

in order to signify different groups of depletion mixtures. 

 

Figure A.6. AEAI lattice layout (left) and SCALE/TRITON representation (right).

None of the lattices discussed in this appendix have described the treatment when gadolinium fuel pins 

are present in the lattice. The treatment is very similar; for all non-gadolinium-bearing fuel locations, the 

same treatment as previously described as applied. In all studies in Section 3 of this report, only the 4.9% 

-enriched fuel pins were allowed to contain gadolinium. In these cases, each gadolinium-bearing pin was 
A-5

modeled using seven radial rings. In each gadolinium-bearing fuel pin, each individual fuel ring 

corresponds to all other gadolinium-bearing fuel pins: the outer rings are identical between all 

gadolinium-bearing fuel pins; the second rings are identical between all fuel pins, etc.

A.2 APPENDIX A REFERENCE

A1 B. J. Ade, SCALE/TRITON Primer: A Primer for Light Water Reactor Lattice Physics Calculations,

NUREG/CR-7041, ORNL/TM-2011/21, U.S. Nuclear Regulatory Commission, Oak Ridge National 

Laboratory, November 2012.

APPENDIX B. GADOLINIUM PATTERNS

B-1

B.1 GADOLINIUM PATTERNS

This appendix contains the 15 gadolinium patterns used in the pattern study documented in Section 3.4.3. 

The base case pattern used in all sections is shown in Figure B.1; the subsequent 14 figures (B.2–B.15) 

show the alternate patterns considered. All patterns contain six gadolinium fuel rods containing 2 wt% 

gadolinium. Only pins with 4.90 weight-percent 235U enrichment are considered for gadolinium in this 

study. The fuel enrichment and gadolinium layout for the full and vanished lattices are illustrated; a box 

with a single number signifies the fuel pin enrichment in wt% 235U, and a box with two numbers signifies 

the enrichment (top) and gadolinium content in wt% gadolinium (bottom). The large boxes containing 

“WR” specify the large central water rod and boxes with a “V” specify a vanished fuel pin.

Figure B.1. Gadolinium patterns 0 (same as used in the Gd-loading study, P0).

Figure B.2. Gadolinium patterns 1 (P1).
B-2

Figure B.3. Gadolinium patterns 2 (P2).

Figure B.4. Gadolinium patterns 3 (P3).
B-3

Figure B.5. Gadolinium patterns 4 (P4).

Figure B.6. Gadolinium patterns 5 (P5).
B-4

Figure B.7. Gadolinium patterns 6 (P6).

Figure B.8. Gadolinium patterns 7 (P7).
B-5

Figure B.9. Gadolinium patterns 8 (P8).

Figure B.10. Gadolinium patterns 9 (P9).
B-6

Figure B.11. Gadolinium patterns 10 (P10).

Figure B.12. Gadolinium patterns 11 (P11).
B-7

Figure B.13. Gadolinium patterns 12 (P12).

Figure B.14. Gadolinium patterns 13 (P13).
B-8

Figure B.15. Gadolinium patterns 14 (P14).
APPENDIX C. EXPERIMENTS CONSIDERED

C-1

C.1 EXPERIMENTS CONSIDERED

This appendix contains the full list of critical experiments considered as candidates for validation in 

Table C.1. This list was compiled from the three sources discussed in Section 4.3 and contains 1643 

unique critical experiments.

Table C.1. Critical experiments considered for validation

LEU-COMP-THERM-001-001 LEU-COMP-THERM-033-025 LEU-COMP-THERM-090-007

LEU-COMP-THERM-001-002 LEU-COMP-THERM-033-026 LEU-COMP-THERM-090-008

LEU-COMP-THERM-001-003 LEU-COMP-THERM-033-027 LEU-COMP-THERM-090-009

LEU-COMP-THERM-001-004 LEU-COMP-THERM-033-028 LEU-COMP-THERM-091-001

LEU-COMP-THERM-001-005 LEU-COMP-THERM-033-029 LEU-COMP-THERM-091-002

LEU-COMP-THERM-001-006 LEU-COMP-THERM-033-030 LEU-COMP-THERM-091-003

LEU-COMP-THERM-001-007 LEU-COMP-THERM-033-031 LEU-COMP-THERM-091-004

LEU-COMP-THERM-001-008 LEU-COMP-THERM-033-032 LEU-COMP-THERM-091-005

LEU-COMP-THERM-002-001 LEU-COMP-THERM-033-033 LEU-COMP-THERM-091-006

LEU-COMP-THERM-002-002 LEU-COMP-THERM-033-034 LEU-COMP-THERM-091-007

LEU-COMP-THERM-002-003 LEU-COMP-THERM-033-035 LEU-COMP-THERM-091-008

LEU-COMP-THERM-002-004 LEU-COMP-THERM-033-036 LEU-COMP-THERM-091-009

LEU-COMP-THERM-002-005 LEU-COMP-THERM-033-037 LEU-COMP-THERM-092-001

LEU-COMP-THERM-003-001 LEU-COMP-THERM-033-038 LEU-COMP-THERM-092-002

LEU-COMP-THERM-003-002 LEU-COMP-THERM-033-039 LEU-COMP-THERM-092-003

LEU-COMP-THERM-003-003 LEU-COMP-THERM-033-040 LEU-COMP-THERM-092-004

LEU-COMP-THERM-003-004 LEU-COMP-THERM-033-041 LEU-COMP-THERM-092-005

LEU-COMP-THERM-003-005 LEU-COMP-THERM-033-042 LEU-COMP-THERM-092-006

LEU-COMP-THERM-003-006 LEU-COMP-THERM-033-043 LEU-COMP-THERM-094-001

LEU-COMP-THERM-003-007 LEU-COMP-THERM-033-044 LEU-COMP-THERM-094-002

LEU-COMP-THERM-003-008 LEU-COMP-THERM-033-045 LEU-COMP-THERM-094-003

LEU-COMP-THERM-003-009 LEU-COMP-THERM-033-046 LEU-COMP-THERM-094-004

LEU-COMP-THERM-003-010 LEU-COMP-THERM-033-047 LEU-COMP-THERM-094-005

LEU-COMP-THERM-003-011 LEU-COMP-THERM-033-048 LEU-COMP-THERM-094-006

LEU-COMP-THERM-003-012 LEU-COMP-THERM-033-049 LEU-COMP-THERM-094-007

LEU-COMP-THERM-003-013 LEU-COMP-THERM-033-050 LEU-COMP-THERM-094-008

LEU-COMP-THERM-003-014 LEU-COMP-THERM-033-051 LEU-COMP-THERM-094-009

LEU-COMP-THERM-003-015 LEU-COMP-THERM-033-052 LEU-COMP-THERM-094-010

LEU-COMP-THERM-003-016 LEU-COMP-THERM-034-001 LEU-COMP-THERM-094-011

LEU-COMP-THERM-003-017 LEU-COMP-THERM-034-002 LEU-MISC-THERM-005-001

LEU-COMP-THERM-003-018 LEU-COMP-THERM-034-003 LEU-MISC-THERM-005-002

LEU-COMP-THERM-003-019 LEU-COMP-THERM-034-004 LEU-MISC-THERM-005-003

LEU-COMP-THERM-003-020 LEU-COMP-THERM-034-005 LEU-MISC-THERM-005-004

LEU-COMP-THERM-003-021 LEU-COMP-THERM-034-006 LEU-MISC-THERM-005-005

LEU-COMP-THERM-003-022 LEU-COMP-THERM-034-007 LEU-MISC-THERM-005-006

LEU-COMP-THERM-004-001 LEU-COMP-THERM-034-008 LEU-MISC-THERM-005-007

LEU-COMP-THERM-004-002 LEU-COMP-THERM-034-009 LEU-MISC-THERM-005-008

LEU-COMP-THERM-004-003 LEU-COMP-THERM-034-010 LEU-MISC-THERM-005-009

LEU-COMP-THERM-004-004 LEU-COMP-THERM-034-011 LEU-MISC-THERM-005-010

LEU-COMP-THERM-004-005 LEU-COMP-THERM-034-012 LEU-MISC-THERM-005-011
C-2

Table C.1. Continued

LEU-COMP-THERM-004-006 LEU-COMP-THERM-034-013 LEU-MISC-THERM-005-012

LEU-COMP-THERM-004-007 LEU-COMP-THERM-034-014 LEU-SOL-THERM-002-001

LEU-COMP-THERM-004-008 LEU-COMP-THERM-034-015 LEU-SOL-THERM-002-002

LEU-COMP-THERM-004-009 LEU-COMP-THERM-034-016 LEU-SOL-THERM-002-003

LEU-COMP-THERM-004-010 LEU-COMP-THERM-034-017 LEU-SOL-THERM-003-001

LEU-COMP-THERM-004-011 LEU-COMP-THERM-034-018 LEU-SOL-THERM-003-002

LEU-COMP-THERM-004-012 LEU-COMP-THERM-034-019 LEU-SOL-THERM-003-003

LEU-COMP-THERM-004-013 LEU-COMP-THERM-034-020 LEU-SOL-THERM-003-004

LEU-COMP-THERM-004-014 LEU-COMP-THERM-034-021 LEU-SOL-THERM-003-005

LEU-COMP-THERM-004-015 LEU-COMP-THERM-034-022 LEU-SOL-THERM-003-006

LEU-COMP-THERM-004-016 LEU-COMP-THERM-034-023 LEU-SOL-THERM-003-007

LEU-COMP-THERM-004-017 LEU-COMP-THERM-034-024 LEU-SOL-THERM-003-008

LEU-COMP-THERM-004-018 LEU-COMP-THERM-035-001 LEU-SOL-THERM-003-009

LEU-COMP-THERM-004-019 LEU-COMP-THERM-035-002 LEU-SOL-THERM-004-001

LEU-COMP-THERM-004-020 LEU-COMP-THERM-035-003 LEU-SOL-THERM-004-002

LEU-COMP-THERM-005-001 LEU-COMP-THERM-036-001 LEU-SOL-THERM-004-003

LEU-COMP-THERM-005-002 LEU-COMP-THERM-036-002 LEU-SOL-THERM-004-004

LEU-COMP-THERM-005-003 LEU-COMP-THERM-036-003 LEU-SOL-THERM-004-005

LEU-COMP-THERM-005-004 LEU-COMP-THERM-036-004 LEU-SOL-THERM-004-006

LEU-COMP-THERM-005-005 LEU-COMP-THERM-036-005 LEU-SOL-THERM-004-007

LEU-COMP-THERM-005-006 LEU-COMP-THERM-036-006 MIX-COMP-THERM-001-001

LEU-COMP-THERM-005-007 LEU-COMP-THERM-036-007 MIX-COMP-THERM-001-002

LEU-COMP-THERM-005-008 LEU-COMP-THERM-036-008 MIX-COMP-THERM-001-003

LEU-COMP-THERM-005-009 LEU-COMP-THERM-036-009 MIX-COMP-THERM-001-004

LEU-COMP-THERM-005-010 LEU-COMP-THERM-036-010 MIX-COMP-THERM-002-001S

LEU-COMP-THERM-005-011 LEU-COMP-THERM-036-011 MIX-COMP-THERM-002-002S

LEU-COMP-THERM-005-012 LEU-COMP-THERM-036-012 MIX-COMP-THERM-002-003S

LEU-COMP-THERM-005-013 LEU-COMP-THERM-036-013 MIX-COMP-THERM-002-004S

LEU-COMP-THERM-005-014 LEU-COMP-THERM-036-014 MIX-COMP-THERM-002-005S

LEU-COMP-THERM-005-015 LEU-COMP-THERM-036-015 MIX-COMP-THERM-002-006S

LEU-COMP-THERM-005-016 LEU-COMP-THERM-036-016 MIX-COMP-THERM-003-001

LEU-COMP-THERM-006-001 LEU-COMP-THERM-036-017 MIX-COMP-THERM-003-002

LEU-COMP-THERM-006-002 LEU-COMP-THERM-036-018 MIX-COMP-THERM-003-003

LEU-COMP-THERM-006-003 LEU-COMP-THERM-036-019 MIX-COMP-THERM-003-004

LEU-COMP-THERM-006-004 LEU-COMP-THERM-036-020 MIX-COMP-THERM-003-005

LEU-COMP-THERM-006-005 LEU-COMP-THERM-036-021 MIX-COMP-THERM-003-006

LEU-COMP-THERM-006-006 LEU-COMP-THERM-036-022 MIX-COMP-THERM-004-001

LEU-COMP-THERM-006-007 LEU-COMP-THERM-036-023 MIX-COMP-THERM-004-002

LEU-COMP-THERM-006-008 LEU-COMP-THERM-036-024 MIX-COMP-THERM-004-003

LEU-COMP-THERM-006-009 LEU-COMP-THERM-036-025 MIX-COMP-THERM-004-004

LEU-COMP-THERM-006-010 LEU-COMP-THERM-036-026 MIX-COMP-THERM-004-005

LEU-COMP-THERM-006-011 LEU-COMP-THERM-036-027 MIX-COMP-THERM-004-006

LEU-COMP-THERM-006-012 LEU-COMP-THERM-036-028 MIX-COMP-THERM-004-007

LEU-COMP-THERM-006-013 LEU-COMP-THERM-036-029 MIX-COMP-THERM-004-008

LEU-COMP-THERM-006-014 LEU-COMP-THERM-036-030 MIX-COMP-THERM-004-009

LEU-COMP-THERM-006-015 LEU-COMP-THERM-036-031 MIX-COMP-THERM-004-010

LEU-COMP-THERM-006-016 LEU-COMP-THERM-036-032 MIX-COMP-THERM-004-011
C-3

Table C.1. Continued

LEU-COMP-THERM-006-017 LEU-COMP-THERM-036-033 MIX-COMP-THERM-005-01

LEU-COMP-THERM-006-018 LEU-COMP-THERM-036-034 MIX-COMP-THERM-005-02

LEU-COMP-THERM-008-001 LEU-COMP-THERM-036-035 MIX-COMP-THERM-005-03

LEU-COMP-THERM-008-002 LEU-COMP-THERM-036-036 MIX-COMP-THERM-005-04

LEU-COMP-THERM-008-003 LEU-COMP-THERM-036-037 MIX-COMP-THERM-005-05

LEU-COMP-THERM-008-004 LEU-COMP-THERM-036-038 MIX-COMP-THERM-005-06

LEU-COMP-THERM-008-005 LEU-COMP-THERM-036-039 MIX-COMP-THERM-005-07

LEU-COMP-THERM-008-006 LEU-COMP-THERM-036-040 MIX-COMP-THERM-006-001

LEU-COMP-THERM-008-007 LEU-COMP-THERM-036-041 MIX-COMP-THERM-006-002

LEU-COMP-THERM-008-008 LEU-COMP-THERM-036-042 MIX-COMP-THERM-006-003

LEU-COMP-THERM-008-009 LEU-COMP-THERM-036-043 MIX-COMP-THERM-006-004

LEU-COMP-THERM-008-010 LEU-COMP-THERM-036-044 MIX-COMP-THERM-006-005

LEU-COMP-THERM-008-011 LEU-COMP-THERM-036-045 MIX-COMP-THERM-006-006

LEU-COMP-THERM-008-012 LEU-COMP-THERM-036-046 MIX-COMP-THERM-006-007

LEU-COMP-THERM-008-013 LEU-COMP-THERM-036-047 MIX-COMP-THERM-006-008

LEU-COMP-THERM-008-014 LEU-COMP-THERM-036-048 MIX-COMP-THERM-006-009

LEU-COMP-THERM-008-015 LEU-COMP-THERM-036-049 MIX-COMP-THERM-006-010

LEU-COMP-THERM-008-016 LEU-COMP-THERM-036-050 MIX-COMP-THERM-006-011

LEU-COMP-THERM-008-017 LEU-COMP-THERM-036-051 MIX-COMP-THERM-006-012

LEU-COMP-THERM-009-001 LEU-COMP-THERM-036-052 MIX-COMP-THERM-006-013

LEU-COMP-THERM-009-002 LEU-COMP-THERM-036-053 MIX-COMP-THERM-006-014

LEU-COMP-THERM-009-003 LEU-COMP-THERM-036-054 MIX-COMP-THERM-006-015

LEU-COMP-THERM-009-004 LEU-COMP-THERM-036-055 MIX-COMP-THERM-006-016

LEU-COMP-THERM-009-005 LEU-COMP-THERM-036-056 MIX-COMP-THERM-006-017

LEU-COMP-THERM-009-006 LEU-COMP-THERM-036-057 MIX-COMP-THERM-006-018

LEU-COMP-THERM-009-007 LEU-COMP-THERM-036-058 MIX-COMP-THERM-006-019

LEU-COMP-THERM-009-008 LEU-COMP-THERM-036-059 MIX-COMP-THERM-006-020

LEU-COMP-THERM-009-009 LEU-COMP-THERM-036-060 MIX-COMP-THERM-006-021

LEU-COMP-THERM-009-010 LEU-COMP-THERM-036-061 MIX-COMP-THERM-006-022

LEU-COMP-THERM-009-011 LEU-COMP-THERM-036-062 MIX-COMP-THERM-006-023

LEU-COMP-THERM-009-012 LEU-COMP-THERM-036-063 MIX-COMP-THERM-006-024

LEU-COMP-THERM-009-013 LEU-COMP-THERM-036-064 MIX-COMP-THERM-006-025

LEU-COMP-THERM-009-014 LEU-COMP-THERM-036-065 MIX-COMP-THERM-006-026

LEU-COMP-THERM-009-015 LEU-COMP-THERM-036-066 MIX-COMP-THERM-006-027

LEU-COMP-THERM-009-016 LEU-COMP-THERM-036-067 MIX-COMP-THERM-006-028

LEU-COMP-THERM-009-017 LEU-COMP-THERM-036-068 MIX-COMP-THERM-006-029

LEU-COMP-THERM-009-018 LEU-COMP-THERM-036-069 MIX-COMP-THERM-006-030

LEU-COMP-THERM-009-019 LEU-COMP-THERM-037-001 MIX-COMP-THERM-006-031

LEU-COMP-THERM-009-020 LEU-COMP-THERM-037-002 MIX-COMP-THERM-006-032

LEU-COMP-THERM-009-021 LEU-COMP-THERM-037-003 MIX-COMP-THERM-006-033

LEU-COMP-THERM-009-022 LEU-COMP-THERM-037-004 MIX-COMP-THERM-006-034

LEU-COMP-THERM-009-023 LEU-COMP-THERM-037-005 MIX-COMP-THERM-006-035

LEU-COMP-THERM-009-024 LEU-COMP-THERM-037-006 MIX-COMP-THERM-006-036

LEU-COMP-THERM-009-025 LEU-COMP-THERM-037-007 MIX-COMP-THERM-006-037

LEU-COMP-THERM-009-026 LEU-COMP-THERM-037-008 MIX-COMP-THERM-006-038

LEU-COMP-THERM-009-027 LEU-COMP-THERM-037-009 MIX-COMP-THERM-006-039

LEU-COMP-THERM-010-001 LEU-COMP-THERM-037-010 MIX-COMP-THERM-006-040
C-4

Table C.1. Continued

LEU-COMP-THERM-010-002 LEU-COMP-THERM-037-011 MIX-COMP-THERM-006-041

LEU-COMP-THERM-010-003 LEU-COMP-THERM-038-001 MIX-COMP-THERM-006-042

LEU-COMP-THERM-010-004 LEU-COMP-THERM-038-002 MIX-COMP-THERM-006-043

LEU-COMP-THERM-010-005 LEU-COMP-THERM-038-003 MIX-COMP-THERM-006-044

LEU-COMP-THERM-010-006 LEU-COMP-THERM-038-004 MIX-COMP-THERM-006-045

LEU-COMP-THERM-010-007 LEU-COMP-THERM-038-005 MIX-COMP-THERM-006-046

LEU-COMP-THERM-010-008 LEU-COMP-THERM-038-006 MIX-COMP-THERM-006-047

LEU-COMP-THERM-010-009 LEU-COMP-THERM-038-007 MIX-COMP-THERM-006-048

LEU-COMP-THERM-010-010 LEU-COMP-THERM-038-008 MIX-COMP-THERM-006-049

LEU-COMP-THERM-010-011 LEU-COMP-THERM-038-009 MIX-COMP-THERM-006-050

LEU-COMP-THERM-010-012 LEU-COMP-THERM-038-010 MIX-COMP-THERM-007-001

LEU-COMP-THERM-010-013 LEU-COMP-THERM-038-011 MIX-COMP-THERM-007-002

LEU-COMP-THERM-010-014 LEU-COMP-THERM-038-012 MIX-COMP-THERM-007-003

LEU-COMP-THERM-010-015 LEU-COMP-THERM-038-013 MIX-COMP-THERM-007-004

LEU-COMP-THERM-010-016 LEU-COMP-THERM-038-014 MIX-COMP-THERM-007-005

LEU-COMP-THERM-010-017 LEU-COMP-THERM-039-001 MIX-COMP-THERM-007-006

LEU-COMP-THERM-010-018 LEU-COMP-THERM-039-002 MIX-COMP-THERM-007-007

LEU-COMP-THERM-010-019 LEU-COMP-THERM-039-003 MIX-COMP-THERM-007-008

LEU-COMP-THERM-010-020 LEU-COMP-THERM-039-004 MIX-COMP-THERM-007-009

LEU-COMP-THERM-010-021 LEU-COMP-THERM-039-005 MIX-COMP-THERM-007-010

LEU-COMP-THERM-010-022 LEU-COMP-THERM-039-006 MIX-COMP-THERM-007-011

LEU-COMP-THERM-010-023 LEU-COMP-THERM-039-007 MIX-COMP-THERM-007-012

LEU-COMP-THERM-010-024 LEU-COMP-THERM-039-008 MIX-COMP-THERM-007-013

LEU-COMP-THERM-010-025 LEU-COMP-THERM-039-009 MIX-COMP-THERM-007-014

LEU-COMP-THERM-010-026 LEU-COMP-THERM-039-010 MIX-COMP-THERM-007-015

LEU-COMP-THERM-010-027 LEU-COMP-THERM-039-011 MIX-COMP-THERM-007-016

LEU-COMP-THERM-010-028 LEU-COMP-THERM-039-012 MIX-COMP-THERM-007-017

LEU-COMP-THERM-010-029 LEU-COMP-THERM-039-013 MIX-COMP-THERM-007-018

LEU-COMP-THERM-010-030 LEU-COMP-THERM-039-014 MIX-COMP-THERM-007-019

LEU-COMP-THERM-011-001 LEU-COMP-THERM-039-015 MIX-COMP-THERM-007-020

LEU-COMP-THERM-011-002 LEU-COMP-THERM-039-016 MIX-COMP-THERM-007-021

LEU-COMP-THERM-011-003 LEU-COMP-THERM-039-017 MIX-COMP-THERM-007-022

LEU-COMP-THERM-011-004 LEU-COMP-THERM-040-001 MIX-COMP-THERM-007-023

LEU-COMP-THERM-011-005 LEU-COMP-THERM-040-002 MIX-COMP-THERM-007-024

LEU-COMP-THERM-011-006 LEU-COMP-THERM-040-003 MIX-COMP-THERM-007-025

LEU-COMP-THERM-011-007 LEU-COMP-THERM-040-004 MIX-COMP-THERM-007-026

LEU-COMP-THERM-011-008 LEU-COMP-THERM-040-005 MIX-COMP-THERM-007-027

LEU-COMP-THERM-011-009 LEU-COMP-THERM-040-006 MIX-COMP-THERM-008-001

LEU-COMP-THERM-011-010 LEU-COMP-THERM-040-007 MIX-COMP-THERM-008-002

LEU-COMP-THERM-011-011 LEU-COMP-THERM-040-008 MIX-COMP-THERM-008-003

LEU-COMP-THERM-011-012 LEU-COMP-THERM-040-009 MIX-COMP-THERM-008-004

LEU-COMP-THERM-011-013 LEU-COMP-THERM-040-010 MIX-COMP-THERM-008-005

LEU-COMP-THERM-011-014 LEU-COMP-THERM-042-001 MIX-COMP-THERM-008-006

LEU-COMP-THERM-011-015 LEU-COMP-THERM-042-002 MIX-COMP-THERM-008-007

LEU-COMP-THERM-012-001 LEU-COMP-THERM-042-003 MIX-COMP-THERM-008-008

LEU-COMP-THERM-012-002 LEU-COMP-THERM-042-004 MIX-COMP-THERM-008-009

LEU-COMP-THERM-012-003 LEU-COMP-THERM-042-005 MIX-COMP-THERM-008-010
C-5

Table C.1. Continued

LEU-COMP-THERM-012-004 LEU-COMP-THERM-042-006 MIX-COMP-THERM-008-011

LEU-COMP-THERM-012-005 LEU-COMP-THERM-042-007 MIX-COMP-THERM-008-012

LEU-COMP-THERM-012-006 LEU-COMP-THERM-043-001 MIX-COMP-THERM-008-013

LEU-COMP-THERM-012-007 LEU-COMP-THERM-043-002 MIX-COMP-THERM-008-014

LEU-COMP-THERM-012-008 LEU-COMP-THERM-043-003 MIX-COMP-THERM-008-015

LEU-COMP-THERM-012-009 LEU-COMP-THERM-043-004 MIX-COMP-THERM-008-016

LEU-COMP-THERM-012-010 LEU-COMP-THERM-043-005 MIX-COMP-THERM-008-017

LEU-COMP-THERM-013-001 LEU-COMP-THERM-043-006 MIX-COMP-THERM-008-018

LEU-COMP-THERM-013-002 LEU-COMP-THERM-043-007 MIX-COMP-THERM-008-019

LEU-COMP-THERM-013-003 LEU-COMP-THERM-043-008 MIX-COMP-THERM-008-020

LEU-COMP-THERM-013-004 LEU-COMP-THERM-043-009 MIX-COMP-THERM-008-021

LEU-COMP-THERM-013-005 LEU-COMP-THERM-044-001 MIX-COMP-THERM-008-022

LEU-COMP-THERM-013-006 LEU-COMP-THERM-044-002 MIX-COMP-THERM-008-023

LEU-COMP-THERM-013-007 LEU-COMP-THERM-044-003 MIX-COMP-THERM-008-024

LEU-COMP-THERM-014-001 LEU-COMP-THERM-044-004 MIX-COMP-THERM-008-025

LEU-COMP-THERM-014-002 LEU-COMP-THERM-044-005 MIX-COMP-THERM-008-026

LEU-COMP-THERM-014-005 LEU-COMP-THERM-044-006 MIX-COMP-THERM-008-027

LEU-COMP-THERM-014-006 LEU-COMP-THERM-044-007 MIX-COMP-THERM-008-028

LEU-COMP-THERM-014-007 LEU-COMP-THERM-044-008 MIX-COMP-THERM-009-01

LEU-COMP-THERM-015-001 LEU-COMP-THERM-044-009 MIX-COMP-THERM-009-02

LEU-COMP-THERM-015-002 LEU-COMP-THERM-044-010 MIX-COMP-THERM-009-03

LEU-COMP-THERM-015-003 LEU-COMP-THERM-045-001 MIX-COMP-THERM-009-04

LEU-COMP-THERM-015-004 LEU-COMP-THERM-045-002 MIX-COMP-THERM-009-05

LEU-COMP-THERM-015-005 LEU-COMP-THERM-045-003 MIX-COMP-THERM-009-06

LEU-COMP-THERM-015-006 LEU-COMP-THERM-045-004 MIX-COMP-THERM-011-01

LEU-COMP-THERM-015-007 LEU-COMP-THERM-045-005 MIX-COMP-THERM-011-02

LEU-COMP-THERM-015-008 LEU-COMP-THERM-045-006 MIX-COMP-THERM-011-03

LEU-COMP-THERM-015-009 LEU-COMP-THERM-045-007 MIX-COMP-THERM-011-04

LEU-COMP-THERM-015-010 LEU-COMP-THERM-045-008 MIX-COMP-THERM-011-05

LEU-COMP-THERM-015-011 LEU-COMP-THERM-045-009 MIX-COMP-THERM-011-06

LEU-COMP-THERM-015-012 LEU-COMP-THERM-045-010 MIX-COMP-THERM-012-001

LEU-COMP-THERM-015-013 LEU-COMP-THERM-045-011 MIX-COMP-THERM-012-002

LEU-COMP-THERM-015-014 LEU-COMP-THERM-045-012 MIX-COMP-THERM-012-003

LEU-COMP-THERM-015-015 LEU-COMP-THERM-045-013 MIX-COMP-THERM-012-004

LEU-COMP-THERM-015-016 LEU-COMP-THERM-045-014 MIX-COMP-THERM-012-005

LEU-COMP-THERM-015-017 LEU-COMP-THERM-045-015 MIX-COMP-THERM-012-006

LEU-COMP-THERM-015-018 LEU-COMP-THERM-045-016 MIX-COMP-THERM-012-007

LEU-COMP-THERM-015-019 LEU-COMP-THERM-045-017 MIX-COMP-THERM-012-008

LEU-COMP-THERM-015-020 LEU-COMP-THERM-045-018 MIX-COMP-THERM-012-009

LEU-COMP-THERM-015-021 LEU-COMP-THERM-045-019 MIX-COMP-THERM-012-010

LEU-COMP-THERM-015-022 LEU-COMP-THERM-045-020 MIX-COMP-THERM-012-011

LEU-COMP-THERM-015-023 LEU-COMP-THERM-045-021 MIX-COMP-THERM-012-012

LEU-COMP-THERM-015-024 LEU-COMP-THERM-046-001 MIX-COMP-THERM-012-013

LEU-COMP-THERM-015-025 LEU-COMP-THERM-046-002 MIX-COMP-THERM-012-014

LEU-COMP-THERM-015-026 LEU-COMP-THERM-046-003 MIX-COMP-THERM-012-015

LEU-COMP-THERM-015-027 LEU-COMP-THERM-046-004 MIX-COMP-THERM-012-016

LEU-COMP-THERM-015-028 LEU-COMP-THERM-046-005 MIX-COMP-THERM-012-017
C-6

Table C.1. Continued

LEU-COMP-THERM-015-029 LEU-COMP-THERM-046-006 MIX-COMP-THERM-012-018

LEU-COMP-THERM-015-030 LEU-COMP-THERM-046-007 MIX-COMP-THERM-012-019

LEU-COMP-THERM-015-031 LEU-COMP-THERM-046-008 MIX-COMP-THERM-012-020

LEU-COMP-THERM-015-032 LEU-COMP-THERM-046-009 MIX-COMP-THERM-012-021

LEU-COMP-THERM-015-033 LEU-COMP-THERM-046-010 MIX-COMP-THERM-012-022

LEU-COMP-THERM-015-034 LEU-COMP-THERM-046-011 MIX-COMP-THERM-012-023

LEU-COMP-THERM-015-035 LEU-COMP-THERM-046-012 MIX-COMP-THERM-012-024

LEU-COMP-THERM-015-036 LEU-COMP-THERM-046-013 MIX-COMP-THERM-012-025

LEU-COMP-THERM-015-037 LEU-COMP-THERM-046-014 MIX-COMP-THERM-012-026

LEU-COMP-THERM-015-038 LEU-COMP-THERM-046-015 MIX-COMP-THERM-012-027

LEU-COMP-THERM-015-039 LEU-COMP-THERM-046-016 MIX-COMP-THERM-012-028

LEU-COMP-THERM-015-040 LEU-COMP-THERM-046-017 MIX-COMP-THERM-012-029

LEU-COMP-THERM-015-041 LEU-COMP-THERM-046-018 MIX-COMP-THERM-012-030

LEU-COMP-THERM-015-042 LEU-COMP-THERM-046-019 MIX-COMP-THERM-012-031

LEU-COMP-THERM-015-043 LEU-COMP-THERM-046-020 MIX-COMP-THERM-012-032

LEU-COMP-THERM-015-044 LEU-COMP-THERM-046-021 MIX-COMP-THERM-012-033

LEU-COMP-THERM-015-045 LEU-COMP-THERM-046-022 MIX-COMP-THERM-013-001

LEU-COMP-THERM-015-046 LEU-COMP-THERM-047-001 MIX-COMP-THERM-013-002

LEU-COMP-THERM-015-047 LEU-COMP-THERM-047-002 MIX-COMP-THERM-013-003

LEU-COMP-THERM-015-048 LEU-COMP-THERM-047-003 MIX-COMP-THERM-013-004

LEU-COMP-THERM-015-049 LEU-COMP-THERM-048-001 MIX-COMP-THERM-013-005

LEU-COMP-THERM-015-050 LEU-COMP-THERM-048-002 MIX-COMP-THERM-013-006

LEU-COMP-THERM-015-051 LEU-COMP-THERM-048-003 MIX-COMP-THERM-013-007

LEU-COMP-THERM-015-052 LEU-COMP-THERM-048-004 MIX-COMP-THERM-013-008

LEU-COMP-THERM-015-053 LEU-COMP-THERM-048-005 MIX-COMP-THERM-013-009

LEU-COMP-THERM-015-054 LEU-COMP-THERM-050-001 MIX-COMP-THERM-013-010

LEU-COMP-THERM-015-055 LEU-COMP-THERM-050-002 MIX-COMP-THERM-013-011

LEU-COMP-THERM-015-056 LEU-COMP-THERM-050-003 MIX-COMP-THERM-013-012

LEU-COMP-THERM-015-057 LEU-COMP-THERM-050-004 MIX-COMP-THERM-013-013

LEU-COMP-THERM-015-058 LEU-COMP-THERM-050-005 MIX-COMP-THERM-013-014

LEU-COMP-THERM-015-059 LEU-COMP-THERM-050-006 MIX-COMP-THERM-013-015

LEU-COMP-THERM-015-060 LEU-COMP-THERM-050-007 MIX-COMP-THERM-013-016

LEU-COMP-THERM-015-061 LEU-COMP-THERM-050-008 MIX-COMP-THERM-013-017

LEU-COMP-THERM-015-062 LEU-COMP-THERM-050-009 MIX-COMP-THERM-013-018

LEU-COMP-THERM-015-063 LEU-COMP-THERM-050-010 MIX-COMP-THERM-013-019

LEU-COMP-THERM-015-064 LEU-COMP-THERM-050-011 MIX-COMP-THERM-013-020

LEU-COMP-THERM-015-065 LEU-COMP-THERM-050-012 MIX-COMP-THERM-013-021

LEU-COMP-THERM-015-066 LEU-COMP-THERM-050-013 MIX-COMP-THERM-013-022

LEU-COMP-THERM-015-067 LEU-COMP-THERM-050-014 MIX-COMP-THERM-013-023

LEU-COMP-THERM-015-068 LEU-COMP-THERM-050-015 MIX-COMP-THERM-013-024

LEU-COMP-THERM-015-069 LEU-COMP-THERM-050-016 MIX-COMP-THERM-013-025

LEU-COMP-THERM-015-070 LEU-COMP-THERM-050-017 MIX-COMP-THERM-013-026

LEU-COMP-THERM-015-071 LEU-COMP-THERM-050-018 MIX-COMP-THERM-013-027

LEU-COMP-THERM-015-072 LEU-COMP-THERM-051-001 MIX-COMP-THERM-013-028

LEU-COMP-THERM-015-073 LEU-COMP-THERM-051-002 MIX-COMP-THERM-013-029

LEU-COMP-THERM-015-074 LEU-COMP-THERM-051-003 MIX-COMP-THERM-013-030

LEU-COMP-THERM-015-075 LEU-COMP-THERM-051-004 MIX-COMP-THERM-014-001
C-7

Table C.1. Continued

LEU-COMP-THERM-015-076 LEU-COMP-THERM-051-005 MIX-COMP-THERM-014-002

LEU-COMP-THERM-015-077 LEU-COMP-THERM-051-006 MIX-COMP-THERM-014-003

LEU-COMP-THERM-015-078 LEU-COMP-THERM-051-007 MIX-COMP-THERM-014-004

LEU-COMP-THERM-015-079 LEU-COMP-THERM-051-008 MIX-COMP-THERM-014-005

LEU-COMP-THERM-015-080 LEU-COMP-THERM-051-009 MIX-COMP-THERM-014-006

LEU-COMP-THERM-015-081 LEU-COMP-THERM-051-010 MIX-COMP-THERM-014-007

LEU-COMP-THERM-015-082 LEU-COMP-THERM-051-011 MIX-COMP-THERM-014-008

LEU-COMP-THERM-015-083 LEU-COMP-THERM-051-012 MIX-COMP-THERM-014-009

LEU-COMP-THERM-015-084 LEU-COMP-THERM-051-013 MIX-COMP-THERM-014-010

LEU-COMP-THERM-015-085 LEU-COMP-THERM-051-014 MIX-COMP-THERM-014-011

LEU-COMP-THERM-015-086 LEU-COMP-THERM-051-015 MIX-COMP-THERM-014-012

LEU-COMP-THERM-015-087 LEU-COMP-THERM-051-016 MIX-COMP-THERM-014-013

LEU-COMP-THERM-015-088 LEU-COMP-THERM-051-017 MIX-COMP-THERM-014-014

LEU-COMP-THERM-015-089 LEU-COMP-THERM-051-018 MIX-COMP-THERM-014-015

LEU-COMP-THERM-015-090 LEU-COMP-THERM-051-019 MIX-COMP-THERM-014-016

LEU-COMP-THERM-015-091 LEU-COMP-THERM-052-001 MIX-COMP-THERM-014-017

LEU-COMP-THERM-015-092 LEU-COMP-THERM-052-002 MIX-COMP-THERM-014-018

LEU-COMP-THERM-015-093 LEU-COMP-THERM-052-003 MIX-COMP-THERM-014-019

LEU-COMP-THERM-015-094 LEU-COMP-THERM-052-004 MIX-COMP-THERM-014-020

LEU-COMP-THERM-015-095 LEU-COMP-THERM-052-005 MIX-COMP-THERM-014-021

LEU-COMP-THERM-015-096 LEU-COMP-THERM-052-006 MIX-COMP-THERM-014-022

LEU-COMP-THERM-015-097 LEU-COMP-THERM-053-001 MIX-COMP-THERM-016-001

LEU-COMP-THERM-015-098 LEU-COMP-THERM-053-002 MIX-COMP-THERM-016-002

LEU-COMP-THERM-015-099 LEU-COMP-THERM-053-003 MIX-COMP-THERM-016-003

LEU-COMP-THERM-015-100 LEU-COMP-THERM-053-004 MIX-COMP-THERM-016-004

LEU-COMP-THERM-015-101 LEU-COMP-THERM-053-005 MIX-COMP-THERM-016-005

LEU-COMP-THERM-015-102 LEU-COMP-THERM-053-006 MIX-COMP-THERM-016-006

LEU-COMP-THERM-015-103 LEU-COMP-THERM-053-007 MIX-COMP-THERM-016-007

LEU-COMP-THERM-015-104 LEU-COMP-THERM-053-008 MIX-COMP-THERM-016-008

LEU-COMP-THERM-015-105 LEU-COMP-THERM-053-009 MIX-COMP-THERM-016-009

LEU-COMP-THERM-015-106 LEU-COMP-THERM-053-010 MIX-COMP-THERM-016-010

LEU-COMP-THERM-015-107 LEU-COMP-THERM-053-011 MIX-COMP-THERM-016-011

LEU-COMP-THERM-015-108 LEU-COMP-THERM-053-012 MIX-COMP-THERM-016-012

LEU-COMP-THERM-015-109 LEU-COMP-THERM-053-013 MIX-COMP-THERM-016-013

LEU-COMP-THERM-015-110 LEU-COMP-THERM-053-014 MIX-COMP-THERM-016-014

LEU-COMP-THERM-015-111 LEU-COMP-THERM-054-001 MIX-COMP-THERM-016-015

LEU-COMP-THERM-015-112 LEU-COMP-THERM-054-002 MIX-COMP-THERM-016-016

LEU-COMP-THERM-015-113 LEU-COMP-THERM-054-003 MIX-COMP-THERM-016-017

LEU-COMP-THERM-015-114 LEU-COMP-THERM-054-004 MIX-COMP-THERM-016-018

LEU-COMP-THERM-015-115 LEU-COMP-THERM-054-005 MIX-COMP-THERM-016-019

LEU-COMP-THERM-015-116 LEU-COMP-THERM-054-006 MIX-COMP-THERM-017-001

LEU-COMP-THERM-015-117 LEU-COMP-THERM-054-007 MIX-COMP-THERM-017-002

LEU-COMP-THERM-015-118 LEU-COMP-THERM-054-008 MIX-COMP-THERM-017-003

LEU-COMP-THERM-015-119 LEU-COMP-THERM-055-001 MIX-COMP-THERM-017-004

LEU-COMP-THERM-015-120 LEU-COMP-THERM-055-002 MIX-COMP-THERM-017-005

LEU-COMP-THERM-015-121 LEU-COMP-THERM-057-001 MIX-COMP-THERM-017-006

LEU-COMP-THERM-015-122 LEU-COMP-THERM-057-002 MIX-COMP-THERM-017-007
C-8

Table C.1. Continued

LEU-COMP-THERM-015-123 LEU-COMP-THERM-057-003 MIX-COMP-THERM-017-008

LEU-COMP-THERM-015-124 LEU-COMP-THERM-057-004 MIX-COMP-THERM-017-009

LEU-COMP-THERM-015-125 LEU-COMP-THERM-057-005 MIX-COMP-THERM-017-010

LEU-COMP-THERM-015-126 LEU-COMP-THERM-057-006 MIX-COMP-THERM-017-011

LEU-COMP-THERM-015-127 LEU-COMP-THERM-057-007 MIX-COMP-THERM-017-012

LEU-COMP-THERM-015-128 LEU-COMP-THERM-057-008 MIX-COMP-THERM-017-013

LEU-COMP-THERM-015-129 LEU-COMP-THERM-057-009 MIX-COMP-THERM-017-014

LEU-COMP-THERM-015-130 LEU-COMP-THERM-057-010 MIX-COMP-THERM-017-015

LEU-COMP-THERM-015-131 LEU-COMP-THERM-057-011 MIX-COMP-THERM-017-016

LEU-COMP-THERM-015-132 LEU-COMP-THERM-057-012 MIX-COMP-THERM-017-017

LEU-COMP-THERM-015-133 LEU-COMP-THERM-057-013 MIX-COMP-THERM-017-018

LEU-COMP-THERM-015-134 LEU-COMP-THERM-057-014 MIX-COMP-THERM-017-019

LEU-COMP-THERM-015-135 LEU-COMP-THERM-057-015 HTC1_001

LEU-COMP-THERM-015-136 LEU-COMP-THERM-057-016 HTC1_002

LEU-COMP-THERM-015-137 LEU-COMP-THERM-057-017 HTC1_003

LEU-COMP-THERM-015-138 LEU-COMP-THERM-057-018 HTC1_004

LEU-COMP-THERM-015-139 LEU-COMP-THERM-057-019 HTC1_005

LEU-COMP-THERM-015-140 LEU-COMP-THERM-057-020 HTC1_006

LEU-COMP-THERM-015-141 LEU-COMP-THERM-057-021 HTC1_007

LEU-COMP-THERM-015-142 LEU-COMP-THERM-057-022 HTC1_008

LEU-COMP-THERM-015-143 LEU-COMP-THERM-057-023 HTC1_009

LEU-COMP-THERM-015-144 LEU-COMP-THERM-057-024 HTC1_010

LEU-COMP-THERM-015-145 LEU-COMP-THERM-057-025 HTC1_011

LEU-COMP-THERM-015-146 LEU-COMP-THERM-057-026 HTC1_012

LEU-COMP-THERM-015-147 LEU-COMP-THERM-057-027 HTC1_013

LEU-COMP-THERM-015-148 LEU-COMP-THERM-057-028 HTC1_014

LEU-COMP-THERM-015-149 LEU-COMP-THERM-057-029 HTC1_015

LEU-COMP-THERM-015-150 LEU-COMP-THERM-057-030 HTC1_016

LEU-COMP-THERM-015-151 LEU-COMP-THERM-057-031 HTC1_017

LEU-COMP-THERM-015-152 LEU-COMP-THERM-057-032 HTC1_018

LEU-COMP-THERM-015-153 LEU-COMP-THERM-057-033 HTC2B_001

LEU-COMP-THERM-015-154 LEU-COMP-THERM-057-034 HTC2B_002

LEU-COMP-THERM-015-155 LEU-COMP-THERM-057-035 HTC2B_003

LEU-COMP-THERM-015-156 LEU-COMP-THERM-057-036 HTC2B_004

LEU-COMP-THERM-015-157 LEU-COMP-THERM-058-001 HTC2B_005

LEU-COMP-THERM-015-158 LEU-COMP-THERM-058-002 HTC2B_006

LEU-COMP-THERM-015-159 LEU-COMP-THERM-058-003 HTC2B_007

LEU-COMP-THERM-015-160 LEU-COMP-THERM-058-004 HTC2B_008

LEU-COMP-THERM-015-161 LEU-COMP-THERM-058-005 HTC2B_009

LEU-COMP-THERM-015-162 LEU-COMP-THERM-058-006 HTC2B_010

LEU-COMP-THERM-015-163 LEU-COMP-THERM-058-007 HTC2B_011

LEU-COMP-THERM-015-164 LEU-COMP-THERM-058-008 HTC2B_012

LEU-COMP-THERM-015-165 LEU-COMP-THERM-058-009 HTC2B_014

LEU-COMP-THERM-016-001 LEU-COMP-THERM-061-001 HTC2B_015

LEU-COMP-THERM-016-002 LEU-COMP-THERM-061-002 HTC2B_016

LEU-COMP-THERM-016-003 LEU-COMP-THERM-061-003 HTC2B_017

LEU-COMP-THERM-016-004 LEU-COMP-THERM-061-004 HTC2B_018
C-9

Table C.1. Continued

LEU-COMP-THERM-016-005 LEU-COMP-THERM-061-005 HTC2B_019

LEU-COMP-THERM-016-006 LEU-COMP-THERM-061-006 HTC2B_020

LEU-COMP-THERM-016-007 LEU-COMP-THERM-061-007 HTC2B_021

LEU-COMP-THERM-016-008 LEU-COMP-THERM-061-008 HTC2G_001

LEU-COMP-THERM-016-009 LEU-COMP-THERM-061-009 HTC2G_002

LEU-COMP-THERM-016-010 LEU-COMP-THERM-061-010 HTC2G_003

LEU-COMP-THERM-016-011 LEU-COMP-THERM-062-001 HTC2G_004

LEU-COMP-THERM-016-012 LEU-COMP-THERM-062-002 HTC2G_005

LEU-COMP-THERM-016-013 LEU-COMP-THERM-062-003 HTC2G_006

LEU-COMP-THERM-016-014 LEU-COMP-THERM-062-004 HTC2G_007

LEU-COMP-THERM-016-015 LEU-COMP-THERM-062-005 HTC2G_008

LEU-COMP-THERM-016-016 LEU-COMP-THERM-062-006 HTC2G_009

LEU-COMP-THERM-016-017 LEU-COMP-THERM-062-007 HTC2G_010

LEU-COMP-THERM-016-018 LEU-COMP-THERM-062-008 HTC2G_011

LEU-COMP-THERM-016-019 LEU-COMP-THERM-062-009 HTC2G_012

LEU-COMP-THERM-016-020 LEU-COMP-THERM-062-010 HTC2G_013

LEU-COMP-THERM-016-021 LEU-COMP-THERM-062-011 HTC2G_014

LEU-COMP-THERM-016-022 LEU-COMP-THERM-062-012 HTC2G_015

LEU-COMP-THERM-016-023 LEU-COMP-THERM-062-013 HTC2G_016

LEU-COMP-THERM-016-024 LEU-COMP-THERM-062-014 HTC2G_017

LEU-COMP-THERM-016-025 LEU-COMP-THERM-062-015 HTC2G_018

LEU-COMP-THERM-016-026 LEU-COMP-THERM-065-001 HTC2G_019

LEU-COMP-THERM-016-027 LEU-COMP-THERM-065-002 HTC2G_020

LEU-COMP-THERM-016-028 LEU-COMP-THERM-065-003 HTC3_001

LEU-COMP-THERM-016-029 LEU-COMP-THERM-065-004 HTC3_002

LEU-COMP-THERM-016-030 LEU-COMP-THERM-065-005 HTC3_003

LEU-COMP-THERM-016-031 LEU-COMP-THERM-065-006 HTC3_004

LEU-COMP-THERM-016-032 LEU-COMP-THERM-065-007 HTC3_005

LEU-COMP-THERM-017-001 LEU-COMP-THERM-065-008 HTC3_006

LEU-COMP-THERM-017-002 LEU-COMP-THERM-065-009 HTC3_007

LEU-COMP-THERM-017-003 LEU-COMP-THERM-065-010 HTC3_008

LEU-COMP-THERM-017-004 LEU-COMP-THERM-065-011 HTC3_009

LEU-COMP-THERM-017-005 LEU-COMP-THERM-065-012 HTC3_010

LEU-COMP-THERM-017-006 LEU-COMP-THERM-065-013 HTC3_011

LEU-COMP-THERM-017-007 LEU-COMP-THERM-065-014 HTC3_012

LEU-COMP-THERM-017-008 LEU-COMP-THERM-065-015 HTC3_013

LEU-COMP-THERM-017-009 LEU-COMP-THERM-065-016 HTC3_014

LEU-COMP-THERM-017-010 LEU-COMP-THERM-065-017 HTC3_015

LEU-COMP-THERM-017-011 LEU-COMP-THERM-066-004 HTC3_016

LEU-COMP-THERM-017-012 LEU-COMP-THERM-066-005 HTC3_017

LEU-COMP-THERM-017-013 LEU-COMP-THERM-066-006 HTC3_018

LEU-COMP-THERM-017-014 LEU-COMP-THERM-066-007 HTC3_019

LEU-COMP-THERM-017-015 LEU-COMP-THERM-066-008 HTC3_020

LEU-COMP-THERM-017-016 LEU-COMP-THERM-066-009 HTC3_021

LEU-COMP-THERM-017-017 LEU-COMP-THERM-066-010 HTC3_022

LEU-COMP-THERM-017-018 LEU-COMP-THERM-069-001 HTC3_023

LEU-COMP-THERM-017-019 LEU-COMP-THERM-069-002 HTC3_024
C-10

Table C.1. Continued

LEU-COMP-THERM-017-020 LEU-COMP-THERM-069-003 HTC3_025

LEU-COMP-THERM-017-021 LEU-COMP-THERM-069-004 HTC3_026

LEU-COMP-THERM-017-022 LEU-COMP-THERM-069-005 HTC4FE_001

LEU-COMP-THERM-017-023 LEU-COMP-THERM-070-001 HTC4FE_002

LEU-COMP-THERM-017-024 LEU-COMP-THERM-070-002 HTC4FE_003

LEU-COMP-THERM-017-025 LEU-COMP-THERM-070-003 HTC4FE_004

LEU-COMP-THERM-017-026 LEU-COMP-THERM-070-004 HTC4FE_005

LEU-COMP-THERM-017-027 LEU-COMP-THERM-070-005 HTC4FE_006

LEU-COMP-THERM-017-028 LEU-COMP-THERM-070-006 HTC4FE_007

LEU-COMP-THERM-017-029 LEU-COMP-THERM-070-007 HTC4FE_008

LEU-COMP-THERM-018-001 LEU-COMP-THERM-070-008 HTC4FE_009

LEU-COMP-THERM-020-001 LEU-COMP-THERM-070-009 HTC4FE_010

LEU-COMP-THERM-020-002 LEU-COMP-THERM-070-010 HTC4FE_011

LEU-COMP-THERM-020-003 LEU-COMP-THERM-070-011 HTC4FE_012

LEU-COMP-THERM-020-004 LEU-COMP-THERM-070-012 HTC4FE_013

LEU-COMP-THERM-020-005 LEU-COMP-THERM-071-001 HTC4FE_014

LEU-COMP-THERM-020-006 LEU-COMP-THERM-071-002 HTC4FE_015

LEU-COMP-THERM-020-007 LEU-COMP-THERM-071-003 HTC4FE_016

LEU-COMP-THERM-021-001 LEU-COMP-THERM-071-004 HTC4FE_017

LEU-COMP-THERM-021-002 LEU-COMP-THERM-072-001 HTC4FE_018

LEU-COMP-THERM-021-003 LEU-COMP-THERM-072-002 HTC4FE_019

LEU-COMP-THERM-021-004 LEU-COMP-THERM-072-003 HTC4FE_020

LEU-COMP-THERM-021-005 LEU-COMP-THERM-072-004 HTC4FE_021

LEU-COMP-THERM-021-006 LEU-COMP-THERM-072-005 HTC4FE_022

LEU-COMP-THERM-022-001 LEU-COMP-THERM-072-006 HTC4FE_023

LEU-COMP-THERM-022-002 LEU-COMP-THERM-072-007 HTC4FE_024

LEU-COMP-THERM-022-003 LEU-COMP-THERM-072-008 HTC4FE_025

LEU-COMP-THERM-022-004 LEU-COMP-THERM-072-009 HTC4FE_026

LEU-COMP-THERM-022-005 LEU-COMP-THERM-073-001 HTC4FE_027

LEU-COMP-THERM-022-006 LEU-COMP-THERM-073-002 HTC4FE_028

LEU-COMP-THERM-022-007 LEU-COMP-THERM-073-003 HTC4FE_029

LEU-COMP-THERM-023-001 LEU-COMP-THERM-073-004 HTC4FE_030

LEU-COMP-THERM-023-002 LEU-COMP-THERM-073-005 HTC4FE_031

LEU-COMP-THERM-023-003 LEU-COMP-THERM-073-006 HTC4FE_032

LEU-COMP-THERM-023-004 LEU-COMP-THERM-073-007 HTC4FE_033

LEU-COMP-THERM-023-005 LEU-COMP-THERM-073-008 HTC4PB_001

LEU-COMP-THERM-023-006 LEU-COMP-THERM-073-009 HTC4PB_002

LEU-COMP-THERM-024-001 LEU-COMP-THERM-073-010 HTC4PB_003

LEU-COMP-THERM-024-002 LEU-COMP-THERM-073-011 HTC4PB_004

LEU-COMP-THERM-026-001 LEU-COMP-THERM-073-012 HTC4PB_005

LEU-COMP-THERM-026-002 LEU-COMP-THERM-073-013 HTC4PB_006

LEU-COMP-THERM-026-003 LEU-COMP-THERM-073-014 HTC4PB_007

LEU-COMP-THERM-026-004 LEU-COMP-THERM-074-001 HTC4PB_008

LEU-COMP-THERM-026-005 LEU-COMP-THERM-074-002 HTC4PB_009

LEU-COMP-THERM-026-006 LEU-COMP-THERM-074-003 HTC4PB_010

LEU-COMP-THERM-027-001 LEU-COMP-THERM-074-004 HTC4PB_011

LEU-COMP-THERM-027-002 LEU-COMP-THERM-075-001 HTC4PB_012
C-11

Table C.1. Continued

LEU-COMP-THERM-027-003 LEU-COMP-THERM-075-002 HTC4PB_013

LEU-COMP-THERM-027-004 LEU-COMP-THERM-075-003 HTC4PB_014

LEU-COMP-THERM-028-001 LEU-COMP-THERM-075-004 HTC4PB_015

LEU-COMP-THERM-028-002 LEU-COMP-THERM-075-005 HTC4PB_016

LEU-COMP-THERM-028-003 LEU-COMP-THERM-075-006 HTC4PB_017

LEU-COMP-THERM-028-004 LEU-COMP-THERM-076-001 HTC4PB_018

LEU-COMP-THERM-028-005 LEU-COMP-THERM-076-002 HTC4PB_019

LEU-COMP-THERM-028-006 LEU-COMP-THERM-076-003 HTC4PB_020

LEU-COMP-THERM-028-007 LEU-COMP-THERM-076-004 HTC4PB_021

LEU-COMP-THERM-028-008 LEU-COMP-THERM-076-005 HTC4PB_022

LEU-COMP-THERM-028-009 LEU-COMP-THERM-076-006 HTC4PB_023

LEU-COMP-THERM-028-010 LEU-COMP-THERM-076-007 HTC4PB_024

LEU-COMP-THERM-028-011 LEU-COMP-THERM-077-001 HTC4PB_025

LEU-COMP-THERM-028-012 LEU-COMP-THERM-077-002 HTC4PB_026

LEU-COMP-THERM-028-013 LEU-COMP-THERM-077-003 HTC4PB_027

LEU-COMP-THERM-028-014 LEU-COMP-THERM-077-004 HTC4PB_028

LEU-COMP-THERM-028-015 LEU-COMP-THERM-077-005 HTC4PB_029

LEU-COMP-THERM-028-016 LEU-COMP-THERM-078-001 HTC4PB_030

LEU-COMP-THERM-028-017 LEU-COMP-THERM-078-002 HTC4PB_031

LEU-COMP-THERM-028-018 LEU-COMP-THERM-078-003 HTC4PB_032

LEU-COMP-THERM-028-019 LEU-COMP-THERM-078-004 HTC4PB_033

LEU-COMP-THERM-028-020 LEU-COMP-THERM-078-005 HTC4PB_034

LEU-COMP-THERM-029-001 LEU-COMP-THERM-078-006 HTC4PB_035

LEU-COMP-THERM-029-002 LEU-COMP-THERM-078-007 HTC4PB_036

LEU-COMP-THERM-029-003 LEU-COMP-THERM-078-008 HTC4PB_037

LEU-COMP-THERM-029-004 LEU-COMP-THERM-078-009 HTC4PB_038

LEU-COMP-THERM-029-005 LEU-COMP-THERM-078-010 MIX-SOL-THERM-001-001

LEU-COMP-THERM-029-006 LEU-COMP-THERM-078-011 MIX-SOL-THERM-001-002

LEU-COMP-THERM-029-007 LEU-COMP-THERM-078-012 MIX-SOL-THERM-001-003

LEU-COMP-THERM-029-008 LEU-COMP-THERM-078-013 MIX-SOL-THERM-001-004

LEU-COMP-THERM-029-009 LEU-COMP-THERM-078-014 MIX-SOL-THERM-001-005

LEU-COMP-THERM-029-010 LEU-COMP-THERM-078-015 MIX-SOL-THERM-001-006

LEU-COMP-THERM-029-011 LEU-COMP-THERM-079-001 MIX-SOL-THERM-001-007

LEU-COMP-THERM-029-012 LEU-COMP-THERM-079-002 MIX-SOL-THERM-001-008

LEU-COMP-THERM-030-001 LEU-COMP-THERM-079-003 MIX-SOL-THERM-001-009

LEU-COMP-THERM-030-002 LEU-COMP-THERM-079-004 MIX-SOL-THERM-001-010

LEU-COMP-THERM-030-003 LEU-COMP-THERM-079-005 MIX-SOL-THERM-001-011

LEU-COMP-THERM-030-004 LEU-COMP-THERM-079-006 MIX-SOL-THERM-001-012

LEU-COMP-THERM-030-005 LEU-COMP-THERM-079-007 MIX-SOL-THERM-001-013

LEU-COMP-THERM-030-006 LEU-COMP-THERM-079-008 MIX-SOL-THERM-002-001

LEU-COMP-THERM-030-007 LEU-COMP-THERM-079-009 MIX-SOL-THERM-002-002

LEU-COMP-THERM-030-008 LEU-COMP-THERM-079-010 MIX-SOL-THERM-002-003

LEU-COMP-THERM-030-009 LEU-COMP-THERM-080-001 MIX-SOL-THERM-003-001

LEU-COMP-THERM-030-010 LEU-COMP-THERM-080-002 MIX-SOL-THERM-003-002

LEU-COMP-THERM-030-011 LEU-COMP-THERM-080-003 MIX-SOL-THERM-003-003

LEU-COMP-THERM-030-012 LEU-COMP-THERM-080-004 MIX-SOL-THERM-003-004

LEU-COMP-THERM-031-001 LEU-COMP-THERM-080-005 MIX-SOL-THERM-003-005
C-12

Table C.1. Continued

LEU-COMP-THERM-031-002 LEU-COMP-THERM-080-006 MIX-SOL-THERM-003-006

LEU-COMP-THERM-031-003 LEU-COMP-THERM-080-007 MIX-SOL-THERM-003-007

LEU-COMP-THERM-031-004 LEU-COMP-THERM-080-008 MIX-SOL-THERM-003-008

LEU-COMP-THERM-031-005 LEU-COMP-THERM-080-009 MIX-SOL-THERM-003-009

LEU-COMP-THERM-031-006 LEU-COMP-THERM-080-010 MIX-SOL-THERM-003-010

LEU-COMP-THERM-032-001 LEU-COMP-THERM-080-011 MIX-SOL-THERM-004-001

LEU-COMP-THERM-032-002 LEU-COMP-THERM-082-002 MIX-SOL-THERM-004-002

LEU-COMP-THERM-032-003 LEU-COMP-THERM-082-003 MIX-SOL-THERM-004-003

LEU-COMP-THERM-032-004 LEU-COMP-THERM-082-004 MIX-SOL-THERM-004-004

LEU-COMP-THERM-032-005 LEU-COMP-THERM-082-005 MIX-SOL-THERM-004-005

LEU-COMP-THERM-032-006 LEU-COMP-THERM-082-006 MIX-SOL-THERM-004-006

LEU-COMP-THERM-032-007 LEU-COMP-THERM-083-001 MIX-SOL-THERM-004-007

LEU-COMP-THERM-032-008 LEU-COMP-THERM-083-002 MIX-SOL-THERM-004-008

LEU-COMP-THERM-032-009 LEU-COMP-THERM-083-003 MIX-SOL-THERM-004-009

LEU-COMP-THERM-033-001 LEU-COMP-THERM-084-001 MIX-SOL-THERM-005-001

LEU-COMP-THERM-033-002 LEU-COMP-THERM-085-001 MIX-SOL-THERM-005-002

LEU-COMP-THERM-033-003 LEU-COMP-THERM-085-002 MIX-SOL-THERM-005-003

LEU-COMP-THERM-033-004 LEU-COMP-THERM-085-003 MIX-SOL-THERM-005-004

LEU-COMP-THERM-033-005 LEU-COMP-THERM-085-004 MIX-SOL-THERM-005-005

LEU-COMP-THERM-033-006 LEU-COMP-THERM-085-005 MIX-SOL-THERM-005-006

LEU-COMP-THERM-033-007 LEU-COMP-THERM-085-006 MIX-SOL-THERM-005-007

LEU-COMP-THERM-033-008 LEU-COMP-THERM-085-007 MIX-SOL-THERM-007-001

LEU-COMP-THERM-033-009 LEU-COMP-THERM-085-008 MIX-SOL-THERM-007-002

LEU-COMP-THERM-033-010 LEU-COMP-THERM-085-009 MIX-SOL-THERM-007-003

LEU-COMP-THERM-033-011 LEU-COMP-THERM-085-010 MIX-SOL-THERM-007-004

LEU-COMP-THERM-033-012 LEU-COMP-THERM-085-011 MIX-SOL-THERM-007-005

LEU-COMP-THERM-033-013 LEU-COMP-THERM-085-012 MIX-SOL-THERM-007-006

LEU-COMP-THERM-033-014 LEU-COMP-THERM-085-013 MIX-SOL-THERM-007-007

LEU-COMP-THERM-033-015 LEU-COMP-THERM-089-001 MIX-SOL-THERM-010-001

LEU-COMP-THERM-033-016 LEU-COMP-THERM-089-002 MIX-SOL-THERM-010-002

LEU-COMP-THERM-033-017 LEU-COMP-THERM-089-003 MIX-SOL-THERM-010-003

LEU-COMP-THERM-033-018 LEU-COMP-THERM-089-004 MIX-SOL-THERM-010-004

LEU-COMP-THERM-033-019 LEU-COMP-THERM-090-001 MIX-SOL-THERM-010-005

LEU-COMP-THERM-033-020 LEU-COMP-THERM-090-002 MIX-SOL-THERM-010-006

LEU-COMP-THERM-033-021 LEU-COMP-THERM-090-003 MIX-SOL-THERM-010-007

LEU-COMP-THERM-033-022 LEU-COMP-THERM-090-004 MIX-SOL-THERM-010-008

LEU-COMP-THERM-033-023 LEU-COMP-THERM-090-005 MIX-SOL-THERM-010-009

LEU-COMP-THERM-033-024 LEU-COMP-THERM-090-006
APPENDIX D. CRITICAL EXPERIMENTS WITH CK VALUES NO 

LESS THAN 0.8

D-1

D1. CRITICAL EXPERIMENTS WITH CK VALUES NO LESS 

THAN 0.8

This appendix provides the cases with ck values of 0.8 or more for GBC-68 models. The results for the 

vanished lattice are contained in Tables D.1 and D.2 for AO and AFP compositions. The results for the 

full lattice with AFP modeling are contained in Table D.3.

Table D.1. Experiments with a ck no less than 0.8, vanished lattice – actinide only

Experiment ck Experiment ck

LEU-COMP-THERM-005-010 0.8044 LEU-COMP-THERM-015-146 0.8021

LEU-COMP-THERM-005-011 0.8020 LEU-COMP-THERM-015-151 0.8268

LEU-COMP-THERM-008-001 0.8859 LEU-COMP-THERM-015-158 0.8083

LEU-COMP-THERM-008-002 0.8889 LEU-COMP-THERM-036-025 0.8032

LEU-COMP-THERM-008-003 0.8900 LEU-COMP-THERM-036-026 0.8023

LEU-COMP-THERM-008-004 0.8889 LEU-COMP-THERM-047-001 0.8522

LEU-COMP-THERM-008-005 0.8888 LEU-COMP-THERM-047-003 0.8025

LEU-COMP-THERM-008-006 0.8900 LEU-COMP-THERM-051-001 0.8488

LEU-COMP-THERM-008-007 0.8892 LEU-COMP-THERM-051-002 0.8789

LEU-COMP-THERM-008-008 0.8892 LEU-COMP-THERM-051-003 0.8763

LEU-COMP-THERM-008-009 0.8891 LEU-COMP-THERM-051-004 0.8752

LEU-COMP-THERM-008-010 0.8883 LEU-COMP-THERM-051-005 0.8718

LEU-COMP-THERM-008-011 0.8880 LEU-COMP-THERM-051-006 0.8702

LEU-COMP-THERM-008-012 0.8881 LEU-COMP-THERM-051-007 0.8719

LEU-COMP-THERM-008-013 0.8873 LEU-COMP-THERM-051-008 0.8628

LEU-COMP-THERM-008-014 0.8878 LEU-COMP-THERM-051-009 0.8690

LEU-COMP-THERM-008-015 0.8892 LEU-COMP-THERM-051-010 0.8613

LEU-COMP-THERM-008-016 0.8913 LEU-COMP-THERM-051-011 0.8621

LEU-COMP-THERM-008-017 0.8929 LEU-COMP-THERM-051-012 0.8631

LEU-COMP-THERM-011-002 0.8610 LEU-COMP-THERM-051-015 0.8642

LEU-COMP-THERM-011-003 0.8694 LEU-COMP-THERM-051-016 0.8591

LEU-COMP-THERM-011-004 0.8703 LEU-COMP-THERM-051-017 0.8620

LEU-COMP-THERM-011-005 0.8682 LEU-COMP-THERM-051-018 0.8592

LEU-COMP-THERM-011-006 0.8674 LEU-COMP-THERM-051-019 0.8464

LEU-COMP-THERM-011-007 0.8635 LEU-COMP-THERM-052-003 0.8049

LEU-COMP-THERM-011-008 0.8593 LEU-COMP-THERM-052-006 0.8053

LEU-COMP-THERM-011-009 0.8563 LEU-COMP-THERM-055-001 0.8124

LEU-COMP-THERM-011-010 0.8634 LEU-COMP-THERM-055-002 0.8067

LEU-COMP-THERM-011-011 0.8584 LEU-COMP-THERM-076-001 0.8347

LEU-COMP-THERM-011-012 0.8498 LEU-COMP-THERM-076-002 0.8440

LEU-COMP-THERM-011-013 0.8509 LEU-COMP-THERM-076-003 0.8394

LEU-COMP-THERM-011-014 0.8416 LEU-COMP-THERM-076-004 0.8353

LEU-COMP-THERM-011-015 0.8375 LEU-COMP-THERM-076-005 0.8364

LEU-COMP-THERM-014-005 0.8432 LEU-COMP-THERM-076-006 0.8339

LEU-COMP-THERM-015-026 0.8007 LEU-COMP-THERM-076-007 0.8340

LEU-COMP-THERM-015-129 0.8023
D-2

Table D.2. Experiments with a ck no less than 0.8, vanished lattice – actinides and fission 

products

Experiment ck Experiment ck

LEU-COMP-THERM-005-010 0.8005 LEU-COMP-THERM-011-015 0.8250

LEU-COMP-THERM-008-001 0.8838 LEU-COMP-THERM-014-005 0.8352

LEU-COMP-THERM-008-002 0.8866 LEU-COMP-THERM-015-151 0.8136

LEU-COMP-THERM-008-003 0.8872 LEU-COMP-THERM-017-026 0.8193

LEU-COMP-THERM-008-004 0.8866 LEU-COMP-THERM-017-027 0.8007

LEU-COMP-THERM-008-005 0.8866 LEU-COMP-THERM-047-001 0.8418

LEU-COMP-THERM-008-006 0.8871 LEU-COMP-THERM-051-001 0.8373

LEU-COMP-THERM-008-007 0.8867 LEU-COMP-THERM-051-002 0.8698

LEU-COMP-THERM-008-008 0.8841 LEU-COMP-THERM-051-003 0.8670

LEU-COMP-THERM-008-009 0.8838 LEU-COMP-THERM-051-004 0.8657

LEU-COMP-THERM-008-010 0.8862 LEU-COMP-THERM-051-005 0.8620

LEU-COMP-THERM-008-011 0.8856 LEU-COMP-THERM-051-006 0.8602

LEU-COMP-THERM-008-012 0.8861 LEU-COMP-THERM-051-007 0.8622

LEU-COMP-THERM-008-013 0.8856 LEU-COMP-THERM-051-008 0.8522

LEU-COMP-THERM-008-014 0.8858 LEU-COMP-THERM-051-009 0.8587

LEU-COMP-THERM-008-015 0.8866 LEU-COMP-THERM-051-010 0.8510

LEU-COMP-THERM-008-016 0.8884 LEU-COMP-THERM-051-011 0.8519

LEU-COMP-THERM-008-017 0.8885 LEU-COMP-THERM-051-012 0.8530

LEU-COMP-THERM-011-002 0.8519 LEU-COMP-THERM-051-015 0.8549

LEU-COMP-THERM-011-003 0.8605 LEU-COMP-THERM-051-016 0.8486

LEU-COMP-THERM-011-004 0.8615 LEU-COMP-THERM-051-017 0.8527

LEU-COMP-THERM-011-005 0.8591 LEU-COMP-THERM-051-018 0.8491

LEU-COMP-THERM-011-006 0.8583 LEU-COMP-THERM-051-019 0.8349

LEU-COMP-THERM-011-007 0.8540 LEU-COMP-THERM-055-001 0.8034

LEU-COMP-THERM-011-008 0.8494 LEU-COMP-THERM-076-001 0.8290

LEU-COMP-THERM-011-009 0.8462 LEU-COMP-THERM-076-002 0.8386

LEU-COMP-THERM-011-010 0.8531 LEU-COMP-THERM-076-003 0.8343

LEU-COMP-THERM-011-011 0.8474 LEU-COMP-THERM-076-004 0.8311

LEU-COMP-THERM-011-012 0.8382 LEU-COMP-THERM-076-005 0.8295

LEU-COMP-THERM-011-013 0.8393 LEU-COMP-THERM-076-006 0.8277

LEU-COMP-THERM-011-014 0.8293 LEU-COMP-THERM-076-007 0.8259
D-3

Table D.3. Experiments with a ck no less than 0.8, full lattice – actinides and fission products

Experiment ck Experiment ck

LEU-COMP-THERM-008-001 0.8679 LEU-COMP-THERM-011-011 0.8095

LEU-COMP-THERM-008-002 0.8677 LEU-COMP-THERM-014-005 0.8062

LEU-COMP-THERM-008-003 0.8672 LEU-COMP-THERM-047-001 0.8002

LEU-COMP-THERM-008-004 0.8682 LEU-COMP-THERM-051-002 0.8371

LEU-COMP-THERM-008-005 0.8683 LEU-COMP-THERM-051-003 0.8336

LEU-COMP-THERM-008-006 0.8679 LEU-COMP-THERM-051-004 0.8324

LEU-COMP-THERM-008-007 0.8684 LEU-COMP-THERM-051-005 0.8277

LEU-COMP-THERM-008-008 0.8611 LEU-COMP-THERM-051-006 0.8260

LEU-COMP-THERM-008-009 0.8606 LEU-COMP-THERM-051-007 0.8283

LEU-COMP-THERM-008-010 0.8680 LEU-COMP-THERM-051-008 0.8169

LEU-COMP-THERM-008-011 0.8671 LEU-COMP-THERM-051-009 0.8223

LEU-COMP-THERM-008-012 0.8677 LEU-COMP-THERM-051-010 0.8166

LEU-COMP-THERM-008-013 0.8679 LEU-COMP-THERM-051-011 0.8175

LEU-COMP-THERM-008-014 0.8678 LEU-COMP-THERM-051-012 0.8188

LEU-COMP-THERM-008-015 0.8673 LEU-COMP-THERM-051-015 0.8209

LEU-COMP-THERM-008-016 0.8669 LEU-COMP-THERM-051-016 0.8111

LEU-COMP-THERM-008-017 0.8620 LEU-COMP-THERM-051-017 0.8184

LEU-COMP-THERM-011-002 0.8207 LEU-COMP-THERM-051-018 0.8114

LEU-COMP-THERM-011-003 0.8255 LEU-COMP-THERM-076-001 0.8287

LEU-COMP-THERM-011-004 0.8267 LEU-COMP-THERM-076-002 0.8367

LEU-COMP-THERM-011-005 0.8241 LEU-COMP-THERM-076-003 0.8356

LEU-COMP-THERM-011-006 0.8229 LEU-COMP-THERM-076-004 0.8359

LEU-COMP-THERM-011-007 0.8179 LEU-COMP-THERM-076-005 0.8249

LEU-COMP-THERM-011-008 0.8127 LEU-COMP-THERM-076-006 0.8251

LEU-COMP-THERM-011-009 0.8090 LEU-COMP-THERM-076-007 0.8147

LEU-COMP-THERM-011-010 0.8187

APPENDIX E. VALIDATION DATA

E-1

E.1 VALIDATION DATA

The data used for the sample validation presented in Section 4.5 are provided here. The C/E ratios, 

enrichments, and EALF values are provided for each experiment in Table E.1. The ck values are provided 

in Table D.2.

Table E.1. Validation data for vanished lattice with actinides and fission products

Experiment C/E C/E

Uncertainty

Enrichment

(wt% 235U)

EALF

(eV)

LEU-COMP-THERM-005-010 0.99697 0.00279 4.31 1.663

LEU-COMP-THERM-008-001 0.99672 0.00120 2.46 0.277

LEU-COMP-THERM-008-002 0.99757 0.00120 2.46 0.244

LEU-COMP-THERM-008-003 0.99784 0.00120 2.46 0.244

LEU-COMP-THERM-008-004 0.99745 0.00120 2.46 0.244

LEU-COMP-THERM-008-005 0.99719 0.00120 2.46 0.244

LEU-COMP-THERM-008-006 0.99780 0.00120 2.46 0.243

LEU-COMP-THERM-008-007 0.99705 0.00120 2.46 0.243

LEU-COMP-THERM-008-008 0.99666 0.00120 2.46 0.242

LEU-COMP-THERM-008-009 0.99739 0.00120 2.46 0.241

LEU-COMP-THERM-008-010 0.99707 0.00120 2.46 0.247

LEU-COMP-THERM-008-011 0.99786 0.00120 2.46 0.252

LEU-COMP-THERM-008-012 0.99753 0.00120 2.46 0.246

LEU-COMP-THERM-008-013 0.99759 0.00120 2.46 0.246

LEU-COMP-THERM-008-014 0.99702 0.00120 2.46 0.248

LEU-COMP-THERM-008-015 0.99686 0.00120 2.46 0.248

LEU-COMP-THERM-008-016 0.99721 0.00120 2.46 0.226

LEU-COMP-THERM-008-017 0.99646 0.00120 2.46 0.197

LEU-COMP-THERM-011-002 0.99578 0.00319 2.46 0.245

LEU-COMP-THERM-011-003 0.99607 0.00319 2.46 0.192

LEU-COMP-THERM-011-004 0.99644 0.00319 2.46 0.193

LEU-COMP-THERM-011-005 0.99627 0.00319 2.46 0.194

LEU-COMP-THERM-011-006 0.99616 0.00319 2.46 0.195

LEU-COMP-THERM-011-007 0.99640 0.00319 2.46 0.196

LEU-COMP-THERM-011-008 0.99666 0.00319 2.46 0.197

LEU-COMP-THERM-011-009 0.99631 0.00319 2.46 0.198

LEU-COMP-THERM-011-010 0.99359 0.00169 2.46 0.187

LEU-COMP-THERM-011-011 0.99328 0.00169 2.46 0.163

LEU-COMP-THERM-011-012 0.99341 0.00169 2.46 0.167

LEU-COMP-THERM-011-013 0.99401 0.00169 2.46 0.147

LEU-COMP-THERM-011-014 0.99380 0.00169 2.46 0.151

LEU-COMP-THERM-011-015 0.99478 0.00179 2.46 0.139

LEU-COMP-THERM-014-005 1.00143 0.00691 4.31 0.583

LEU-COMP-THERM-015-151 1.00034 0.00300 3.56 0.175

LEU-COMP-THERM-017-026 0.99496 0.00279 2.35 0.375

LEU-COMP-THERM-017-027 0.99696 0.00279 2.35 0.321

LEU-COMP-THERM-047-001 1.00000 0.00200 3.01 0.165

LEU-COMP-THERM-051-001 0.99594 0.00199 2.46 0.147
E-2

Table E.1. (continued)

Experiment C/E C/E

Uncertainty

Enrichment

(wt% 235U)

EALF

(eV)

LEU-COMP-THERM-051-002 0.99730 0.00239 2.46 0.197

LEU-COMP-THERM-051-003 0.99708 0.00239 2.46 0.196

LEU-COMP-THERM-051-004 0.99709 0.00239 2.46 0.198

LEU-COMP-THERM-051-005 0.99709 0.00239 2.46 0.198

LEU-COMP-THERM-051-006 0.99718 0.00239 2.46 0.200

LEU-COMP-THERM-051-007 0.99682 0.00239 2.46 0.200

LEU-COMP-THERM-051-008 0.99700 0.00239 2.46 0.201

LEU-COMP-THERM-051-009 0.99655 0.00189 2.46 0.167

LEU-COMP-THERM-051-010 0.99609 0.00189 2.46 0.192

LEU-COMP-THERM-051-011 0.99332 0.00189 2.46 0.193

LEU-COMP-THERM-051-012 0.99213 0.00189 2.46 0.195

LEU-COMP-THERM-051-015 0.99070 0.00238 2.46 0.201

LEU-COMP-THERM-051-016 0.99088 0.00198 2.46 0.169

LEU-COMP-THERM-051-017 0.99226 0.00268 2.46 0.202

LEU-COMP-THERM-051-018 0.99215 0.00208 2.46 0.169

LEU-COMP-THERM-051-019 0.99213 0.00189 2.46 0.151

LEU-COMP-THERM-055-001 0.99707 0.00249 3.01 1.216

LEU-COMP-THERM-076-001 0.99653 0.00249 3.00 1.482

LEU-COMP-THERM-076-002 0.99653 0.00249 3.00 1.482

LEU-COMP-THERM-076-003 0.99668 0.00249 3.00 1.400

LEU-COMP-THERM-076-004 0.99540 0.00249 3.00 1.481

LEU-COMP-THERM-076-005 1.00027 0.00250 3.00 1.477

LEU-COMP-THERM-076-006 0.99762 0.00250 3.00 1.491

LEU-COMP-THERM-076-007 1.00308 0.00251 3.00 1.362
APPENDIX F. ISOTOPIC VALIDATION DATA

F-1

F.1 SELECTION OF DATA FOR BWR ISOTOPIC 

VALIDATION

A review of the Spent Fuel Isotopic Composition Database (SFCOMPO) [F1] and the literature was 

performed to identify radiochemical assay (RCA) data for boiling water reactor (BWR) spent nuclear fuel 

(SNF) in the burnup range of interest for this report. The samples considered were expanded to 

encompass RCA data that included gadolinium measurements of PWR SNF samples selected from 

gadolinium fuel rods since the data available for BWR fuel was limited. The results of the review are 

summarized in Table F.1, which presents the RCA data that were further evaluated for applicability in this 

report. This table shows 14 sets of RCA data, 11 of which contain samples irradiated in BWRs. 

Table F.1. Sources of RCA data for BWR isotopic validation 

Reactor

name

Reactor 

type

Lattice 

type

Measured 

fuel rod 

type(s)

Number of

samples

Sample burnup

(GWd/MTU)

Gd rods

in

assembly?

Gd 

nuclides

measured?

JPDR BWR 6×6 UO2 30 2.2–7.2 No No

FukushimaDaini-2BWR 8×8 UO2, 

UO2-Gd2O3

18 4.1–44.0 Yes No

FukishimaDaichi-3BWR 8×8 UO2, 

UO2-Gd2O3

36 4.1–33.6 Yes No

Garigliano BWR 9×9 UO2 30 8.0–13.7 No No

Tsuruga-1 BWR 7×7 UO2 10 8.6–27.7 No No

Gundremmingen

-A

BWR 6×6 UO2 12 14.4–27.4 No No

Cooper BWR 7×7 UO2 6 17.8–33.9 No No

FukushimaDaini-1BWR 9×9 UO2, 

UO2-Gd2O3

8 35.6–68.3 Yes No

Forsmark3 BWR 10×10 UO2 6 38.3–56.0 Yes Yes

Monticello BWR 8×8 UO2, 

UO2-Gd2O3

30 40.3–58.7 Yes No

Dodeward BWR 6×6 UO2 1 54.4 Yes No

Takahama-3 PWR 17×17 UO2, 

UO2-Gd2O3

16 7.8–47.3 Yes No

Ohi-2 PWR 17×17 UO2, 

UO2-Gd2O3

3 21.5–25.1 Yes Yes

Many of the BWR samples in Table F.1 correspond to older lattice designs that do not contain gadolinium 

fuel rods. The pressurized water reactor (PWR) data sets were selected because they include measurement 

data performed for gadolinium fuel rods. The sample burnups range from 2.2 to 68.3 gigawatt days per 

metric ton of uranium (GWd/MTU). 

Older measurements, such as those for SNF from the Japan Power Demonstration Reactor (JPDR) and the 

Gundremmingen-A reactor, include only major actinides and limited fission product data. Only three of 

the measurement sets in Table F.1 include gadolinium measurements. Measurement data from the 

Forsmark-3 reactor include gadolinium; however the measured fuel rod did not contain any gadolinium 

poison. The only samples where gadolinium measurements were performed on fuel containing 

gadolinium poison were the PWR samples from Takahama-3 and Ohi-2. 
F-2

The measurement data included in Table F.1 represent a wide range of burnups and assembly types. The 

burnup and enrichment ranges for the BWR samples included in this table are illustrated in Figure F.1. 

Each color in the figure represents samples from one of the reactors listed in Table F.1. Not all of these 

measurements would be applicable to validating nuclide compositions near peak reactivity burnup credit 

(BUC). The uncertainties and biases calculated from isotopic validation can vary as a function of fuel 

burnup and core conditions. The measurement data listed in Table F.1 were evaluated using several 

selection criteria, as further presented in this section, for applicability to the analyses discussed in the 

current report. 

Figure F.1. Burnup vs. enrichment for available BWR RCA data.

The first criterion for sample selection was the burnup of the measured samples. Peak reactivity can 

generally occur at burnups up to ~20 GWd/MTU, but the reactivity effects in assemblies with high 

gadolinium content can extend to ~30 GWd/MTU. Therefore, all samples with burnups less than 30 

GWd/MTU were selected for inclusion in the isotopic validation set. Gadolinium measurements were 

only available at burnups greater than 20 GWd/MTU, with a few of these data corresponding to burnups 

larger than 25 GWd/MTU. Seven BWR RCA data sets listed in Table F.1 meet this selection criterion. 

Another sample selection criterion relates to the availability of adequate operation data for the measured 

samples to enable accurate depletion modeling. The older RCA measurements usually lack detailed 

operating history data for the measured samples. Depending on the reactor type and isotope of interest, 

the effect of the missing data on the isotopic prediction, and consequently on the calculated bias and 

uncertainty for that isotope, can vary. For example, the fuel temperature history generally has a small 

effect on isotopic prediction, whereas the coolant void fraction history can be a very important factor in 

prediction of major actinides. 

Unlike PWRs, the axial change in the coolant density in BWRs is large, leading to isotopic variations 

along the axial direction of the fuel rod due to the hardening of the neutron spectrum with increased void 

fraction. Figure F.2 illustrates the high sensitivity to void fraction of calculated plutonium isotopic 

contents. This example shows the percent change in the isotopic content of selected actinides and fission 

products due to a 10% decrease in the void fraction for a JPDR fuel sample with a 5 GWd/MTU burnup. 

This example emphasizes the importance of void fraction data availability to accurately model the fuel 

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

0

10

20

30

40

50

60

70

Burnup (GWd/MTU)

Enrichment (wt%)
F-3

depletion. The samples from the Cooper, Fukishima-Daichi-3, and Tsuruga reactors listed in Table F.1 

were not included in the final isotopic validation data set because no void fraction information was 

available for these samples. 

Figure F.2. Effect of void fraction change (-10%) on isotopic content for 5 GWd/MTU BWR fuel.

A third criterion for sample selection was the availability of complete design data important to the 

accuracy of the depletion models. All samples from the Garigliano reactor and some of the samples from 

the JPDR were eliminated due to unavailability of relevant design data. The Garigliano reactor and the 

JPDR employed first generation BWR designs, with boron curtains and erbium-loaded fuel rods used as 

burnable poisons in the reactor cycle at the times the samples were irradiated. However, no specifications 

for the boron curtains or the erbium loading of the fuel rods are available. Because both of these burnable 

absorbers—boron and erbium—are expected to change the neutron spectrum significantly, the samples 

adjacent to the boron curtains in JPDR assemblies were eliminated from the validation data set in this 

study, as were all Garigliano samples. 

The samples that resulted from the down-selection process are listed in Table F.2. Sixteen of the 19 

samples are from BWRs. However, none of these BWR samples include gadolinium nuclide 

measurements, and only four samples (Fukushima-Daini-2) are from gadolinium-loaded assemblies. 

Clearly there is a need for additional RCA measurements of BWR SNF with burnup in the peak reactivity 

burnup range. 
F-4

Table F.2. Selected RCA isotopic validation data set

Reactor

name

Lattice 

type

Reactor 

type

Measured fuel rod 

type

Number of 

samples

Sample burnup 

(GWd/MTU)

Gadolinium 

nuclides 

measurements

Gundremmingen-A 6×6 BWR UO2 8 14.4 - 25.2 No

JPDR 6×6 BWR UO2 4 2.8 - 4.4 No

Fukushima-Daini-2 8×8 BWR UO2, UO2- Gd2O3 4 16.6 - 26.5 No

Ohi-2 a 17×17 PWR UO2, UO2- Gd2O3 3 21.5 - 28.7 Yes

a fuel samples analyzed to obtain isotopic validation data for 155Gd 

To provide additional data for validating gadolinium depletion three samples from the Ohi-2 PWR were 

included in the isotopic validation dataset. This PWR assembly included gadolinium-loaded fuel rods, 

which are also present in modern BWR assemblies. The Ohi-2 samples are the only available RCA data 

that include gadolinium isotope measurements at relatively low burnups for fuel rods that include 

gadolinium poison. Although BWRs and PWRs differ in their fuel assembly design and operation, the 

fuel-to-moderator ratio for the Ohi-2 and a modern GE14 10×10 assembly are similar, and these 

particular PWR samples provide data representative of non-boiling regions of a BWR assembly.

F.2 ISOTOPIC VALIDATION MODELING 

This section presents the modeling assumptions used for BWR depletion modeling in the peak reactivity 

burnup range. The SCALE depletion simulation models used for isotopic validation include several 

assumptions in cases of missing operation and design data for the validation samples. These assumptions 

are listed below.

1. It is assumed that the in-channel void fraction is radially uniform across the sample axial node. 

Although high or low power fuel rods may exhibit gradients from the average value, in-channel 

radial void fraction distribution data are not available. 

2. It is assumed that the void fraction is constant with burnup. The available void history is averaged 

over irradiation time.

3. Unless specified, the clad temperature is set equal to the moderator temperature. In normal reactor 

operations, the clad temperature is at a value between the temperature of the fuel pin outer surface 

and the coolant temperature. However, the sensitivity of the clad neutron absorption to the clad 

temperature is negligible.

4. The fuel temperature is assumed to be radially uniform across the fuel assembly and constant 

over the irradiation history of the assembly. The basis for this assumption is that the effect of fuel 

temperature history on fuel isotopics diminishes over long assembly exposures. 

5. It is assumed that the modeling of the fuel channel as a square has a negligible impact on the 

calculated isotopic results. Although the fuel channel corners are rounded, this geometrical 

approximation would impact only the corner fuel rods to some extent, and not the non-corner fuel 

rods. None of the samples included in the isotopic validation set were selected from rods located 

at the corner of the assembly.
F-5

F.3 ANALYSIS OF ISOTOPIC MEASUREMENTS

F.3.1 JPDR

The Japanese Power Demonstration Reactor (JPDR) was a small, natural circulation BWR operated at the 

Japanese Atomic Energy Research Institute (JAERI). The RCA measurements of the JPDR samples were 

performed by JAERI. These JPDR samples offer a unique set of data for the validation of major actinides 

at very low burnups [F1, F2]. Note that the poison rods used in this reactor, as discussed in Section F.1, 

are an early implementation of burnable poison rods in BWRs. The void history data are available for 

these samples. However, there are missing data on the use of boron poison curtains, as no information 

was provided about the material content of the curtains. 

The JPDR measured samples were extracted from three assemblies with locations in the core as illustrated 

in Figure F.3. Based on the assembly locations, the samples from the A-20 assembly were not included in 

the isotopic validation set. The A-20 assembly is located adjacent to poison curtains on two sides and a

control blade nearby. The missing control blade information increases the uncertainty in modeling the 

depletion of the samples. Considering that the majority of the samples are located at the edge of the 

assembly, the samples from A-20 are not included in the analysis for this report. 

The fuel assembly design data and operating characteristics are listed in Table F.3. The operating data for 

the samples from A-14 and A-18 assemblies are given in Table F.4. The samples’ axial locations are 

shown in Figure F.4. The SCALE/TRITON assembly model used for depletion simulations is illustrated 

in Figure F.5. This figure indicates the location of the measured rod in the assembly. As indicated in the 

figure by different colors for fuel zones, the measured fuel rod and each of its nearest neighbors are 

depleted individually.

The TRITON-calculated isotopic contents for the four considered samples were compared with reported 

isotopic measured data. As shown in Table F.5, there is very good agreement between calculation and 

measurement for the major actinide 235U. The Pu nuclides are generally overpredicted. The largest 

discrepancies for Pu are seen for sample A18-5, which is near a Dy2O3 pellet. The effect of this pellet

cannot be modeled in the TRITON 2D model of A18-5 and likely contributes to the larger discrepancies 

in results for this sample.
F-6

Figure F.3. JPDR core map [F1].

Table F.3. JPDR assembly design data [F1, F2]

Parameter Data

Fuel Rod Data

 Fuel Type UO2

 Fuel Density (g/cm3) 10.4

 Fuel Pitch (cm) 1.956

 Fuel Diameter (cm) 1.25

 Fuel Temperature (K) 840

 Initial U Isotopics

234U 0.0153 wt% 235U 2.5966 wt% 236U0.0161 wt% 238U 97.372 wt%

 Clad Inner Diameter (cm) 1.26

 Clad Thickness (mm) 0.76

 Clad Material Zircaloy-2

 Clad Temperature (K) 620

Moderator Data

 Temperature (K) 550

Assembly Data

 Assembly Pitch (cm) 13.26

 Channel Material Zircaloy-4

 Assembly Pitch (cm) 11.736

 Fuel Rod Active Height (cm) 366
F-7

Table F.4. JPDR samples data [F1, F2]

Sample Assembly Burnup

(GWd/MTU)

Void 

fraction (%)

Coolant density 

(g/cm3)

Sample location

(cm)*

A14-1 A14 4.13 0 0.7541 -293

A14-3 3.38 20.0 0.6075 +538

A18-5 A18 4.35 11.8 0.6700 +49

A18-6 2.77 26.6 0.5629 +538

* See Figure F.12

Figure F.4. JPDR samples axial locations [F1].
F-8

Figure F.5. Illustration of SCALE/TRITON model for JPDR assembly.

Table F.5. Comparison calculation-measurement 

for JPDR samples

C/M-1 (%)

Sample ID A14-1 A14-3 A18-5 A18-6

GWd/MTU 4.13 3.38 4.35 2.77

U234 1.79 -0.92 -1.31 0.12

U235 0.31 -0.67 0.90 0.00

U236 0.01 -0.64 2.78 -1.18

U238 0.00 0.03 0.11 -0.01

Pu238 -5.52 -8.68 3.98 36.92

Pu239 8.66 9.07 15.39 6.45

Pu240 7.51 10.54 16.09 8.90

Pu241 11.79 10.45 25.66 3.09

Pu242 8.45 10.76 20.26 35.23

Nd143 -0.08 -0.05 0.01 0.00

Nd144 -1.21 -0.62 -1.19 -0.51

Nd145 0.46 0.13 0.32 0.43

Nd146 0.65 0.53 0.92 0.66

Nd148 1.18 0.70 1.37 0.44

Nd150 0.58 0.20 1.48 -1.06

Cs137 -10.70 -11.01 -7.59 -6.95

Sample Rod
F-9

F.3.2 Gundremmingen-A

Located in Germany, the Gundremmingen power plant was one of the first commercial BWRs. Like the 

JPDR plant, the Gundremmingen employed poison curtains in the reactor core. The poison curtains were 

boron-loaded, stainless steel plates located along the narrow gap edges of the fuel assembly [F1, F2]. 

Post-irradiation examination of two 6×6 fuel assemblies from Gundremmingen Unit A was performed by 

the Karlsruhe and Ispra institutes [F3]. Both assemblies—identified as B23 and C16—had low assembly 

average burnups of 22 GWd/MTU and 17 GWd/MTU, respectively, and they also had similar enrichment 

profiles. Each assembly had seven fuel rods with 1.87 wt% 235U enrichment and 29 fuel rods with 

2.53 wt% 235U enrichment. The configuration of the assemblies, including the location of the measured 

fuel rods, is illustrated in Figure F.6. All measured samples were selected from rods with 2.53 wt% 235U 

enrichment. 

Relevant assembly design data are listed in Table F.6. Burnup, coolant density, and sample location for 

the eight samples analyzed in this report are shown in Table F.7. The majority of the design information 

used for modeling was obtained from a report released by the European Commission Joint Research 

Center [F3], with other modeling data gathered from several other sources [F1, F4]. An example of the 

SCALE/TRITON models used for analysis of these samples is illustrated in Figure F.7, which 

corresponds to sample C16-B3 analysis. Note that the model makes use of the symmetry along the 

assembly diagonal. The measured rod and its nearest neighbor rods are depleted individually as indicated 

by the use of different colors in Figure F.7.

Table F.8 presents a comparison of the calculated and measured data. The major actinides show good 

agreement, while some of the minor actinides show larger discrepancies, especially 241Am, which requires 

further investigation.

Figure F.6. Diagram of assembly C16 enrichment profile [F1].
F-10

Table F.6. Gundremmingen-A assembly design data

Parameter Data

Assembly and reactor data

Lattice type 6×6

Active core height (m) 3.302

Assembly pitch wide-wide (cm) 13.098

Assembly pitch narrow-narrow (cm) 12.303

Fuel rod data

Fuel material UO2

Fresh fuel pellet density (g/cm3) 10.5

Smeared fuel pellet density (g/cm3) 10.07

Fuel pellet diameter (cm) 1.224

Rod pitch (cm) 1.78

Fuel temperature (K) 923

Clad material Zircaloy-2

Pellet-cladding gap (cm) 0.01375

Clad thickness (cm) 0.0889

Clad inner diameter (cm) 1.25

Moderator data

Nominal pressure (bar) 69

Nominal outlet temperature (K) 559

Channel box data

Channel box outside width (cm) 11.352

Channel box thickness (cm) 0.15

Channel box material Zircaloy-4

Table F.7. Gundremmingen-A samples data

Sample Assembly Burnup

(GWd/MTU)

Coolant density 

(g/cm3)

Sample location

(cm)*

C16-B3

C16

14.39 0.388 268

C16-C5 15.84 0.388 268

C16-E5 17.49 0.388 268

B23-B3

B23

21.24 0.388 268

B23-B4 22.25 0.388 268

B23-C5 22.97 0.388 268

B23-E3 23.51 0.388 268

B23-E5 25.19 0.388 268

* axial distance from bottom of active length 
F-11

Figure F.7. Illustration of SCALE/TRITON model for Gundremmingen sample C16-B3.

Table F.8. Comparison calculation-measurement for Gundremmingen-A samples

C/M-1 (%)

Sample ID C16-B3 C16-C5 C16-E5 B23-B3 B23-B4 B23-C5 B23-E3 B23-E5

GWd/MTU 14.39 15.84 17.49 21.24 22.25 22.97 23.51 25.19

U235 2.16 -1.61 3.71 0.23 3.24 0.44 -2.80 4.86

U236 -7.78 -3.73 -5.98 -3.81 -2.69 -5.76 -4.13 -4.91

U238 -0.02 0.01 0.00 -0.04 -0.09 0.00 0.01 0.07

Pu238 -6.56 -3.50 -9.94 -7.64 -10.65 -8.33 1.41 -9.92

Pu239 3.18 2.57 1.11 4.70 9.37 3.79 6.77 1.64

Pu240 -0.26 2.94 -3.52 -0.56 4.00 -0.31 8.72 -0.79

Pu241 -16.13 -11.91 -17.47 -13.57 -10.39 -14.89 -11.49 -16.41

Pu242 -9.31 -0.14 -16.88 -8.09 -3.02 -8.34 4.74 -10.05

Am141 -11.04 167.88 -28.14 -51.78 -20.26 -8.54

Cm242 -99.18 -98.82 -98.96 -98.94 -99.00 -99.06 -99.55 -99.03

Cm244 -21.35 -17.26 -25.06 -16.94 -10.02 -18.75 3.66 -23.82

Nd148 -0.89 0.75 -1.07 -0.68 -0.41 -0.45 -3.09 -3.24

Cs137 -13.28 -18.36 -6.08 -9.28 -7.04 -15.50 -4.71 -9.73
F-12

F.3.3 Fukushima Daini-2

The Fukushima Daini-2 Nuclear Power Station, operated by Tokyo Electric Power Company (TEPCO), 

used Hitachi BWR fuel bundles with an 8×8 lattice for the reactor cycles considered in this report [0]. A 

nuclide composition benchmark data set was generated by JAERI as part of a BUC research project [F5]. 

The JAERI-generated data set included 18 BWR samples which were selected from two rods with initial 

235U enrichments of 3.41 and 3.91 wt%, respectively. The samples had burnups ranging from 4.2 to 

44.0 GWd/MTU. The two measured rods, identified as SF98 and SF99, were part of the same assembly—

2F2DN23—which was irradiated in the reactor for a total of 1174 days. 

The layout of assembly 2F2DN23 and its axially averaged enrichment distribution are shown in 

Figure F.8. The SF98 rod corresponds to position B-2 within the assembly. The SF99 rod corresponds to 

position C-2 and contains gadolinium as a burnable poison. Both fuel rods contain a natural uranium 

blanket segment at the upper and lower tips of the rods. 

Destructive and non-destructive analyses were performed at JAERI from 1995 through 1997. The 

destructive analyses were conducted to determine nuclide compositions. Non-destructive gamma scans 

were performed to determine axial burnup distributions. For destructive analyses, the samples were 

collected by cutting 0.5 mm-thick slices axially at different locations along the rod, as shown in 

Figure F.9. Based on the reported sample burnups [0], four of the SF98 and SF99 samples have burnups 

smaller than 20 GWd/MTU; however, three of these samples are located in the natural uranium blanket 

region and are therefore not applicable for the study in this report. 

Relevant design and operation data used in the SCALE models of the considered samples are presented in 

Tables F.9 and F.10 [0, F4, F5, F6]. The SCALE/TRITON model for SF99 samples is illustrated in 

Figure F.10. The comparison of calculated and measured isotopic concentrations is presented in 

Table F.11.
F-13

Figure F.8. Radial loading diagram of assembly 2F2DN23.

Figure F.9. Measurement positions for rod SF99.
F-14

Table F.9. Fukushima-Daini-2 assembly design data

Parameter Data

Assembly and reactor data

Lattice type 8×8-2

Active core height (m) 3.71

Assembly pitch (cm) 15.2

Fuel rod data

Fuel material UO2, UO2-Gd2O3

Fuel density (g/cm3) 10.412

Smeared fuel pellet density (g/cm3)

* 9.943

Fuel pellet diameter (cm) 1.03

Pellet-clad gap clearance (cm) 0.024

Clad material Zircaloy-2

Clad thickness (cm) 0.086

Clad outer diameter (cm) 1.23

Rod pitch (cm) 1.63

Fuel temperature (K) 900

Water rod data

Water rod material Zircaloy

 Water rod inner diameter (cm) 1.35

Water rod outer diameter (cm) 1.50

Channel Box Data

Channel box inner width (cm) 13.4

 Channel box thickness (cm) 0.203

*Based on fresh fuel diameter + gap distance.

Table F.10. Fukushima-Daini-2 samples data

Sample Burnup

(GWd/MTU)

Enrichment 

(wt% 235U)

Coolant density 

(g/cm3)

Sample location* 

(cm)

SF99-9 16.65 3.41 0.2272 354.0

SF99-8 21.83 3.41 0.2356 338.8

SF99-2 22.63 3.41 0.7303 28.6

SF98-8 27.18 3.91 0.2265 339.7

* distance from bottom of active fuel
F-15

Figure F.10. Illustration of SCALE/TRITON model for Fukushima Daini-2 SF99 samples.

Table F.11. Comparison calculation-measurement for Fukushima Daini-2 samples

C/M-1 (%)

Sample ID SF99-9 SF99-8 SF99-2 SF98-8

GWd/MTU 16.65 21.83 22.63 27.18

U234 4.85 7.86 10.77 3.47

U235 4.53 5.20 2.47 1.97

U236 -1.82 -2.84 -2.30 -1.99

U238 -0.14 -0.09 0.30 -0.07

Np237 -10.03 -9.74 -13.14 6.50

Pu238 2.09 -3.58 -1.47 -12.38

Pu239 9.99 3.98 -2.71 2.09

Pu240 4.70 1.65 -1.50 0.49

Pu241 7.27 -1.23 -10.28 -0.34

Pu242 2.53 -4.86 -13.03 -4.08

Am241 0.87 7.88 30.05 16.11

Am242m -13.44 -26.49 -35.11 -31.35

Am243 13.98 1.03 -7.27 13.27

Cm244 4.06 -15.05 -22.92 -4.31

Nd143 -2.71 -1.20 0.23 1.39

Nd144 -3.09 5.40 0.32 5.88

Nd145 -1.88 -0.59 1.13 1.68

Nd146 -0.79 -0.53 1.42 2.34

Nd148 -0.65 -0.42 0.65 1.86

Nd150 0.38 -0.53 -0.20 1.46

Cs137 -6.87 -6.92 -5.04 3.95

Cs134 -11.06 -14.64 -11.96 4.69

Eu154 -3.11 -6.73 -10.29 -0.93

Ce144 -6.19 -21.25 -0.64 -12.13

Ru106 2.34 73.27 111.58 23.16

Sm147 -2.07 -2.02 -7.49

Sm148 -5.54 -12.53 -14.66

Sm149 7.27 -3.60 -26.18

Sm150 -1.74 -4.21 -6.23

Sm151 3.61 -4.60 -9.07

Sm152 -2.20 -2.08 -7.66

Sm154 -2.41 -4.71 -12.00

Sample Rod
F-16

F.3.4 Ohi-2

The Ohi-2 reactor is a PWR operated in Japan by JAERI. Post irradiation evaluation of five samples from 

fuel irradiated in this reactor was performed by JAERI [F7]. All samples were cut from three fuel rods 

located in the same 17×17 fuel assembly, identified as 17G. Although the assembly’s average burnup is 

relatively high, the samples located at the top of the fuel have burnups less than 30 GWd/MTU. Three of 

these samples were selected from two gadolinium fuel rods placed at symmetric locations in the fuel 

assembly. 

The measurements include data for actinides (U, Pu, Am, Cm) and fission products (selected nuclides of 

Nd, Ru, Ag, Sb, Cs, Ce, Eu, Gd). The experimental actinides data are reported for discharge time, 

whereas the fission products data are reported at a cooling time in the range 1100–1390 days after 

discharge. All the measurement data except for gadolinium are expressed in grams of measured nuclide 

per initial MTU. For the gadolinium nuclides, the data are reported as atomic ratios of a gadolinium 

isotope relative to the total gadolinium content. 

Relevant design and operating data for the analyzed gadolinium rod samples are listed in Tables F.12 and 

F.13. The SCALE/TRITON model used for the depletion simulations is illustrated in Figure F.11.

The results of the calculated to measured isotopic comparisons for actinides and the burnup indicator

fission product 148Nd are presented in Table F.14. As seen from this table, the prediction for actinides is 

similar to that observed for other reported data for PWR fuel. However, for UO2, 235U is slightly 

overpredicted for the gadolinium rod. The calculated and measured data for 148Nd are in very good 

agreement. 

The experimental and the calculated data for the gadolinium nuclides are presented in Table F.15. The 

results shown in this table indicate a systematic large underestimation for 155Gd. This underestimation is 

consistent with other published results for these samples, which were obtained using the Step Wise 

Burnup Analysis Code System (SWAT) with the Japanese Evaluated Nuclear Data Library (JENDL)-

3.2 cross sections [F7]. Note that the 155Gd content in the measured samples is less than 2% of the total 

gadolinium content.
F-17

Table F.12. Ohi-2 assembly design data [F7]

Parameter Data

Fuel rod data 

 Fuel Type UO2, UO2- Gd2O3

 Pellet Density (g/cm3) 10.4

 Pin Pitch (cm) 1.265

 Fuel Pellet Diameter. (cm) 0.805

 Fuel Temperature (K) 900

 Fuel Enrichment (UO2) 3.2 wt % 235U

 Fuel Enrichment (UO2-Gd2O3) 1.68 wt % 235U, 6wt% Gd2O3

 Clad Inner Diameter (cm) 0.822

 Clad Outer Diameter (cm) 0.950

 Clad Material Zircaloy-4

 Clad Temperature (K) 600

Moderator data

 Coolant Inlet Temperature (K) 289

 Coolant Outlet Temperature (K) 325

Assembly data

 Assembly Pitch (cm) 21.4

 Channel Material Zircaloy-4

 Operating Pressure (kg/cm2) 32

 Fuel Active Height (cm) 364.8

Table F.13. Ohi-2 samples data

Sample ID Burnup

(GWd/MTU)

Coolant density

(g/cm3)

Sample location*

(mm)

89G01 21.92 0.740 267

89G03 29.45 0.726 737

89G05 25.73 0.726 733

* with respect to bottom of active fuel
F-18

Figure F.11. Illustration of SCALE/TRITON model for Ohi-2 assembly.

Sample Rod
F-19

Table F.14. Comparison calculation-measurement for 

Ohi-2 samples (actinides)

C/M-1 (%)

Sample ID 89G01 89G05 89G03 Average

GWd/MTU 21.47 25.14 28.72

U234 2.5 2.3 3.6 2.8

U235 4.1 5.2 4.7 4.7

U238 0.1 0.2 0.1 0.1

Np237 -5.1 0.9 -0.5 -1.6

Pu238 -10.8 -15.9 -14.5 -13.7

Pu239 -1.7 -2.9 -1.8 -2.1

Pu240 -1.5 -2.5 -1.9 -2.0

Pu241 -4.4 -6.0 -5.3 -5.2

Pu242 -5.5 -9.2 -7.9 -7.5

Am241 13.0 3.5 -6.7 3.3

Am243 6.2 -14.8 1.6 -2.3

Nd148 -0.7 -0.3 -0.2 -0.4

Table F.15. Comparison calculation-measurement for Ohi-2 samples (Gd)

89G01 89G05 89G03

GWd/

MTU 21.47 25.14 28.72

M (measured 

data)*

C C/M M (measured 

data)

C C/M M (measured 

data)

C C/M

Gdn/

Gdtotal uncert

Gdn/

Gdtotal uncert

Gdn/

Gdtotal uncert

Gd152 0.056 0.001 0.057 1.024 0.044 0.001 0.046 1.340 0.034 0.001 0.036 0.828

Gd154 1.818 0.002 1.863 1.025 1.748 0.002 1.806 1.079 1.674 0.002 1.754 1.003

Gd155 0.018 0.001 0.012 0.675 0.019 0.001 0.012 0.226 0.053 0.003 0.013 0.707

Gd156 34.600 0.020 34.665 1.002 34.545 0.023 34.567 1.009 34.26 0.030 34.467 0.998

Gd157 0.007 0.001 0.007 0.964 0.009 0.001 0.007 0.843 0.008 0.001 0.007 0.745

Gd158 41.520 0.020 41.406 0.997 41.640 0.030 41.556 0.992 41.870 0.030 41.699 1.001

Gd160 21.990 0.010 21.990 1.000 21.994 0.004 22.008 0.996 22.100 0.010 22.023 1.001

* reported measured data consists of the ratio of atoms of a Gd isotope and total number of Gd atoms.

F.4 STATISTICAL ANALYSIS OF THE BWR ISOTOPIC 

VALIDATION DATA

Relevant statistical data for the analyzed BWR samples are shown in Table F.16. For each of the BUC 

nuclides, the table includes the mean, the standard deviation around the mean, and the number of samples. 

The variation with burnup in the 16 considered samples of (C/M-1) is presented in Figure F.12 for the 

major actinides 235U and 239Pu. On average, the comparison calculation-measurement for these two major 

actinides, obtained for the 16 BWR samples with burnups less than 27 GWd/MTU, is quite similar with 

the data obtained for PWR fuel. For the considered 16 BWR samples, 235U and 239Pu are predicted on 

average within 1.6 and 5.4% of the measurement, respectively. Corresponding standard deviations are 2.4 

and 4.4%. Results reported [F8] for 92 PWR fuel samples with burnups in the range of 

7–70 GWd/MTU, based on calculations performed with SCALE6.1 and ENDF/B-VII.0 cross sections, 
F-20

show predictions for 235U and 239Pu that are on average within 1.2 and 4.1% of the measurement, 

respectively; the corresponding standard deviations are 3.5 and 3.5%. 

Table F.16. Statistical data for the BWR samples 

(BUC nuclides)

Nuclide Average

%(C/M-1)

Standard

deviation

Number

of samples

U234 3.33 4.32 8

U235 1.56 2.36 16

U236 -2.92 2.58 16

U238 0.00 0.10 16

Pu238 -2.74 11.64 16

Pu239 5.38 4.40 16

Pu240 3.66 5.37 16

Pu241 -4.12 12.72 16

Pu242 0.26 13.40 16

Am241 10.30 60.02 10

Am243 5.25 10.25 4

Nd143 -0.30 1.20 8

Nd145 0.21 1.08 8

Sm147 -3.86 3.14 3

Sm149 -7.50 17.06 3

Sm150 -4.06 2.25 3

Sm151 -3.35 6.43 3

Sm152 -3.98 3.19 3

Figure F.12. Variation with burnup of (C/M-1) for 235U and 239Pu.

0 5 10 15 20 25 30

-10

-5

0

5

10

15

20

AvgU235 = 1.56

 U-235

 Pu-239

C/M-1 (%)

Burnup (GWd/MTU)

AvgPu239 = 5.4
F-21

F.5 APPENDIX F REFERENCES

F1. SFCOMPO - Spent Fuel Isotopic Composition Database, http://www.nea.fr/sfcompo/, retrieved 

November 2014.

F2. O. W. Hermann and M. D. DeHart, “Validation of SCALE (SAS2H) Isotopic Predictions for 

BWR Spent Fuel,” ORNL/TM-13315, Oak Ridge National Laboratory, September 1998.

F3. “Post-Irradiation Analysis of the Gundremmingen BWR Spent Fuel,” Nucl. Sci. and Tech., 

Commission of the European Communities, ISBN 92-825-1099-9, 1979.

T. Yamamoto, “Compilation of Measurement and Analysis Results of Isotopic Inventories of 

Spent BWR Fuels,”

https://www.oecd-nea.org/science/wpncs/ADSNF/reports/JNES/JNESreport2009.pdf.

F4. T. Yamamoto and M. Yamamoto, “Nuclear Analysis of [Postirradiation Examination] PIE Data 

of Irradiated BWR 8×8-2 and 8x8-4 UO2 Fuel Assemblies,” Journal of Nuclear Science and 

Technology, Vol. 45, No.11, (November 2008).

F5. Y. Nakahara, K Suyama, and T. Suzaki, “Technical Development on Burnup Credit for Spent 

LWR Fuels,” JAERI-Tech 2000-071, ORNL/TR-2001/01, English Translation, Oak Ridge 

National Laboratory, January 2002.

F6. U. Mertyurek, M. W. Francis, and I. C. Gauld, “SCALE 5 Analysis of BWR Spent Nuclear Fuel 

Isotopic Compositions for Safety Studies,” ORNL/TM-2010/286, Oak Ridge National 

Laboratory, December 2010.

F7. K. Suyama, M. Murazaki, K. Ohkubo, Y. Nakahara, G. Uchiyama, “Re-evaluation of Assay Data 

of Spent Nuclear Fuel obtained at Japan Atomic Energy Research Institute for Validation of 

Burnup Calculation Code Systems,” Annals of Nuclear Energy, Volume 38, pp. 930–941, 2011. 

F8. G. Ilas, I. C. Gauld, and G. Radulescu, “Validation of new depletion capabilities and ENDF/VII 

data libraries in SCALE,” Annals of Nuclear Energy Volume 46, pp. 43–55, August 2012.







NUREG/CR-7194 Technical Basis for Peak Reactivity Burnup Credit for BWR Spent Nuclear

Fuel in Storage and Transportation Systems