Computational Benchmark for 

Estimated Reactivity Margin 

from Fission Products and 

Minor Actinides in BWR 

Burnup Credit

Office of Nuclear Regulatory Research

NUREG/CR-7157

ORNL/TM-2012/96
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NUREG/CR-7157

ORNL/TM-2012/96

Computational Benchmark for Estimated Reactivity 

Margin from Fission Products and Minor Actinides in 

BWR Burnup Credit

Manuscript Completed: September 2012 

Date Published: February 2013 

Prepared by

D. E. Mueller 

J. M. Scaglione

J. C. Wagner

S. M. Bowman

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6170

M. Aissa, NRC Project Manager

Prepared for

Division of Systems Analysis

Office of Nuclear Regulatory Research

U. S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code V6061

Office of Nuclear Regulatory Research

iii

ABSTRACT

This report proposes and documents a computational benchmark for the estimation of the 

additional reactivity margin available in spent nuclear fuel (SNF) from fission products and minor 

actinides in a burnup-credit storage/transport environment, relative to SNF compositions 

containing only the major actinides. The benchmark problem/configuration is a generic burnupcredit cask designed to hold 68 boiling water reactor (BWR) spent nuclear fuel assemblies. The 

purpose of this computational benchmark is to provide a reference configuration for the 

estimation of the additional reactivity margin for partial burnup credit (ISG-8) and document 

reference estimations of the additional reactivity margin as a function of initial enrichment, 

burnup, and cooling time. This benchmark model will also be used as the base case in future 

sensitivity studies, to be documented in a companion NUREG/CR. The geometry and material 

specifications are provided in sufficient detail to enable independent evaluations. Estimates of 

additional reactivity margin for this reference configuration may be compared to those of similar 

burnup-credit casks to provide an indication of the validity of design-specific estimates of fissionproduct margin. The reference solutions were generated with the SCALE 6.1 package. The

SCALE depletion and criticality sequences have been extensively validated elsewhere for a 

variety of applications, including light water reactor fuel. Note that the reference solutions 

presented in this report are not directly or indirectly based on experimental results. 

Consequently, this computational benchmark cannot be used to satisfy the ANS 8.1, 8.24, and 

8.27 requirements for validation of calculational methods and is not intended to be used to 

establish biases and bias uncertainties for burnup-credit analyses.

v

CONTENTS

Section Page

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

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

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

ACKNOWLEDGMENTS.............................................................................................................xi

ACRONYMS ............................................................................................................................ xiii

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

1.1 PURPOSE.......................................................................................................................1

1.2 BACKGROUND...............................................................................................................2

1.3 REGULATORY GUIDANCE............................................................................................3

2. BENCHMARK SPECIFICATION ............................................................................................5

2.1 GBC-68 CASK SPECIFICATION.....................................................................................5

2.2 BWR FUEL ASSEMBLY SPECIFICATIONS ...................................................................7

3. ANALYSIS............................................................................................................................11

3.1 COMPUTATIONAL METHODS.....................................................................................11

3.2 GBC-68 COMPUTATIONAL MODEL ............................................................................13

3.3 RESULTS......................................................................................................................18

3.3.1 Reference Results................................................................................................18

3.3.2 Related Information..............................................................................................28

3.3.3 Additional Results with Non-Uniform Axial Burnup ...............................................28

4. CONCLUSIONS...................................................................................................................37

5. REFERENCES.....................................................................................................................39

APPENDIX A. TRITON Input File Example .............................................................................A-1

APPENDIX B. STARBUCS Input File Example.......................................................................B-1

APPENDIX C. CSAS5 Input File Example ..............................................................................C-1

APPENDIX D. DISCUSSION OF REFERENCE RESULTS ....................................................D-1

D.1 DISCUSSION OF REFERENCE RESULTS................................................................D-1

D.2 APPENDIX D REFERENCES...................................................................................D-23

APPENDIX E. LIMITED NUCLIDE COMPOSITION DATA......................................................E-1

vii

LIST OF FIGURES

Figure Page

Figure 1. TRITON depletion model used to generate the rodded ORIGEN-ARP 

libraries..........................................................................................................12

Figure 2. Radial cross section of the GBC-68 model with .............................................15

Figure 3. Cross-sectional view of assembly cell in GBC-68 model................................16

Figure 4. Cutaway view of bottom part GBC-68 model. Poison panel and cell 

walls removed to reveal fuel assembly axial zoning. Note that the 

reference cases utilized a single axial zone. ..................................................17

Figure 5. Normalized axial burnup distributions used. These distributions are 

based on data for assembly B2 from the LaSalle Unit 1 CRC data. ...............30

Figure D.1. Values of keff in the GBC-68 cask as a function of burnup using the 

different nuclide sets and 5-year cooling time for fuel of 2 wt% 235U 

initial enrichment..........................................................................................D-4

Figure D.2. Values of keff in the GBC-68 cask as a function of burnup using the 

different nuclide sets and 5-year cooling time for fuel of 3 wt% 235U 

initial enrichment..........................................................................................D-5

Figure D.3. Values of keff in the GBC-68 cask as a function of burnup using the 

different nuclide sets and 5-year cooling time for fuel of 4 wt% 235U 

initial enrichment..........................................................................................D-6

Figure D.4. Values of keff in the GBC-68 cask as a function of burnup using the 

different nuclide sets and 5-year cooling time for fuel of 5 wt% 235U 

initial enrichment..........................................................................................D-7

Figure D.5. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of 

burnup using the different nuclide sets and 5-year cooling time for fuel 

of 2 wt% 235U initial enrichment....................................................................D-8

Figure D.6. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of 

burnup using the different nuclide sets and 5-year cooling time for fuel 

of 3 wt% 235U initial enrichment....................................................................D-9

Figure D.7. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of 

burnup using the different nuclide sets and 5-year cooling time for fuel 

of 4 wt% 235U initial enrichment..................................................................D-10

Figure D.8. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of 

burnup using the different nuclide sets and 5-year cooling time for fuel 

of 5 wt% 235U initial enrichment..................................................................D-11

Figure D.9. Individual contributions to the total reduction in keff for the different 

nuclide sets as a function of burnup for fuel of 2 wt% 235U initial 

enrichment with a 5-year cooling time........................................................D-12

Figure D.10. Individual contributions to the total reduction in keff for the different 

nuclide sets as a function of burnup for fuel of 3 wt% 235U initial 

enrichment with a 5-year cooling time........................................................D-13
viii

Figure D.11. Individual contributions to the total reduction in keff for the different 

nuclide sets as a function of burnup for fuel of 4 wt% 235U initial 

enrichment with a 5-year cooling time........................................................D-14

Figure D.12. Individual contributions to the total reduction in keff for the different 

nuclide sets as a function of burnup for fuel of 5 wt% 235U initial 

enrichment with a 5-year cooling time........................................................D-15

Figure D.13. Δk values (relative to fresh fuel) in the GBC-68 cask due to major 

actinides (set 1) as a function of burnup for various initial enrichments 

with a 5-year cooling time. .........................................................................D-16

Figure D.14. Δk values (relative to fresh fuel) in the GBC-68 cask due to additional 

nuclides (set 3) as a function of burnup for various initial enrichments 

with a 5-year cooling time. .........................................................................D-17

Figure D.15. Contribution to total reduction in keff due to the major actinides (set 1) 

as a function of burnup for various enrichments with a 5-year cooling 

time. ..........................................................................................................D-18

Figure D.16. Contribution of total reduction in keff due to the additional nuclides 

(set 3) as a function of burnup for various enrichments with a 5-year 

cooling time. ..............................................................................................D-19

Figure D.17. Δk (relative to fresh fuel) in the GBC-68 cask due to the major actinides 

(set 1) as a function of burnup for 4 wt% 235U initial enrichment fuel with 

various cooling times. ................................................................................D-20

Figure D.18. Δk (relative to fresh fuel) in the GBC-68 cask due to the minor actinides 

and fission products (set 3) as a function of burnup for 4 wt% 235U initial 

enrichment fuel with various cooling times.................................................D-21

Figure D.19. Range of Δk in the GBC-68 cask due to the additional nuclides (set 3) 

as a function of burnup for all cooling times and initial enrichments 

considered.................................................................................................D-22
ix

LIST OF TABLES

Table Page

Table 1. Physical dimensions for the GBC-68 cask.............................................................6

Table 2. Material compositions for the GBC-68 cask model ................................................7

Table 3. BWR fuel assembly specification...........................................................................8

Table 4. Initial material compositions for the unburned fuel assemblies ..............................9

Table 5. Fuel depletion parameters...................................................................................11

Table 6. Nuclide sets defined for the benchmark problem analysis ...................................18

Table 7. Nuclides in "set 3," on which the additional reactivity margin available from 

fission products and minor actinides is based......................................................18

Table 8. keff values for the GBC-68 cask as a function of burnup and cooling time 

for 2 wt% 235U initial enrichment ..........................................................................20

Table 9. keff values for the GB C-68 cask as a function of burnup and cooling time 

for 3 wt% 235U initial enrichment ..........................................................................21

Table 10. keff values for the GBC-68 cask as a function of burnup and cooling time 

for 4 wt% 235U initial enrichment ..........................................................................22

Table 11. keff values for the GBC-68 cask as a function of burnup and cooling time 

for 5 wt% 235U initial enrichment ..........................................................................23

Table 12. Individual components of the reduction in keff as a function of burnup and 

cooling time for fuel of 2 wt% 235U initial enrichment............................................24

Table 13. Individual components of the reduction in keff as a function of burnup and 

cooling time for fuel of 3 wt% 235U initial enrichment............................................25

Table 14. Individual components of the reduction in keff as a function of burnup and 

cooling time for fuel in 4 wt% 235U initial enrichment ............................................26

Table 15. Individual components of the reduction in keff as a function of burnup and 

cooling time for fuel of 5 wt% 235U initial enrichment............................................27

Table 16. Normalized axial burnup distributions used for benchmark problem† ...................31

Table 17. keff and Δk values using axial burnup profiles with and without axial blankets 

as a function of burnup for fuel with 2 wt% 235U initial enrichment and a 

5-year cooling time ..............................................................................................32

Table 18. keff and Δk values using axial burnup profiles with and without axial blankets 

as a function of burnup for fuel with 3 wt% 235U initial enrichment and a 

5-year cooling time ..............................................................................................33

Table 19. keff and Δk values using axial burnup profiles with and without axial blankets 

as a function of burnup for fuel with 4 wt% 235U initial enrichment and a 

5-year cooling time ..............................................................................................34
x

Table 20. keff and Δk values using axial burnup profiles with and without axial blankets 

as a function of burnup for fuel with 5 wt% 235U initial enrichment and a 

5-year cooling time ..............................................................................................35

Table 21. Axially dependent design of LaSalle Unit 1 assembly B2.....................................36

Table D.1. Nuclide sets defined for the benchmark problem analysis .................................D-3

Table D.2. Nuclides in "set 3," on which the additional reactivity margin available from 

fission products and minor actinides is based....................................................D-3

Table E.1. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, zero cooling time and various burnups......................................................E-1

Table E.2. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 5-year cooling time and various burnups...................................................E-2

Table E.3. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt%, 

235U, 10-year cooling time and various burnups.................................................E-3

Table E.4. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 20-year cooling time and various burnups.................................................E-4

Table E.5. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 40-year cooling time and various burnups.................................................E-5
xi

ACKNOWLEDGMENTS

This work was performed under contract with the Office of Nuclear Regulatory Research, U.S. 

Nuclear Regulatory Commission (NRC). The authors thank M. Aissa, the NRC Project Manager, 

D. R. Algama and R. Y. Lee of the Office of Nuclear Research (RES), T. T. Nakanishi and K. A. 

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

Nuclear Material Safety and Safeguards (NMSS) for their support and guidance. The authors 

acknowledge W. J. Marshall of ORNL for computational support. The careful reviews of the draft 

manuscript by W. J. Marshall and G. Radulescu are very much appreciated. Finally, the authors 

are thankful to A. C. Alford for her preparation of the final report.

xiii

ACRONYMS

ANS: American Nuclear Society

ANSI: American National Standards Institute

BUC: burnup credit

BWR: boiling water reactor

CRC: commercial reactor critical

DOE: U.S. Department of Energy

FP: fission product

GBC generic burnup credit cask

Gd: gadolinium

GWd/MTU: unit of nuclear fuel burnup; gigawatt-days per initial metric ton of uranium

ISG: interim staff guidance

LWR: light water reactor

NRC: U.S. Nuclear Regulatory Commission

ORNL: Oak Ridge National Laboratory

PWR: pressurized water reactor

SNF: spent nuclear fuel

1

1. INTRODUCTION

This report develops and documents a computational benchmark for the estimation of the 

additional reactivity margin available from fission products and minor actinides, relative to 

calculations based on major actinides only, in a boiling water reactor (BWR) burnup-credit 

storage/transport environment. Relevant reference configurations for baseline and comparative 

analyses are provided, similar to what was developed for pressurized water reactor (PWR) fuel

in NUREG/CR-6747 [1]. Herein, the major actinides are consistent with those specified in 

NUREG/CR-6747 (i.e., 234U, 235U, 238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, and 241Am). Although 

additional reactivity margin is primarily due to fission products, a few minor actinides (236U, 

237Np, and 243Am) that have been identified as being relevant to burnup credit [2] have been 

included in this benchmark to provide a more complete assessment of the additional reactivity 

margin beyond the major actinides. The proposed benchmark problem was developed to be 

similar to current burnup-credit-style casks, including similar materials and dimensions. While 

preserving all of the important features, it approximates (or eliminates) nonessential details and 

proprietary information. The documentation of this computational benchmark includes all of the 

necessary geometric and material specifications to permit independent evaluations and 

sufficiently detailed reference solutions to enable meaningful comparisons. Select isotopic 

compositions are provided to facilitate comparisons. The reference solutions were generated 

with depletion (TRITON and ORIGEN-ARP) and criticality (STARBUCS and CSAS5) sequences 

of the SCALE 6.1 package [3] and the SCALE 238-group library based on ENDF/B-VII.0 nuclear 

data. It is important that the reader and potential users of this report understand that this is a 

computational benchmark, and as such, the reference solutions are based on calculations. 

Although the CSAS5 and TRITON sequences have been validated using laboratory critical 

experiments, commercial reactor criticals (CRCs), measured radiochemical assay data, and 

reactivity worth measurements with individual fission products important to burnup credit, the 

reference solutions provided herein are not directly or indirectly based on experimental results.

1.1 PURPOSE

The purpose of this computational benchmark is to provide a reference configuration to help 

establish a method for the estimation of reactivity margin available from fission products and 

minor actinides, and document estimates of the additional reactivity margin as a function of 

initial enrichment, burnup, and cooling time. Estimates of the additional reactivity margin for this 

reference configuration may be compared to those of similar burnup-credit-style casks to 

provide an indication of the validity of design-specific estimates of the additional reactivity 

margin. Detailed geometry and material specifications are provided to enable independent 

estimations and comparisons. As reference solutions are provided in terms of differences in 

effective neutron multiplication factors (Δk values), benchmarking of depletion and criticality 

codes, individually, is not the intent. Comparison of calculated results to the reference solutions 

does not satisfy the ANSI/ANS 8.1 (Section 4.3 of Ref. 4), ANSI/ANS 8.24 (Section 6 of Ref. 5),

and ANSI/ANS-8.27 (Section 5 of Ref. 6) requirements for validation of calculational methods. 

In particular, footnote 11 of ANSI/ANS 8.1 states that validation of a calculational method by 

comparing the results with those of another calculational method is unacceptable. 

Consequently, this computational benchmark is not intended to be used to establish biases for 

burnup-credit analyses.

The computational benchmark model described in this report is presented for use as a 

reference model for sensitivity study calculations to quantify potential impacts on the calculated 
2

system keff values. Additional sensitivity studies, to be documented in a companion report, will 

explore the effects of varying reactor depletion parameters and burnup-credit analysis modeling 

approximations.

1.2 BACKGROUND

In the past, some criticality safety analyses for commercial light-water reactor (LWR) spent fuel 

storage and transport canisters [7,8] have assumed the SNF to be fresh (unirradiated) fuel with 

uniform isotopic compositions corresponding to the maximum allowable enrichment. This “freshfuel assumption” generally provides a well-defined, bounding approach for the criticality safety 

analysis that eliminates concerns related to the fuel operating history, and thus considerably 

simplifies the safety analysis. However, because this assumption ignores the decrease in fuel 

reactivity due to irradiation, it is very conservative and can limit the SNF capacity for a given 

package volume.

The concept of taking credit for the reduction in reactivity due to fuel burnup is commonly 

referred to as burnup credit. The reduction in reactivity due to fuel burnup is caused by the 

change in concentration (net reduction) of fissile nuclides and the production of actinide and 

fission-product neutron absorbers. If criticality calculations are performed based on all fissile 

nuclides and a limited subset of absorber nuclides present in the burned fuel, the calculated 

neutron multiplication factor (keff ) is less than the calculated keff value using the fresh fuel 

assumption but remains conservative (i.e., keff is overestimated), because some absorber 

nuclides are omitted. The typical approach for burnup credit in storage and transportation casks 

has been to qualify calculated isotopic predictions via validation against destructive assay 

measurements from SNF samples. Thus, utilization of nuclides in a safety analysis process has 

been primarily limited by the availability of measured assay data. An additional consideration 

has been the chemical characteristics (e.g., volatility) that could potentially allow the nuclide to 

escape the fuel region.

Numerous studies have been performed nationally and internationally to develop a detailed 

understanding of the issues and phenomena associated with PWR burnup credit. The findings

from these studies have supported the allowance of burnup credit for PWR fuel in transportation 

and storage casks. Although some studies have been performed [9, 10, 11] to support burnup 

credit for BWR fuel, the issues and phenomena have not been addressed in a thorough and

systematic manner for relevant dry cask storage and transport systems as has been done for 

PWR fuel. This has been due in part to the complexity in modeling and analysis of BWR SNF 

caused by radial and axial variations in fuel enrichment, extensive use of fuel rods that also 

contain Gd2O3 as a burnable absorber, and significant axial moderator density variation due to a 

combination of two-phase flow and varying core flow. However, current conditions have caused 

the industry to consider burnup-credit applications for BWR SNF. This report is part of a larger 

effort to establish the requisite technical basis for allowance of burnup credit for BWR fuel in 

storage and transportation casks. The computational benchmark defined in this report provides 

a framework for future studies into the issues associated with implementation of burnup credit 

for BWR fuel. 
3

1.3 REGULATORY GUIDANCE

The NRC issued Interim Staff Guidance 8 (ISG-8), Revision 0 [12] “Limited Burnup Credit” in 

May 1999, providing the first allowance of burnup credit for PWR fuel. Based on technical work 

performed at ORNL and elsewhere, ISG-8 has undergone two revisions, which have eliminated 

or lessened a number of the restrictions present in ISG-8, Revision 0. However, ISG-8 is 

specific to PWR fuel in transportation and storage casks, and no such similar guidance 

permitting burnup credit for BWR fuel in storage and transport casks has been developed. The 

regulatory standard review plans for dry cask storage [7] and transport [8] do not allow credit for 

BWR fuel burnup or fixed burnable absorbers. Relevant excerpts from NUREG-1617 include the 

following: “For BWR fuel assemblies, NRC staff does not currently allow any credit for burnup of 

the fissile material or increase in actinide or fission product poisons during irradiation; therefore, 

the enrichment should be that of the un-irradiated fuel” and “because of differences in net 

reactivity due to depletion of fissile material and burnable poisons, no credit should be taken for 

burnable poisons in the fuel.”

5

2. BENCHMARK SPECIFICATION

To provide a reference burnup-credit-style cask configuration that is not constrained by 

unnecessary detail or proprietary information, a generic 68 BWR-assembly burnup-credit cask 

design was developed. This generic cask design is proposed as a reference configuration to 

normalize analyses and estimations of the additional reactivity margin available from fission 

product and minor actinide nuclides. A physical description of the generic burnup-credit (GBC) 

cask, referred to herein as the GBC-68 cask, is provided in this section. Reference fuel 

assembly dimensions, corresponding to a 10×10 BWR fuel assembly design, are also provided 

in this section. 

2.1 GBC-68 CASK SPECIFICATION

The primary motivation for burnup credit is to increase storage and transportation cask 

capacities for a constant canister volume. A variety of BWR dry-storage casks are available 

from different vendors with significant variation in capacity (44 to 89 BWR fuel assemblies). 

They also vary in dimensionality and incorporate different attributes to account for design 

objectives. However, a common feature is the use of neutron absorber panels between fuel 

assembly basket cells. A basic space optimization study was conducted by Bahney and Doering 

[13] to evaluate assembly capacity versus amount of free volume space. Based on this 

assessment, 68-assembly and the 89-assembly capacity configurations had the least amount of 

space wasted, 24.5% and 21.6%, respectively. From a criticality perspective, having 68 

assemblies or 89 assemblies represented will have little impact on the neutron leakage rate;

consequently, the smaller 68-capacity configuration was selected for the generic cask design. 

The physical dimensions for the generic cask design are provided in Table 1 with material 

compositions provided in Table 2.
6

Table 1. Physical dimensions for the GBC-68 cask

Parameter inches cm

Cell inside dimension 5.9226 15.0435

Cell outside dimension 6.5132 16.5435

Cell wall (stainless steel 304) thickness 0.2953 0.75

Boral panel, overall thickness† 0.1010 0.2565

Boral panel, B4C/Al thickness 0.0810 0.2057

Boral panel, Al plate thickness, 2 per 

panel 0.0100 0.0254

Cell pitch 6.6142 16.80

Cell height‡ 150.0 381.0

BoralTM panel height 150.0 381.0

Cask inside diameter 68.8976 175.0

Cask outside diameter 84.6457 215.0

Cask wall (stainless steel 304) radial 

thickness 7.8740 20.0

Cask base plate thickness 11.8110 30.0

Cask lid thickness 7.8740 20.0

Cask inside height 161.7165 410.76

Active fuel height 150.0 381.0

Bottom assembly hardware length‡‡ 5.9055 15.0

Top assembly hardware length‡‡ 5.8110 14.76

† BoralTM is a clad composite of aluminum and boron carbide. A Boral panel or plate 

consists of three distinct layers. The outer layers are aluminum cladding, which form a 

sandwich with a central layer of uniform aggregate of fine boron carbide particles with 

an aluminum alloy matrix.

‡ The cell height, Boral panel height, and active fuel height are all equivalent and their 

lower boundaries are coincident, 15 cm above the base plate. The 381 cm value is 

from the LaSalle Unit 1 reactor and was used to facilitate use of publicly available 

commercial reactor critical data [14] in sensitivity studies that are planned to be 

presented in a future report.

‡‡ Top and bottom hardware is not modeled. This axial zone is modeled as water.
7

Table 2. Material compositions for the GBC-68 cask model

Isotope Atom density 

(atoms/b-cm) Weight percent

Water (Density = 0.99821 g/cm3) [3]

Hydrogen 6.6753 × 10-2 11.19

Oxygen 3.3377 × 10-2 88.81

Total 1.0013 × 10-1 100.0

Stainless steel 304 (Density 7.94 g/cm3) [3]

Carbon 3.1849 × 10-4 0.08

Silicon 1.7025 × 10-3 1.0

Phosphorus 6.9469 × 10-5 0.045

Chromium 1.7472 × 10-2 19.0

Manganese 1.7407 × 10-3 2.0

Iron 5.8546 × 10-2 68.375

Nickel 7.7402 × 10-3 9.5

Total 8.7589 × 10-2 100.0

Boral panel aluminum cladding (density = 2.6972 g/cm3)

Aluminum (Al) 6.0200 × 10-2 [15] 100.0

Boral panel central layer (0.0200 g 10B/cm2)

Boron-10 5.8465 × 10-3 3.55

Boron-11 2.3532 × 10-2 15.70

Carbon 7.3447 × 10-3 5.35

Aluminum 4.6120 × 10-2 75.41

Total 8.2843 × 10-2 100.0

2.2 BWR FUEL ASSEMBLY SPECIFICATIONS

BWR fuel assembly lattices have considerable variability. BWRs have used a variety of array 

configurations including 6 × 6, 7 × 7, 8 × 8, 9 × 9, and 10 × 10, as well as a quad design with an 

internal “water cross” feature. Within each of these different lattice configurations there are other 

design features, including differences in numbers and placement of water rods, numbers and 

placement of gadolinium fuel rods, Gd2O3 content of gadolinium fuel rods, radial and axial

variation of 235U enrichments, use of part-length fuel rods, and the use of axial blankets. Each of 

these design features in conjunction with different reactor operating strategies will impact fuel 

assembly residual reactivity at discharge. Many BWR plants have a variety of lattice designs 

currently stored on-site, which provides an additional complexity to criticality safety evaluations 

for spent fuel storage and transportation. 

For the GBC-68 benchmark model, a simplified BWR assembly design was adopted. The 

design, similar to a GE14 lattice, utilizes a 10 × 10 lattice in which eight of the fuel rods have 

been replaced with two large water rods. The base GBC-68 model uses the same initial 235U 
8

enrichment for all fuel rods and does not include gadolinium fuel rods or part-length fuel rods or 

axial blankets. Evaluation of the impact of these simplifications may be performed in future 

studies. 

Fuel assembly geometry information used in the GBC-68 benchmark model is presented in

Table 3. With the exception of the active fuel length and fuel channel dimensions, fuel assembly 

dimensional information was taken from Table D1.A.3 in the SCALE 6.1 manual [3] for the 

GE14 assembly design. The active fuel length and fuel channel dimensions from the LaSalle 

Unit 1 CRC data [14] were used, because sensitivity studies based on the LaSalle CRC data 

are planned for future work. The initial (fresh) fuel assembly material composition data are

provided in Table 4, where the UO2 density used is 96% of the UO2 theoretical maximum 

density (10.96 g/cm3

) [3]. 

Table 3. BWR fuel assembly specification

Parameter inches cm

Fuel pellet outside diameter 0.3449 0.876

Cladding inside diameter 0.3520 0.894

Cladding outside diameter 0.4039 1.026

Cladding thickness 0.0260 0.066

Fuel rod pitch 0.5098 1.295

Water rod inside diameter 0.9138 2.321

Water rod outside diameter 0.9925 2.521

Water rod radial thickness 0.0394 0.100

Active fuel length 150.0 381.0

Array size 10 × 10

Number of fuel rods 92

Number of water rods 2

Fuel channel inner dimension 5.278 13.406

Fuel channel outer dimension 5.478 13.914

Fuel channel thickness 0.100 0.2540

 
9

Table 4. Initial material compositions for the unburned fuel assemblies

Components

Atom density 

(atoms/b-cm) Weight percent

Fuel rod clad, water rod, and fuel channel (density = 6.41 g/cm3)

Zirconium 4.2300 × 10-2[15] 100.0

UO2, 2 wt% 235U initial enrichment (density = 10.5216 g/cm3)

Oxygen 4.6939 × 10-2 11.8490

234U 4.2480 × 10-6 0.0157

235U 4.7527 × 10-4 1.7630

236U 2.1770 × 10-6 0.0081

238U 2.2988 × 10-2 86.3642

Total 7.0408 × 10-2 100.0

UO2, 3 wt% 235U initial enrichment (density = 10.5216 g/cm3)

Oxygen 4.6944 × 10-2 11.8504

234U 6.3720 × 10-6 0.0235

235U 7.1290 × 10-4 2.6445

236U 3.2654 × 10-6 0.0122

238U 2.2750 × 10-2 85.4694

Total 7.0416 × 10-2 100.0

UO2, 4 wt% 235U initial enrichment (density = 10.5216 g/cm3)

Oxygen 4.6950 × 10-2 11.8517

234U 8.4958 × 10-6 0.0314

235U 9.5051 × 10-4 3.5259

236U 4.3538 × 10-6 0.0162

238U 2.2512 × 10-2 84.5748

Total 7.0425 × 10-2 100.0

UO2, 5 wt% 235U initial enrichment (density = 10.5216 g/cm3)

Oxygen 4.6955 × 10-2 11.8531

234U 1.0620 × 10-5 0.0392

235U 1.1881 × 10-3 4.4073

236U 5.4422 × 10-6 0.0203

238U 2.2273 × 10-2 83.6801

Total 7.0432 × 10-2 100.0

11

3. ANALYSIS

3.1 COMPUTATIONAL METHODS

The computational methods necessary for this benchmark analysis include codes for fuel 

depletion and criticality simulation. All calculations were performed using the publicly released 

version of SCALE 6.1[3] and the ENDF/B-VII 238 neutron energy group library distributed with 

SCALE 6.1.

Depletion calculations were performed using the STARBUCS sequence and ORIGEN-ARP 

libraries generated using the TRITON T-DEPL 2-D lattice depletion sequence, which utilizes the 

NEWT module for flux calculations and the ORIGEN module to calculate burned fuel 

compositions. New ORIGEN-ARP libraries were generated for the generic 10 x 10 assembly for 

use in the GBC-68 benchmark model. New libraries were needed, because the GE14 ORIGENARP libraries distributed with SCALE included some fuel rods with Gd2O3 and the existing 

libraries were generated without control blades being inserted. The GE14 lattice was depleted in 

TRITON with the control blades fully inserted for the entire depletion. To create the ORIGENARP libraries used by STARBUCS, depletion calculations were performed with initial 

enrichments varying from 1.5 to 6 wt% 235U, with moderator densities varying from 0.1 to 0.8 

g/cm3

, and for fuel assembly average burnup values up to 88.5 GWd/MTU. The parameters 

used in the TRITON depletion model are provided in Table 5, and the fuel depletion model is 

shown in Figure 1. The depletion parameters used are generally consistent with the parameters 

used to generate the GE14 ORIGEN-ARP library distributed with SCALE 6.1 and are 

considered representative of average conditions fuel might experience during irradiation. These 

TRITON calculations produced ORIGEN-ARP libraries for initial enrichments between 1.5 and 6 

wt % 235U and burnup values up to 88.5 GWd/MTU. These libraries were used in STARBUCS 

calculations, for determining the nuclide concentrations in the burned fuel used in the GBC-68 

model. Assembly average burnup values up to 60 GWd/MTU were used for the actinide and 

fission product reactivity margin calculations. The maximum assembly average burnup value 

for the non-uniform axial burnup case described in Section 3.3.3 was 79 GWd/MTU.

Table 5. Fuel depletion parameters

Parameter Value

Pellet average fuel temperature (K) 840

Pellet average power density (MW/MTU) 40

Clad average temperature (K) 567

Moderator temperature (K) 512

Moderator density (g/cm3)

Water around fuel rods 0.1 to 0.8

Water inside water rod 0.776

Water between channels 0.776

A 512 K moderator temperature was used during the depletion calculations that generated the 

new ORIGEN-ARP libraries to be consistent with the conditions used to generate the GE14 

ORIGEN-ARP libraries distributed with SCALE 6.1. This moderator temperature is low for a 

BWR operating around 1030 psia where Tsat is about 560 K. However, the moderator 
12

temperature has only a minor impact on the depletion calculations because the water density, 

which has the primary impact on the flux spectrum, is modeled explicitly and independent of the

moderator temperature. The moderator temperature variation has only a minor impact through 

temperature-dependent adjustments to the scattering cross sections.

Figure 1. TRITON depletion model used to generate the rodded ORIGEN-ARP libraries.

The STARBUCS sequence automates calculation of burned fuel compositions using the 

ORIGEN-ARP methodology to perform a series of cross-section preparation and depletion 

calculations to generate a comprehensive set of spent fuel isotopic inventories for each burnup 

region of an assembly. The spent fuel nuclide concentrations are subsequently input to CSAS5, 

which performs a KENO V.a criticality calculation of the GBC-68 model to determine the neutron 
13

multiplication factor (keff) for the system. The user can specify the assembly-average irradiation 

history, the axial variation of the moderator density, axial and horizontal-burnup profiles, and the 

nuclides that are to be applied in the criticality safety analysis. Nuclide correction factors may 

also be applied to the predicted concentrations to account for known bias and/or uncertainty in 

the predicted SNF compositions. Nuclide correction factors and horizontal burnup gradients

were not used for the GBC-68 calculations.

The STARBUCS sequence was used when it was necessary to calculate burned fuel 

compositions. The CSAS5 sequence was used when burned fuel compositions were already 

available from a previously performed STARBUCS calculation. All criticality calculations 

performed to determine keff used 11,000 neutrons per generation and skipped the first 

100 generations. Calculations were run until the standard deviation on the average keff value 

reached 0.0001 ∆k. This criterion resulted in 20 to 80 million individual neutron histories for 

each criticality calculation, with an average of 44 million neutron histories per KENO V.a 

calculation.

Example input files for the TRITON, STARBUCS, and CSAS5 calculations are provided in 

Appendices A, B, and C, respectively. 

3.2 GBC-68 COMPUTATIONAL MODEL

Based on the benchmark specification provided in Section 2, a computational model of the 

GBC-68 cask, loaded with BWR fuel assemblies, was developed for KENO V.a. Cross-sectional 

views of the computational model are shown in Figure 2 and Figure 3. A 3-D cutaway view,

generated by KENO3D, is shown in Figure 4. To aid users of this proposed benchmark in 

verification of their criticality models, calculated keff values corresponding to fresh fuel without 

axial or radial enrichment variation and without gadolinium fuel rods are provided in the next 

section for initial enrichments of 2, 3, 4 and 5 wt% 235U.

The active fuel length of the assemblies is divided into 25 equal-length axial regions to facilitate 

the variation in axial composition due to the axial burnup distribution, which will be considered 

later in this report. The reference calculations were performed with a uniform axial burnup 

profile. Calculations using more realistic burnup profiles were also performed and are discussed 

later in this report.

For the criticality calculations, it is necessary to define the isotopes considered. Many studies 

have been performed to rank the reactivity worth of the actinide and fission product nuclides. 

Based on these analyses, Ref. 2 lists “prime candidates” for inclusion in burnup-credit analyses 

related to dry storage and transport, including several nuclides for which measured chemical 

assay data are not currently available in the United States. Cross-section data are generally 

available for all nuclides identified in Ref. 2 as being the most important for burnup-credit 

criticality calculations. Therefore, in this benchmark, all of the actinide and fission product 

nuclides identified in Ref. 2, including those for which little or no chemical assay data are 

available, are used in the estimation of the additional reactivity margin. 

The two “nuclide sets” used here for the estimation of the additional reactivity margin are listed 

in Table 6. The first set, which corresponds to the major actinides specified in a DOE topical 

report [16], is used for the reference actinide-only calculations. The second set includes all of 

the actinide and fission product nuclides identified in Ref. 2 as being important for burnup credit 

criticality calculations; the first set is a subset of the second set. These nuclide sets are 
14

consistent with those used in NUREG/CR-6747[1], NUREG/CR-7108[17], and NUREG/CR7109[18]. 

For the purpose of this benchmark report and the cited results, the additional reactivity margin 

available from fission products and minor actinides is due to the nuclides that are exclusive to 

the second set. These “additional nuclides,” which are exclusive to the second set, are listed in 

Table 7 for clarity and are designated as “set 3.” Throughout this report, where reference is 

made to the additional reactivity margin due to the additional actinide and fission product 

nuclides, the additional reactivity margin is due to the nuclides listed in Table 6.

Finally, it should be noted that these “nuclide sets” are defined for the purposes of this analysis 

only; other terminology and specific sets of nuclides have been defined and used by individuals 

studying burnup-credit phenomena. 
15

Figure 2. Radial cross section of the GBC-68 model with 

reflective left boundary condition.
16

Figure 3. Cross-sectional view of assembly cell in GBC-68 model.
17

Figure 4. Cutaway view of bottom part GBC-68 model. Poison panel and cell walls 

removed to reveal fuel assembly axial zoning. Note that the reference cases 

utilized a single axial zone.
18

Table 6. Nuclide sets defined for the benchmark problem analysis

Set 1: Major actinides (9 total)

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

Set 2: Actinides and major fission products (28 total)

234U 235U 236U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 241Am

243Am 237Np 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm

150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd O+

+

Oxygen is neither an actinide nor a fission product, but is included in this list because it is 

included in the calculations.

Table 7. Nuclides in "set 3," on which the additional reactivity margin 

available from fission products and minor actinides is based

Set 3: Minor actinides and major fission products (19 total)

236U 243Am 237Np 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm

149Sm 150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd

3.3 RESULTS

Results for the computational benchmark are presented in this section. Based on the nuclide 

sets identified in the previous section, calculated keff values are provided as a function of initial 

enrichment, burnup, and cooling times, within the ranges relevant to storage and transportation. 

A rather large volume of results is included for completeness. It is not anticipated that users of 

this benchmark problem will attempt to reproduce the complete set of results, but rather 

compare to a subset of the reference results that are relevant to their application.

3.3.1 Reference Results

Calculated keff values for the GBC-68 cask as a function of burnup and cooling time for initial 

enrichments of 2, 3, 4, and 5 wt % 235U are listed in Tables 8 through 11. Values are provided 

for the burnup range of 0 to 60 GWd/MTU, in increments of 10 GWd/MTU, and for postirradiation cooling times of 0, 5, 10, 20, and 40 years. The keff values were calculated with a 

uniform axial burnup profile and a moderator density value of 0.6 g/cm3

. Control blades were 

present (i.e., fully inserted for the entire depletion) in ORIGEN-ARP calculations to generate 

nuclide concentrations based on the initial fuel enrichment, assembly burnup, and cooling time 

values. Standard deviations for all calculated keff values were approximately 0.00010. 

The individual components of reduction in keff (∆k), relative to fresh fuel, associated with (a) the 

major actinides and (b) the additional nuclides as a function of burnup and cooling time are 

listed in Tables 12 through 15 for each initial fuel enrichment. The second column from the left 

in Tables 12 through 15 lists the ∆k reductions due to the presence of the major actinides alone 

(nuclide set 1, see Table 6), while the third column lists the ∆k reduction due to the presence of 
19

the fission products and additional actinides (i.e., due to the nuclides present in set 3, see Table 

7). Thus, the results listed in the third column may be interpreted as the additional ∆k margin 

associated with the fission products and additional actinides. The fourth column from the left in 

Table 12 through Table 15 lists the total ∆k reduction as a function of burnup for the cooling 

times considered. Finally, the two columns on the right-hand side of the table list the percent 

contributions from the two sets of nuclides to the total ∆k reduction, and thus provide an 

assessment of the reactivity reduction, relative to fresh fuel, associated with (a) the major 

actinides and (b) the fission products and additional nuclides.

When associating practical meaning to these results, it is important that the reader and potential 

users of this report understand that this is a computational benchmark, and as such, the 

reference solutions are based on calculations alone (e.g., no isotopic correction factors are 

applied). The reference solutions are not directly or indirectly based on experimental results. 

However, note that the computational tools used to generate the reference solutions have been 

validated elsewhere [18,19].

As noted above, the reference results presented in Tables 8 through 15 are for a uniform axial 

burnup profile. Because conservative axial burnup profiles are not available, the reference 

results were generated using a uniform axial profile. Future BWR burnup-credit work should 

include identification of conservative axial burnup profiles and generation of reference results 

using those axial burnup profiles.

In addition to the uniform axial burnup distribution simplification, the computational benchmark 

uses a uniform axial moderator density for simplification. This is necessary because, as with 

axial burnup distribution data, very little work has been done to collect and evaluate realistic 

axial moderator density profiles. The potential impact of varying the average moderator density 

and of modeling the axial distribution of moderator density will be addressed in future reports 

designed to improve the bases for BWR burnup credit.
20

Table 8. keff values for the GBC-68 cask as a function of burnup 

 and cooling time for 2 wt% 235U initial enrichment

Major actinides (nuclide set 1, see Table 6)

Cooling time 

(years) 0 5 10 20 40

Burnup 

(GWd/MTU) keff values*

0 0.77303 0.77303 0.77303 0.77303 0.77303

10 0.73639 0.73359 0.72996 0.72497 0.71992

20 0.69217 0.68232 0.67262 0.65872 0.64533

30 0.65632 0.64069 0.62630 0.60585 0.58546

40 0.63322 0.61353 0.59593 0.57068 0.54558

50 0.62082 0.59861 0.57869 0.55013 0.52179

60 0.61586 0.59202 0.57074 0.54020 0.50961

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.77303 0.77303 0.77303 0.77303 0.77303

10 0.71181 0.70289 0.69840 0.69294 0.68785

20 0.65391 0.63560 0.62443 0.60999 0.59692

30 0.60817 0.58227 0.56553 0.54450 0.52542

40 0.57756 0.54625 0.52593 0.50049 0.47721

50 0.55906 0.52400 0.50148 0.47350 0.44795

60 0.54892 0.51158 0.48744 0.45796 0.43106

*Standard deviation is approximately 0.0001 for all calculations
21

Table 9. keff values for the GB C-68 cask as a function of burnup 

and cooling time for 3 wt% 235U initial enrichment

Major actinides (nuclide set 1, see Table 6)

Cooling time 

(years) 0 5 10 20 40

Burnup 

(GWd/MTU) keff values*

0 0.87624 0.87624 0.87624 0.87624 0.87624

10 0.83454 0.83328 0.83126 0.82834 0.82561

20 0.78600 0.77877 0.77195 0.76254 0.75363

30 0.73777 0.72498 0.71356 0.69780 0.68231

40 0.69550 0.67821 0.66285 0.64136 0.62023

50 0.66306 0.64214 0.62399 0.59806 0.57272

60 0.64214 0.61908 0.59889 0.56996 0.54121

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.87624 0.87624 0.87624 0.87624 0.87624

10 0.80845 0.80168 0.79866 0.79567 0.79257

20 0.74503 0.73009 0.72216 0.71203 0.70338

30 0.68519 0.66292 0.64963 0.63293 0.61818

40 0.63456 0.60594 0.58834 0.56607 0.54628

50 0.59618 0.56272 0.54182 0.51586 0.49255

60 0.57056 0.53422 0.51108 0.48283 0.45724

*Standard deviation is approximately 0.0001 for all calculations
22

Table 10. keff values for the GBC-68 cask as a function of burnup 

and cooling time for 4 wt% 235U initial enrichment

Major actinides (nuclide set 1, see Table 6)

Cooling time 

(years) 0 5 10 20 40

Burnup 

(GWd/MTU) keff values*

0 0.94283 0.94283 0.94283 0.94283 0.94283

10 0.90466 0.90380 0.90241 0.90076 0.89892

20 0.86015 0.85491 0.85023 0.84382 0.83729

30 0.81393 0.80387 0.79532 0.78323 0.77161

40 0.76734 0.75282 0.74028 0.72273 0.70570

50 0.72381 0.70533 0.68951 0.66723 0.64547

60 0.68789 0.66636 0.64755 0.62129 0.59546

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.94283 0.94283 0.94283 0.94283 0.94283

10 0.87755 0.87177 0.86989 0.86774 0.86614

20 0.81780 0.80611 0.80031 0.79316 0.78722

30 0.75899 0.74066 0.73015 0.71734 0.70591

40 0.70263 0.67746 0.66269 0.64438 0.62793

50 0.65165 0.62134 0.60230 0.57965 0.55930

60 0.61060 0.57592 0.55452 0.52822 0.50466

*Standard deviation is approximately 0.0001 for all calculations
23

Table 11. keff values for the GBC-68 cask as a function of burnup 

and cooling time for 5 wt% 235U initial enrichment

Major actinides (nuclide set 1, see Table 6)

Cooling time 

(years) 0 5 10 20 40

Burnup 

(GWd/MTU) keff values*

0 0.99048 0.99048 0.99048 0.99048 0.99048

10 0.95634 0.95594 0.95486 0.95384 0.95284

20 0.91693 0.91296 0.90967 0.90472 0.90017

30 0.87603 0.86791 0.86112 0.85196 0.84290

40 0.83235 0.82040 0.81035 0.79646 0.78269

50 0.78825 0.77202 0.75854 0.74015 0.72182

60 0.74533 0.72573 0.70932 0.68665 0.66397

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.99048 0.99048 0.99048 0.99048 0.99048

10 0.92921 0.92403 0.92260 0.92110 0.92015

20 0.87425 0.86466 0.85996 0.85476 0.85022

30 0.82004 0.80458 0.79646 0.78634 0.77752

40 0.76554 0.74412 0.73199 0.71679 0.70370

50 0.71246 0.68544 0.66915 0.64965 0.63246

60 0.66326 0.63115 0.61182 0.58828 0.56737

*Standard deviation is approximately 0.0001 for all calculations
24

Table 12. Individual components of the reduction in keff as a function of burnup

and cooling time for fuel of 2 wt% 235U initial enrichment

Δk values due to the various nuclide sets Contribution (%) to total 

reduction in keff 

Burnup 

(GWd/MTU)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

Total 

(set 2)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

0-year cooling time

10 0.03664 0.02458 0.06122 59.84 40.16

20 0.08085 0.03827 0.11912 67.88 32.12

30 0.11670 0.04815 0.16485 70.79 29.21

40 0.13980 0.05567 0.19547 71.52 28.48

50 0.15221 0.06175 0.21396 71.14 28.86

60 0.15717 0.06694 0.22411 70.13 29.87

5-year cooling time

10 0.03943 0.03070 0.07013 56.23 43.77

20 0.09071 0.04672 0.13743 66.00 34.00

30 0.13234 0.05842 0.19076 69.37 30.63

40 0.15950 0.06728 0.22678 70.33 29.67

50 0.17442 0.07461 0.24903 70.04 29.96

60 0.18101 0.08043 0.26144 69.23 30.77

10-year cooling time

10 0.04306 0.03156 0.07462 57.71 42.29

20 0.10040 0.04819 0.14859 67.57 32.43

30 0.14673 0.06076 0.20750 70.72 29.28

40 0.17710 0.07000 0.24710 71.67 28.33

50 0.19434 0.07721 0.27155 71.57 28.43

60 0.20229 0.08330 0.28559 70.83 29.17

20-year cooling time

10 0.04806 0.03203 0.08009 60.01 39.99

20 0.11431 0.04872 0.16303 70.11 29.89

30 0.16717 0.06135 0.22853 73.15 26.85

40 0.20235 0.07018 0.27253 74.25 25.75

50 0.22290 0.07662 0.29952 74.42 25.58

60 0.23283 0.08224 0.31507 73.90 26.10

40-year cooling time

10 0.05310 0.03208 0.08518 62.34 37.66

20 0.12769 0.04841 0.17611 72.51 27.49

30 0.18757 0.06004 0.24761 75.75 24.25

40 0.22744 0.06837 0.29581 76.89 23.11

50 0.25124 0.07383 0.32508 77.29 22.71

60 0.26342 0.07855 0.34197 77.03 22.97
25

Table 13. Individual components of the reduction in keff as a function of burnup 

and cooling time for fuel of 3 wt% 235U initial enrichment

Δk values due to the various nuclide sets Contribution (%) to total 

reduction in keff 

Burnup 

(GWd/MTU)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

Total 

(set 2)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

0-year cooling time

10 0.04170 0.02609 0.06779 61.51 38.49

20 0.09023 0.04098 0.13121 68.77 31.23

30 0.13847 0.05257 0.19104 72.48 27.52

40 0.18074 0.06094 0.24168 74.79 25.21

50 0.21318 0.06688 0.28006 76.12 23.88

60 0.23409 0.07158 0.30568 76.58 23.42

5-year cooling time

10 0.04296 0.03159 0.07455 57.62 42.38

20 0.09746 0.04868 0.14614 66.69 33.31

30 0.15125 0.06207 0.21332 70.90 29.10

40 0.19803 0.07227 0.27030 73.26 26.74

50 0.23410 0.07942 0.31352 74.67 25.33

60 0.25716 0.08485 0.34201 75.19 24.81

10-year cooling time

10 0.04497 0.03260 0.07757 57.98 42.02

20 0.10428 0.04980 0.15408 67.68 32.32

30 0.16268 0.06393 0.22661 71.79 28.21

40 0.21339 0.07451 0.28790 74.12 25.88

50 0.25225 0.08216 0.33441 75.43 24.57

60 0.27734 0.08781 0.36515 75.95 24.05

20-year cooling time

10 0.04790 0.03267 0.08057 59.45 40.55

20 0.11369 0.05052 0.16421 69.24 30.76

30 0.17844 0.06487 0.24331 73.34 26.66

40 0.23488 0.07529 0.31017 75.73 24.27

50 0.27818 0.08219 0.36037 77.19 22.81

60 0.30628 0.08712 0.39340 77.85 22.15

40-year cooling time

10 0.05062 0.03304 0.08366 60.51 39.49

20 0.12261 0.05025 0.17285 70.93 29.07

30 0.19392 0.06413 0.25806 75.15 24.85

40 0.25600 0.07396 0.32996 77.59 22.41

50 0.30352 0.08017 0.38368 79.11 20.89

60 0.33503 0.08396 0.41899 79.96 20.04
26

Table 14. Individual components of the reduction in keff as a function of burnup 

and cooling time for fuel in 4 wt% 235U initial enrichment

Δk values due to the various nuclide sets Contribution (%) to total 

reduction in keff 

Burnup 

(GWd/MTU)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

Total 

(set 2)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

0-year cooling time

10 0.03817 0.02711 0.06527 58.48 41.52

20 0.08268 0.04235 0.12503 66.12 33.88

30 0.12890 0.05494 0.18384 70.11 29.89

40 0.17549 0.06471 0.24020 73.06 26.94

50 0.21902 0.07216 0.29118 75.22 24.78

60 0.25494 0.07729 0.33223 76.74 23.26

5-year cooling time

10 0.03903 0.03203 0.07106 54.93 45.07

20 0.08792 0.04880 0.13672 64.31 35.69

30 0.13896 0.06321 0.20217 68.73 31.27

40 0.19001 0.07535 0.26537 71.60 28.40

50 0.23750 0.08399 0.32149 73.88 26.12

60 0.27647 0.09045 0.36691 75.35 24.65

10-year cooling time

10 0.04042 0.03252 0.07294 55.42 44.58

20 0.09260 0.04992 0.14252 64.97 35.03

30 0.14751 0.06518 0.21268 69.36 30.64

40 0.20255 0.07759 0.28013 72.30 27.70

50 0.25332 0.08721 0.34053 74.39 25.61

60 0.29528 0.09302 0.38830 76.04 23.96

20-year cooling time

10 0.04207 0.03301 0.07509 56.03 43.97

20 0.09900 0.05066 0.14966 66.15 33.85

30 0.15959 0.06590 0.22549 70.78 29.22

40 0.22010 0.07836 0.29845 73.75 26.25

50 0.27560 0.08758 0.36318 75.89 24.11

60 0.32154 0.09307 0.41461 77.55 22.45

40-year cooling time

10 0.04391 0.03278 0.07669 57.25 42.75

20 0.10554 0.05007 0.15561 67.82 32.18

30 0.17122 0.06570 0.23692 72.27 27.73

40 0.23713 0.07777 0.31489 75.30 24.70

50 0.29736 0.08617 0.38353 77.53 22.47

60 0.34737 0.09080 0.43817 79.28 20.72
27

Table 15. Individual components of the reduction in keff as a function of burnup 

and cooling time for fuel of 5 wt% 235U initial enrichment

Δk values due to the various nuclide sets Contribution (%) to total 

reduction in keff 

Burnup 

(GWd/MTU)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

Total 

(set 2)

Major 

actinides 

(set 1)

Additional 

nuclides 

(set 3)

0-year cooling time

10 0.03414 0.02713 0.06127 55.72 44.28

20 0.07355 0.04268 0.11623 63.28 36.72

30 0.11445 0.05599 0.17043 67.15 32.85

40 0.15812 0.06681 0.22494 70.30 29.70

50 0.20222 0.07579 0.27801 72.74 27.26

60 0.24515 0.08206 0.32721 74.92 25.08

5-year cooling time

10 0.03454 0.03191 0.06645 51.97 48.03

20 0.07752 0.04830 0.12581 61.61 38.39

30 0.12256 0.06333 0.18589 65.93 34.07

40 0.17008 0.07628 0.24636 69.04 30.96

50 0.21845 0.08659 0.30504 71.61 28.39

60 0.26475 0.09458 0.35933 73.68 26.32

10-year cooling time

10 0.03561 0.03226 0.06788 52.47 47.53

20 0.08081 0.04972 0.13052 61.91 38.09

30 0.12936 0.06466 0.19401 66.67 33.33

40 0.18012 0.07837 0.25849 69.68 30.32

50 0.23194 0.08939 0.32133 72.18 27.82

60 0.28116 0.09750 0.37865 74.25 25.75

20-year cooling time

10 0.03663 0.03274 0.06937 52.80 47.20

20 0.08576 0.04996 0.13572 63.19 36.81

30 0.13851 0.06562 0.20414 67.85 32.15

40 0.19402 0.07967 0.27369 70.89 29.11

50 0.25032 0.09051 0.34083 73.45 26.55

60 0.30383 0.09837 0.40220 75.54 24.46

40-year cooling time

10 0.03763 0.03269 0.07033 53.51 46.49

20 0.09031 0.04995 0.14025 64.39 35.61

30 0.14757 0.06539 0.21296 69.30 30.70

40 0.20779 0.07899 0.28678 72.46 27.54

50 0.26866 0.08936 0.35801 75.04 24.96

60 0.32651 0.09660 0.42311 77.17 22.83
28

3.3.2 Related Information

Additional results and supplementary discussion, which should not be considered part of this 

computational benchmark, are available in Appendix D. Discussion of the reference results, 

including graphical representations and relevant observations, is given in Appendix D.

3.3.3 Additional Results with Non-Uniform Axial Burnup

Considerable work has been done to characterize and develop axial burnup profiles for PWR 

fuel. A review of this subject as applied to PWRs is provided in NUREG/CR-6801 [19]. For 

BWRs, assessment of the impact of axial burnup distribution is significantly more complicated 

than for PWRs because of the extensive use of axial design features such as axially varying 

235U enrichment, part-length fuel rods, axial blankets of natural uranium, and axial variation of 

initial gadolinia burnable absorber in some fuel rods. Reactor operations affect axial burnup by

the use of control blades for long-term reactivity control and the significant axial variation in 

effective moderator density, which is caused by both reduction in density due to increased 

temperature and the presence of steam voids generated by boiling. For example, in the LaSalle 

Unit 1 CRC data, the effective moderator density varies from 0.74 g/cm3 at the bottom of the 

core to 0.17 g/cm3 at the tops of some assemblies [14]. 

Due to the axially dependent complexities associated with BWR SNF and the lack of an 

established database of evaluated axial burnup distribution information for BWR fuel, the GBC68 benchmark model in Sect. 3.2 did not include axial design features or axial burnup or 

moderator density distributions. Recognizing that these issues are still relevant for BWR SNF, 

two additional series of calculations were performed to provide an example of the potential 

impact of using axial burnup distributions and of modeling natural uranium blankets. 

To demonstrate the potential effects associated with axial burnup distribution, a few calculations 

were performed with axial burnup distributions extracted from the CRC data for LaSalle Unit 1 

While it is not clear from the reference, these data were most likely inferred using a nodal code 

and Transverse Incore Probe (TIP) measurements. The 25-node burnup data for assembly ID 

B2 from Ref. 14 were used, because this assembly reached the highest assembly average 

burnup in the LaSalle Unit 1 CRC data. The axial burnup distributions used in this report are 

shown in Figure 5 and Table 16. These five profiles had assembly average burnups closest to 

the assembly average burnup values of interest.

From Figure 5, there appears to be an axial shift in the power distribution between the 10 and 

20 GWd/MTU profiles. This is likely due to control blade withdrawal near the assembly. 

Because of the extensive and long-term usage of control blades to control reactivity and power 

peaking, axial power shifts due to control blade movements are likely seen by most assemblies. 

The example provided in this section is a single sample being used to show that modeling of 

axial burnup distributions will be necessary for application of BWR burnup-credit. 

In the first series of calculations, the burnup-dependent normalized axial burnup profiles (see 

Table 16) from LaSalle Unit 1 assembly B2 were applied to the benchmark model with initial 

enrichments of 2, 3, 4, and 5 wt % 235U, burned to 10, 20, 30, 40, 50, and 60 GWd/MTU, and 

cooled for 5 years following irradiation. Note that these calculations did not include modeling of 

natural uranium blankets. The resulting keff values and the ∆k values with respect to the base 

model are provided in the middle two columns of Tables 17 through 20. The comparison 

demonstrates that the “end effect” previously seen for PWR burnup credit also exists for BWR 
29

burnup credit. Note that, as was seen for PWR burnup credit, the reactivity increases are 

significantly larger for the actinide plus fission products cases (set 2 nuclides) than for the major 

actinide only cases (set 1 nuclides). 

A description of LaSalle Unit 1 assembly B2 design is provided in Table 21. Note that only the 

axial burnup distribution data were used. No attempt was made to model the axially dependent 

enrichments, axial variation in gadolinium rod loading, or the axial dependence of the moderator 

density. Comprehensive detailed studies of the impact of such axially varying features should 

be performed, but is beyond the scope of the work presented in this report. Modeling the 

additional axial detail shown in Table 21 would not impact the general conclusion that it will be 

necessary to model axial burnup distributions for BWR BUC at middle to high burnup values. 

The actual relative burnup in the natural uranium blanket zones is significantly lower than it 

would be for unblanketed fuel. An additional series of calculations was performed with natural 

uranium blankets modeled in the two end fuel zones. These calculations provide a more realistic 

assessment of the impact of axial burnup distribution on the GBC-68 models. The results are 

provided in the two right-most columns of Tables 17 through 20. These results from the models 

with blankets show an increase in keff that is significantly smaller than the increase observed 

when a blanketed normalized assembly burnup profile is applied to unblanketed fuel. 

Note that the reactivity worth of the fission products increases with burnup and that, with the 

axial burnup distribution present, the lower burnup region near the top of the assembly controls 

the reactivity. Thus, for a given assembly-average burnup, the reactivity margin due to fission 

products will be overestimated if the axial burnup distribution is not included in the model. 

Therefore, it should be emphasized that the computational benchmark results with uniform axial 

burnup are provided to enable comparison with a simpler benchmark problem and should not be 

considered to be representative of actual reactivity margins. This modeling simplification 

reduces the volume of composition data by a factor of 25 (i.e., the number of axial regions used 

to represent the axial burnup distribution). Nuclide compositions for fuel with initial enrichment of 

4 wt % 235U at various burnup and cooling time combinations are provided in Appendix E to 

enable comparisons of calculated spent fuel compositions.

Comparison of the results within Tables 17 through 20 shows that, with the uniform axial burnup 

distribution, the calculated total reactivity reduction due to actinides and actinides with fission 

products is overestimated for burnups greater than approximately 10 GWd/MTU. Thus, for 

typical discharge burnups (30–50 GWd/MTU), the individual components of reactivity reduction 

associated with (a) the major actinides and (b) the additional nuclides are both overestimated 

with the uniform axial burnup distribution. Additionally, at the higher burnup values the keff

values calculated for the uniform axial burnup distribution appear to be significantly nonconservative.
30

Figure 5. Normalized axial burnup distributions used. These distributions are based on

data for assembly B2 from the LaSalle Unit 1 CRC data.
31

Table 16. Normalized axial burnup distributions used for benchmark problem†

Upper bound of axial region, 

measured from bottom of 

active fuel (cm)

GBC-68 assembly average burnup (GWd/MTU)

10 20 30 40 >40

15.24 0.205 0.210 0.204 0.223 0.230

30.48 0.719 0.747 0.706 0.732 0.735

45.72 0.964 1.018 0.939 0.953 0.945

60.96 1.095 1.164 1.067 1.046 1.054

76.2 1.156 1.229 1.140 1.138 1.114

91.44 1.187 1.256 1.186 1.180 1.151

106.68 1.207 1.269 1.216 1.209 1.178

121.92 1.224 1.278 1.233 1.231 1.200

137.16 1.268 1.316 1.274 1.272 1.240

152.4 1.275 1.313 1.290 1.287 1.257

167.64 1.274 1.301 1.289 1.288 1.262

182.88 1.267 1.282 1.279 1.281 1.261

198.12 1.255 1.258 1.266 1.269 1.255

213.36 1.239 1.230 1.248 1.253 1.246

228.6 1.219 1.198 1.225 1.230 1.231

243.84 1.194 1.160 1.196 1.201 1.210

259.08 1.162 1.115 1.161 1.163 1.180

274.32 1.113 1.051 1.112 1.112 1.137

289.56 1.065 0.995 1.064 1.060 1.091

304.8 1.009 0.935 1.009 1.002 1.036

320.04 0.925 0.854 0.924 0.915 0.949

335.28 0.816 0.748 0.814 0.806 0.838

350.52 0.679 0.622 0.674 0.664 0.691

365.76 0.308 0.282 0.306 0.307 0.324

381.0 0.179 0.168 0.177 0.177 0.186

Assembly B2 average 

burnup (GWd/MTU) 6.9 19.0 28.9 39.4 44.3

† Calculated using axial burnup information for LaSalle Unit 1 assembly B2 [14].
32

Table 17. keff and Δk values using axial burnup profiles with and without axial 

blankets as a function of burnup for fuel with 2 wt% 235U initial enrichment 

and a 5-year cooling time

Axial model

1 axial zone, 

no blankets

25 axial zones,

no blankets

25 axial zones,

with blankets

Burnup 

(GWd/MTU)

keff value* keff value* ∆k from 1 

axial zone keff value* ∆k from 1 axial zone

Major actinides (nuclide set 1, see Table 6)

0 0.77303 0.77303 0.00000 0.77280 -0.00023

10 0.73359 0.73443 0.00083 0.73020 -0.00339

20 0.68232 0.70575 0.02343 0.69352 0.01120

30 0.64069 0.67723 0.03654 0.65515 0.01446

40 0.61353 0.65838 0.04485 0.63174 0.01821

50 0.59861 0.63940 0.04080 0.61071 0.01210

60 0.59202 0.62591 0.03389 0.59854 0.00652

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.77303 0.77303 0.00000 0.77280 -0.00023

10 0.70289 0.71071 0.00781 0.70272 -0.00018

20 0.63560 0.67909 0.04349 0.65976 0.02416

30 0.58227 0.64667 0.06440 0.61588 0.03362

40 0.54625 0.62452 0.07827 0.58839 0.04215

50 0.52400 0.60162 0.07762 0.56190 0.03790

60 0.51158 0.58454 0.07296 0.54452 0.03294

*0.0001 ∆k Monte Carlo uncertainty for all calculations
33

Table 18. keff and Δk values using axial burnup profiles with and without axial 

blankets as a function of burnup for fuel with 3 wt% 235U initial enrichment 

and a 5-year cooling time

Axial model

1 axial zone, 

no blankets

25 axial zones,

no blankets

25 axial zones,

with blankets

Burnup 

(GWd/MTU)

keff value* keff value* ∆k from 1 

axial zone keff value* ∆k from 1 axial zone

Major actinides (nuclide set 1, see Table 6)

0 0.87624 0.87624 0.00000 0.87609 -0.00015

10 0.83328 0.83313 -0.00014 0.82807 -0.00520

20 0.77877 0.80239 0.02362 0.78843 0.00966

30 0.72498 0.77046 0.04548 0.74321 0.01822

40 0.67821 0.74872 0.07051 0.71175 0.03355

50 0.64214 0.72533 0.08319 0.67970 0.03756

60 0.61908 0.70794 0.08887 0.65706 0.03798

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.87624 0.87624 0.00000 0.87609 -0.00015

10 0.80168 0.80782 0.00614 0.79860 -0.00309

20 0.73009 0.77331 0.04321 0.75184 0.02175

30 0.66292 0.73822 0.07530 0.70063 0.03771

40 0.60594 0.71349 0.10755 0.66570 0.05977

50 0.56272 0.68704 0.12432 0.62973 0.06701

60 0.53422 0.66726 0.13304 0.60486 0.07064

*0.0001 ∆k Monte Carlo uncertainty for all calculations
34

Table 19. keff and Δk values using axial burnup profiles with and without axial 

blankets as a function of burnup for fuel with 4 wt% 235U initial enrichment 

and a 5-year cooling time

Axial model

1 axial zone, 

no blankets

25 axial zones,

no blankets

25 axial zones,

with blankets

Burnup 

(GWd/MTU)

keff value* keff value* ∆k from 1 

axial zone keff value* ∆k from 1 axial zone

Major actinides (nuclide set 1, see Table 6)

0 0.94283 0.94283 0.00000 0.94243 -0.00040

10 0.90380 0.90193 -0.00187 0.89793 -0.00587

20 0.85491 0.87243 0.01753 0.86006 0.00515

30 0.80387 0.84107 0.03720 0.81632 0.01246

40 0.75282 0.81902 0.06620 0.78376 0.03095

50 0.70533 0.79487 0.08955 0.74811 0.04278

60 0.66636 0.77667 0.11030 0.72125 0.05489

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.94283 0.94283 0.00000 0.94243 -0.00040

10 0.87177 0.87504 0.00327 0.86738 -0.00439

20 0.80611 0.84111 0.03500 0.82189 0.01578

30 0.74066 0.80606 0.06540 0.77034 0.02969

40 0.67746 0.78140 0.10394 0.73419 0.05672

50 0.62134 0.75442 0.13308 0.69484 0.07351

60 0.57592 0.73396 0.15804 0.66627 0.09035

*0.0001 ∆k Monte Carlo uncertainty for all calculations
35

Table 20. keff and Δk values using axial burnup profiles with and without axial 

blankets as a function of burnup for fuel with 5 wt% 235U initial enrichment 

and a 5-year cooling time

Axial model

1 axial zone, 

no blankets

25 axial zones,

no blankets

25 axial zones,

with blankets

Burnup 

(GWd/MTU)

keff value* keff value* ∆k from 1 

axial zone keff value* ∆k from 1 axial zone

Major actinides (nuclide set 1, see Table 6)

0 0.99048 0.99048 0.00000 0.99009 -0.00039

10 0.95594 0.95276 -0.00318 0.95004 -0.00590

20 0.91296 0.92483 0.01187 0.91485 0.00189

30 0.86791 0.89491 0.02699 0.87404 0.00612

40 0.82040 0.87362 0.05323 0.84263 0.02224

50 0.77202 0.85008 0.07805 0.80719 0.03517

60 0.72573 0.83194 0.10621 0.77949 0.05377

Actinides and major fission products (nuclide set 2, see Table 6)

0 0.99048 0.99048 0.00000 0.99009 -0.00039

10 0.92403 0.92513 0.00111 0.91873 -0.00529

20 0.86466 0.89227 0.02760 0.87518 0.01052

30 0.80458 0.85770 0.05312 0.82621 0.02163

40 0.74412 0.83398 0.08987 0.79048 0.04636

50 0.68544 0.80740 0.12197 0.75103 0.06559

60 0.63115 0.78735 0.15620 0.72081 0.08966

*0.0001 ∆k Monte Carlo uncertainty for all calculations
36

Table 21. Axially dependent design of LaSalle Unit 1 assembly B2

Axial 

Zone

Zone 

thickness 

(cm)

Lattice 

number†

Number 

of fuel 

rods

Initial 

enrichment 

(wt% 235U)

Number of 

Gd rods

Gd content 

(wt% Gd2O3)

25 (top) 15.24 106 49 0.71 0 0

24 15.24 107 60 0.71 0 0

23 15.24 108 60 3.23 9 3

22 15.24 108 60 3.23 9 3

21 15.24 108 60 3.23 9 3

20 15.24 109 60 3.37 2 & 9‡ 4 & 3‡

19 15.24 109 60 3.37 3 & 9 5 & 3

18 15.24 109 60 3.37 4 & 9 6 & 3

17 15.24 110 60 3.37 9 3

16 15.24 110 60 3.37 9 3

15 15.24 110 60 3.37 9 3

14 15.24 110 60 3.37 9 3

13 15.24 110 60 3.37 9 3

12 15.24 110 60 3.37 9 3

11 15.24 110 60 3.37 9 3

10 15.24 110 60 3.37 9 3

9 15.24 110 60 3.37 9 3

8 15.24 111 60 3.23 5 & 4 4 & 3

7 15.24 111 60 3.23 6 & 4 5 & 3

6 15.24 111 60 3.23 7 & 4 6 & 3

5 15.24 111 60 3.23 8 & 4 7 & 3

4 15.24 111 60 3.23 9 & 4 8 & 3

3 15.24 111 60 3.23 10 & 4 9 & 3

2 15.24 111 60 3.23 11 & 4 10 & 3

1 15.24 107 60 0.71 0 0

† Lattice number from Table 3-4 of LaSalle Unit 1 CRC data [14]

‡ "2 & 9" rods with "4 & 3" gadolinium content means two fuel rods with 4 wt% Gd2O3 and nine

fuel rods with 3 wt% Gd2O3.
37

4. CONCLUSIONS

This report proposes and documents a computational benchmark model for use as a reference 

case in the estimation of the additional reactivity margin available from fission products and 

minor actinides in a BWR burnup-credit storage/transport environment, based on a generic 68

BWR-assembly cask. The proposed benchmark problem was developed to be similar to existing

designs for burnup-credit casks, including similar materials and dimensions. While preserving all 

of the important features, the proposed benchmark problem approximates (or eliminates) 

nonessential details and proprietary information. The documentation of this computational 

benchmark includes all of the necessary geometric and material specifications to permit 

independent evaluations and sufficiently detailed reference solutions to enable meaningful 

comparisons. This benchmark model will also be used as the base case in future sensitivity 

studies exploring the impact of varying reactor depletion parameters and burnup-credit analysis 

modeling approximations. 

The purpose of this computational benchmark is to provide a reference configuration to help 

establish a method for the estimation of the additional reactivity margin and document reference 

estimations of the additional reactivity margin as a function of initial enrichment, burnup, and 

cooling time. Calculated keff values for the benchmark problem are provided as a function of 

burnup and cooling time for initial enrichments of 2, 3, 4, and 5 wt% 235U. Values are provided 

for the burnup range of 0 to 60 GWd/MTU, in increments of 10 GWd/MTU, and for cooling times 

of 0, 5, 10, 20, and 40 years. The individual components of the reactivity reduction associated 

with (a) the major actinides and (b) the additional nuclides as a function of burnup, cooling time, 

and initial enrichment are also provided. In addition, results for 2, 3, 4, and 5 wt% 235U initial fuel 

enrichment with a 5-year post-irradiation cooling time are given for two cases to provide an 

indication of the potential impact associated with modeling axial burnup profiles with and without 

axial blankets. The reference estimations were all based on the SCALE 6.1 code package and 

the SCALE 238-group ENDF/B-VII library.

The reference results are plotted and examined in Appendix D, and in some cases, 

observations and conclusions are offered. For typical discharge enrichment and burnup 

combinations, the results show that approximately 70% of the reactivity reduction is due to the 

major actinides, with the remaining 30% being attributed to the additional nuclides (major fission 

products and minor actinides). For a given burnup, an increase in the initial enrichment is shown 

to result in a small decrease in the fractional contribution from the major actinides and a 

simultaneous increase in the contribution from the additional nuclides. During the time frame of 

interest, the reactivity reduction associated with the major actinides is shown to increase with 

cooling time. In contrast, the reactivity reduction associated with the fission products and minor 

actinides is shown to increase initially with cooling time, but then decrease somewhat in the 5-

to 40-year time frame. Finally, the minimum additional reactivity margin available from fission 

products and minor actinides is quantified for the burnup, initial enrichments, and cooling times 

considered in this report..

Where applicable, estimates of the reactivity margin for this reference configuration may be 

compared to those of actual burnup-credit-style casks to provide a check of the design-specific 

estimates. However, when associating practical meaning to these results, it is important that the 

reader and potential users of this report understand that this is a computational benchmark, and 

as such, the reference solutions are based on calculations alone. Although reference solutions 

are not directly or indirectly based on experimental results, it should be noted that the SCALE

depletion (TRITON) and criticality (CSAS5) sequences have been validated using laboratory 
38

critical experiments, commercial reactor criticals (CRCs), measured chemical assay data, and 

reactivity worth measurements with individual fission products important to burnup credit [2]. 

An additional purpose for development of the GBC-68 computational benchmark model is to 

provide a reference model to be used in future sensitivity studies exploring the impact of varying 

fuel depletion parameters and the use of burnup-credit analysis techniques, approximations,

and simplifications. 

The work described in this report does not include evaluation of the impact of realistic axial 

variations in BWR fuel assembly designs. Such features include axial zoning of fuel rod initial 

enrichment, axial zoning of gadolinium content in fuel rods, use of part-length fuel rods, and 

reduced or natural uranium enrichment blankets on the ends of the fuel. It is possible that the 

reactivity reduction associated with the major actinides and the additional actinides and fission 

products will be affected by modeling such axial design features. 

Additional work is needed to identify bounding axial burnup distributions appropriate for 

application to BWR fuel assemblies and to evaluate the interdependence of axial burnup 

distributions and axial design features. From experience with PWR burnup credit, and as was 

demonstrated with one example in this report, neglecting the axial burnup distribution may result

in conservative keff value estimates at low assembly average burnup values and in nonconservative estimates of keff values for assembly average burnups greater than 10 to 20 

GWd/MTU. The actual crossover point where using a uniform axial profile changes from 

conservative to non-conservative will vary with assembly axial design features used and with 

reactor operations (e.g., control rod usage). It is expected that usage of bounding axial burnup 

profiles would yield lower estimates for the reactivity margin available from burnup credit 

nuclides. 

Further work is also recommended to quantify the impact of the use of realistic axially 

dependent reactor operation conditions during fuel depletion calculations. Such conditions 

include long-term partial insertion of control rods, moderator density axial variation, and fuel 

temperature axial variation. In the case of the LaSalle Unit 1 CRC data [14], the effective 

moderator density varies from 0.74 to 0.17 g/cm3 as the moderator moves from the bottom to 

the top of the fuel. This will lead to a significantly harder neutron spectrum near the top of the 

fuel and, consequently, higher plutonium generation in this axial region.

 
39

5. REFERENCES

1 J. C. Wagner, Computational Benchmark for Estimation of Reactivity Margin from Fission 

Products and Minor Actinides in PWR Burnup Credit, NUREG/CR-6747 (ORNL/TM2000/306), U. S. Nuclear Regulatory Commission, Oak Ridge National Laboratory, 

October 2001.

2 C. V. Parks, M. D. DeHart and J. C. Wagner, Review and Prioritization of Technical Issues 

Related to Burnup Credit for LWR Fuel, NUREG/CR-6665 (ORNL/TM-1999/303), U. S. 

Nuclear Regulatory Commission, Oak Ridge National Laboratory, February 2000.

3 SCALE: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and 

Design, ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory, Oak Ridge, 

Tennessee, June 2011. Available from Radiation Safety Information Computational Center 

at Oak Ridge National Laboratory as CCC-785.

4 Nuclear Criticality Safety in Operations with Fissionable Material Outside Reactors, 

ANSI/ANS-8.1-1998 (R2007).

5 Validation of Neutron Transport Methods for Nuclear Criticality Safety Calculations, 

ANSI/ANS-8.24-2007.

6 Burnup Credit for LWR Fuel, ANSI/ANS-8.27-2008.

7 Standard Review Plan for Dry Cask Storage Systems, NUREG-1536, U.S. NRC, 

Washington, D.C., January 1997.

8 Standard Review Plan for Transportation Packages for Spent Nuclear Fuel – Draft 

Report for Comment, NUREG-1617, U.S. NRC, Washington, D.C., March 1998.

9 J. C. Wagner, M. DeHart, and B. L. Broadhead, Investigation of Burnup Credit Modeling 

Issues Associated with BWR Fuel, ORNL/TM-1999/193, Oak Ridge National Laboratory, 

October 2000.

10 K. W. Cummings and S. E. Turner, “Design of Wet Storage Racks for Spent BWR Fuel,” 

Proc. 2001 ANS Embedded Topical Meeting on Practical Implementation of Nuclear 

Criticality Safety, American Nuclear Society, Reno, NV, 2001.

11 C. Casado, J. Sabater, and J. Serrano, “Peak Reactivity Characterization and Isotopic 

Inventory Calculations for BWR Criticality Applications,” International Workshop on 

Advances in Applications of Burnup Credit for Spent Fuel Storage, Trasnport, 

Reprocessing, and Disposition, International Atomic Energy Agency, Cordoba, Spain, 

2009.

12 Spent Fuel Project Office Interim Staff Guidance – 8, Revision 0, “Limited Burnup Credit,” 

U.S. Nuclear Regulatory Commission, May 1999.
40

13 R. Bahney and T. Doering, Interoffice Correspondence to S. Saterlie; R. Memory; and J. 

Stringer on Waste Package Sizes Efficiencies and Weights, LV.WP.RHB.05/93-086, TRW 

Environmental Safety Systems Inc., Las Vegas, NV, 1993.

14 D. P. Henderson, Summary Report of Commercial Reactor Criticality Data for LaSalle Unit 

1, B00000000-01717-5705-00138 REV 00, CRWMS/M&O, Las Vegas, NV, September 

1999. B0000000001717.

15 J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, 1976.

16 Topical Report on Actinide-Only Burnup Credit for PWR Spent Nuclear Fuel Packages, 

DOE/RW-0472, Rev. 2, U.S. Department of Energy, September 1998.

17 G. Radulescu, I. C. Gauld, G. Ilas, and J. C. Wagner, An Approach for Validating Actinide 

and Fission Product Burnup Credit Criticality Safety Analyses – Isotopic Composition 

Predictions, NUREG/CR-7108 (ORNL/TM-2011/509), U.S. Nuclear Regulatory 

Commission, Oak Ridge National Laboratory, May 2012.

18 J. M. Scaglione, D. E. Mueller, J. C. Wagner, and W. J. Marshall, An Approach for 

Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses –

Criticality (keff)Predictions, NUREG/CR-7109 (ORNL/TM-2011/514), U.S. Nuclear 

Regulatory Commission, Oak Ridge National Laboratory, May 2012.

19 J. C. Wagner, M. D. DeHart, and C. V. Parks, Recommendations for Addressing Axial 

Burnup in PWR Burnup Credit Analyses, NUREG/CR-6801 (ORNL/TM-2001/273), U.S. 

Nuclear Regulatory Commission, Oak Ridge National Laboratory, March 2003.
A-1

APPENDIX A. TRITON INPUT FILE EXAMPLE

(Used to generate ORIGEN-ARP Libraries)

=t-depl parm=(addnux=4)

BWR GE 10x10 

v7-238

' ----------------------------------------------------------------

' template to generate libraries for ORIGEN

' parameters are: 5.0 - wt% enrichment U-235

' 95.0 - wt% U-238

' 0.8 - coolant density (g/cc)

' ge14_uni_rod_5wo_0.8.lib - name of ORIGEN library created

' ----------------------------------------------------------------

' Mixture data

' ----------------------------------------------------------------

read comp

' fuel 1 (no gadolinia)

uo2 1 0.95 840 92235 5.0 

 92238 95.0 end

' clad 

zirc2 2 1 567 end

' water coolant 

h2o 3 den=0.8 1 512 end

' clad 

zirc2 6 1 567 end

' water coolant 

h2o 7 den=0.8 1 512 end

' channel tube 

zirc2 9 1 512 end

' water in water rod and channel

h2o 10 den=0.776 1 512 end

'

'-----------------------Control rod blades---------------------------------

'

' Material: B4C absorber

' ss304 clad 7.94 g/cc SCALE default density

 ss304 21 den=7.94 1.0000 512 end

 b4c 22 den=1.76 1.0000 512 end

 h2o 23 den=0.776 1.0000 512 end

end comp

' ----------------------------------------------------------------

' Cell data

' ----------------------------------------------------------------

read celldata

latticecell squarepitch pitch=1.295 3

 fueld=0.876 1

cladd=1.026 2 end

end celldata

' ----------------------------------------------------------------

' Depletion data

' ----------------------------------------------------------------

read depletion

1 

end depletion

' ----------------------------------------------------------------
A-2

' Burn data

' ----------------------------------------------------------------

read burndata

power=40 burn=1e-15 down=0 end

power=40 burn=4 down=0 end

power=40 burn=71 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

power=40 burn=75 down=0 end

end burndata

' ----------------------------------------------------------------

' NEWT model data

' ----------------------------------------------------------------

read model

BWR GE 10x10

read parm

fillmix=10 echo=yes drawit=no run=yes

cmfd=yes xycmfd=4 epsilon=1e-5

end parm

READ materials

1 1 ! fuel ! end

2 1 ! clad ! end

3 2 ! coolant ! end

9 1 ! channel tube ! end

10 2 ! moderator ! end

21 1 ! blade ss304 ! end

22 1 ! blade b4c ! end

23 2 ! blade water ! end

end materials

read geom

unit 1
A-3

com='fuel pin'

cylinder 10 .438

cylinder 20 .513

cuboid 40 4p0.6475

media 1 1 10

media 2 1 20 -10

media 3 1 40 -20

boundary 40 4 4

unit 3

com='water rod'

cylinder 10 1.1605

cylinder 20 1.2605

media 10 1 10

media 9 1 20 -10

boundary 20 8 8

'-----------------------------------------------------------------------

' control blade geometry

'-----------------------------------------------------------------------

' - GE OEM B4C blade

' - adjusted so that the poison tubes are evenly

' dispersed in the wing of the blade

unit 90

com='control poison tube - north wing'

cylinder 1 0.2108 chord -y=0

cylinder 2 0.2794 chord -y=0

cuboid 3 2p0.2876 0 -0.30226

media 22 1 1

media 21 1 2 -1

media 23 1 3 -2

boundary 3 2 1

'

unit 91

com='control poison tube - north wing - end tube'

cylinder 1 0.2108 chord -y=0 chord -x=0

cylinder 2 0.2794 chord -y=0 chord -x=0

cuboid 3 0 -0.2876 0 -0.30226

media 22 1 1

media 21 1 2 -1

media 23 1 3 -2

boundary 3 1 1

'

unit 92

com='control poison tube - west wing'

cylinder 1 0.2108 chord +x=0

cylinder 2 0.2794 chord +x=0

cuboid 3 0.30226 0 2p0.2876

media 22 1 1

media 21 1 2 -1

media 23 1 3 -2

boundary 3 1 2

unit 93

com='control poison tube - west wing - end tube'

cylinder 1 0.2108 chord +x=0 chord +y=0

cylinder 2 0.2794 chord +x=0 chord +y=0

cuboid 3 0.30226 0 0.2876 0

media 22 1 1

media 21 1 2 -1
A-4

media 23 1 3 -2

boundary 3 1 1

'

' note: the extra chords on the outer cylinder are to prevent tracer errors –

‘ the tips of the

' 'circle' (polygon) stick out of the unit boundary

unit 94

com='control blade wing end tube and rounded edge'

cylinder 1 0.2108 chord +x=0 chord -y=0 com='b4c'

cylinder 2 0.2794 chord +x=0 chord -y=0 com='clad'

cylinder 3 0.30226 chord +x=0 chord -y=0 com='inner wing radius'

cylinder 4 0.41656 chord +x=0 chord -y=0 chord -x=0.41656 chord +y=-0.41656 

com='outer wing radius'

media 22 1 1

media 21 1 2 -1

media 23 1 3 -2

media 21 1 4 -3

boundary 4 1 1

'

unit 95

com='control blade north wing'

cuboid 1 10.066 0 0 -0.41656

media 21 1 1

array 2 1 place 1 1 0.2875 0

boundary 1

'

unit 96

com='control blade west wing'

cuboid 1 0.41656 0 0 -10.066

media 21 1 1

array 3 1 place 1 18 0 -0.2875

boundary 1

unit 97 com='control central support'

cuboid 1 1.9685 0 0 -0.41656

media 21 1 1

boundary 1

unit 98 com='control central support'

cuboid 1 0.41656 0 0 -1.55194

media 21 1 1

boundary 1

'

' end of control blade geometry

'-----------------------------------------------------------------------

global unit 5

com='assembly'

cuboid 51 4p6.475

cuboid 52 4p6.675

cuboid 53 4p7.62

hole 3 origin x=1.295 y=1.295 

hole 3 origin x=-1.295 y=-1.295 

array 1 51 place 1 1 -5.8275 -5.8275

media 3 1 51

media 9 1 52 -51

media 10 1 53 -52 

' insert control blade units

' comment out these lines to withdraw the blade

hole 95 origin x=-5.6515 y=7.62 com='north wing'
A-5

hole 96 origin x=-7.62 y=5.6515 com='west wing'

hole 97 origin x=-7.62 y=7.62 com='north support'

hole 98 origin x=-7.62 y=7.20344 com='west support' 

hole 94 origin x=4.4145 y=7.62 com='north wing tip'

hole 94 origin x=-7.62 y=-4.4145 com='west wing tip'

'

boundary 53 36 36

end geom

read array

ara=1 nux=10 nuy=10

fill

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 0 0 1 1 1 1 1

1 1 1 0 0 1 1 1 1 1

1 1 1 1 1 0 0 1 1 1

1 1 1 1 1 0 0 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1

end fill

' control blade poison tubes array - north wing

ara=2

nux=18 nuy=1

fill

 17r90 91 end fill

' control blade poison tubes array - west wing

ara=3

nux=1 nuy=18

fill

 93 17r92 end fill

end array

read bounds

all=refl

end bounds

end data

end

' ----------------------------------------------------------------

=shell

mv ft33f001.cmbined $OUTDIR/ge14_uni_rod_5wo_0.8.lib

end

B-1

APPENDIX B. STARBUCS INPUT FILE EXAMPLE

=starbucs

GBC-68 - BUC GE10x10, 5.0 w/o, 60 GWd/MTU, 28Act&FP, cooling time of 40 years

v7-238

read comp

' - UO2 for fuel pellet

uo2 1 den=10.5216 1 293.0 

 92234 .0445

92235 5.0

92236 .0230

92238 94.9325 end

' - Zr cladding

zr 2 0 0.04230 293.0 end

' - water for fuel pin moderator

h2o 3 1 293.0 end

' - water for fuel pin pellet/clad gap

h2o 4 1 293.0 end

' - water in water tube

h2o 5 1 293.0 end

' - zirc for water tube

zr 6 0 0.04230 293.0 end

' - water outside water tube

h2o 7 1 293.0 end

' - water in fuel channel

h2o 8 1 293.0 end

' - zr fuel channel

zr 9 0 0.04230 293.0 end

' - water outside fuel channel

h2o 10 1 293.0 end

' - steel cell wall

ss304 11 1 293.0 end

' - Boral (9.721e-2 gb10/cm3)

b-10 12 0 5.8465e-03 293.0 end

b-11 12 0 2.3532e-02 293.0 end

c 12 0 7.3447e-03 293.0 end

al 12 0 4.6120e-02 293.0 end

' - Al plate

al 13 0 0.0602 293.0 end

' - water in poison panel gap

h2o 14 1 293.0 end

' - water outside cells

h2o 15 1 293.0 end

' - steel cask body

ss304 16 1 293.0 end

end comp
B-2

read celldata

 latticecell squarepitch

 fuelr=0.438 1

 gapr= 0.447 4

 cladr=0.513 2

 pitch=1.295 3 end

end celldata

'

read control

 arp=rodded_ge14

 axp=1 end

 mod=0.6 end

 nax=1 

 nuc=u-234 1.0

 u-235 1.0

 u-236 1.0

 u-238 1.0

 pu-238 1.0

 pu-239 1.0

 pu-240 1.0

 pu-241 1.0

 pu-242 1.0

 am-241 1.0

 am-243 1.0

 np-237 1.0

 mo-95 1.0

 tc-99 1.0

 ru-101 1.0

 rh-103 1.0

 ag-109 1.0

 cs-133 1.0

 sm-147 1.0

 sm-149 1.0

 sm-150 1.0

 sm-151 1.0

 sm-152 1.0

 nd-143 1.0

 nd-145 1.0

 eu-151 1.0

 eu-153 1.0

 gd-155 1.0 end

end control

read hist

 power=30 burn=2000.00 down=14610.00 nlib=30 end

end hist

'

read keno

'

read parm

 gen=10000 nsk=100 npg=11000

 sig=10.e-5

 htm=no

end parm

read geom

'UO2 fuel pin

unit 1

 cylinder 101 1 0.438 381.0 0

 cylinder 4 1 0.447 381.0 0

 cylinder 2 1 0.513 381.0 0

 cuboid 3 1 0.6475 -0.6475 0.6475 -0.6475 381.0 0
B-3

'water tube

unit 2

 cylinder 5 1 1.1605 381.0 0

 cylinder 6 1 1.2605 381.0 0

 cuboid 7 1 1.295 -1.295 1.295 -1.295 381.0 0

'2x2 array of pins

unit 3

 array 1 0 0 0

'3x3 array of pins

unit 4

 array 2 0 0 0

'2x3 array of pins

unit 5

 array 3 0 0 0

'3x2 array of pins

unit 6

 array 4 0 0 0

'fuel assembly

unit 7

 array 5 0 0 0

' Top Half Horizontal Boral Panel

unit 40

 cuboid 13 1 6.475 -6.475 0.0254 0 381.0 0

 cuboid 12 1 6.475 -6.475 0.12826 0 381.0 0

' Right-Hand Side Half Vertical Boral Panel

unit 50

 cuboid 13 1 0.0254 0 6.475 -6.475 381.0 0

 cuboid 12 1 0.12826 0 6.475 -6.475 381.0 0

' Bottom Half Horizontal Boral Panel

unit 60

 cuboid 13 1 6.475 -6.475 0 -0.0254 381.0 0

 cuboid 12 1 6.475 -6.475 0 -0.12826 381.0 0

' Left-Hand Side Half Vertical Boral Panel

unit 70

 cuboid 13 1 0 -0.0254 6.475 -6.475 381.0 0

 cuboid 12 1 0 -0.12826 6.475 -6.475 381.0 0

' Assembly Basket Cell

unit 101

' assembly

 array 5 -6.475 -6.475 0

' water inside the channel

 cuboid 8 1 6.70306 -6.70306 6.70306 -6.70306 381.0 0

' Zr channel

 cuboid 9 1 6.95706 -6.95706 6.95706 -6.95706 381.0 0

' water between channel and basket SS plate

 cuboid 10 1 7.52173 -7.52173 7.52173 -7.52173 381.0 0

' SS basket plate is cell width - boral panel thickness

 cuboid 11 1 8.27173 -8.27173 8.27173 -8.27173 381.0 0

 cuboid 14 1 8.4 -8.4 8.4 -8.4 381.0 0

 hole 40 0 8.27173 0

 hole 50 8.27173 0 0

 hole 60 0 -8.27173 0

 hole 70 -8.27173 0 0
B-4

' Top Boral/Basket Plate

unit 110

 cuboid 12 1 6.475 -6.475 0.10287 0 381.0 0

 cuboid 13 1 6.475 -6.475 0.12827 0 381.0 0

 cuboid 14 1 8.27173 -8.27173 0.12827 0 381.0 0

 cuboid 11 1 8.27173 -8.27173 0.87827 0 381.0 0

' Left-Hand Side Boral/Basket Plate

unit 112

 cuboid 12 1 0 -0.10287 6.475 -6.475 381.0 0

 cuboid 13 1 0 -0.12827 6.475 -6.475 381.0 0

 cuboid 14 1 0 -0.12827 7.52172 -7.52172 381.0 0

 cuboid 11 1 0 -0.87827 7.52172 -7.52172 381.0 0

' Right-Hand Side Boral/Basket Plate

unit 113

 cuboid 12 1 0.10287 0 6.475 -6.475 381.0 0

 cuboid 13 1 0.12827 0 6.475 -6.475 381.0 0

 cuboid 14 1 0.12827 0 7.52172 -7.52172 381.0 0

 cuboid 11 1 0.87827 0 7.52172 -7.52172 381.0 0

' 1x3 array

unit 114

 array 7 -8.4 0 0

' 2x1 array

unit 115

 array 8 -16.8 0 0

' Cask Inner Volume

global unit 200

 array 6 -50.4 0 0

 zhemicyl+y 15 1 87.5 395.76 -15

' holes for side and top assemblies

 hole 115 0 67.2001 0

 hole 114 -58.8001 0 0

 hole 114 58.8001 0 0

 hole 101 75.6002 8.4 0

 hole 101 -75.6002 8.4 0

' Exterior Half Boral Panels

' Top Plates

 hole 110 -8.4 84.0002 0

 hole 110 8.4 84.0002 0

 hole 110 -25.2 67.2002 0

 hole 110 25.2 67.2002 0

 hole 110 -42 67.2002 0

 hole 110 42 67.2002 0

 hole 110 -58.8001 50.4002 0

 hole 110 58.8001 50.4002 0

 hole 110 75.6002 16.8002 0

 hole 110 -75.6002 16.8002 0

' Left-Hand Side Plates

 hole 112 -16.8001 75.6002 0

 hole 112 -50.4002 58.8003 0

 hole 112 -67.2002 25.2003 0

 hole 112 -67.2002 42.0004 0

 hole 112 -84.0003 8.4 0

' Right-Hand Side Plates

 hole 113 16.8001 75.6002 0

 hole 113 50.4002 58.8003 0

 hole 113 67.2002 25.2003 0

 hole 113 67.2002 42.0004 0
B-5

 hole 113 84.0003 8.4 0

'

' Steel Cask/Overpack

 zhemicyl+y 16 1 92.5 400.76 -25

 zhemicyl+y 16 1 97.5 405.76 -35

 zhemicyl+y 16 1 107.5 415.76 -45

'

' Cube Surrounding Cask

 cuboid 0 1 108 -108 108 0 415.76 -45

end geom

'

' Assembly Type: GE 10x10A01

read array

 ara=1 nux=2 nuy=2 nuz=1 fill f1 end fill

 ara=2 nux=3 nuy=3 nuz=1 fill f1 end fill

 ara=3 nux=2 nuy=3 nuz=1 fill f1 end fill

 ara=4 nux=3 nuy=2 nuz=1 fill f1 end fill

 ara=5 nux=4 nuy=4 nuz=1

 fill 4 5 5 4

 6 3 2 6

 6 2 3 6

 4 5 5 4 end fill

 ara=6 nux=6 nuy=4 nuz=1 fill f101 end fill

 ara=7 nux=1 nuy=3 nuz=1 fill f101 end fill

 ara=8 nux=2 nuy=1 nuz=1 fill f101 end fill

end array

read bounds

 +xb=specular

 -xb=specular

 +yb=specular

 +zb=void

 -zb=void

' the -yb must be kept at specular because only half of cask is modeled

 -yb=specular

end bounds

end data

end keno

end

=shell

 cp sysin2 $INPDIR/$BASENAME.bu.inp

end

C-1

APPENDIX C. CSAS5 INPUT FILE EXAMPLE

=csas5 parm=()

gbc-68 - buc ge10x10, 5.0 w/o, 60 gwd/mtu, 28act&fp, cooling time of 40 years 

v7-238n 

read comp

'Node[01][01] gbc-68 - buc ge10x10, 5.0 w/o, 60 gwd/mtu, 28act&fp, cooling 

tim

 u-234 101 0 7.6567E-06 293.0 end

 u-235 101 0 1.6455E-04 293.0 end

 u-236 101 0 1.7046E-04 293.0 end

 u-238 101 0 2.1343E-02 293.0 end

np-237 101 0 2.1855E-05 293.0 end

pu-238 101 0 7.6774E-06 293.0 end

pu-239 101 0 1.4696E-04 293.0 end

pu-240 101 0 7.5564E-05 293.0 end

pu-241 101 0 5.7785E-06 293.0 end

pu-242 101 0 2.2062E-05 293.0 end

am-241 101 0 3.4818E-05 293.0 end

am-243 101 0 6.2444E-06 293.0 end

mo-95 101 0 7.7774E-05 293.0 end

tc-99 101 0 7.7847E-05 293.0 end

ru-101 101 0 7.6055E-05 293.0 end

rh-103 101 0 3.9853E-05 293.0 end

ag-109 101 0 6.7615E-06 293.0 end

cs-133 101 0 7.9871E-05 293.0 end

nd-143 101 0 4.8263E-05 293.0 end

nd-145 101 0 4.3580E-05 293.0 end

sm-147 101 0 1.4892E-05 293.0 end

sm-149 101 0 1.2901E-07 293.0 end

sm-150 101 0 1.8791E-05 293.0 end

sm-151 101 0 4.0258E-07 293.0 end

eu-151 101 0 1.4592E-07 293.0 end

sm-152 101 0 5.7591E-06 293.0 end

eu-153 101 0 7.4564E-06 293.0 end

gd-155 101 0 5.7754E-07 293.0 end

 o-16 101 0 4.6949E-02 293.0 end

zr-90 2 0 2.1763E-02 293.0 end

zr-91 2 0 4.7461E-03 293.0 end

zr-92 2 0 7.2545E-03 293.0 end

zr-94 2 0 7.3517E-03 293.0 end

zr-96 2 0 1.1844E-03 293.0 end

o-16 3 0 3.3377E-02 293.0 end

h-1 3 0 6.6753E-02 293.0 end

o-16 4 0 3.3377E-02 293.0 end

h-1 4 0 6.6753E-02 293.0 end

o-16 5 0 3.3377E-02 293.0 end

h-1 5 0 6.6753E-02 293.0 end

zr-90 6 0 2.1763E-02 293.0 end

zr-91 6 0 4.7461E-03 293.0 end

zr-92 6 0 7.2545E-03 293.0 end

zr-94 6 0 7.3517E-03 293.0 end

zr-96 6 0 1.1844E-03 293.0 end

o-16 7 0 3.3377E-02 293.0 end
C-2

h-1 7 0 6.6753E-02 293.0 end

o-16 8 0 3.3377E-02 293.0 end

h-1 8 0 6.6753E-02 293.0 end

zr-90 9 0 2.1763E-02 293.0 end

zr-91 9 0 4.7461E-03 293.0 end

zr-92 9 0 7.2545E-03 293.0 end

zr-94 9 0 7.3517E-03 293.0 end

zr-96 9 0 1.1844E-03 293.0 end

o-16 10 0 3.3377E-02 293.0 end

h-1 10 0 6.6753E-02 293.0 end

c 11 0 3.1849E-04 293.0 end

si-28 11 0 1.5701E-03 293.0 end

si-29 11 0 7.9763E-05 293.0 end

si-30 11 0 5.2642E-05 293.0 end

p-31 11 0 6.9469E-05 293.0 end

cr-50 11 0 7.5918E-04 293.0 end

cr-52 11 0 1.4640E-02 293.0 end

cr-53 11 0 1.6599E-03 293.0 end

cr-54 11 0 4.1322E-04 293.0 end

mn-55 11 0 1.7407E-03 293.0 end

fe-54 11 0 3.4542E-03 293.0 end

fe-56 11 0 5.3698E-02 293.0 end

fe-57 11 0 1.2295E-03 293.0 end

fe-58 11 0 1.6393E-04 293.0 end

ni-58 11 0 5.2842E-03 293.0 end

ni-60 11 0 2.0202E-03 293.0 end

ni-61 11 0 8.7463E-05 293.0 end

ni-62 11 0 2.7787E-04 293.0 end

ni-64 11 0 7.0435E-05 293.0 end

c 12 0 7.3447E-03 293.0 end

b-10 12 0 5.8465E-03 293.0 end

b-11 12 0 2.3532E-02 293.0 end

al-27 12 0 4.6120E-02 293.0 end

al-27 13 0 6.0200E-02 293.0 end

o-16 14 0 3.3377E-02 293.0 end

h-1 14 0 6.6753E-02 293.0 end

o-16 15 0 3.3377E-02 293.0 end

h-1 15 0 6.6753E-02 293.0 end

c 16 0 3.1849E-04 293.0 end

si-28 16 0 1.5701E-03 293.0 end

si-29 16 0 7.9763E-05 293.0 end

si-30 16 0 5.2642E-05 293.0 end

p-31 16 0 6.9469E-05 293.0 end

cr-50 16 0 7.5918E-04 293.0 end

cr-52 16 0 1.4640E-02 293.0 end

cr-53 16 0 1.6599E-03 293.0 end

cr-54 16 0 4.1322E-04 293.0 end

mn-55 16 0 1.7407E-03 293.0 end

fe-54 16 0 3.4542E-03 293.0 end

fe-56 16 0 5.3698E-02 293.0 end

fe-57 16 0 1.2295E-03 293.0 end

fe-58 16 0 1.6393E-04 293.0 end

ni-58 16 0 5.2842E-03 293.0 end

ni-60 16 0 2.0202E-03 293.0 end

ni-61 16 0 8.7463E-05 293.0 end

ni-62 16 0 2.7787E-04 293.0 end

ni-64 16 0 7.0435E-05 293.0 end
C-3

end comp

read celldata

latticecell squarepitch pitch= 1.29500 3 fueld= 0.87600 101 cladd= 

1.02600 2

gapd= 0.89400 4 end

end celldata

'

read param

res=1000000

 gen=10000 nsk=100 npg=11000

 sig=10.e-5

 htm=no

end parm

read geom

'UO2 fuel pin

unit 1

 cylinder 101 1 0.438 381.0 0

 cylinder 4 1 0.447 381.0 0

 cylinder 2 1 0.513 381.0 0

 cuboid 3 1 0.6475 -0.6475 0.6475 -0.6475 381.0 0

'water tube

unit 2

 cylinder 5 1 1.1605 381.0 0

 cylinder 6 1 1.2605 381.0 0

 cuboid 7 1 1.295 -1.295 1.295 -1.295 381.0 0

'2x2 array of pins

unit 3

 array 1 0 0 0

'3x3 array of pins

unit 4

 array 2 0 0 0

'2x3 array of pins

unit 5

 array 3 0 0 0

'3x2 array of pins

unit 6

 array 4 0 0 0

'fuel assembly

unit 7

 array 5 0 0 0

' Top Half Horizontal Boral Panel

unit 40

 cuboid 13 1 6.475 -6.475 0.0254 0 381.0 0

 cuboid 12 1 6.475 -6.475 0.12826 0 381.0 0

' Right-Hand Side Half Vertical Boral Panel

unit 50

 cuboid 13 1 0.0254 0 6.475 -6.475 381.0 0
C-4

 cuboid 12 1 0.12826 0 6.475 -6.475 381.0 0

' Bottom Half Horizontal Boral Panel

unit 60

 cuboid 13 1 6.475 -6.475 0 -0.0254 381.0 0

 cuboid 12 1 6.475 -6.475 0 -0.12826 381.0 0

' Left-Hand Side Half Vertical Boral Panel

unit 70

 cuboid 13 1 0 -0.0254 6.475 -6.475 381.0 0

 cuboid 12 1 0 -0.12826 6.475 -6.475 381.0 0

' Assembly Basket Cell

unit 101

' assembly

 array 5 -6.475 -6.475 0

' water inside the channel

 cuboid 8 1 6.70306 -6.70306 6.70306 -6.70306 381.0 0

' Zr channel

 cuboid 9 1 6.95706 -6.95706 6.95706 -6.95706 381.0 0

' water between channel and basket SS plate

 cuboid 10 1 7.52173 -7.52173 7.52173 -7.52173 381.0 0

' SS basket plate is cell width - boral panel thickness

 cuboid 11 1 8.27173 -8.27173 8.27173 -8.27173 381.0 0

 cuboid 14 1 8.4 -8.4 8.4 -8.4 381.0 0

 hole 40 0 8.27173 0

 hole 50 8.27173 0 0

 hole 60 0 -8.27173 0

 hole 70 -8.27173 0 0

' Top Boral/Basket Plate

unit 110

 cuboid 12 1 6.475 -6.475 0.10287 0 381.0 0

 cuboid 13 1 6.475 -6.475 0.12827 0 381.0 0

 cuboid 14 1 8.27173 -8.27173 0.12827 0 381.0 0

 cuboid 11 1 8.27173 -8.27173 0.87827 0 381.0 0

' Left-Hand Side Boral/Basket Plate

unit 112

 cuboid 12 1 0 -0.10287 6.475 -6.475 381.0 0

 cuboid 13 1 0 -0.12827 6.475 -6.475 381.0 0

 cuboid 14 1 0 -0.12827 7.52172 -7.52172 381.0 0

 cuboid 11 1 0 -0.87827 7.52172 -7.52172 381.0 0

' Right-Hand Side Boral/Basket Plate

unit 113

 cuboid 12 1 0.10287 0 6.475 -6.475 381.0 0

 cuboid 13 1 0.12827 0 6.475 -6.475 381.0 0

 cuboid 14 1 0.12827 0 7.52172 -7.52172 381.0 0

 cuboid 11 1 0.87827 0 7.52172 -7.52172 381.0 0

' 1x3 array

unit 114

 array 7 -8.4 0 0

' 2x1 array

unit 115
C-5

 array 8 -16.8 0 0

' Cask Inner Volume

global unit 200

 array 6 -50.4 0 0

 zhemicyl+y 15 1 87.5 395.76 -15

' holes for side and top assemblies

 hole 115 0 67.2001 0

 hole 114 -58.8001 0 0

 hole 114 58.8001 0 0

 hole 101 75.6002 8.4 0

 hole 101 -75.6002 8.4 0

' Exterior Half Boral Panels

' Top Plates

 hole 110 -8.4 84.0002 0

 hole 110 8.4 84.0002 0

 hole 110 -25.2 67.2002 0

 hole 110 25.2 67.2002 0

 hole 110 -42 67.2002 0

 hole 110 42 67.2002 0

 hole 110 -58.8001 50.4002 0

 hole 110 58.8001 50.4002 0

 hole 110 75.6002 16.8002 0

 hole 110 -75.6002 16.8002 0

' Left-Hand Side Plates

 hole 112 -16.8001 75.6002 0

 hole 112 -50.4002 58.8003 0

 hole 112 -67.2002 25.2003 0

 hole 112 -67.2002 42.0004 0

 hole 112 -84.0003 8.4 0

' Right-Hand Side Plates

 hole 113 16.8001 75.6002 0

 hole 113 50.4002 58.8003 0

 hole 113 67.2002 25.2003 0

 hole 113 67.2002 42.0004 0

 hole 113 84.0003 8.4 0

'

' Steel Cask/Overpack

 zhemicyl+y 16 1 92.5 400.76 -25

 zhemicyl+y 16 1 97.5 405.76 -35

 zhemicyl+y 16 1 107.5 415.76 -45

'

' Cube Surrounding Cask

 cuboid 0 1 108 -108 108 0 415.76 -45

end geom

'

' Assembly Type: GE 10x10A01

read array

 ara=1 nux=2 nuy=2 nuz=1 fill f1 end fill

 ara=2 nux=3 nuy=3 nuz=1 fill f1 end fill

 ara=3 nux=2 nuy=3 nuz=1 fill f1 end fill

 ara=4 nux=3 nuy=2 nuz=1 fill f1 end fill

 ara=5 nux=4 nuy=4 nuz=1

 fill 4 5 5 4

 6 3 2 6

 6 2 3 6

 4 5 5 4 end fill
C-6

 ara=6 nux=6 nuy=4 nuz=1 fill f101 end fill

 ara=7 nux=1 nuy=3 nuz=1 fill f101 end fill

 ara=8 nux=2 nuy=1 nuz=1 fill f101 end fill

end array

read bounds

 +xb=specular

 -xb=specular

 +yb=specular

 +zb=void

 -zb=void

' the -yb must be kept at specular because only half of cask is modeled

 -yb=specular

end bounds

end data

end
D-1

APPENDIX D. DISCUSSION OF REFERENCE RESULTS

D.1 DISCUSSION OF REFERENCE RESULTS

Although the intended scope of this report does not include analysis and interpretation of the 

results, some limited examination, discussion, and conclusions related to the reference results 

are offered in this appendix.

To assist in the examination of the reference results, plots of a select set of the reference results 

are presented for a cooling time of 5 years. Figures D.1 through D.4 plot the keff values in the 

GBC-68 cask for the two nuclide sets (refer to Tables D.1 and D.2 for specification of nuclide 

sets) as a function of burnup for initial enrichments of 2, 3, 4, and 5 wt% 235U, respectively. 

Although, for consistency, results were generated for burnups up to 60 GWd/MTU for each of 

the enrichments, it should be noted that typical discharge burnups for fuel assemblies with initial

enrichments below 3 wt % 235U are below 40 GWd/MTU. Similarly, for initial enrichments above 

3 wt % 235U, typical discharge burnups are greater than 30 GWd/MTU. Thus, one should be 

cognizant of these facts when examining the results for the various burnup and enrichment 

combinations. Limited data for actual initial enrichment and discharge burnup combinations for 

SNF discharged from U.S. reactors through 2002 are available in Ref. D.1.

The reactivity reductions due to the major actinides (set 1 in Table D.1), additional nuclides 

(set 3 in Table D.2), and all of the nuclides considered (set 2 in Table D.1) are plotted in Figures 

D.5 through D.8 as a function of burnup for each of the initial enrichments considered. Finally, 

bar charts showing the individual contributions from (a) the major actinides and (b) the 

additional nuclides to the total reactivity reduction for 5-year cooling as a function of burnup are 

plotted in Figures D.9 through D.12. The relative reactivity reductions due to (a) the major 

actinides and (b) the additional nuclides are similar at low burnups, but quickly diverge for 

higher burnups. For typical enrichment and discharge burnup combinations, the figures show 

that approximately 70% of the reactivity reduction is due to the major actinides, with the 

remaining 30% being attributed to the additional nuclides (major fission products and minor 

actinides).

To compare the reactivity reductions for various initial enrichments, Figure D.13 shows the 

reactivity reductions (in terms of ∆k values) for the major actinides as a function of burnup from 

Figures D.5 through D.8 for initial enrichments of 2, 3, 4, and 5 wt % 235U. Similarly, Figure D.14

shows the reactivity reductions for the additional nuclides as a function of burnup from Figures 

D.5 through D.8 for initial enrichments of 2, 3, 4, and 5 wt % 235U. The variation in these 

contributions to the reactivity reduction versus initial enrichment is shown to be relatively minor. 

However, Figure D.14 does reveal that, for a given burnup, an increase in the initial enrichment 

results in a slight increase in the contribution from the additional nuclides. The individual 

contributions to the total reactivity reduction from (a) the major actinides and (b) the additional 

nuclides from Figures D.9 through D.12 are compared for various initial enrichments in Figures 

D.15 and D.16, respectively.

To examine the effect of cooling time, Figures D.17 and D.18 show the reactivity reductions (in 

terms of ∆k values) as a function of burnup, for an initial enrichment of 4 wt % 235U, for (a) the 

major actinides and (b) the additional nuclides, respectively. During the time frame of interest to 

storage and transport, the reactivity reduction associated with the major actinides increases with 
D-2

cooling time, primarily due to the decay of the 241Pu fissile nuclide (t1/2 = 14.4 years) and the 

buildup of the neutron absorber 241Am (from decay of 241Pu). This behavior has been well 

documented [D.2,D.3]. For the fission products and minor actinides considered as the 

“additional nuclides” (see Table D.2), the associated reactivity reduction increases initially with 

cooling time due to the buildup of 155Gd (from 155Eu which decays with t1/2 = 4.7 years), but then 

decreases somewhat due to the decay of 151Sm. In general, however, the reactivity reduction 

due to the additional nuclides does not vary significantly in the 5-to-40 year time frame.

As there has been a great deal of interest in quantifying the minimum additional reactivity 

margin available from fission products and minor actinides, Figure D.19 plots the range of 

calculated reactivity margin (in terms of ∆k values) for all of the burnup, initial enrichments, and 

cooling times considered in this report. Specifically, the range for burnups from 10 to 

60 GWd/MTU, initial enrichments of 2, 3, 4, and 5 wt % 235U, and cooling times of 0, 5, 10, 20, 

and 40 years. In all cases, the minimum values correspond to zero cooling time.
D-3

Table D.1. Nuclide sets defined for the benchmark problem analysis

set 1: Major actinides (9 total)

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

set 2: Actinides and major fission products (28 total)

234U 235U 236U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 241Am

243Am 237Np 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm

150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd

Table D.2. Nuclides in "set 3," on which the additional reactivity margin 

available from fission products and minor actinides is based

set 3: Minor actinides and major fission products (19 total)

236U 243Am 237Np 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm

149Sm 150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd
D-4

Figure D.1. Values of keff in the GBC-68 cask as a function of burnup using the different

nuclide sets and 5-year cooling time for fuel of 2 wt% 235U initial enrichment.
D-5

Figure D.2. Values of keff in the GBC-68 cask as a function of burnup using the different

nuclide sets and 5-year cooling time for fuel of 3 wt% 235U initial enrichment.
D-6

Figure D.3. Values of keff in the GBC-68 cask as a function of burnup using the different

nuclide sets and 5-year cooling time for fuel of 4 wt% 235U initial enrichment.
D-7

Figure D.4. Values of keff in the GBC-68 cask as a function of burnup using the different

nuclide sets and 5-year cooling time for fuel of 5 wt% 235U initial enrichment.
D-8

Figure D.5. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of burnup

using the different nuclide sets and 5-year cooling time for fuel of 2 wt% 235U 

initial enrichment.
D-9

Figure D.6. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of burnup

using the different nuclide sets and 5-year cooling time for fuel of 3 wt% 235U 

initial enrichment.
D-10

Figure D.7. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of burnup

using the different nuclide sets and 5-year cooling time for fuel of 4 wt% 235U 

initial enrichment.
D-11

Figure D.8. Δk values (relative to fresh fuel) in the GBC-68 cask as a function of burnup

using the different nuclide sets and 5-year cooling time for fuel of 5 wt% 235U 

initial enrichment.
D-12

Figure D.9. Individual contributions to the total reduction in keff for the different nuclide

sets as a function of burnup for fuel of 2 wt% 235U initial enrichment with a 5-

year cooling time.
D-13

Figure D.10. Individual contributions to the total reduction in keff for the different nuclide

sets as a function of burnup for fuel of 3 wt% 235U initial enrichment with a 

5-year cooling time.
D-14

Figure D.11. Individual contributions to the total reduction in keff for the different nuclide

sets as a function of burnup for fuel of 4 wt% 235U initial enrichment with a 

5-year cooling time.
D-15

Figure D.12. Individual contributions to the total reduction in keff for the different nuclide

sets as a function of burnup for fuel of 5 wt% 235U initial enrichment with a 

5-year cooling time.
D-16

Figure D.13. Δk values (relative to fresh fuel) in the GBC-68 cask due to major actinides

(set 1) as a function of burnup for various initial enrichments with a 5-year 

cooling time.
D-17

Figure D.14. Δk values (relative to fresh fuel) in the GBC-68 cask due to additional 

nuclides (set 3) as a function of burnup for various initial enrichments 

with a 5-year cooling time.
D-18

Figure D.15. Contribution to total reduction in keff due to the major actinides (set 1) as 

a function of burnup for various enrichments with a 5-year cooling time.
D-19

Figure D.16. Contribution of total reduction in keff due to the additional nuclides (set 3) as 

a function of burnup for various enrichments with a 5-year cooling time.
D-20

Figure D.17. Δk (relative to fresh fuel) in the GBC-68 cask due to the major actinides (set 

1) as a function of burnup for 4 wt% 235U initial enrichment fuel with various 

cooling times. 
D-21

Figure D.18. Δk (relative to fresh fuel) in the GBC-68 cask due to the minor actinides and

fission products (set 3) as a function of burnup for 4 wt% 235U initial 

enrichment fuel with various cooling times.
D-22

Figure D.19. Range of Δk in the GBC-68 cask due to the additional nuclides (set 3) as a

function of burnup for all cooling times and initial enrichments considered.
D-23

D.2 APPENDIX D REFERENCES

D.1 RW-859, “Nuclear Fuel Data”, Energy Information Administration, Washington, D.C., 

October 2004.

D. 2 B. L. Broadhead et al., Investigation of Nuclide Importance to Functional Requirements 

Related to Transport and Long-Term Storage for LWR Spent Fuel, ORNL/TM-12742, 

Lockheed Martin Energy Systems, Inc., Oak Ridge National Laboratory, June 1995.

D.3 T. Suto, S. M. Bowman, and C. V. Parks, “The Reactivity of Nuclide Buildup and Decay 

During Long-Term Fuel Storage,” Proceedings of the Fifth Annual International 

Conference on High Level Radioactive Waste Management, Vol. 2, p. 831, May 22–26, 

1994, Las Vegas, NV, (1994).

APPENDIX E. LIMITED NUCLIDE COMPOSITION DATA

E-1

Table E.1. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, zero cooling time and various burnups

Nuclide

10 

GWd/MTU

20 

GWd/MTU

30 

GWd/MTU

40 

GWd/MTU

50 

GWd/MTU

60 

GWd/MTU

234U 7.47E-06 6.52E-06 5.63E-06 4.82E-06 4.08E-06 3.43E-06

235U 6.97E-04 4.98E-04 3.43E-04 2.24E-04 1.39E-04 8.22E-05

236U 4.98E-05 8.36E-05 1.08E-04 1.24E-04 1.33E-04 1.36E-04

238U 2.24E-02 2.22E-02 2.21E-02 2.19E-02 2.17E-02 2.15E-02

237Np 1.85E-06 5.00E-06 8.65E-06 1.23E-05 1.57E-05 1.85E-05

238Pu 1.41E-07 7.92E-07 2.16E-06 4.29E-06 6.98E-06 9.89E-06

239Pu 7.75E-05 1.15E-04 1.31E-04 1.37E-04 1.37E-04 1.35E-04

240Pu 1.00E-05 2.59E-05 4.22E-05 5.68E-05 6.85E-05 7.71E-05

241Pu 3.91E-06 1.38E-05 2.36E-05 3.12E-05 3.65E-05 3.97E-05

242Pu 2.60E-07 2.15E-06 6.20E-06 1.21E-05 1.94E-05 2.75E-05

241Am 4.48E-08 3.20E-07 7.64E-07 1.20E-06 1.52E-06 1.69E-06

243Am 1.19E-08 2.24E-07 1.02E-06 2.65E-06 5.13E-06 8.25E-06

95Mo 9.16E-06 2.34E-05 3.67E-05 4.87E-05 5.95E-05 6.93E-05

99Tc 1.51E-05 2.93E-05 4.25E-05 5.46E-05 6.56E-05 7.54E-05

101Ru 1.32E-05 2.63E-05 3.92E-05 5.18E-05 6.41E-05 7.60E-05

103Rh 6.84E-06 1.48E-05 2.19E-05 2.81E-05 3.31E-05 3.70E-05

109Ag 4.98E-07 1.51E-06 2.84E-06 4.38E-06 6.03E-06 7.70E-06

133Cs 1.58E-05 3.09E-05 4.45E-05 5.68E-05 6.75E-05 7.69E-05

143Nd 1.25E-05 2.31E-05 3.11E-05 3.67E-05 3.99E-05 4.12E-05

145Nd 9.27E-06 1.75E-05 2.48E-05 3.12E-05 3.67E-05 4.13E-05

147Sm 4.86E-07 1.59E-06 2.85E-06 3.99E-06 4.88E-06 5.49E-06

149Sm 9.01E-08 9.17E-08 8.80E-08 8.24E-08 7.68E-08 7.24E-08

150Sm 2.86E-06 6.11E-06 9.45E-06 1.28E-05 1.59E-05 1.88E-05

151Sm 3.26E-07 3.76E-07 4.11E-07 4.38E-07 4.62E-07 4.86E-07

152Sm 1.42E-06 2.77E-06 3.76E-06 4.55E-06 5.20E-06 5.76E-06

151Eu 4.98E-10 5.82E-10 5.80E-10 5.52E-10 5.21E-10 5.00E-10

153Eu 7.11E-07 1.96E-06 3.50E-06 5.02E-06 6.39E-06 7.56E-06

155Gd 4.36E-10 1.02E-09 1.86E-09 2.77E-09 3.59E-09 4.32E-09

16O 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
E-2

Table E.2. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 5-year cooling time and various burnups

Nuclide 10 

GWd/MTU

20 

GWd/MTU

30 

GWd/MTU

40 

GWd/MTU

50 

GWd/MTU

60 

GWd/MTU

234U 7.48E-06 6.55E-06 5.72E-06 4.99E-06 4.37E-06 3.84E-06

235U 6.97E-04 4.98E-04 3.43E-04 2.24E-04 1.39E-04 8.22E-05

236U 4.98E-05 8.36E-05 1.08E-04 1.24E-04 1.33E-04 1.36E-04

238U 2.24E-02 2.22E-02 2.21E-02 2.19E-02 2.17E-02 2.15E-02

237Np 1.94E-06 5.15E-06 8.85E-06 1.26E-05 1.60E-05 1.88E-05

238Pu 1.43E-07 8.22E-07 2.27E-06 4.50E-06 7.28E-06 1.03E-05

239Pu 7.88E-05 1.16E-04 1.33E-04 1.38E-04 1.39E-04 1.37E-04

240Pu 1.00E-05 2.59E-05 4.22E-05 5.69E-05 6.89E-05 7.78E-05

241Pu 3.07E-06 1.08E-05 1.85E-05 2.45E-05 2.86E-05 3.12E-05

242Pu 2.60E-07 2.15E-06 6.20E-06 1.21E-05 1.94E-05 2.75E-05

241Am 8.84E-07 3.28E-06 5.81E-06 7.89E-06 9.33E-06 1.02E-05

243Am 1.20E-08 2.24E-07 1.02E-06 2.65E-06 5.13E-06 8.26E-06

95Mo 1.55E-05 2.96E-05 4.26E-05 5.43E-05 6.49E-05 7.44E-05

99Tc 1.53E-05 2.95E-05 4.27E-05 5.48E-05 6.58E-05 7.56E-05

101Ru 1.32E-05 2.63E-05 3.92E-05 5.18E-05 6.41E-05 7.60E-05

103Rh 8.49E-06 1.67E-05 2.40E-05 3.03E-05 3.55E-05 3.95E-05

109Ag 5.00E-07 1.51E-06 2.85E-06 4.39E-06 6.04E-06 7.71E-06

133Cs 1.63E-05 3.13E-05 4.50E-05 5.72E-05 6.80E-05 7.73E-05

143Nd 1.33E-05 2.39E-05 3.19E-05 3.75E-05 4.07E-05 4.20E-05

145Nd 9.28E-06 1.75E-05 2.48E-05 3.12E-05 3.67E-05 4.13E-05

147Sm 3.63E-06 6.41E-06 8.48E-06 9.92E-06 1.08E-05 1.13E-05

149Sm 1.22E-07 1.28E-07 1.27E-07 1.24E-07 1.20E-07 1.17E-07

150Sm 2.86E-06 6.11E-06 9.45E-06 1.28E-05 1.59E-05 1.88E-05

151Sm 3.20E-07 3.69E-07 4.03E-07 4.30E-07 4.53E-07 4.76E-07

152Sm 1.42E-06 2.77E-06 3.76E-06 4.55E-06 5.20E-06 5.76E-06

151Eu 1.31E-08 1.51E-08 1.64E-08 1.74E-08 1.83E-08 1.92E-08

153Eu 7.22E-07 1.98E-06 3.52E-06 5.05E-06 6.43E-06 7.61E-06

155Gd 2.46E-08 5.98E-08 1.17E-07 1.86E-07 2.54E-07 3.14E-07

16O 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
E-3

Table E.3. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 10-year cooling time and various burnups

Nuclide 10 

GWd/MTU

20 

GWd/MTU

30 

GWd/MTU

40 

GWd/MTU

50 

GWd/MTU

60 

GWd/MTU

234U 7.48E-06 6.58E-06 5.81E-06 5.17E-06 4.65E-06 4.24E-06

235U 6.97E-04 4.98E-04 3.43E-04 2.24E-04 1.39E-04 8.22E-05

236U 4.99E-05 8.37E-05 1.08E-04 1.24E-04 1.33E-04 1.36E-04

238U 2.24E-02 2.22E-02 2.21E-02 2.19E-02 2.17E-02 2.15E-02

237Np 1.95E-06 5.19E-06 8.91E-06 1.27E-05 1.61E-05 1.89E-05

238Pu 1.37E-07 7.90E-07 2.18E-06 4.33E-06 7.00E-06 9.86E-06

239Pu 7.88E-05 1.16E-04 1.33E-04 1.38E-04 1.39E-04 1.37E-04

240Pu 1.00E-05 2.59E-05 4.22E-05 5.70E-05 6.91E-05 7.84E-05

241Pu 2.41E-06 8.51E-06 1.45E-05 1.92E-05 2.25E-05 2.45E-05

242Pu 2.60E-07 2.15E-06 6.20E-06 1.21E-05 1.94E-05 2.75E-05

241Am 1.54E-06 5.58E-06 9.74E-06 1.31E-05 1.54E-05 1.68E-05

243Am 1.20E-08 2.24E-07 1.02E-06 2.65E-06 5.13E-06 8.25E-06

95Mo 1.55E-05 2.96E-05 4.26E-05 5.43E-05 6.49E-05 7.44E-05

99Tc 1.53E-05 2.95E-05 4.27E-05 5.48E-05 6.58E-05 7.56E-05

101Ru 1.32E-05 2.63E-05 3.92E-05 5.18E-05 6.41E-05 7.60E-05

103Rh 8.49E-06 1.67E-05 2.40E-05 3.03E-05 3.55E-05 3.95E-05

109Ag 5.00E-07 1.51E-06 2.85E-06 4.39E-06 6.04E-06 7.71E-06

133Cs 1.63E-05 3.13E-05 4.50E-05 5.72E-05 6.80E-05 7.73E-05

143Nd 1.33E-05 2.39E-05 3.19E-05 3.75E-05 4.07E-05 4.20E-05

145Nd 9.28E-06 1.75E-05 2.48E-05 3.12E-05 3.67E-05 4.13E-05

147Sm 4.48E-06 7.70E-06 9.98E-06 1.15E-05 1.24E-05 1.28E-05

149Sm 1.22E-07 1.28E-07 1.27E-07 1.24E-07 1.20E-07 1.17E-07

150Sm 2.86E-06 6.11E-06 9.45E-06 1.28E-05 1.59E-05 1.88E-05

151Sm 3.08E-07 3.55E-07 3.88E-07 4.14E-07 4.36E-07 4.58E-07

152Sm 1.42E-06 2.77E-06 3.76E-06 4.55E-06 5.20E-06 5.76E-06

151Eu 2.52E-08 2.90E-08 3.17E-08 3.37E-08 3.54E-08 3.72E-08

153Eu 7.22E-07 1.98E-06 3.52E-06 5.05E-06 6.43E-06 7.61E-06

155Gd 3.63E-08 8.82E-08 1.72E-07 2.74E-07 3.75E-07 4.64E-07

16O 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
E-4

Table E.4. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 20-year cooling time and various burnups

Nuclide 10 

GWd/MTU

20

GWd/MTU

30 

GWd/MTU

40 

GWd/MTU

50 

GWd/MTU

60 

GWd/MTU

234U 7.49E-06 6.64E-06 5.98E-06 5.50E-06 5.18E-06 4.99E-06

235U 6.97E-04 4.98E-04 3.43E-04 2.25E-04 1.39E-04 8.22E-05

236U 4.99E-05 8.37E-05 1.08E-04 1.24E-04 1.33E-04 1.37E-04

238U 2.24E-02 2.22E-02 2.21E-02 2.19E-02 2.17E-02 2.15E-02

237Np 1.99E-06 5.30E-06 9.12E-06 1.29E-05 1.64E-05 1.92E-05

238Pu 1.27E-07 7.30E-07 2.02E-06 4.00E-06 6.47E-06 9.11E-06

239Pu 7.88E-05 1.16E-04 1.33E-04 1.38E-04 1.39E-04 1.37E-04

240Pu 1.00E-05 2.59E-05 4.22E-05 5.71E-05 6.95E-05 7.93E-05

241Pu 1.48E-06 5.24E-06 8.94E-06 1.18E-05 1.38E-05 1.51E-05

242Pu 2.60E-07 2.15E-06 6.20E-06 1.21E-05 1.94E-05 2.75E-05

241Am 2.43E-06 8.73E-06 1.51E-05 2.02E-05 2.37E-05 2.59E-05

243Am 1.19E-08 2.24E-07 1.02E-06 2.65E-06 5.13E-06 8.25E-06

95Mo 1.55E-05 2.96E-05 4.26E-05 5.43E-05 6.49E-05 7.44E-05

99Tc 1.53E-05 2.95E-05 4.27E-05 5.48E-05 6.58E-05 7.56E-05

101Ru 1.32E-05 2.63E-05 3.92E-05 5.18E-05 6.41E-05 7.60E-05

103Rh 8.49E-06 1.67E-05 2.40E-05 3.03E-05 3.55E-05 3.95E-05

109Ag 5.00E-07 1.51E-06 2.85E-06 4.39E-06 6.04E-06 7.71E-06

133Cs 1.63E-05 3.13E-05 4.50E-05 5.72E-05 6.80E-05 7.73E-05

143Nd 1.33E-05 2.39E-05 3.19E-05 3.75E-05 4.07E-05 4.20E-05

145Nd 9.28E-06 1.75E-05 2.48E-05 3.12E-05 3.67E-05 4.13E-05

147Sm 4.76E-06 8.13E-06 1.05E-05 1.20E-05 1.29E-05 1.33E-05

149Sm 1.22E-07 1.28E-07 1.27E-07 1.24E-07 1.20E-07 1.17E-07

150Sm 2.86E-06 6.11E-06 9.45E-06 1.28E-05 1.59E-05 1.88E-05

151Sm 2.85E-07 3.29E-07 3.59E-07 3.83E-07 4.04E-07 4.24E-07

152Sm 1.42E-06 2.77E-06 3.76E-06 4.55E-06 5.20E-06 5.76E-06

151Eu 4.80E-08 5.53E-08 6.04E-08 6.43E-08 6.77E-08 7.12E-08

153Eu 7.22E-07 1.98E-06 3.52E-06 5.05E-06 6.43E-06 7.61E-06

155Gd 4.46E-08 1.08E-07 2.12E-07 3.37E-07 4.61E-07 5.71E-07

16O 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
E-5

Table E.5. Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt% 

235U, 40-year cooling time and various burnups

Nuclide 10 

GWd/MTU

20 

GWd/MTU

30 

GWd/MTU

40 

GWd/MTU

50 

GWd/MTU

60 

GWd/MTU

234U 7.51E-06 6.75E-06 6.27E-06 6.08E-06 6.13E-06 6.32E-06

235U 6.97E-04 4.98E-04 3.43E-04 2.25E-04 1.40E-04 8.23E-05

236U 4.99E-05 8.37E-05 1.08E-04 1.24E-04 1.34E-04 1.37E-04

238U 2.24E-02 2.22E-02 2.21E-02 2.19E-02 2.17E-02 2.15E-02

237Np 2.08E-06 5.64E-06 9.70E-06 1.37E-05 1.73E-05 2.02E-05

238Pu 1.08E-07 6.24E-07 1.72E-06 3.41E-06 5.53E-06 7.78E-06

239Pu 7.88E-05 1.16E-04 1.33E-04 1.38E-04 1.39E-04 1.37E-04

240Pu 1.00E-05 2.58E-05 4.22E-05 5.72E-05 6.99E-05 8.02E-05

241Pu 5.62E-07 1.99E-06 3.39E-06 4.48E-06 5.24E-06 5.71E-06

242Pu 2.60E-07 2.15E-06 6.20E-06 1.21E-05 1.94E-05 2.75E-05

241Am 3.26E-06 1.17E-05 2.01E-05 2.68E-05 3.14E-05 3.42E-05

243Am 1.19E-08 2.23E-07 1.01E-06 2.64E-06 5.12E-06 8.23E-06

95Mo 1.55E-05 2.96E-05 4.26E-05 5.43E-05 6.49E-05 7.44E-05

99Tc 1.53E-05 2.95E-05 4.27E-05 5.48E-05 6.58E-05 7.56E-05

101Ru 1.32E-05 2.63E-05 3.92E-05 5.18E-05 6.41E-05 7.60E-05

103Rh 8.49E-06 1.67E-05 2.40E-05 3.03E-05 3.55E-05 3.95E-05

109Ag 5.00E-07 1.51E-06 2.85E-06 4.39E-06 6.04E-06 7.71E-06

133Cs 1.63E-05 3.13E-05 4.50E-05 5.72E-05 6.80E-05 7.73E-05

143Nd 1.33E-05 2.39E-05 3.19E-05 3.75E-05 4.07E-05 4.20E-05

145Nd 9.28E-06 1.75E-05 2.48E-05 3.12E-05 3.67E-05 4.13E-05

147Sm 4.78E-06 8.17E-06 1.05E-05 1.21E-05 1.30E-05 1.34E-05

149Sm 1.22E-07 1.28E-07 1.27E-07 1.24E-07 1.20E-07 1.17E-07

150Sm 2.86E-06 6.11E-06 9.45E-06 1.28E-05 1.59E-05 1.88E-05

151Sm 2.45E-07 2.82E-07 3.08E-07 3.28E-07 3.46E-07 3.64E-07

152Sm 1.42E-06 2.77E-06 3.76E-06 4.55E-06 5.20E-06 5.76E-06

151Eu 8.88E-08 1.02E-07 1.12E-07 1.19E-07 1.25E-07 1.32E-07

153Eu 7.22E-07 1.98E-06 3.52E-06 5.05E-06 6.43E-06 7.61E-06

155Gd 4.70E-08 1.14E-07 2.23E-07 3.55E-07 4.86E-07 6.01E-07

16O 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02






UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/CR-7157 Computational Benchmark for Estimated Reactivity Margin from 

Fission Products and Minor Actinides in BWR Burnup Credit