NUREG/CR-6747

ORNL/TM-2000/306

Computational Benchmark for

Estimation of Reactivity

Margin from Fission Products

and Minor Actinides in

PWR Burnup Credit

Prepared by

J. C. Wagner, ORNL

Oak Ridge National Laboratory

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
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NUREG/CR–6747

ORNL/TM–2000/306

Computational Benchmark for

Estimation of Reactivity

Margin from Fission Products

and Minor Actinides in

PWR Burnup Credit

Manuscript Completed: July 2001

Date Published: October 2001

Prepared by

J. C. Wagner, ORNL

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831–6370

R. Y. Lee, NRC Project Manager

Prepared for

Division of System Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555–0001

NRC Job Code W6479

iii

ABSTRACT

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

reactivity margin available in spent nuclear fuel (SNF) from fission products and minor actinides in a burnupcredit storage/transport environment, relative to SNF compositions containing only the major actinides. The

benchmark problem/configuration is a generic burnup credit cask designed to hold 32 pressurized water reactor

(PWR) assemblies. The purpose of this computational benchmark is to provide a reference configuration for the

estimation of the additional reactivity margin, which is encouraged in the U.S. Nuclear Regulatory Commission

(NRC) guidance for partial burnup credit (ISG8), and document reference estimations of the additional reactivity

margin as a function of initial enrichment, burnup, and cooling time. Consequently, 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 fission-product margin. The reference

solutions were generated with the SAS2H-depletion and CSAS25-criticality sequences of the SCALE 4.4a

package. Although the SAS2H and CSAS25 sequences have been extensively validated elsewhere, the reference

solutions are not directly or indirectly based on experimental results. Consequently, this computational

benchmark cannot be used to satisfy the ANS 8.1 requirements for validation of calculational methods and is not

intended to be used to establish biases for burnup credit analyses.

v

CONTENTS

Page

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

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

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

ACKNOWLEDGEMENT................................................................................................................................... xi

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

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

1.2 BACKGROUND ................................................................................................................................1

1.3 ESTIMATION OF ADDITIONAL REACTIVITY MARGIN.............................................................2

1.3.1 Regulatory Guidance ...............................................................................................................2

1.3.2 Available Resources for Meeting the Regulatory Guidance ......................................................3

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

2.1 GBC-32 CASK SPECIFICATION......................................................................................................5

2.2 PWR FUEL ASSEMBLY SPECIFICATION......................................................................................7

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

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

3.2 GBC-32 COMPUTATIONAL MODEL............................................................................................ 11

3.3 RESULTS ........................................................................................................................................ 19

3.3.1 Reference Results .................................................................................................................. 19

3.3.2 Related Information ............................................................................................................... 19

3.3.3 Additional Results with Uniform Axial Burnup...................................................................... 19

4 CONCLUSIONS ....................................................................................................................................... 31

5. REFERENCES .......................................................................................................................................... 33

APPENDIX A — SAMPLE INPUT FILE FOR SAS2H .................................................................................... 35

APPENDIX B — SAMPLE INPUT FILE FOR CSAS25................................................................................... 41

APPENDIX C — SUPPLEMENTARY RESULTS FOR ADDITIONAL NUCLIDE SETS............................... 55

REFERENCES .......................................................................................................................................... 66

APPENDIX D — DISCUSSION OF REFERENCE RESULTS......................................................................... 67

REFERENCES .......................................................................................................................................... 90

APPENDIX E — LIMITED NUCLIDE COMPOSITION DATA ...................................................................... 91

vii

LIST OF FIGURES

Figure Page

1 Radial cross section of one quarter of the KENO V.a model for the GBC-32 cask.................................. 12

2 Cross-sectional view of assembly cell in KENO V.a model for the GBC-32 cask................................... 13

3 Cutaway view of KENO V.a model for the GBC-32 cask (one-half full height) ..................................... 15

4 Axial burnup profile used for calculations ............................................................................................. 16

C.1 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 5-year cooling time for fuel of 2 wt % 235U initial enrichment.......................................................... 58

C.2 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 20-year cooling time for fuel of 2 wt % 235U initial enrichment........................................................ 59

C.3 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 5-year cooling time for fuel of 3 wt % 235U initial enrichment.......................................................... 60

C.4 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 20-year cooling time for fuel of 3 wt % 235U initial enrichment........................................................ 61

C.5 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 5-year cooling time for fuel of 4 wt % 235U initial enrichment.......................................................... 62

C.6 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 20-year cooling time for fuel of 4 wt % 235U initial enrichment........................................................ 63

C.7 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 5-year cooling time for fuel of 5 wt % 235U initial enrichment.......................................................... 64

C.8 Values of keff in the GBC-32 cask as a function of the burnup using various nuclide sets

and 20-year cooling time for fuel of 5 wt % 235U initial enrichment........................................................ 65

D.1 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide sets and

5-year cooling time for fuel of 2 wt % 235U initial enrichment ................................................................ 71

D.2 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide sets and

5-year cooling time for fuel of 3 wt % 235U initial enrichment ................................................................ 72

D.3 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide sets and

5-year cooling time for fuel of 4 wt % 235U initial enrichment ................................................................ 73

D.4 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide sets and

5-year cooling time for fuel of 5 wt % 235U initial enrichment ................................................................ 74

D.5 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the different

nuclide sets and 5-year cooling time for fuel of 2 wt % 235U initial enrichment....................................... 75
viii

LIST OF FIGURES (continued)

Figure Page

D.6 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

different nuclide sets and 5-year cooling time for fuel of 3 wt % 235U initial enrichment......................... 76

D.7 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

different nuclide sets and 5-year cooling time for fuel of 4 wt % 235U initial enrichment......................... 77

D.8 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

different nuclide sets and 5-year cooling time for fuel of 5 wt % 235U initial enrichment......................... 78

D.9 Individual contributions to the total reduction in keff for the different nuclide sets as a function

of burnup and 5-year cooling time for fuel of 2 wt % 235U initial enrichment ......................................... 79

D.10 Individual contributions to the total reduction in keff for the different nuclide sets as a function

of burnup and 5-year cooling time for fuel of 3 wt % 235U initial enrichment ......................................... 80

D.11 Individual contributions to the total reduction in keff for the different nuclide sets as a function

of burnup and 5-year cooling time for fuel of 4 wt % 235U initial enrichment ......................................... 81

D.12 Individual contributions to the total reduction in keff for the different nuclide sets as a function

of burnup and 5-year cooling time for fuel of 5 wt % 235U initial enrichment.......................................... 82

D.13 ∆k (relative to fresh fuel) in GBC-32 cask due to the major actinides (set 1) as a function

of burnup for various initial enrichments and 5-year cooling time ......................................................... 83

D.14 ∆k in GBC-32 cask due to the additional nuclides (set 3) as a function of burnup for various

initial enrichments and 5-year cooling time............................................................................................ 84

D.15 Effect of initial enrichment on the contribution to total reduction in keff due to the major actinides

(set 1) as a function of burnup for 5-year cooling time ........................................................................... 85

D.16 Effect of initial enrichment on the contribution to total reduction in keff due to the additional

nuclides (set 3) as a function of burnup for 5-year cooling time.............................................................. 86

D.17 ∆k (relative to fresh fuel) in the GBC-32 cask due to the major actinides (set 1) as a function

of burnup for various cooling times and 4 wt % 235U initial enrichment.................................................. 87

D.18 ∆k in the GBC-32 cask due to the additional nuclides (set 3) as a function of burnup

for various cooling times and 4 wt % 235U initial enrichment.................................................................. 88

D.19 Range of ∆k values in the GBC-32 cask due to the additional nuclides (set 3) as a function

of burnup for all cooling times and initial enrichments considered ......................................................... 89
ix

LIST OF TABLES

Table Page

1 Physical dimensions for the GBC-32 cask ...................................................................................................6

2 Material compositions for GBC-32 cask model ...........................................................................................7

3 PWR fuel assembly specifications...............................................................................................................8

4 Material compositions for the fuel assembly................................................................................................9

5 Specification of axial burnup distribution used for benchmark problem .....................................................17

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

7 Nuclides in “set 3,” on which the additional reactivity margin available from fission products

and minor actinides is based......................................................................................................................18

8 keff values for the GBC-32 cask as a function of burnup and cooling time for 2 wt % 235U

initial enrichment ..................................................................................................................................21

9 keff values for the GBC-32 cask as a function of burnup and cooling time for 3 wt % 235U

initial enrichment .................................................................................................................................22

10 keff values for the GBC-32 cask as a function of burnup and cooling time for 4 wt % 235U

initial enrichment .................................................................................................................................23

11 keff values for the GBC-32 cask as a function of burnup and cooling time for 5 wt % 235U

initial enrichment .................................................................................................................................24

12 Individual components of the reduction in keff as a function of burnup and cooling time

for fuel of 2 wt % 235U initial enrichment ..................................................................................................25

13 Individual components of the reduction in keff as a function of burnup and cooling time

for fuel of 3 wt % 235U initial enrichment ..................................................................................................26

14 Individual components of the reduction in keff as a function of burnup and cooling time

for fuel of 4 wt % 235U initial enrichment ..................................................................................................27

15 Individual components of the reduction in keff as a function of burnup and cooling time

for fuel of 5 wt % 235U initial enrichment ..................................................................................................28

16 keff values with UNIFORM axial burnup for the GBC-32 cask as a function of burnup and

cooling time for 4 wt % 235U initial enrichment .........................................................................................29

17 Individual components of the reduction in keff for UNIFORM axial burnup as a function

of burnup and cooling time for fuel of 4 wt % 235U initial enrichment ........................................................30
LIST OF TABLES (continued)

Table Page

C.1 Nuclides used for supplementary analysis of the benchmark problem..................................................... 57

D.1 Nuclide sets defined for the benchmark problem analysis....................................................................... 70

D.2 Nuclides in “set 3,” on which the additional reactivity margin available from fission products

and minor actinides is based .................................................................................................................. 70

E.1 Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt % 235U,

zero cooling time, and various burnups.................................................................................................. 93

E.2 Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt % 235U,

5-year cooling time, and various burnups............................................................................................... 94

E.3 Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt % 235U,

20-year cooling time, and various burnups............................................................................................. 95
xi

ACKNOWLEDGEMENT

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

Regulatory Commission (NRC). The author acknowledges C. V. Parks of Oak Ridge National Laboratory

(ORNL) for providing guidance for this report and C. J. Withee of the NRC Spent Fuel Project Office for his

review and useful comments. The careful review of the draft manuscript by M. D. DeHart, I. C. Gauld, and

C. E. Sanders is very much appreciated. Finally, the author is thankful to W. C. Carter for her preparation of the

final report.

1

1 INTRODUCTION

This report proposes 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 pressurized water reactor (PWR) burnup credit storage/transport environment. Herein, the major actinides are

consistent with those specified in a Department of Energy (DOE) topical report1

 on burnup credit (i.e., 234U, 235U,

238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, and 241Am). Although the additional reactivity margin is primarily due to

fission products, a few minor actinides (i.e., 236U, 237Np, and 243Am) that have been identified as being relevant to

burnup credit2

 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 the SAS2H-depletion and CSAS25-criticality modules of the SCALE 4.4a package.3

 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 SAS2H and CSAS25 sequences have

been validated using laboratory critical experiments, commercial reactor criticals (CRCs), measured chemical

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

reference solutions 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 normalize 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 (∆k values),

benchmarking of depletion and criticality codes, individually, is not the intent. Comparison of calculated results

to the reference solutions does not satisfy the ANS 8.1 (Ref. 4) requirements for validation of calculational

methods, which 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.

1.2 BACKGROUND

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

canisters5,6 have assumed the spent nuclear fuel (SNF) to be fresh (unirradiated) fuel with uniform isotopic

compositions corresponding to the maximum allowable enrichment. This “fresh-fuel assumption” provides a

well-defined, bounding approach for the criticality safety analysis that eliminates all concerns related to the fuel

operating history, and thus considerably simplifies the safety analysis. However, because this assumption ignores

the decrease in reactivity as a result of 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 that occurs with fuel burnup is due to the change in concentration (net

reduction) of fissile nuclides and the production of actinide and fission-product neutron absorbers. Consequently,
Introduction Section 1

2

it has been recognized that if criticality calculations are performed based on all fissile nuclides and a limited

subset of absorbers, the calculated neutron multiplication factor (keff ) is conservative (i.e., keff is overestimated).

To date, the proposed approach1,7 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.8

Isotopic validation studies using the SCALE/SAS2H depletion sequence and available measured assay data have

been performed for PWR spent fuel9,10,11 and boiling water reactor (BWR) spent fuel.12 For the most part, the

fission product data available in the United States for PWR fuel are limited to 3–6 samples,9

 and calculational

methods for these nuclides may not be considered to be fully validated. Note that additional chemical assay data

are becoming available that will enable improved validation for fission products. However, the paucity of

available chemical assay data for fission products is the major reason that only partial or “actinide-only” burnup

credit was considered in a topical report1

 prepared by the DOE and the U.S. Nuclear Regulatory Commission

(NRC) interim staff guidance (ISG8)13 on burnup credit. “Actinide-only burnup credit” refers to criticality

analyses that include only a limited set of actinide isotopes in the SNF (i.e., fission products and certain other

actinides are not included in the criticality analysis). The additional reduction in reactivity due to the presence of

the fission products, often referred to as the fission product margin, is still present in reality; but since sufficient

measured data for isotopic validation do not exist, credit for their negative reactivity worth has not generally been

recommended for inclusion in safety analyses for storage and transport.

Studies14,15,1 have been performed to quantify the incremental reactivity worth of actinides and fission products for

an infinite lattice of fuel pins. The results indicate that, for typical discharge burnup values, approximately 2/3 of

the reactivity decrease is due to actinides, with the remaining 1/3 due to fission products. However, it is

important to note that the competing effect of external absorbers in cask designs affect this ratio for finite cask

analysis, resulting in a relative reduction in the reactivity worth of the fission products.2,16 This reduced effect has

been demonstrated and has led to some concerns regarding the estimation of fission product margin in different

systems.16

1.3 ESTIMATION OF ADDITIONAL REACTIVITY MARGIN

1.3.1 Regulatory Guidance

The NRC interim staff guidance (ISG8)13 on burnup credit in storage/transport casks permits partial credit for

burnup in PWR fuel. ISG8 limits credit for the reactivity reduction associated with burnup to that available from

actinide compositions (i.e., actinide-only burnup credit). Moreover, the actinides are limited to those that are

established by validation (e.g., benchmarks of applicable fuel assay measurements). Credit for the reactivity

reduction due to fission products is not currently included due to the greater uncertainties associated with

inventory prediction and cross-section data for fission products. Consequently, an added margin of subcriticality

exists due to the presence of fission product and actinide nuclides not included in the design-basis safety analysis.

To assess the effect of fission products, and thus gain a greater understanding of the actual subcritical margin,

ISG8 calls for design-specific analyses to estimate the additional reactivity margins available from the fission

products and actinide nuclides not included in the design-basis safety analysis. Additionally, ISG8 states that,

“the analysis methods used for determining the estimated reactivity margins should be verified using available

experimental data (e.g., isotopic assay data) and computational benchmarks that demonstrate the performance of

the applicant's methods in comparison with independent methods and analyses.” Further, ISG8 states that,

“design-specific margins should be evaluated over the full range of initial enrichments and burnups on the burnup

credit loading curve(s).”
Section 1 Introduction

3

Besides assessing the actual subcritical margin as recommended in the regulatory guidance, the potential

utilization of some portion of the additional reactivity margin provides added incentive for its estimation. ISG8

recommends that the estimated margins be assessed against estimates of (a) any uncertainties not directly

evaluated in the modeling or validation processes and (b) any potential nonconservatisms in the models for

calculating the licensing safety basis actinide inventories.

1.3.2 Available Resources for Meeting the Regulatory Guidance

The Nuclear Energy Agency (NEA) of the Organization for Economic Cooperation and Development (OECD)

sponsors an Expert Group tasked with the study of burnup credit issues. The Expert Group on Burnup Credit

(EGBUC), formerly known as the BUCWG, defines and analyzes computational benchmarks for the purpose of

international comparison of computer code/data packages used for the analysis of spent fuel. The broad scope of

international participants enables comparison of a wide range of codes, data, and methods for each benchmark

problem. To date, the EGBUC has studied a number of different configurations relevant to burnup credit in LWR

fuel.17 The studies (or phases) relevant to PWR burnup credit include: Phase I, which investigated the calculation

of the neutron multiplication factor for an infinite lattice of PWR pins and the prediction of isotopic composition

of spent PWR fuel under simplified operating conditions15,18 and Phase II, which investigated the effect of the

axial burnup distribution in a radially infinite array of PWR pins and in a conceptual burnup credit cask.19,20 

The ISG8 refers to the OECD/NEA’s EGBUC as a source of computational benchmarks that may be considered.

Another resource for meeting the regulatory guidance is the limited isotopic assay data available for fission

products.9

 Finally, it should be noted that this discussion of available resources is not exhaustive. A number of

ongoing research projects, both domestically and internationally, have already or soon will contribute to the pool

of available resources and experimental data for validating estimations of the additional reactivity margin

available from fission product and minor actinide nuclides.
4
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 32 PWR-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 cask, referred to herein as the GBC-32 cask, is provided in this section. Reference fuel assembly

dimensions, corresponding to a 17 × 17 Westinghouse optimized fuel assembly (OFA), are also provided in this

section.

2.1 GBC-32 CASK SPECIFICATION

The primary motivation for burnup credit is to eliminate the need for flux-traps between PWR assembly storage

cells, and thus increase storage and transport cask capacities for a constant canister volume. For the current large,

rail-type cask internal dimensions, this could enable an increase in the assembly capacity by as much as one-third

(e.g., increasing total assembly capacity from ~24 to ~32). Although individual canister capacities will vary

depending on the inner diameter and assembly cell size, typical burnup credit rail casks are expected to

accommodate between 24 and 40 assemblies. Canisters designed to accommodate large PWR assemblies

(e.g., 15 × 15 & 17 × 17) are expected to have maximum capacities of approximately 32 assemblies, while

canisters designed to accommodate the smaller PWR assemblies (e.g., 14 × 14 & 16 × 16) are expected to have

maximum capacities nearing 40 assemblies.

With these thoughts in mind, a review of various cask designs, and consideration of the OECD/NEA conceptual

PWR spent fuel transportation cask,20 a generic burnup credit cask design was developed. The design was

developed to meet the following criteria: (1) the internal dimensions and geometry should be representative of

typical U.S. rail-type casks, (2) the canister must accommodate at least 30 fuel assemblies, (3) the assembly cell

size must be large enough to accommodate all common PWR fuel assembly designs, and (4) the design must be

general (i.e., no proprietary information and no unique features that would unnecessarily limit its applicability for

analyses). The generic design employs features from several U.S. cask vendor’s designs (e.g., similar canister

inside diameter and Boral21 for fixed neutron poison), as well as features from the OECD benchmark cask.20

The generic cask design, designated GBC-32, will accommodate 32 PWR fuel assemblies. Dimensions for the

GBC-32 cask are listed in Table 1. For simplicity, the fuel assemblies are centered in the storage cells and the

assembly upper and lower hardware are modeled as water. The height of the fuel assembly cell, which includes

the Boral panel, is equivalent to the active fuel length, and the upper and lower boundaries are coincident.

Material specifications are provided in Table 2.
Benchmark Specification Section 2

6

Table 1 Physical dimensions for the GBC-32 cask

Parameter inches cm

Cell inside dimension (I.D.) 8.6614 22.0000

Cell outside dimension (O.D.) 9.2520 23.5000

Cell wall thickness 0.2953 0.7500

Boral panel thickness† 0.1010 0.2565

Boral center thickness 0.0810 0.2057

Boral Al plate thickness 0.0100 0.0254

Cell pitch 9.3530 23.7565

Boral panel width 7.5000 19.0500

Cell height‡ 144.0000 365.76

Boral panel height‡ 144.0000 365.76

Cask inside diameter (I.D.) 68.8976 175.0000

Cask outside diameter (O.D.) 84.6457 215.0000

Cask radial thickness 7.8740 20.0000

Base plate thickness 11.8110 30.0000

Cask lid thickness 11.8110 30.0000

Cask inside height 161.7165 410.7600

Active fuel height‡ 144.0000 365.76

Bottom assembly hardware thickness 5.9055 15.0000

Top assembly hardware thickness 11.8110 30.0000

† Boral 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 that consists of a uniform aggregate of fine boron carbide

 particles within 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.
Section 2 Benchmark Specification

7

Table 2 Material compositions for GBC-32 cask model

Isotope Atom density (atoms/b-cm) Weight percent

Water (Density = 0.9983 g/cm3)

Hydrogen (H) 0.06674 11.19

Oxygen (O) 0.03337 88.81

Total 0.10011 100.0

Stainless steel 304 (Density = 7.92 g/cm3) [22]

Chromium (Cr) 0.01743 19.0

Manganese (Mn) 0.00174 2.0

Iron (Fe) 0.05936 69.5

Nickel (Ni) 0.00772 9.5

Total 0.08625 100.0

Boral panel Aluminum cladding (Density = 2.699 g/cm3)

Aluminum (Al) 0.0602 [23] 100.0

Total 0.0602 100.0

Boral panel central layer (0.0225 g B-10/cm2)

†

Boron-10 (B-10) 6.5794E-03 4.13

Boron-11 (B-11) 2.7260E-02 18.81

Carbon (C) 8.4547E-03 6.37

Aluminum (Al) 4.1795E-02 70.69

Total 8.4089E-02 100.0

†

 Note: 0.030 g B-10/cm2 is the loading from the manufacturer (AAR21) that corresponds to the

 modeled Boral panel thickness of 0.101 inches. However, current NRC regulations5

 allow only 75%

 credit for fixed neutron absorbers, and thus 75% of 0.030, or 0.0225 g B-10/cm2

 is used.

2.2 PWR FUEL ASSEMBLY SPECIFICATION

The reference fuel assembly design used in the GBC-32 cask is the Westinghouse 17 × 17 OFA. This assembly

was selected as the reference because it has been shown to be the most reactive assembly in most fresh-fuel cask

designs.5

 However, it is acknowledged that this assembly design will likely not be the most reactive in a burnup

credit cask design. The characteristic that makes this assembly design so reactive at zero burnup (fresh), namely

the high moderator-to-fuel ratio, is also responsible for making this assembly less reactive, as compared to a

similar assembly design with lower moderator-to-fuel ratio (e.g., Westinghouse 17 × 17 Standard), at typical
Benchmark Specification Section 2

8

discharge burnups. The assembly physical specifications are listed in Table 3. The initial (fresh) fuel material

specifications for the various initial enrichments considered are listed in Table 4.

Table 3 PWR fuel assembly specifications

Parameter inches cm

Fuel outside diameter 0.3088 0.7844

Cladding inside diameter 0.3150 0.8001

Cladding outside diameter 0.3600 0.9144

Cladding radial thickness 0.0225 0.0572

Rod pitch 0.4960 1.2598

Guide tube/thimble inside diameter 0.4420 1.1227

Guide tube/thimble outside diameter 0.4740 1.2040

Thimble radial thickness 0.0160 0.0406

Instrument tube inside diameter 0.4420 1.1227

Instrument tube outside diameter 0.4740 1.2040

Instrument tube radial thickness 0.0160 0.0406

Active fuel length 144 365.76

Array size 17 × 17

Number of fuel rods 264

Number of guide tubes/thimbles 24

Number of instrument tubes 1
Section 2 Benchmark Specification

9

Table 4 Material compositions for the fuel assembly

Isotope Atom density (atoms/b-cm) Weight percent

Cladding (Density = 6.40 g/cm3)

Zirconium (Zr) 0.0423 [23] 100.0

Total 0.0423 100.0

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

Oxygen (O) 4.686E-02 11.8519

234U 3.905E-06 0.0144

235U 4.745E-04 1.7630

236U 2.173E-06 0.0081

238U 2.295E-02 86.3626

Total 7.029E-02 100.0

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

Oxygen (O) 4.686E-02 11.8532

234U 6.058E-06 0.0224

235U 7.117E-04 2.6444

236U 3.260E-06 0.0122

238U 2.271E-02 85.4678

Total 7.030E-02 100.0

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

Oxygen (O) 4.687E-02 11.8545

234U 8.274E-06 0.0306

235U 9.489E-04 3.5258

236U 4.346E-06 0.0162

238U 2.247E-02 84.5728

Total 7.030E-02 100.0

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

Oxygen (O) 4.687E-02 11.8558

234U 1.054E-05 0.0390

235U 1.186E-03 4.4072

236U 5.433E-06 0.0203

238U 2.224E-02 83.6777

Total 7.031E-02 100.0
10
11

3 ANALYSIS

3.1 COMPUTATIONAL METHODS

The computational methods necessary for this benchmark analysis include codes for depletion and criticality

simulation. A prototype control module designed to automate burnup credit criticality safety analyses by

coupling the depletion and criticality modules of SCALE (Ref. 3) was used for this analysis. This module,

referred to as STARBUCS, couples a number of SCALE code modules, including ARP, ORIGEN-S, CSASI,

WAX, and KENO V.a, to achieve this automation. The ARP code prepares cross sections for each irradiation

cycle based on interpolation for the fuel enrichment and the mid-cycle burnup. The use of ARP requires that an

ARP library containing the required cross sections be available. These may be obtained from pre-made libraries

available with SCALE, or the user may generate problem-specific libraries. For this analysis, problem-specific

libraries were generated with the SAS2H sequence of SCALE. All SAS2H calculations utilized the SCALE

44-group (ENDF/B-V) library. The depletion calculations were performed using reasonably conservative cycleaverage operational parameters for fuel temperature (1000 K), clad temperature (620 K), moderator temperature

(600 K), soluble boron concentration (650 ppm) and specific power (60 MW/MTU). The sensitivity of keff to

variations in these parameters is discussed in Ref. 8. However, it should be noted that this is not a safety

evaluation, and thus there is no requirement for the depletion parameters to be bounding. A sample SAS2H input

file, which was used to generate the ARP libraries, is provided in Appendix A.

Using an ARP-generated cross-section library, ORIGEN-S performs the depletion calculation to generate the fuel

compositions for the burnup and decay time requested for a single axial fuel region. Subsequently, ARP and

ORIGEN-S calculations are performed for each of the axial fuel regions. After the fuel compositions from all

axial regions have been generated, the CSASI module is called to automate resonance self-shielding and prepare

macroscopic fuel cross sections for each axial region. Sequentially with CSASI, the WAX module is executed to

append the cross sections into a single cross-section library for all axial fuel regions. Finally, the STARBUCS

module executes the three-dimensional (3-D) KENO V.a Monte Carlo criticality code using the generated axiallyvarying cross sections and isotopic compositions. To ensure proper convergence and reduce statistical

uncertainty, the KENO V.a calculations simulated 1100 generations, with 2000 neutron histories per generation,

and skipped the first 100 generations before averaging; thus, each calculated keff value is based on 2 million

neutron histories. These calculations utilized the SCALE 238-group cross-section library, which is primarily

based on ENDF/B-V data, and required ~18 CPU-minutes for each keff calculation (on a DEC AlphaStation 500).

Since the STARBUCS module is not currently publicly available, and the CSAS25 module is a standard part of

SCALE, an equivalent sample input file for CSAS25 is provided in Appendix B.

3.2 GBC-32 COMPUTATIONAL MODEL

Based on the benchmark specification provided in Section 2, a computational model of the GBC-32 cask, loaded

with PWR fuel assemblies, was developed for KENO V.a (Ref. 3). Cross-sectional views of the computational

model, as generated by KENO V.a, are shown in Figure 1 and Figure 2. A 3-D cutaway view, as generated by

KENO3D (Ref. 24), is shown in Figure 3. To aid users of this proposed benchmark in verification of their

criticality models, keff values corresponding to fresh fuel are provided in the next section for initial enrichments of

2, 3, 4, and 5 wt % 235U.
Analysis Section 3

12

Figure 1 Radial cross section of one quarter of the KENO V.a model for the GBC-32 cask
Section 3 Analysis

13

Figure 2 Cross-sectional view of assembly cell in KENO V.a model for the GBC-32 cask

22.0 cm

0.75 cm

1.7565 cm
Analysis Section 3

14

The active fuel length of the assemblies is divided into 18 equal-length axial regions to facilitate the variation in

axial composition due to the axial burnup distribution.25 Although the shape of the axial burnup distribution is

known to vary as a function of burnup, a single axial burnup profile was used for this analysis to facilitate the

estimation of the additional reactivity margin and corresponding discussion. The profile used corresponds to the

bounding profile suggested in Ref. 1 for PWR fuel with average-assembly discharge burnup greater than

30 GWd/MTU. The axial burnup profile is plotted in Figure 4 and the specifications necessary for modeling the

axial burnup profile are provided in Table 5. Horizontal variations in burnup are not included in this

computational benchmark problem. Finally, for simplicity, isotopic correction factors (used to “correct” predicted

isotopic compositions to that determined from comparisons with measured assay data) are not considered for this

benchmark problem.

For the criticality calculations, it is necessary to define the isotopes considered. As mentioned, the use of a subset

of possible actinides in burnup credit calculations is referred to as “actinide-only” burnup credit. The nuclides

used here for actinide-only calculations are consistent with those specified in the DOE topical report on actinideonly burnup credit.1

 Other actinides of minor importance to burnup credit, for which measured assay data are

available, are 236U and 237Np (Ref. 26), but these actinides are omitted from the actinide-only calculations due to

large deviations between calculated and measured values for 237Np and the lack of sufficient critical experiments

with 236U (Ref. 1).

In determining which additional nuclides to include for the estimation of the additional reactivity margin, the

following two criteria were considered: (1) reactivity worth and (2) availability of cross-section data. It was

recognized that the availability of nuclides in the various cross-section libraries is an important consideration.

Thus, it was decided not to consider all of the nuclides for which cross-section data are available (in SCALE),

because doing so may make it difficult for others to analyze the benchmark with other codes/data (e.g., other code

systems may not have data available for all of the included nuclides).

Regarding reactivity worth, 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 to the primary

criticality codes for all of the 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 Table 2 of

Ref. 2, including those for which no chemical assay data are available, are used in the estimation of the additional

reactivity margin. This decision is based on the objective of estimating the residual margins associated with

actinide-only burnup credit. Additionally, it should be noted that the selected actinide and fission product

nuclides account for less than the total negative worth of all of the nuclides in SNF.2

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,1

 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. 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 7.
Section 3 Analysis

15

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.

Figure 3 Cutaway view of KENO V.a model for the GBC-32 cask (one-half full height)

 
Analysis Section 3

16

Figure 4 Axial burnup profile used for calculations (Source: Ref. 1)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 50 100 150 200 250 300 350

Distance from Bottom of Assembly (cm)

Normalized Burnup
Section 3 Analysis

17

Table 5 Specification of axial burnup distribution used for benchmark problem (Source: Ref. 1)

Upper bound of axial region, measured

from bottom of active fuel

(cm) Normalized burnup

20.32 0.652

40.64 0.967

60.95 1.074

81.27 1.103

101.61 1.108

121.93 1.106

142.28 1.102

162.60 1.097

182.88 1.094

203.20 1.094

223.52 1.095

243.83 1.096

264.15 1.095

284.49 1.086

304.81 1.059

325.12 0.971

345.44 0.738

365.76 0.462
Analysis Section 3

18

Table 6 Nuclide sets defined for the benchmark problem analysis

set 1: Major actinides (10 total)

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

set 2: Actinides and major fission products (29 total)

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

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

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

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

Sm-149 Sm-150 Sm-151 Sm-152 Nd-143 Nd-145 Eu-151 Eu-153 Gd-155
Section 3 Analysis

19

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 time,

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-32 cask as a function of burnup and cooling time for initial enrichments of 2, 3,

4, and 5 wt % 235U are listed in Tables 8–11. Values are provided for the burnup range of 0-60 GWd/MTU, in

increments of 10 GWd/MTU, and for cooling times of 0, 5, 10, 20, and 40 years. Standard deviations are also

listed in the tables and are all less than 0.00075. The individual components of keff reduction (∆k) associated with

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

Tables 12–15. The second column from the left in Tables 12–15 lists the ∆k reductions (relative to fresh fuel) 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 the major 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

Tables 12–15 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 relative reactivity reduction associated with (a) the

major actinides and (b) the 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.2

3.3.2 Related Information

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

benchmark, are available in Appendices C and D. Results for various additional nuclide sets as a function of

burnup for each initial enrichment and cooling times of 5 and 20 years are provided in Appendix C. Discussion of

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

3.3.3 Additional Results with Uniform Axial Burnup

As it is recognized that the presence of the axial burnup distribution in the benchmark problem adds complexity

and, depending on the computational tools available to the analyst, may substantially increase the effort associated

with analyzing this computational benchmark problem, additional reference results are presented in this section

for uniform axial burnup. Note, however, 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
Analysis Section 3

20

that the computational benchmark results in this section 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 18

(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 and various burnup and cooling time combinations are included in

Appendix E to enable comparisons of calculated spent fuel compositions.

Calculated keff values, based on the nuclide sets identified in the Section 2, as a function of burnup and cooling

time, within the ranges relevant to storage and transportation, are provided for a single initial fuel enrichment of

4 wt % 235U. The calculated keff values are listed in Table 16 and the individual components of the reactivity

reduction associated with (a) the major actinides and (b) the additional nuclides as a function of burnup and

cooling time are listed in Table 17. The second column from the left in Table 17 lists the ∆k reactivity reductions

(relative to fresh fuel) due to the presence of the major actinides alone (nuclide set 1, see Table 6), while the third

column lists the reactivity reduction due to the presence of the major 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 reactivity margin associated with the fission products and additional actinides.

The fourth column from the left in Table 17 lists the total reactivity 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 reactivity reduction, and thus provide an assessment of the

relative reactivity reduction associated with (a) the major actinides and (b) the additional nuclides.

Comparison of the results in Table 17 with those listed in Table 14 shows that, with the uniform axial burnup

distribution, the calculated total reactivity reduction is overestimated for burnups greater than approximately

10 GWd/MTU. The individual components of reactivity reduction due to (a) the major actinides and (b) the

additional nuclides are shown to be overestimated for burnups greater than approximately 20 GWd/MTU and

10 GWd/MTU, respectively. Thus, for typical discharge burnups (30–50 GWd/MTU for 4 wt % 235U

enrichment), 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. Further, the overestimation

increases with cooling time.
Section 3 Analysis

21

Table 8 keff values for the GBC-32 cask as a function of burnup and cooling time for 2 wt % 235U initial 

Major actinides (nuclide set 1, see Table 6)

Cooling time

(years)

0 5 10 20 

Burnup

(GWd/MTU)

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

 0 0.94797 0.00058 0.94797 0.00058 0.94797 0.00058 0.94797 0.00058 0.9

10 0.90142 0.00051 0.89928 0.00046 0.89373 0.00055 0.88818 0.00051 0.20 0.85376 0.00049 0.84486 0.00048 0.83519 0.00046 0.82165 0.00055 0.30 0.81963 0.00053 0.80657 0.00044 0.79199 0.00053 0.77240 0.00048 0.740 0.79629 0.00048 0.77814 0.00049 0.75867 0.00042 0.73439 0.00048 0.750 0.78326 0.00054 0.75996 0.00045 0.73669 0.00047 0.70568 0.00051 0.660 0.77869 0.00045 0.74930 0.00039 0.72356 0.00041 0.68805 0.00040 0.6

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

 0 0.94797 0.00058 0.94797 0.00058 0.94797 0.00058 0.94797 0.00058 0.9

10 0.86946 0.00049 0.85380 0.00048 0.85015 0.00051 0.84444 0.00053 0.20 0.80832 0.00048 0.78712 0.00045 0.77769 0.00045 0.76753 0.00052 0.730 0.76508 0.00046 0.73685 0.00047 0.72437 0.00043 0.70679 0.00048 0.640 0.73163 0.00040 0.70005 0.00046 0.68218 0.00057 0.66012 0.00040 0.650 0.70701 0.00043 0.67103 0.00044 0.64977 0.00043 0.62388 0.00044 0.660 0.68844 0.00051 0.64783 0.00047 0.62443 0.00041 0.59499 0.00040 0.5

21
Analysis Section 3

22

Table 9 keff values for the GBC-32 cask as a function of burnup and cooling time for 3 wt % 235U initial 

Major actinides (nuclide set 1, see Table 6)

Cooling time

(years)

0 5 10 20 

Burnup

(GWd/MTU)

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

 0 1.06633 0.00059 1.06633 0.00059 1.06633 0.00059 1.06633 0.00059 1.0

10 1.01277 0.00055 1.01232 0.00058 1.00913 0.00055 1.00438 0.00054 1.020 0.95973 0.00055 0.95288 0.00046 0.94668 0.00053 0.93680 0.00047 0.930 0.91723 0.00053 0.90684 0.00054 0.89573 0.00052 0.88210 0.00055 0.40 0.88025 0.00051 0.86807 0.00058 0.85486 0.00058 0.83711 0.00056 0.50 0.85158 0.00053 0.83412 0.00054 0.81885 0.00047 0.79703 0.00047 0.760 0.82720 0.00050 0.80870 0.00050 0.78895 0.00046 0.76269 0.00049 0.7

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

 0 1.06633 0.00059 1.06633 0.00059 1.06633 0.00059 1.06633 0.00059 1.0

10 0.97915 0.00052 0.96674 0.00044 0.96348 0.00050 0.96000 0.00055 0.920 0.91232 0.00054 0.89556 0.00053 0.88923 0.00053 0.87974 0.00060 0.30 0.86008 0.00049 0.83836 0.00061 0.82832 0.00056 0.81603 0.00052 0.40 0.81703 0.00055 0.79134 0.00060 0.77723 0.00057 0.76236 0.00059 0.750 0.78077 0.00053 0.75040 0.00050 0.73375 0.00051 0.71466 0.00043 0.660 0.74946 0.00047 0.71563 0.00051 0.69751 0.00047 0.67412 0.00044 0.6

22
Section 3 Analysis

23

Table 10 keff values for the GBC-32 cask as a function of burnup and cooling time for 4 wt % 235U initial 

Major actinides (nuclide set 1, see Table 6)

Cooling time

(years)

0 5 10 20 

Burnup

(GWd/MTU)

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

 0 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.

10 1.09164 0.00058 1.09080 0.00065 1.08835 0.00056 1.08607 0.00061 1.020 1.04031 0.00068 1.03480 0.00062 1.03061 0.00061 1.02341 0.00061 1.030 0.99712 0.00058 0.98852 0.00057 0.98179 0.00050 0.97011 0.00058 0.940 0.96212 0.00056 0.94987 0.00061 0.93875 0.00069 0.92537 0.00054 0.950 0.92785 0.00057 0.91323 0.00058 0.90156 0.00053 0.88338 0.00059 0.60 0.89973 0.00057 0.88209 0.00057 0.86666 0.00054 0.84654 0.00063 0.

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

 0 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.

10 1.05711 0.00060 1.04583 0.00058 1.04295 0.00062 1.03927 0.00055 1.020 0.98981 0.00065 0.97480 0.00054 0.96995 0.00055 0.96340 0.00060 0.930 0.93904 0.00055 0.91944 0.00057 0.91224 0.00048 0.90120 0.00061 0.40 0.89470 0.00058 0.87156 0.00058 0.86051 0.00053 0.84925 0.00053 0.50 0.85564 0.00061 0.82811 0.00056 0.81489 0.00057 0.80009 0.00051 0.760 0.82032 0.00053 0.79043 0.00056 0.77525 0.00054 0.75693 0.00062 0.7

23
Analysis Section 3

24

Table 11 keff values for the GBC-32 cask as a function of burnup and cooling time for 5 wt % 235U initial 

Major actinides (nuclide set 1, see Table 6)

Cooling time

(years)

0 5 10 20 

Burnup

(GWd/MTU)

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

 0 1.19142 0.00056 1.19142 0.00056 1.19142 0.00056 1.19142 0.00056 1.

10 1.14856 0.00057 1.14808 0.00063 1.14680 0.00058 1.14482 0.00058 1.20 1.10288 0.00064 1.09803 0.00059 1.09310 0.00056 1.08810 0.00061 1.030 1.06231 0.00057 1.05430 0.00065 1.04805 0.00049 1.03898 0.00054 1.040 1.02689 0.00062 1.01604 0.00058 1.00786 0.00059 0.99584 0.00063 0.950 0.99396 0.00057 0.98203 0.00064 0.97055 0.00055 0.95624 0.00055 0.960 0.96403 0.00056 0.94944 0.00055 0.93655 0.00059 0.91956 0.00056 0.9

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

 0 1.19142 0.00056 1.19142 0.00056 1.19142 0.00056 1.19142 0.00056 1.

10 1.11293 0.00062 1.10270 0.00061 1.10083 0.00060 1.09906 0.00061 1.020 1.05132 0.00057 1.03554 0.00055 1.03228 0.00057 1.02738 0.00052 1.030 1.00087 0.00059 0.98376 0.00061 0.97800 0.00062 0.96914 0.00063 0.940 0.95883 0.00051 0.93748 0.00053 0.92718 0.00060 0.91822 0.00055 0.950 0.91844 0.00054 0.89442 0.00058 0.88344 0.00056 0.87030 0.00047 0.60 0.88140 0.00048 0.85549 0.00052 0.84317 0.00055 0.82850 0.00050 0.

24
Section 3 Analysis

25

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

∆k 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 0.04655 0.03196 0.07851 59.29% 40.71%

20 0.09421 0.04544 0.13965 67.46% 32.54%

30 0.12834 0.05455 0.18289 70.17% 29.83%

40 0.15168 0.06466 0.21634 70.11% 29.89%

50 0.16471 0.07625 0.24096 68.36% 31.64%

60 0.16928 0.09025 0.25953 65.23% 34.77%

5-year cooling time

10 0.04869 0.04548 0.09417 51.70% 48.30%

20 0.10311 0.05774 0.16085 64.10% 35.90%

30 0.14140 0.06972 0.21112 66.98% 33.02%

40 0.16983 0.07809 0.24792 68.50% 31.50%

50 0.18801 0.08893 0.27694 67.89% 32.11%

60 0.19867 0.10147 0.30014 66.19% 33.81%

10-year cooling time

10 0.05424 0.04358 0.09782 55.45% 44.55%

20 0.11278 0.05750 0.17028 66.23% 33.77%

30 0.15598 0.06762 0.22360 69.76% 30.24%

40 0.18930 0.07649 0.26579 71.22% 28.78%

50 0.21128 0.08692 0.29820 70.85% 29.15%

60 0.22441 0.09913 0.32354 69.36% 30.64%

20-year cooling time

10 0.05979 0.04374 0.10353 57.75% 42.25%

20 0.12632 0.05412 0.18044 70.01% 29.99%

30 0.17557 0.06561 0.24118 72.80% 27.20%

40 0.21358 0.07427 0.28785 74.20% 25.80%

50 0.24229 0.08180 0.32409 74.76% 25.24%

60 0.25992 0.09306 0.35298 73.64% 26.36%

40-year cooling time

10 0.06684 0.04198 0.10882 61.42% 38.58%

20 0.13867 0.05309 0.19176 72.31% 27.69%

30 0.19442 0.06167 0.25609 75.92% 24.08%

40 0.23804 0.06901 0.30705 77.52% 22.48%

50 0.27040 0.07746 0.34786 77.73% 22.27%

60 0.29415 0.08486 0.37901 77.61% 22.39%
Analysis Section 3

26

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

∆k 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 0.05356 0.03362 0.08718 61.44% 38.56%

20 0.10660 0.04741 0.15401 69.22% 30.78%

30 0.14910 0.05715 0.20625 72.29% 27.71%

40 0.18608 0.06322 0.24930 74.64% 25.36%

50 0.21475 0.07081 0.28556 75.20% 24.80%

60 0.23913 0.07774 0.31687 75.47% 24.53%

5-year cooling time

10 0.05401 0.04558 0.09959 54.23% 45.77%

20 0.11345 0.05732 0.17077 66.43% 33.57%

30 0.15949 0.06848 0.22797 69.96% 30.04%

40 0.19826 0.07673 0.27499 72.10% 27.90%

50 0.23221 0.08372 0.31593 73.50% 26.50%

60 0.25763 0.09307 0.35070 73.46% 26.54%

10-year cooling time

10 0.05720 0.04565 0.10285 55.61% 44.39%

20 0.11965 0.05745 0.17710 67.56% 32.44%

30 0.17060 0.06741 0.23801 71.68% 28.32%

40 0.21147 0.07763 0.28910 73.15% 26.85%

50 0.24748 0.08510 0.33258 74.41% 25.59%

60 0.27738 0.09144 0.36882 75.21% 24.79%

20-year cooling time

10 0.06195 0.04438 0.10633 58.26% 41.74%

20 0.12953 0.05706 0.18659 69.42% 30.58%

30 0.18423 0.06607 0.25030 73.60% 26.40%

40 0.22922 0.07475 0.30397 75.41% 24.59%

50 0.26930 0.08237 0.35167 76.58% 23.42%

60 0.30364 0.08857 0.39221 77.42% 22.58%

40-year cooling time

10 0.06615 0.04419 0.11034 59.95% 40.05%

20 0.13639 0.05712 0.19351 70.48% 29.52%

30 0.19708 0.06422 0.26130 75.42% 24.58%

40 0.24648 0.07263 0.31911 77.24% 22.76%

50 0.28987 0.07915 0.36902 78.55% 21.45%

60 0.32868 0.08406 0.41274 79.63% 20.37%
Section 3 Analysis

27

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

for fuel of 4 wt % 235U initial enrichment

∆k 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 0.04819 0.03453 0.08272 58.26% 41.74%

20 0.09952 0.05050 0.15002 66.34% 33.66%

30 0.14271 0.05808 0.20079 71.07% 28.93%

40 0.17771 0.06742 0.24513 72.50% 27.50%

50 0.21198 0.07221 0.28419 74.59% 25.41%

60 0.24010 0.07941 0.31951 75.15% 24.85%

5-year cooling time

10 0.04903 0.04497 0.09400 52.16% 47.84%

20 0.10503 0.06000 0.16503 63.64% 36.36%

30 0.15131 0.06908 0.22039 68.66% 31.34%

40 0.18996 0.07831 0.26827 70.81% 29.19%

50 0.22660 0.08512 0.31172 72.69% 27.31%

60 0.25774 0.09166 0.34940 73.77% 26.23%

10-year cooling time

10 0.05148 0.04540 0.09688 53.14% 46.86%

20 0.10922 0.06066 0.16988 64.29% 35.71%

30 0.15804 0.06955 0.22759 69.44% 30.56%

40 0.20108 0.07824 0.27932 71.99% 28.01%

50 0.23827 0.08667 0.32494 73.33% 26.67%

60 0.27317 0.09141 0.36458 74.93% 25.07%

20-year cooling time

10 0.05376 0.04680 0.10056 53.46% 46.54%

20 0.11642 0.06001 0.17643 65.99% 34.01%

30 0.16972 0.06891 0.23863 71.12% 28.88%

40 0.21446 0.07612 0.29058 73.80% 26.20%

50 0.25645 0.08329 0.33974 75.48% 24.52%

60 0.29329 0.08961 0.38290 76.60% 23.40%

40-year cooling time

10 0.05682 0.04619 0.10301 55.16% 44.84%

20 0.12454 0.05569 0.18023 69.10% 30.90%

30 0.17779 0.06739 0.24518 72.51% 27.49%

40 0.22783 0.07455 0.30238 75.35% 24.65%

50 0.27294 0.08168 0.35462 76.97% 23.03%

60 0.31294 0.08688 0.39982 78.27% 21.73%
Analysis Section 3

28

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

∆k 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 0.04286 0.03563 0.07849 54.61% 45.39%

20 0.08854 0.05156 0.14010 63.20% 36.80%

30 0.12911 0.06144 0.19055 67.76% 32.24%

40 0.16453 0.06806 0.23259 70.74% 29.26%

50 0.19746 0.07552 0.27298 72.33% 27.67%

60 0.22739 0.08263 0.31002 73.35% 26.65%

5-year cooling time

10 0.04334 0.04538 0.08872 48.85% 51.15%

20 0.09339 0.06249 0.15588 59.91% 40.09%

30 0.13712 0.07054 0.20766 66.03% 33.97%

40 0.17538 0.07856 0.25394 69.06% 30.94%

50 0.20939 0.08761 0.29700 70.50% 29.50%

60 0.24198 0.09395 0.33593 72.03% 27.97%

10-year cooling time

10 0.04462 0.04597 0.09059 49.25% 50.75%

20 0.09832 0.06082 0.15914 61.78% 38.22%

30 0.14337 0.07005 0.21342 67.18% 32.82%

40 0.18356 0.08068 0.26424 69.47% 30.53%

50 0.22087 0.08711 0.30798 71.72% 28.28%

60 0.25487 0.09338 0.34825 73.19% 26.81%

20-year cooling time

10 0.04660 0.04576 0.09236 50.45% 49.55%

20 0.10332 0.06072 0.16404 62.98% 37.02%

30 0.15244 0.06984 0.22228 68.58% 31.42%

40 0.19558 0.07762 0.27320 71.59% 28.41%

50 0.23518 0.08594 0.32112 73.24% 26.76%

60 0.27186 0.09106 0.36292 74.91% 25.09%

40-year cooling time

10 0.04969 0.04302 0.09271 53.60% 46.40%

20 0.10848 0.05918 0.16766 64.70% 35.30%

30 0.16049 0.06857 0.22906 70.06% 29.94%

40 0.20565 0.07535 0.28100 73.19% 26.81%

50 0.24857 0.08340 0.33197 74.88% 25.12%

60 0.28913 0.08774 0.37687 76.72% 23.28%
Section 3 Analysis

29

Table 16 keff values with UNIFORM axial burnup for the GBC-32 cask as a function of burnup and co

for 4 wt % 235U initial enrichment 

Major actinides (nuclide set 1, see Table 6)

Cooling time

(years)

0 5 10 20 

Burnup

(GWd/MTU)

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

keff Standard

deviation

0 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.

10 1.09551 0.00062 1.09461 0.00060 1.09357 0.00048 1.09151 0.00062 1.020 1.04608 0.00054 1.03990 0.00060 1.03287 0.00060 1.02437 0.00051 1.030 0.99684 0.00065 0.98484 0.00055 0.97349 0.00055 0.95796 0.00058 0.940 0.94988 0.00059 0.93184 0.00052 0.91554 0.00057 0.89278 0.00056 0.50 0.90678 0.00050 0.88361 0.00053 0.86267 0.00050 0.83281 0.00051 0.60 0.87012 0.00049 0.84299 0.00047 0.81871 0.00054 0.78489 0.00044 0.7

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

0 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.13983 0.00065 1.

10 1.06057 0.00053 1.05023 0.00058 1.04736 0.00060 1.04493 0.00051 1.020 0.99105 0.00053 0.97162 0.00048 0.96457 0.00048 0.95614 0.00054 0.930 0.92418 0.00053 0.89802 0.00051 0.88551 0.00052 0.86861 0.00044 0.40 0.86305 0.00051 0.82865 0.00045 0.81073 0.00050 0.78732 0.00046 0.750 0.80905 0.00050 0.76758 0.00041 0.74515 0.00045 0.71642 0.00041 0.660 0.76355 0.00049 0.71736 0.00040 0.69119 0.00038 0.65827 0.00041 0.6

29
Analysis Section 3

30

Table 17 Individual components of the reduction in keff for UNIFORM axial burnup as a function

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

∆k 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 0.04432 0.03494 0.07926 55.92% 44.08%

20 0.09375 0.05503 0.14878 63.01% 36.99%

30 0.14299 0.07266 0.21565 66.31% 33.69%

40 0.18995 0.08683 0.27678 68.63% 31.37%

50 0.23305 0.09773 0.33078 70.45% 29.55%

60 0.26971 0.10657 0.37628 71.68% 28.32%

5-year cooling time

10 0.04522 0.04438 0.08960 50.47% 49.53%

20 0.09993 0.06828 0.16821 59.41% 40.59%

30 0.15499 0.08682 0.24181 64.10% 35.90%

40 0.20799 0.10319 0.31118 66.84% 33.16%

50 0.25622 0.11603 0.37225 68.83% 31.17%

60 0.29684 0.12563 0.42247 70.26% 29.74%

10-year cooling time

10 0.04626 0.04621 0.09247 50.03% 49.97%

20 0.10696 0.06830 0.17526 61.03% 38.97%

30 0.16634 0.08798 0.25432 65.41% 34.59%

40 0.22429 0.10481 0.32910 68.15% 31.85%

50 0.27716 0.11752 0.39468 70.22% 29.78%

60 0.32112 0.12752 0.44864 71.58% 28.42%

20-year cooling time

10 0.04832 0.04658 0.09490 50.92% 49.08%

20 0.11546 0.06823 0.18369 62.86% 37.14%

30 0.18187 0.08935 0.27122 67.06% 32.94%

40 0.24705 0.10546 0.35251 70.08% 29.92%

50 0.30702 0.11639 0.42341 72.51% 27.49%

60 0.35494 0.12662 0.48156 73.71% 26.29%

40-year cooling time

10 0.05130 0.04535 0.09665 53.08% 46.92%

20 0.12371 0.06842 0.19213 64.39% 35.61%

30 0.19769 0.08827 0.28596 69.13% 30.87%

40 0.27017 0.10318 0.37335 72.36% 27.64%

50 0.33523 0.11449 0.44972 74.54% 25.46%

60 0.38982 0.12220 0.51202 76.13% 23.87%
Section 4 Conclusions

31

4 CONCLUSIONS

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

reactivity margin available from fission products and minor actinides in a PWR burnup credit storage/transport

environment, based on a generic 32 PWR-assembly cask. The proposed benchmark problem was developed to be

similar to proposed 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.

The purpose of this computational benchmark is to provide a reference configuration to help normalize 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 0–60 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, reference results for a single initial fuel enrichment of 4 wt % 235U are given for a

simplification of the computational benchmark problem involving a uniform axial burnup distribution. The

reference estimations were all based on the SCALE4.4a code package.

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 decrease in the 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. The minimum values are shown to occur at zero cooling time and increase as a function

of burnup from ~0.03 ∆k at 10 GWd/MTU to ~0.08 ∆k at 60 GWd/MTU.

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 depletion (SAS2H) and criticality (CSAS25) sequences have been validated using laboratory critical

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

measurements with individual fission products important to burnup credit.2

 Although the minor modeling

simplifications employed in this evaluation are not expected to have a significant impact on the calculated

reactivity margins, analyses to support this assertion have not been performed.

One modeling characteristic that is known to notably impact the calculated reactivity margins, however, is the

axial burnup profile. The use a of more bounding profile (i.e., one that results in greater reactivity) than the one

specified in Section 2 for this benchmark problem will yield lower estimates for the reactivity margin available

from the additional nuclides, as well as from the major actinides. The amount by which the estimates are lower

will depend on the actual axial burnup profile.
32
33

5. REFERENCES

1. 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.

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 Modular Code System for Performing Standardized Computer Analyses for Licensing

Evaluation, NUREG/CR-0200, Rev. 6 (ORNL/NUREG/CSD-2/R6), Vols. I, II, III, May 2000. Available

from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-545.

4. Nuclear Criticality Safety in Operations with Fissionable Material Outside Reactors, ANSI/ANS-8.1-

1998.

5. Standard Review Plan for Dry Cask Storage Systems, NUREG-1536, U.S. NRC, Washington, D.C.,

January 1997.

6. Standard Review Plan for Transportation Packages for Spent Nuclear Fuel – Draft Report for Comment,

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

7. T. L. Sanders, editor, Proceedings of a Workshop on the Use of Burnup Credit in Spent Fuel Transport

Casks, Washington, D.C., February 21–22, 1988, SAND89-0018, TTC-0884, UC-820, Sandia National

Laboratory, October 1989.

8. M. D. DeHart, Sensitivity and Parametric Evaluations of Significant Aspects of Burnup Credit for PWR

Spent Fuel Packages, ORNL/TM-12973, Lockheed Martin Energy Research Corp., Oak Ridge Natl. Lab.,

May 1996.

9. O. W. Hermann, S. M. Bowman, M. C. Brady, and C. V. Parks, Validation of the SCALE System for PWR

Spent Fuel Isotopic Composition Analyses, ORNL/TM-12667, Martin Marietta Energy Systems, Inc.,

Oak Ridge National Laboratory, March 1995.

10. M. D. DeHart and O. W. Hermann, An Extension of the Validation of SCALE (SAS2H) Isotopic

Predictions for PWR Spent Fuel, ORNL/TM-13317, Lockheed Martin Energy Research Corp., Oak Ridge

National Laboratory, September 1996.

11. M. Rahimi, E. Fuentes, D. Lancaster, Isotopic and Criticality Validation for PWR Actinide-Only Burnup

Credit, DOE/RW-0497, U.S. Department of Energy, May 1997.

12. O. W. Hermann and M. D. DeHart, Validation of SCALE (SAS2H) Isotopic Predictions for BWR Spent

Fuel, ORNL/TM-13315, Lockheed Martin Energy Research Corp., Oak Ridge National Laboratory,

September 1998.

13. Spent Fuel Project Office Interim Staff Guidance – 8, Rev. 1 – Limited Burnup Credit, U.S. Nuclear

Regulatory Commission, July 30, 1999.
References Section 5

34

14. C. V. Parks, “Parametric Neutronic Analyses Related to Burnup Credit Cask Design,” pp. 21–43 in

Proceedings of a Workshop on the Use of Burnup Credit in Spent Fuel Transport Casks, Washington

D.C., February 21–22, 1988, SAND89-0018, TTC-0884, UC-820, Sandia National Laboratory (October

1989).

15. M. Takano, OECD/NEA Burnup Credit Criticality Benchmark — Result of Phase-1A, JAERI-M 94-003

(NEA/NSC/DOC(93)22, Japan Atomic Energy Research Institute, 1994.

16. D. E. Carlson, C. J. Withee and C. V. Parks, “Spent Fuel Burnup Credit in Casks: An NRC Perspective,”

U.S. Nuclear Regulatory Commission, Proceedings of the Twenty-Seventh Water Reactor Safety

Information Meeting, October 25–27, 1999, Bethesda, Maryland, NUREG/CP-0169, pp. 419–436, March

2000.

17. M. C. Brady, H. Okuno, M. D. DeHart, A. Nouri, and E. Sartori, “International Studies on Burnup Credit

Criticality Safety by an OECD/NEA Working Group,” Int. Conf. Physics of Nuclear Science and

Technology, Long Island, New York, October 5–8, 1998.

18. M. D. DeHart et al., OECD/NEA Burnup Credit Calculational Criticality Benchmark Phase I-B Results,

ORNL-6901 (NEA/NSC/DOC(96)-06), Lockheed Martin Energy Research Corp., Oak Ridge Natl. Lab.,

June 1996.

19. M. Takano and H. Okuno, OECD/NEA Burnup Credit Criticality Benchmark — Result of Phase IIA,

JAERI-Research-96-003 (NEA/NSC/DOC(61)01), Japan Atomic Energy Research Institute, 1996.

20. A. Nouri, OECD/NEA Burnup Credit Criticality Benchmark — Analysis of Phase II-B Results:

Conceptual PWR Spent Fuel Transportation Cask, IPSN/98-05 (NEA/NSC/DOC(98)1), Institut de

Protection et de Surete Nucleaire, May 1998.

21. Boral – The Proven Neutron Absorber, AAR Advanced Structures, Livonia, MI.

22. C. D. Harmon II, R. D. Busch, J. F. Briesmeister, and R. A. Forster, Criticality Calculations with MCNP:

A Primer, LA-12827-M, Los Alamos National Laboratory (1994).

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

24. J. E. Horwedel and S. M. Bowman, KENO3D Visualization Tool for KENO V.a and KENO-VI Geometry

Models, NUREG/CR-6662 (ORNL/TM-1999/284), U.S. Nuclear Regulatory Commission, Oak Ridge

National Laboratory, June 2000.

25. J. C. Wagner and M. D. DeHart, Review of Axial Burnup Distribution Considerations for Burnup Credit

Calculations, ORNL/TM-1999/246, Lockheed Martin Energy Research Corp., Oak Ridge National

Laboratory, February 2000.

26. B. L. Broadhead, M. D. DeHart, J. C. Ryman, J. S. Tang, and C. V. Parks, 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.
35

APPENDIX A

SAMPLE INPUT FILE FOR SAS2H
36
Appendix A Sample Input File for SAS2H

37

=sas2 parm=’halt31,skipshipdata’

sas2 pwr-buc westinghouse 17×17OFA, 4.0 wt % U-235, B_total=60 GWd/MTU

44groupndf5 latticecell

’

’ ASS= Westinghouse 17×17 OFA assembly design

’ IE = initial enrichment of 4.0 wt % U-235

’ Tm = moderator temperature = 600K

’ Tf = fuel temperature = 1000K

’ SB = soluble boron concentration = 650ppm

’ SP = Specific Power = 60 MW/MTU

’

’ mixtures of fuel-pin-unit-cell

’

’ U-234, U-236, & U-238 isotopics calculated based on relations

’ in NUREG/CR-5625(ORNL-6698)

’ Fuel Density reduced to account for pellet expansion

uo2 1 den=10.5216

 1 1000.0 92234 0.03473

 92235 4.0

 92236 0.01840

 92238 95.94687 end

’

’ Following list contains all Important nuclides from

’ Table 1 of ORNL/TM-12294/V1

u-232 1 0 1.00e-20 1000.0 end

u-233 1 0 1.00e-20 1000.0 end

u-237 1 0 1.00e-20 1000.0 end

np-237 1 0 1.00e-20 1000.0 end

pu-236 1 0 1.00e-20 1000.0 end

pu-237 1 0 1.00e-20 1000.0 end

pu-238 1 0 1.00e-20 1000.0 end

pu-239 1 0 1.00e-20 1000.0 end

pu-240 1 0 1.00e-20 1000.0 end

pu-241 1 0 1.00e-20 1000.0 end

pu-242 1 0 1.00e-20 1000.0 end

pu-243 1 0 1.00e-20 1000.0 end

pu-244 1 0 1.00e-20 1000.0 end

am-241 1 0 1.00e-20 1000.0 end

am-242m 1 0 1.00e-20 1000.0 end

am-243 1 0 1.00e-20 1000.0 end

cm-241 1 0 1.00e-20 1000.0 end

cm-242 1 0 1.00e-20 1000.0 end

cm-243 1 0 1.00e-20 1000.0 end

cm-244 1 0 1.00e-20 1000.0 end

cm-245 1 0 1.00e-20 1000.0 end

cm-246 1 0 1.00e-20 1000.0 end

cm-247 1 0 1.00e-20 1000.0 end

cm-248 1 0 1.00e-20 1000.0 end

ge-72 1 0 1.00e-20 1000.0 end

ge-73 1 0 1.00e-20 1000.0 end

ge-74 1 0 1.00e-20 1000.0 end

as-75 1 0 1.00e-20 1000.0 end

ge-76 1 0 1.00e-20 1000.0 end

se-76 1 0 1.00e-20 1000.0 end

se-77 1 0 1.00e-20 1000.0 end

se-78 1 0 1.00e-20 1000.0 end

br-79 1 0 1.00e-20 1000.0 end

se-80 1 0 1.00e-20 1000.0 end

kr-80 1 0 1.00e-20 1000.0 end

br-81 1 0 1.00e-20 1000.0 end

se-82 1 0 1.00e-20 1000.0 end

kr-82 1 0 1.00e-20 1000.0 end

kr-83 1 0 1.00e-20 1000.0 end

kr-84 1 0 1.00e-20 1000.0 end

kr-85 1 0 1.00e-20 1000.0 end

rb-85 1 0 1.00e-20 1000.0 end

kr-86 1 0 1.00e-20 1000.0 end

rb-86 1 0 1.00e-20 1000.0 end

sr-86 1 0 1.00e-20 1000.0 end

rb-87 1 0 1.00e-20 1000.0 end

sr-87 1 0 1.00e-20 1000.0 end
Sample Input File for SAS2H Appendix A

38

sr-88 1 0 1.00e-20 1000.0 end

sr-89 1 0 1.00e-20 1000.0 end

y-89 1 0 1.00e-20 1000.0 end

sr-90 1 0 1.00e-20 1000.0 end

y-90 1 0 1.00e-20 1000.0 end

zr-90 1 0 1.00e-20 1000.0 end

y-91 1 0 1.00e-20 1000.0 end

zr-91 1 0 1.00e-20 1000.0 end

zr-92 1 0 1.00e-20 1000.0 end

zr-93 1 0 1.00e-20 1000.0 end

nb-93 1 0 1.00e-20 1000.0 end

zr-94 1 0 1.00e-20 1000.0 end

nb-94 1 0 1.00e-20 1000.0 end

zr-95 1 0 1.00e-20 1000.0 end

nb-95 1 0 1.00e-20 1000.0 end

mo-95 1 0 1.00e-20 1000.0 end

zr-96 1 0 1.00e-20 1000.0 end

mo-96 1 0 1.00e-20 1000.0 end

mo-97 1 0 1.00e-20 1000.0 end

mo-98 1 0 1.00e-20 1000.0 end

mo-99 1 0 1.00e-20 1000.0 end

tc-99 1 0 1.00e-20 1000.0 end

ru-99 1 0 1.00e-20 1000.0 end

mo-100 1 0 1.00e-20 1000.0 end

ru-100 1 0 1.00e-20 1000.0 end

ru-101 1 0 1.00e-20 1000.0 end

ru-102 1 0 1.00e-20 1000.0 end

pd-102 1 0 1.00e-20 1000.0 end

ru-103 1 0 1.00e-20 1000.0 end

rh-103 1 0 1.00e-20 1000.0 end

ru-104 1 0 1.00e-20 1000.0 end

pd-104 1 0 1.00e-20 1000.0 end

ru-105 1 0 1.00e-20 1000.0 end

rh-105 1 0 1.00e-20 1000.0 end

pd-105 1 0 1.00e-20 1000.0 end

ru-106 1 0 1.00e-20 1000.0 end

pd-106 1 0 1.00e-20 1000.0 end

pd-107 1 0 1.00e-20 1000.0 end

ag-107 1 0 1.00e-20 1000.0 end

pd-108 1 0 1.00e-20 1000.0 end

cd-108 1 0 1.00e-20 1000.0 end

ag-109 1 0 1.00e-20 1000.0 end

pd-110 1 0 1.00e-20 1000.0 end

cd-110 1 0 1.00e-20 1000.0 end

ag-111 1 0 1.00e-20 1000.0 end

cd-111 1 0 1.00e-20 1000.0 end

cd-112 1 0 1.00e-20 1000.0 end

cd-113 1 0 1.00e-20 1000.0 end

in-113 1 0 1.00e-20 1000.0 end

cd-114 1 0 1.00e-20 1000.0 end

sn-114 1 0 1.00e-20 1000.0 end

cd-115m 1 0 1.00e-20 1000.0 end

in-115 1 0 1.00e-20 1000.0 end

sn-115 1 0 1.00e-20 1000.0 end

cd-116 1 0 1.00e-20 1000.0 end

sn-116 1 0 1.00e-20 1000.0 end

sn-117 1 0 1.00e-20 1000.0 end

sn-118 1 0 1.00e-20 1000.0 end

sn-119 1 0 1.00e-20 1000.0 end

sn-120 1 0 1.00e-20 1000.0 end

sb-121 1 0 1.00e-20 1000.0 end

sn-122 1 0 1.00e-20 1000.0 end

te-122 1 0 1.00e-20 1000.0 end

sn-123 1 0 1.00e-20 1000.0 end

sb-123 1 0 1.00e-20 1000.0 end

te-123 1 0 1.00e-20 1000.0 end

sn-124 1 0 1.00e-20 1000.0 end

sb-124 1 0 1.00e-20 1000.0 end

te-124 1 0 1.00e-20 1000.0 end

sn-125 1 0 1.00e-20 1000.0 end
Appendix A Sample Input File for SAS2H

39

sb-125 1 0 1.00e-20 1000.0 end

te-125 1 0 1.00e-20 1000.0 end

sn-126 1 0 1.00e-20 1000.0 end

sb-126 1 0 1.00e-20 1000.0 end

te-126 1 0 1.00e-20 1000.0 end

xe-126 1 0 1.00e-20 1000.0 end

te-127m 1 0 1.00e-20 1000.0 end

i-127 1 0 1.00e-20 1000.0 end

te-128 1 0 1.00e-20 1000.0 end

xe-128 1 0 1.00e-20 1000.0 end

te-129m 1 0 1.00e-20 1000.0 end

i-129 1 0 1.00e-20 1000.0 end

xe-129 1 0 1.00e-20 1000.0 end

te-130 1 0 1.00e-20 1000.0 end

i-130 1 0 1.00e-20 1000.0 end

xe-130 1 0 1.00e-20 1000.0 end

i-131 1 0 1.00e-20 1000.0 end

xe-131 1 0 1.00e-20 1000.0 end

te-132 1 0 1.00e-20 1000.0 end

xe-132 1 0 1.00e-20 1000.0 end

xe-133 1 0 1.00e-20 1000.0 end

cs-133 1 0 1.00e-20 1000.0 end

xe-134 1 0 1.00e-20 1000.0 end

cs-134 1 0 1.00e-20 1000.0 end

ba-134 1 0 1.00e-20 1000.0 end

i-135 1 0 1.00e-20 1000.0 end

xe-135 1 0 1.00e-20 1000.0 end

cs-135 1 0 1.00e-20 1000.0 end

ba-135 1 0 1.00e-20 1000.0 end

xe-136 1 0 1.00e-20 1000.0 end

cs-136 1 0 1.00e-20 1000.0 end

ba-136 1 0 1.00e-20 1000.0 end

cs-137 1 0 1.00e-20 1000.0 end

ba-137 1 0 1.00e-20 1000.0 end

ba-138 1 0 1.00e-20 1000.0 end

la-139 1 0 1.00e-20 1000.0 end

ba-140 1 0 1.00e-20 1000.0 end

la-140 1 0 1.00e-20 1000.0 end

ce-140 1 0 1.00e-20 1000.0 end

ce-141 1 0 1.00e-20 1000.0 end

pr-141 1 0 1.00e-20 1000.0 end

ce-142 1 0 1.00e-20 1000.0 end

pr-142 1 0 1.00e-20 1000.0 end

nd-142 1 0 1.00e-20 1000.0 end

ce-143 1 0 1.00e-20 1000.0 end

pr-143 1 0 1.00e-20 1000.0 end

nd-143 1 0 1.00e-20 1000.0 end

ce-144 1 0 1.00e-20 1000.0 end

nd-144 1 0 1.00e-20 1000.0 end

nd-145 1 0 1.00e-20 1000.0 end

nd-146 1 0 1.00e-20 1000.0 end

nd-147 1 0 1.00e-20 1000.0 end

pm-147 1 0 1.00e-20 1000.0 end

sm-147 1 0 1.00e-20 1000.0 end

nd-148 1 0 1.00e-20 1000.0 end

pm-148 1 0 1.00e-20 1000.0 end

pm-148m 1 0 1.00e-20 1000.0 end

sm-148 1 0 1.00e-20 1000.0 end

pm-149 1 0 1.00e-20 1000.0 end

sm-149 1 0 1.00e-20 1000.0 end

nd-150 1 0 1.00e-20 1000.0 end

sm-150 1 0 1.00e-20 1000.0 end

pm-151 1 0 1.00e-20 1000.0 end

sm-151 1 0 1.00e-20 1000.0 end

eu-151 1 0 1.00e-20 1000.0 end

sm-152 1 0 1.00e-20 1000.0 end

eu-152 1 0 1.00e-20 1000.0 end

gd-152 1 0 1.00e-20 1000.0 end

sm-153 1 0 1.00e-20 1000.0 end

eu-153 1 0 1.00e-20 1000.0 end

sm-154 1 0 1.00e-20 1000.0 end
Sample Input File for SAS2H Appendix A

40

eu-154 1 0 1.00e-20 1000.0 end

gd-154 1 0 1.00e-20 1000.0 end

eu-155 1 0 1.00e-20 1000.0 end

gd-155 1 0 1.00e-20 1000.0 end

eu-156 1 0 1.00e-20 1000.0 end

gd-156 1 0 1.00e-20 1000.0 end

eu-157 1 0 1.00e-20 1000.0 end

gd-157 1 0 1.00e-20 1000.0 end

gd-158 1 0 1.00e-20 1000.0 end

tb-159 1 0 1.00e-20 1000.0 end

gd-160 1 0 1.00e-20 1000.0 end

tb-160 1 0 1.00e-20 1000.0 end

dy-160 1 0 1.00e-20 1000.0 end

dy-161 1 0 1.00e-20 1000.0 end

dy-162 1 0 1.00e-20 1000.0 end

dy-163 1 0 1.00e-20 1000.0 end

dy-164 1 0 1.00e-20 1000.0 end

ho-165 1 0 1.00e-20 1000.0 end

er-166 1 0 1.00e-20 1000.0 end

er-167 1 0 1.00e-20 1000.0 end

’

zirc2 2 1 620.0 end

h2o 3 den=0.670 1 600.0 end

arbm-bormod 0.670 1 1 0 0 5000 100 3 650.0E-06 600.0 end

end comp

’

’ base reactor lattice specification

squarepitch 1.2598 0.7844 1 3 0.9144 2 0.8001 3 end

more data szf=0.50 end

’

’ assembly and cycle parameters

npin/assembly=264 fuelngth=845.0 ncycles=21 nlib/cyc=1

printlevel=2 lightel=9 inplevel=1

numinstr=1 ortube=0.60198 srtube=0.56134 asmpitch=21.5

facmesh=0.50 end

’

’ assembly depletion/decay parameters

power=60.0 burn=1.0e-15 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

power=60.0 burn=50.0 down=0.0 end

’

’ light-elements taken from SAS2H input listing in

’ ORNL/TM-12294/V5 Appendix B, not verified to be accurate

 o 135 cr 5.9 mn 0.33

 fe 12.9 co 0.075 ni 9.9

 zr 221 nb 0.71 sn 3.60

’

’ end of input

end
41

APPENDIX B

SAMPLE INPUT FILE FOR CSAS25
42
Appendix B Sample Input File for CSAS25

43

=csas25 parm=size=5000000

Generic 32-Assembly Burnup Credit Cask (GBC-32) w/Axial Brnp Profile

238groupndf5 latticecell

’

’ ********** GBC-32: Generic 32-Assembly Cask **********

’ *

’ * -GBC-32 Characteristics-

’ * Basket Cell ID: 22.0 cm

’ * Basket Cell OD: 23.5 cm, basket wall thickness = 0.75 cm

’ * Basket Cell Height: 365.76

’ * Boral Thickness: 0.2565 cm (0.101 in)

’ * Boral Width: 19.05 cm (7.5 in)

’ * Boral B-10 Loading: 0.0225 g/sqcm (75% of 0.030)

’ * Boral Panel Height: 365.76

’ * Cask ID: 175.0 cm

’ * Cask OD: 215.0 cm

’ * Cask Top & Bottom Thickness: 30.0 cm

’ *

’ * -Assembly Characteristics-

’ * Assembly Type: Westinghouse 17×17 OFA/V5

’ * Assembly Initial Enrichment: 4.0 wt % U-235

’ * Assembly Burnup: 40 GWd/MTU

’ * Assembly Cooling Time: 5 Years

’ *

’ * -Modeling Characteristics-

’ * 18-equi-length node axial profile (365.76cm total fuel height)

’ * Axial Burnup Profile consistent with that suggested in

’ * DOE TR Rev. 2 for Burnups > 30 GWd/MTU

’ *

’ ********** GBC-32: Generic 32-Assembly Cask **********

’

’ Node-01 Burnup=26.08GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 101 0 5.8176E-06 293.0 end

 u-235 101 0 4.0950E-04 293.0 end

 u-236 101 0 9.9756E-05 293.0 end

 u-238 101 0 2.2105E-02 293.0 end

 np-237 101 0 7.9002E-06 293.0 end

 pu-238 101 0 1.6561E-06 293.0 end

 pu-239 101 0 1.3192E-04 293.0 end

 pu-240 101 0 3.9078E-05 293.0 end

 pu-241 101 0 1.7872E-05 293.0 end

 pu-242 101 0 5.1651E-06 293.0 end

 am-241 101 0 5.1831E-06 293.0 end

 am-243 101 0 7.5598E-07 293.0 end

’ fission products

 mo-95 101 0 3.7734E-05 293.0 end

 tc-99 101 0 3.7770E-05 293.0 end

 ru-101 101 0 3.3623E-05 293.0 end

 rh-103 101 0 2.1908E-05 293.0 end

 ag-109 101 0 2.8370E-06 293.0 end

 cs-133 101 0 3.9691E-05 293.0 end

 nd-143 101 0 2.9313E-05 293.0 end

 nd-145 101 0 2.1983E-05 293.0 end

 sm-147 101 0 7.0810E-06 293.0 end

 sm-149 101 0 2.0986E-07 293.0 end

 sm-150 101 0 8.8377E-06 293.0 end

 sm-151 101 0 5.9274E-07 293.0 end

 eu-151 101 0 2.3732E-08 293.0 end

 sm-152 101 0 3.8060E-06 293.0 end

 eu-153 101 0 2.8524E-06 293.0 end

 gd-155 101 0 6.3214E-08 293.0 end

 o-16 101 0 4.6948E-02 293.0 end

’ Node-02 Burnup=38.68 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 102 0 4.8790E-06 293.0 end

 u-235 102 0 2.5447E-04 293.0 end

 u-236 102 0 1.2187E-04 293.0 end

 u-238 102 0 2.1873E-02 293.0 end

 np-237 102 0 1.3147E-05 293.0 end
Sample Input File for CSAS25 Appendix B

44

 pu-238 102 0 4.2966E-06 293.0 end

 pu-239 102 0 1.4269E-04 293.0 end

 pu-240 102 0 5.7000E-05 293.0 end

 pu-241 102 0 2.7388E-05 293.0 end

 pu-242 102 0 1.3158E-05 293.0 end

 am-241 102 0 8.0958E-06 293.0 end

 am-243 102 0 2.8810E-06 293.0 end

’ fission products

 mo-95 102 0 5.3059E-05 293.0 end

 tc-99 102 0 5.3269E-05 293.0 end

 ru-101 102 0 4.9411E-05 293.0 end

 rh-103 102 0 3.0421E-05 293.0 end

 ag-109 102 0 4.9976E-06 293.0 end

 cs-133 102 0 5.5684E-05 293.0 end

 nd-143 102 0 3.7678E-05 293.0 end

 nd-145 102 0 3.0398E-05 293.0 end

 sm-147 102 0 8.5409E-06 293.0 end

 sm-149 102 0 2.1895E-07 293.0 end

 sm-150 102 0 1.3693E-05 293.0 end

 sm-151 102 0 6.9918E-07 293.0 end

 eu-151 102 0 2.7946E-08 293.0 end

 sm-152 102 0 5.3941E-06 293.0 end

 eu-153 102 0 4.9658E-06 293.0 end

 gd-155 102 0 1.2078E-07 293.0 end

 o-16 102 0 4.6946E-02 293.0 end

’ Node-03 Burnup=42.96 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 103 0 4.5993E-06 293.0 end

 u-235 103 0 2.1363E-04 293.0 end

 u-236 103 0 1.2668E-04 293.0 end

 u-238 103 0 2.1790E-02 293.0 end

 np-237 103 0 1.4857E-05 293.0 end

 pu-238 103 0 5.4578E-06 293.0 end

 pu-239 103 0 1.4399E-04 293.0 end

 pu-240 103 0 6.1987E-05 293.0 end

 pu-241 103 0 2.9794E-05 293.0 end

 pu-242 103 0 1.6465E-05 293.0 end

 am-241 103 0 8.8447E-06 293.0 end

 am-243 103 0 3.9712E-06 293.0 end

’ fission products

 mo-95 103 0 5.7866E-05 293.0 end

 tc-99 103 0 5.8118E-05 293.0 end

 ru-101 103 0 5.4667E-05 293.0 end

 rh-103 103 0 3.2880E-05 293.0 end

 ag-109 103 0 5.7639E-06 293.0 end

 cs-133 103 0 6.0625E-05 293.0 end

 nd-143 103 0 3.9755E-05 293.0 end

 nd-145 103 0 3.2959E-05 293.0 end

 sm-147 103 0 8.8457E-06 293.0 end

 sm-149 103 0 2.1999E-07 293.0 end

 sm-150 103 0 1.5298E-05 293.0 end

 sm-151 103 0 7.3084E-07 293.0 end

 eu-151 103 0 2.9194E-08 293.0 end

 sm-152 103 0 5.8819E-06 293.0 end

 eu-153 103 0 5.7012E-06 293.0 end

 gd-155 103 0 1.4254E-07 293.0 end

 o-16 103 0 4.6945E-02 293.0 end

’ Node-04 Burnup=44.12 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 104 0 4.5268E-06 293.0 end

 u-235 104 0 2.0350E-04 293.0 end

 u-236 104 0 1.2777E-04 293.0 end

 u-238 104 0 2.1766E-02 293.0 end

 np-237 104 0 1.5307E-05 293.0 end

 pu-238 104 0 5.7912E-06 293.0 end

 pu-239 104 0 1.4422E-04 293.0 end

 pu-240 104 0 6.3243E-05 293.0 end

 pu-241 104 0 3.0374E-05 293.0 end

 pu-242 104 0 1.7398E-05 293.0 end

 am-241 104 0 9.0255E-06 293.0 end

 am-243 104 0 4.2966E-06 293.0 end
Appendix B Sample Input File for CSAS25

45

’ fission products

 mo-95 104 0 5.9135E-05 293.0 end

 tc-99 104 0 5.9395E-05 293.0 end

 ru-101 104 0 5.6081E-05 293.0 end

 rh-103 104 0 3.3508E-05 293.0 end

 ag-109 104 0 5.9725E-06 293.0 end

 cs-133 104 0 6.1921E-05 293.0 end

 nd-143 104 0 4.0255E-05 293.0 end

 nd-145 104 0 3.3628E-05 293.0 end

 sm-147 104 0 8.9143E-06 293.0 end

 sm-149 104 0 2.2014E-07 293.0 end

 sm-150 104 0 1.5726E-05 293.0 end

 sm-151 104 0 7.3907E-07 293.0 end

 eu-151 104 0 2.9518E-08 293.0 end

 sm-152 104 0 6.0099E-06 293.0 end

 eu-153 104 0 5.8995E-06 293.0 end

 gd-155 104 0 1.4852E-07 293.0 end

 o-16 104 0 4.6945E-02 293.0 end

’ Node-05 Burnup=44.32 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 105 0 4.5145E-06 293.0 end

 u-235 105 0 2.0179E-04 293.0 end

 u-236 105 0 1.2795E-04 293.0 end

 u-238 105 0 2.1762E-02 293.0 end

 np-237 105 0 1.5384E-05 293.0 end

 pu-238 105 0 5.8494E-06 293.0 end

 pu-239 105 0 1.4426E-04 293.0 end

 pu-240 105 0 6.3455E-05 293.0 end

 pu-241 105 0 3.0471E-05 293.0 end

 pu-242 105 0 1.7560E-05 293.0 end

 am-241 105 0 9.0558E-06 293.0 end

 am-243 105 0 4.3539E-06 293.0 end

’ fission products

 mo-95 105 0 5.9352E-05 293.0 end

 tc-99 105 0 5.9614E-05 293.0 end

 ru-101 105 0 5.6324E-05 293.0 end

 rh-103 105 0 3.3615E-05 293.0 end

 ag-109 105 0 6.0084E-06 293.0 end

 cs-133 105 0 6.2142E-05 293.0 end

 nd-143 105 0 4.0338E-05 293.0 end

 nd-145 105 0 3.3742E-05 293.0 end

 sm-147 105 0 8.9256E-06 293.0 end

 sm-149 105 0 2.2016E-07 293.0 end

 sm-150 105 0 1.5799E-05 293.0 end

 sm-151 105 0 7.4047E-07 293.0 end

 eu-151 105 0 2.9573E-08 293.0 end

 sm-152 105 0 6.0317E-06 293.0 end

 eu-153 105 0 5.9336E-06 293.0 end

 gd-155 105 0 1.4955E-07 293.0 end

 o-16 105 0 4.6945E-02 293.0 end

’ Node-06 Burnup=44.24 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 106 0 4.5194E-06 293.0 end

 u-235 106 0 2.0247E-04 293.0 end

 u-236 106 0 1.2788E-04 293.0 end

 u-238 106 0 2.1764E-02 293.0 end

 np-237 106 0 1.5353E-05 293.0 end

 pu-238 106 0 5.8261E-06 293.0 end

 pu-239 106 0 1.4424E-04 293.0 end

 pu-240 106 0 6.3371E-05 293.0 end

 pu-241 106 0 3.0432E-05 293.0 end

 pu-242 106 0 1.7495E-05 293.0 end

 am-241 106 0 9.0437E-06 293.0 end

 am-243 106 0 4.3309E-06 293.0 end

’ fission products

 mo-95 106 0 5.9265E-05 293.0 end

 tc-99 106 0 5.9526E-05 293.0 end

 ru-101 106 0 5.6227E-05 293.0 end

 rh-103 106 0 3.3572E-05 293.0 end

 ag-109 106 0 5.9940E-06 293.0 end

 cs-133 106 0 6.2054E-05 293.0 end
Sample Input File for CSAS25 Appendix B

46

 nd-143 106 0 4.0305E-05 293.0 end

 nd-145 106 0 3.3696E-05 293.0 end

 sm-147 106 0 8.9211E-06 293.0 end

 sm-149 106 0 2.2016E-07 293.0 end

 sm-150 106 0 1.5770E-05 293.0 end

 sm-151 106 0 7.3991E-07 293.0 end

 eu-151 106 0 2.9551E-08 293.0 end

 sm-152 106 0 6.0230E-06 293.0 end

 eu-153 106 0 5.9200E-06 293.0 end

 gd-155 106 0 1.4914E-07 293.0 end

 o-16 106 0 4.6945E-02 293.0 end

’ Node-07 Burnup=44.08 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 107 0 4.5293E-06 293.0 end

 u-235 107 0 2.0384E-04 293.0 end

 u-236 107 0 1.2773E-04 293.0 end

 u-238 107 0 2.1767E-02 293.0 end

 np-237 107 0 1.5292E-05 293.0 end

 pu-238 107 0 5.7796E-06 293.0 end

 pu-239 107 0 1.4421E-04 293.0 end

 pu-240 107 0 6.3200E-05 293.0 end

 pu-241 107 0 3.0354E-05 293.0 end

 pu-242 107 0 1.7366E-05 293.0 end

 am-241 107 0 9.0195E-06 293.0 end

 am-243 107 0 4.2852E-06 293.0 end

’ fission products

 mo-95 107 0 5.9091E-05 293.0 end

 tc-99 107 0 5.9351E-05 293.0 end

 ru-101 107 0 5.6032E-05 293.0 end

 rh-103 107 0 3.3487E-05 293.0 end

 ag-109 107 0 5.9653E-06 293.0 end

 cs-133 107 0 6.1876E-05 293.0 end

 nd-143 107 0 4.0238E-05 293.0 end

 nd-145 107 0 3.3605E-05 293.0 end

 sm-147 107 0 8.9120E-06 293.0 end

 sm-149 107 0 2.2014E-07 293.0 end

 sm-150 107 0 1.5711E-05 293.0 end

 sm-151 107 0 7.3879E-07 293.0 end

 eu-151 107 0 2.9507E-08 293.0 end

 sm-152 107 0 6.0055E-06 293.0 end

 eu-153 107 0 5.8927E-06 293.0 end

 gd-155 107 0 1.4831E-07 293.0 end

 o-16 107 0 4.6945E-02 293.0 end

’ Node-08 Burnup=43.88 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 108 0 4.5417E-06 293.0 end

 u-235 108 0 2.0556E-04 293.0 end

 u-236 108 0 1.2755E-04 293.0 end

 u-238 108 0 2.1771E-02 293.0 end

 np-237 108 0 1.5215E-05 293.0 end

 pu-238 108 0 5.7216E-06 293.0 end

 pu-239 108 0 1.4418E-04 293.0 end

 pu-240 108 0 6.2987E-05 293.0 end

 pu-241 108 0 3.0256E-05 293.0 end

 pu-242 108 0 1.7204E-05 293.0 end

 am-241 108 0 8.9888E-06 293.0 end

 am-243 108 0 4.2282E-06 293.0 end

’ fission products

 mo-95 108 0 5.8873E-05 293.0 end

 tc-99 108 0 5.9132E-05 293.0 end

 ru-101 108 0 5.5789E-05 293.0 end

 rh-103 108 0 3.3379E-05 293.0 end

 ag-109 108 0 5.9293E-06 293.0 end

 cs-133 108 0 6.1654E-05 293.0 end

 nd-143 108 0 4.0153E-05 293.0 end

 nd-145 108 0 3.3490E-05 293.0 end

 sm-147 108 0 8.9006E-06 293.0 end

 sm-149 108 0 2.2012E-07 293.0 end

 sm-150 108 0 1.5638E-05 293.0 end

 sm-151 108 0 7.3737E-07 293.0 end

 eu-151 108 0 2.9451E-08 293.0 end
Appendix B Sample Input File for CSAS25

47

 sm-152 108 0 5.9835E-06 293.0 end

 eu-153 108 0 5.8585E-06 293.0 end

 gd-155 108 0 1.4728E-07 293.0 end

 o-16 108 0 4.6945E-02 293.0 end

’ Node-09 Burnup=43.76 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 109 0 4.5491E-06 293.0 end

 u-235 109 0 2.0660E-04 293.0 end

 u-236 109 0 1.2744E-04 293.0 end

 u-238 109 0 2.1774E-02 293.0 end

 np-237 109 0 1.5168E-05 293.0 end

 pu-238 109 0 5.6869E-06 293.0 end

 pu-239 109 0 1.4416E-04 293.0 end

 pu-240 109 0 6.2858E-05 293.0 end

 pu-241 109 0 3.0197E-05 293.0 end

 pu-242 109 0 1.7107E-05 293.0 end

 am-241 109 0 8.9703E-06 293.0 end

 am-243 109 0 4.1943E-06 293.0 end

’ fission products

 mo-95 109 0 5.8743E-05 293.0 end

 tc-99 109 0 5.9000E-05 293.0 end

 ru-101 109 0 5.5642E-05 293.0 end

 rh-103 109 0 3.3315E-05 293.0 end

 ag-109 109 0 5.9077E-06 293.0 end

 cs-133 109 0 6.1521E-05 293.0 end

 nd-143 109 0 4.0102E-05 293.0 end

 nd-145 109 0 3.3421E-05 293.0 end

 sm-147 109 0 8.8936E-06 293.0 end

 sm-149 109 0 2.2010E-07 293.0 end

 sm-150 109 0 1.5593E-05 293.0 end

 sm-151 109 0 7.3653E-07 293.0 end

 eu-151 109 0 2.9418E-08 293.0 end

 sm-152 109 0 5.9703E-06 293.0 end

 eu-153 109 0 5.8380E-06 293.0 end

 gd-155 109 0 1.4666E-07 293.0 end

 o-16 109 0 4.6945E-02 293.0 end

’ Node-10 Burnup=43.76 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 110 0 4.5491E-06 293.0 end

 u-235 110 0 2.0660E-04 293.0 end

 u-236 110 0 1.2744E-04 293.0 end

 u-238 110 0 2.1774E-02 293.0 end

 np-237 110 0 1.5168E-05 293.0 end

 pu-238 110 0 5.6869E-06 293.0 end

 pu-239 110 0 1.4416E-04 293.0 end

 pu-240 110 0 6.2858E-05 293.0 end

 pu-241 110 0 3.0197E-05 293.0 end

 pu-242 110 0 1.7107E-05 293.0 end

 am-241 110 0 8.9703E-06 293.0 end

 am-243 110 0 4.1943E-06 293.0 end

’ fission products

 mo-95 110 0 5.8743E-05 293.0 end

 tc-99 110 0 5.9000E-05 293.0 end

 ru-101 110 0 5.5642E-05 293.0 end

 rh-103 110 0 3.3315E-05 293.0 end

 ag-109 110 0 5.9077E-06 293.0 end

 cs-133 110 0 6.1521E-05 293.0 end

 nd-143 110 0 4.0102E-05 293.0 end

 nd-145 110 0 3.3421E-05 293.0 end

 sm-147 110 0 8.8936E-06 293.0 end

 sm-149 110 0 2.2010E-07 293.0 end

 sm-150 110 0 1.5593E-05 293.0 end

 sm-151 110 0 7.3653E-07 293.0 end

 eu-151 110 0 2.9418E-08 293.0 end

 sm-152 110 0 5.9703E-06 293.0 end

 eu-153 110 0 5.8380E-06 293.0 end

 gd-155 110 0 1.4666E-07 293.0 end

 o-16 110 0 4.6945E-02 293.0 end

’ Node-11 Burnup=43.80 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides
Sample Input File for CSAS25 Appendix B

48

 u-234 111 0 4.5466E-06 293.0 end

 u-235 111 0 2.0625E-04 293.0 end

 u-236 111 0 1.2748E-04 293.0 end

 u-238 111 0 2.1773E-02 293.0 end

 np-237 111 0 1.5184E-05 293.0 end

 pu-238 111 0 5.6985E-06 293.0 end

 pu-239 111 0 1.4416E-04 293.0 end

 pu-240 111 0 6.2901E-05 293.0 end

 pu-241 111 0 3.0216E-05 293.0 end

 pu-242 111 0 1.7139E-05 293.0 end

 am-241 111 0 8.9765E-06 293.0 end

 am-243 111 0 4.2056E-06 293.0 end

’ fission products

 mo-95 111 0 5.8786E-05 293.0 end

 tc-99 111 0 5.9044E-05 293.0 end

 ru-101 111 0 5.5691E-05 293.0 end

 rh-103 111 0 3.3336E-05 293.0 end

 ag-109 111 0 5.9149E-06 293.0 end

 cs-133 111 0 6.1565E-05 293.0 end

 nd-143 111 0 4.0119E-05 293.0 end

 nd-145 111 0 3.3444E-05 293.0 end

 sm-147 111 0 8.8959E-06 293.0 end

 sm-149 111 0 2.2011E-07 293.0 end

 sm-150 111 0 1.5608E-05 293.0 end

 sm-151 111 0 7.3681E-07 293.0 end

 eu-151 111 0 2.9429E-08 293.0 end

 sm-152 111 0 5.9747E-06 293.0 end

 eu-153 111 0 5.8449E-06 293.0 end

 gd-155 111 0 1.4687E-07 293.0 end

 o-16 111 0 4.6945E-02 293.0 end

’ Node-12 Burnup=43.84 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 112 0 4.5442E-06 293.0 end

 u-235 112 0 2.0591E-04 293.0 end

 u-236 112 0 1.2751E-04 293.0 end

 u-238 112 0 2.1772E-02 293.0 end

 np-237 112 0 1.5199E-05 293.0 end

 pu-238 112 0 5.7100E-06 293.0 end

 pu-239 112 0 1.4417E-04 293.0 end

 pu-240 112 0 6.2944E-05 293.0 end

 pu-241 112 0 3.0236E-05 293.0 end

 pu-242 112 0 1.7172E-05 293.0 end

 am-241 112 0 8.9827E-06 293.0 end

 am-243 112 0 4.2169E-06 293.0 end

’ fission products

 mo-95 112 0 5.8830E-05 293.0 end

 tc-99 112 0 5.9088E-05 293.0 end

 ru-101 112 0 5.5740E-05 293.0 end

 rh-103 112 0 3.3358E-05 293.0 end

 ag-109 112 0 5.9221E-06 293.0 end

 cs-133 112 0 6.1610E-05 293.0 end

 nd-143 112 0 4.0136E-05 293.0 end

 nd-145 112 0 3.3467E-05 293.0 end

 sm-147 112 0 8.8983E-06 293.0 end

 sm-149 112 0 2.2011E-07 293.0 end

 sm-150 112 0 1.5623E-05 293.0 end

 sm-151 112 0 7.3709E-07 293.0 end

 eu-151 112 0 2.9440E-08 293.0 end

 sm-152 112 0 5.9791E-06 293.0 end

 eu-153 112 0 5.8517E-06 293.0 end

 gd-155 112 0 1.4707E-07 293.0 end

 o-16 112 0 4.6945E-02 293.0 end

’ Node-13 Burnup=43.80 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 113 0 4.5466E-06 293.0 end

 u-235 113 0 2.0625E-04 293.0 end

 u-236 113 0 1.2748E-04 293.0 end

 u-238 113 0 2.1773E-02 293.0 end

 np-237 113 0 1.5184E-05 293.0 end

 pu-238 113 0 5.6985E-06 293.0 end

 pu-239 113 0 1.4416E-04 293.0 end
Appendix B Sample Input File for CSAS25

49

 pu-240 113 0 6.2901E-05 293.0 end

 pu-241 113 0 3.0216E-05 293.0 end

 pu-242 113 0 1.7139E-05 293.0 end

 am-241 113 0 8.9765E-06 293.0 end

 am-243 113 0 4.2056E-06 293.0 end

’ fission products

 mo-95 113 0 5.8786E-05 293.0 end

 tc-99 113 0 5.9044E-05 293.0 end

 ru-101 113 0 5.5691E-05 293.0 end

 rh-103 113 0 3.3336E-05 293.0 end

 ag-109 113 0 5.9149E-06 293.0 end

 cs-133 113 0 6.1565E-05 293.0 end

 nd-143 113 0 4.0119E-05 293.0 end

 nd-145 113 0 3.3444E-05 293.0 end

 sm-147 113 0 8.8959E-06 293.0 end

 sm-149 113 0 2.2011E-07 293.0 end

 sm-150 113 0 1.5608E-05 293.0 end

 sm-151 113 0 7.3681E-07 293.0 end

 eu-151 113 0 2.9429E-08 293.0 end

 sm-152 113 0 5.9747E-06 293.0 end

 eu-153 113 0 5.8449E-06 293.0 end

 gd-155 113 0 1.4687E-07 293.0 end

 o-16 113 0 4.6945E-02 293.0 end

’ Node-14 Burnup=43.44 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 114 0 4.5691E-06 293.0 end

 u-235 114 0 2.0939E-04 293.0 end

 u-236 114 0 1.2714E-04 293.0 end

 u-238 114 0 2.1780E-02 293.0 end

 np-237 114 0 1.5044E-05 293.0 end

 pu-238 114 0 5.5948E-06 293.0 end

 pu-239 114 0 1.4409E-04 293.0 end

 pu-240 114 0 6.2512E-05 293.0 end

 pu-241 114 0 3.0038E-05 293.0 end

 pu-242 114 0 1.6850E-05 293.0 end

 am-241 114 0 8.9207E-06 293.0 end

 am-243 114 0 4.1044E-06 293.0 end

’ fission products

 mo-95 114 0 5.8393E-05 293.0 end

 tc-99 114 0 5.8648E-05 293.0 end

 ru-101 114 0 5.5252E-05 293.0 end

 rh-103 114 0 3.3142E-05 293.0 end

 ag-109 114 0 5.8502E-06 293.0 end

 cs-133 114 0 6.1163E-05 293.0 end

 nd-143 114 0 3.9965E-05 293.0 end

 nd-145 114 0 3.3237E-05 293.0 end

 sm-147 114 0 8.8748E-06 293.0 end

 sm-149 114 0 2.2006E-07 293.0 end

 sm-150 114 0 1.5475E-05 293.0 end

 sm-151 114 0 7.3426E-07 293.0 end

 eu-151 114 0 2.9329E-08 293.0 end

 sm-152 114 0 5.9351E-06 293.0 end

 eu-153 114 0 5.7833E-06 293.0 end

 gd-155 114 0 1.4501E-07 293.0 end

 o-16 114 0 4.6945E-02 293.0 end

’ Node-15 Burnup=42.36 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 115 0 4.6373E-06 293.0 end

 u-235 115 0 2.1903E-04 293.0 end

 u-236 115 0 1.2608E-04 293.0 end

 u-238 115 0 2.1802E-02 293.0 end

 np-237 115 0 1.4622E-05 293.0 end

 pu-238 115 0 5.2882E-06 293.0 end

 pu-239 115 0 1.4385E-04 293.0 end

 pu-240 115 0 6.1322E-05 293.0 end

 pu-241 115 0 2.9482E-05 293.0 end

 pu-242 115 0 1.5988E-05 293.0 end

 am-241 115 0 8.7473E-06 293.0 end

 am-243 115 0 3.8077E-06 293.0 end

’ fission products

 mo-95 115 0 5.7204E-05 293.0 end
Sample Input File for CSAS25 Appendix B

50

 tc-99 115 0 5.7451E-05 293.0 end

 ru-101 115 0 5.3934E-05 293.0 end

 rh-103 115 0 3.2549E-05 293.0 end

 ag-109 115 0 5.6561E-06 293.0 end

 cs-133 115 0 5.9947E-05 293.0 end

 nd-143 115 0 3.9486E-05 293.0 end

 nd-145 115 0 3.2609E-05 293.0 end

 sm-147 115 0 8.8079E-06 293.0 end

 sm-149 115 0 2.1988E-07 293.0 end

 sm-150 115 0 1.5076E-05 293.0 end

 sm-151 115 0 7.2652E-07 293.0 end

 eu-151 115 0 2.9024E-08 293.0 end

 sm-152 115 0 5.8150E-06 293.0 end

 eu-153 115 0 5.5984E-06 293.0 end

 gd-155 115 0 1.3946E-07 293.0 end

 o-16 115 0 4.6946E-02 293.0 end

’ Node-16 Burnup=38.84 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 116 0 4.8682E-06 293.0 end

 u-235 116 0 2.5284E-04 293.0 end

 u-236 116 0 1.2207E-04 293.0 end

 u-238 116 0 2.1870E-02 293.0 end

 np-237 116 0 1.3212E-05 293.0 end

 pu-238 116 0 4.3378E-06 293.0 end

 pu-239 116 0 1.4275E-04 293.0 end

 pu-240 116 0 5.7196E-05 293.0 end

 pu-241 116 0 2.7486E-05 293.0 end

 pu-242 116 0 1.3277E-05 293.0 end

 am-241 116 0 8.1262E-06 293.0 end

 am-243 116 0 2.9185E-06 293.0 end

’ fission products

 mo-95 116 0 5.3242E-05 293.0 end

 tc-99 116 0 5.3454E-05 293.0 end

 ru-101 116 0 4.9608E-05 293.0 end

 rh-103 116 0 3.0517E-05 293.0 end

 ag-109 116 0 5.0261E-06 293.0 end

 cs-133 116 0 5.5873E-05 293.0 end

 nd-143 116 0 3.7763E-05 293.0 end

 nd-145 116 0 3.0496E-05 293.0 end

 sm-147 116 0 8.5538E-06 293.0 end

 sm-149 116 0 2.1900E-07 293.0 end

 sm-150 116 0 1.3754E-05 293.0 end

 sm-151 116 0 7.0040E-07 293.0 end

 eu-151 116 0 2.7994E-08 293.0 end

 sm-152 116 0 5.4127E-06 293.0 end

 eu-153 116 0 4.9933E-06 293.0 end

 gd-155 116 0 1.2158E-07 293.0 end

 o-16 116 0 4.6946E-02 293.0 end

’ Node-17 Burnup=29.52 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 117 0 5.5443E-06 293.0 end

 u-235 117 0 3.6164E-04 293.0 end

 u-236 117 0 1.0706E-04 293.0 end

 u-238 117 0 2.2044E-02 293.0 end

 np-237 117 0 9.3347E-06 293.0 end

 pu-238 117 0 2.2501E-06 293.0 end

 pu-239 117 0 1.3627E-04 293.0 end

 pu-240 117 0 4.4429E-05 293.0 end

 pu-241 117 0 2.0813E-05 293.0 end

 pu-242 117 0 7.0354E-06 293.0 end

 am-241 117 0 6.0735E-06 293.0 end

 am-243 117 0 1.1752E-06 293.0 end

’ fission products

 mo-95 117 0 4.2096E-05 293.0 end

 tc-99 117 0 4.2180E-05 293.0 end

 ru-101 117 0 3.7975E-05 293.0 end

 rh-103 117 0 2.4415E-05 293.0 end

 ag-109 117 0 3.4048E-06 293.0 end

 cs-133 117 0 4.4270E-05 293.0 end

 nd-143 117 0 3.1943E-05 293.0 end

 nd-145 117 0 2.4412E-05 293.0 end
Appendix B Sample Input File for CSAS25

51

 sm-147 117 0 7.5738E-06 293.0 end

 sm-149 117 0 2.1350E-07 293.0 end

 sm-150 117 0 1.0170E-05 293.0 end

 sm-151 117 0 6.2399E-07 293.0 end

 eu-151 117 0 2.4972E-08 293.0 end

 sm-152 117 0 4.2632E-06 293.0 end

 eu-153 117 0 3.4113E-06 293.0 end

 gd-155 117 0 7.7532E-08 293.0 end

 o-16 117 0 4.6947E-02 293.0 end

’ Node-18 Burnup=18.48 GWd/MTU w17×17 pwr 18-axial nodes gbc-32 model

’ actinides

 u-234 118 0 6.4660E-06 293.0 end

 u-235 118 0 5.3166E-04 293.0 end

 u-236 118 0 7.9832E-05 293.0 end

 u-238 118 0 2.2234E-02 293.0 end

 np-237 118 0 4.8683E-06 293.0 end

 pu-238 118 0 6.9462E-07 293.0 end

 pu-239 118 0 1.1629E-04 293.0 end

 pu-240 118 0 2.6299E-05 293.0 end

 pu-241 118 0 1.0804E-05 293.0 end

 pu-242 118 0 2.0446E-06 293.0 end

 am-241 118 0 3.0829E-06 293.0 end

 am-243 118 0 2.0341E-07 293.0 end

’ fission products

 mo-95 118 0 2.7605E-05 293.0 end

 tc-99 118 0 2.6628E-05 293.0 end

 ru-101 118 0 2.3913E-05 293.0 end

 rh-103 118 0 1.5926E-05 293.0 end

 ag-109 118 0 1.6800E-06 293.0 end

 cs-133 118 0 2.9023E-05 293.0 end

 nd-143 118 0 2.2535E-05 293.0 end

 nd-145 118 0 1.6246E-05 293.0 end

 sm-147 118 0 5.6918E-06 293.0 end

 sm-149 118 0 1.9729E-07 293.0 end

 sm-150 118 0 5.9405E-06 293.0 end

 sm-151 118 0 5.1675E-07 293.0 end

 eu-151 118 0 2.0704E-08 293.0 end

 sm-152 118 0 2.7262E-06 293.0 end

 eu-153 118 0 1.7157E-06 293.0 end

 gd-155 118 0 3.6864E-08 293.0 end

 o-16 118 0 4.6947E-02 293.0 end

’

’ - Zr cladding

zr 2 0 0.04230 293.0 end

’

’ - water moderator

h 3 0 0.06674 293.0 end

o-16 3 0 0.03337 293.0 end

’

’ - Stainless Steel [Ref. LA-12827-M, page C-10]

cr 4 0 0.01743 293.0 end

mn 4 0 0.00174 293.0 end

fe 4 0 0.05936 293.0 end

ni 4 0 0.00772 293.0 end

’

’ - Boral Center - B-10 loading of 0.0225 g/sqcm

b-10 5 0 6.5795E-03 293.0 end

b-11 5 0 2.7260E-02 293.0 end

c 5 0 8.4547E-03 293.0 end

al 5 0 4.1795E-02 293.0 end

’

’ - Stainless Steel [Ref. LA-12827-M, page C-10]

cr 6 0 0.01743 293.0 end

mn 6 0 0.00174 293.0 end

fe 6 0 0.05936 293.0 end

ni 6 0 0.00772 293.0 end

’

’ - Aluminum [Ref. Duderstadt & Hamilton]

al 7 0 0.0602 293.0 end

end comp

’
Sample Input File for CSAS25 Appendix B

52

’ pitch fuel OD mfuel mmod clad OD mclad cladid mgap

squarepitch 1.2598 0.7844 101 3 0.9144 2 0.8001 3 end

more data

res=102 cylinder 0.3922 dan(102)=0.22877

res=103 cylinder 0.3922 dan(103)=0.22877

res=104 cylinder 0.3922 dan(104)=0.22877

res=105 cylinder 0.3922 dan(105)=0.22877

res=106 cylinder 0.3922 dan(106)=0.22877

res=107 cylinder 0.3922 dan(107)=0.22877

res=108 cylinder 0.3922 dan(108)=0.22877

res=109 cylinder 0.3922 dan(109)=0.22877

res=110 cylinder 0.3922 dan(110)=0.22877

res=111 cylinder 0.3922 dan(111)=0.22877

res=112 cylinder 0.3922 dan(112)=0.22877

res=113 cylinder 0.3922 dan(113)=0.22877

res=114 cylinder 0.3922 dan(114)=0.22877

res=115 cylinder 0.3922 dan(115)=0.22877

res=116 cylinder 0.3922 dan(116)=0.22877

res=117 cylinder 0.3922 dan(117)=0.22877

res=118 cylinder 0.3922 dan(118)=0.22877 end

Generic 32-Assembly Burnup Credit Cask (GBC-32) w/Axial Brnp Profile

read param tme=10000 gen=1100 nsk=100 npg=2000 end parm

read geom

’

’ Fuel Pin

unit 1

cylinder 101 1 0.3922 20.318 0.

cylinder 102 1 0.3922 40.636 0.

cylinder 103 1 0.3922 60.954 0.

cylinder 104 1 0.3922 81.272 0.

cylinder 105 1 0.3922 101.608 0.

cylinder 106 1 0.3922 121.926 0.

cylinder 107 1 0.3922 142.281 0.

cylinder 108 1 0.3922 162.599 0.

cylinder 109 1 0.3922 182.880 0.

cylinder 110 1 0.3922 203.198 0.

cylinder 111 1 0.3922 223.516 0.

cylinder 112 1 0.3922 243.834 0.

cylinder 113 1 0.3922 264.152 0.

cylinder 114 1 0.3922 284.488 0.

cylinder 115 1 0.3922 304.806 0.

cylinder 116 1 0.3922 325.124 0.

cylinder 117 1 0.3922 345.442 0.

cylinder 118 1 0.3922 365.760 0.

cylinder 3 1 0.4001 365.76 0.

cylinder 2 1 0.4572 365.76 0.

cuboid 3 1 0.6299 -0.6299 0.6299 -0.6299 365.76 0.

’

’ Guide Thimble/Instrument Tube (assumed to be same)

unit 2

cylinder 3 1 0.5613 365.76 0.

cylinder 2 1 0.6020 365.76 0.

cuboid 3 1 0.6299 -0.6299 0.6299 -0.6299 365.76 0.

’

’ Top Half Horizontal Boral Panel

unit 4

cuboid 7 1 9.5250 -9.5250 0.02540 -0.0 365.76 0.

cuboid 5 1 9.5250 -9.5250 0.128270 -0.0 365.76 0.

’

’ Right-Hand Side Half Vertical Boral Panel

unit 5

cuboid 7 1 0.02540 -0.0 9.5250 -9.5250 365.76 0.

cuboid 5 1 0.128270 -0.0 9.5250 -9.5250 365.76 0.

’

’ Bottom Half Horizontal Boral Panel

unit 6

cuboid 7 1 9.5250 -9.5250 0.0 -0.02540 365.76 0.

cuboid 5 1 9.5250 -9.5250 0.0 -0.128270 365.76 0.

’

’ Left-Hand Side Half Vertical Boral Panel

unit 7
Appendix B Sample Input File for CSAS25

53

cuboid 7 1 0.0 -0.02540 9.5250 -9.5250 365.76 0.

cuboid 5 1 0.0 -0.128270 9.5250 -9.5250 365.76 0.

’

’ Assembly Basket Cell

unit 101 ARRAY 1 -10.7086 -10.7086 0.

cuboid 3 1 11.0000 -11.0000 11.0000 -11.0000 365.76 0.

cuboid 4 1 11.7500 -11.7500 11.7500 -11.7500 365.76 0.

cuboid 3 1 11.87827 -11.87827 11.87827 -11.87827 365.76 0.

hole 4 0. 11.75000 0.

hole 5 11.75000 0. 0.

hole 6 0. -11.75000 0.

hole 7 -11.75000 0. 0.

’

’ Top Boral/Basket Plate

unit 110

cuboid 4 1 11.7500 -11.7500 0.0000 -0.7500 365.76 0.

cuboid 3 1 11.7500 -11.7500 0.0000 -0.8783 365.76 0.

hole 6 0. -0.7500 0.

’

’ Bottom Boral/Basket Plate

unit 111

cuboid 4 1 11.7500 -11.7500 0.7500 -0.0000 365.76 0.

cuboid 3 1 11.7500 -11.7500 0.8783 -0.0000 365.76 0.

hole 4 0. 0.7500 0.

’

’ Left-Hand Side Boral/Basket Plate

unit 112

cuboid 4 1 0.0000 -0.7500 10.9999 -10.9999 365.76 0.

cuboid 3 1 0.0000 -0.8783 10.9999 -10.9999 365.76 0.

hole 7 -0.75000 0. 0.

’

’ Right-Hand Side Boral/Basket Plate

unit 113

cuboid 4 1 0.7500 -0.0000 10.9999 -10.9999 365.76 0.

cuboid 3 1 0.8783 -0.0000 10.9999 -10.9999 365.76 0.

hole 5 0.75000 0. 0.

’

’ Cask Inner Volume

global unit 200

cylinder 3 1 87.500 395.76 -30.00

’ Assemblies

hole 101 -35.634840 59.391400 0.

hole 101 -11.878270 59.391400 0.

hole 101 11.878270 59.391400 0.

hole 101 35.634840 59.391400 0.

’

hole 101 -59.391400 35.634840 0.

hole 101 -35.634840 35.634840 0.

hole 101 -11.878270 35.634840 0.

hole 101 11.878270 35.634840 0.

hole 101 35.634840 35.634840 0.

hole 101 59.391400 35.634840 0.

’

hole 101 -59.391400 11.878270 0.

hole 101 -35.634840 11.878270 0.

hole 101 -11.878270 11.878270 0.

hole 101 11.878270 11.878270 0.

hole 101 35.634840 11.878270 0.

hole 101 59.391400 11.878270 0.

’

hole 101 -59.391400 -11.878270 0.

hole 101 -35.634840 -11.878270 0.

hole 101 -11.878270 -11.878270 0.

hole 101 11.878270 -11.878270 0.

hole 101 35.634840 -11.878270 0.

hole 101 59.391400 -11.878270 0.

’

hole 101 -59.391400 -35.634840 0.

hole 101 -35.634840 -35.634840 0.

hole 101 -11.878270 -35.634840 0.

hole 101 11.878270 -35.634840 0.
Sample Input File for CSAS25 Appendix B

54

hole 101 35.634840 -35.634840 0.

hole 101 59.391400 -35.634840 0.

’

hole 101 -35.634840 -59.391400 0.

hole 101 -11.878270 -59.391400 0.

hole 101 11.878270 -59.391400 0.

hole 101 35.634840 -59.391400 0.

’

’ Exterior Half Boral Panels

’ Top Plates

hole 110 -35.634840 72.147980 0.

hole 110 -11.878270 72.147980 0.

hole 110 11.878270 72.147980 0.

hole 110 35.634840 72.147980 0.

hole 110 59.391400 48.391420 0.

hole 110 -59.391400 48.391420 0.

’ Bottom Plates

hole 111 -35.634840 -72.147980 0.

hole 111 -11.878270 -72.147980 0.

hole 111 11.878270 -72.147980 0.

hole 111 35.634840 -72.147980 0.

hole 111 59.391400 -48.391420 0.

hole 111 -59.391400 -48.391420 0.

’ Left-Hand Side Plates

hole 113 -48.391420 59.391400 0.

hole 113 -72.147980 35.634840 0.

hole 113 -72.147980 11.878270 0.

hole 113 -72.147980 -11.878270 0.

hole 113 -72.147980 -35.634840 0.

hole 113 -48.391420 -59.391400 0.

’ Right-Hand Side Plates

hole 112 48.391420 59.391400 0.

hole 112 72.147980 35.634840 0.

hole 112 72.147980 11.878270 0.

hole 112 72.147980 -11.878270 0.

hole 112 72.147980 -35.634840 0.

hole 112 48.391420 -59.391400 0.

’

’ Steel Cask/Overpack

cylinder 6 1 107.5 425.76 -60.

’

’ Cube of Water Surrounding Cask

cuboid 0 1 108 -108 108 -108 425.76 -60.

end geom

’

’ Assembly Type: Westinghouse 17×17 OFA/V5

read array

ara=1 nux=17 nuy=17 nuz=1

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 1

 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1

 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1

 1 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

end fill

end array

read bounds xyf=specular end bounds

end data

end
55

APPENDIX C

SUPPLEMENTARY RESULTS FOR ADDITIONAL

NUCLIDE SETS
56
57

APPENDIX C

SUPPLEMENTARY RESULTS FOR ADDITIONAL

NUCLIDE SETS

This appendix contains supplementary results for nuclide sets in addition to those defined in the main body of this

report. One of the more difficult decisions that was required during the preparation of this computational

benchmark was the decision related to which nuclides to consider for the estimation of the additional reactivity

margin. Given the number of nuclides that have been identified as being important to burnup credit, one could

group them in many different ways. It has become a common practice for the nuclides to be divided in terms of

actinides and fission products. Another useful guideline for dividing the nuclides into subsets is the existence of

measured chemical assay data. In this appendix, the nuclides that have been previous identified as being

important to burnup credit are divided into 4 subsets and reactivity comparisons are made between calculations

with these nuclide subsets and calculations using all nuclides for which cross-section data are available, which

corresponds to 233 nuclides in the SCALE 238-group library. The nuclides are divided into subsets according to

their classification as actinide or fission product, and based on the existence of measured assay data.

Reference C.1 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. Therefore, for this benchmark, all of the actinide and fission product nuclides identified in

Ref. C.1, including those for which no chemical assay data are available, were used in the estimation of the

additional reactivity margin. This decision was based on the objective of estimating the residual margins with

actinide-only burnup credit. However, questions often arise regarding the reactivity margin associated with

various subsets of the actinides and fission products. To investigate the reactivity worth of the nuclides in a bit

more detail, results were also generated for the computational benchmark problem using additional nuclide sets,

based on those listed in Table C.1.

Calculated keff values for the benchmark problem (the GBC-32 cask) for various nuclide sets as a function of

burnup for initial enrichments of 2, 3, 4, and 5 wt % 235U and cooling times of 5- and 20-years are plotted in

Figures C.1–C.8.

Table C.1 Nuclides used for supplementary analysis of the benchmark problem

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

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

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

 Notes: (1) Underlined nuclides are consistent with those specified in a DOE Topical Report.C.2

(2) Nuclides identified with asterisks are nuclides for which measured chemical assay data

are not currently available or are not readily available at this time in the United States.
Supplementary Results Appendix C

58

Figure C.1 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

5-year cooling time for fuel of 2 wt % 235U initial enrichment

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Appendix C Supplementary Results

59

Figure C.2 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

20-year cooling time for fuel of 2 wt % 235U initial enrichment

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Supplementary Results Appendix C

60

Figure C.3 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

5-year cooling time for fuel of 3 wt % 235U initial enrichment

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Appendix C Supplementary Results

61

Figure C.4 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

20-year cooling time for fuel of 3 wt % 235U initial enrichment

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Supplementary Results Appendix C

62

Figure C.5 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

5-year cooling time for fuel of 4 wt % 235U initial enrichment

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Appendix C Supplementary Results

63

Figure C.6 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

20-year cooling time for fuel of 4 wt % 235U initial enrichment

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Supplementary Results Appendix C

64

Figure C.7 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

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

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Appendix C Supplementary Results

65

Figure C.8 Values of keff in the GBC-32 cask as a function of burnup using various nuclide sets and

20-year cooling time for fuel of 5 wt % 235U initial enrichment

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel All Measured Nuclides in Table C.1

DOE TR Rev. 2 Actinides All Nuclides in Table C.1

11 Measured Actinides in Table C.1 All Nuclides Available (233)
Supplementary Results Appendix C

66

REFERENCES

C.1 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.

C.2 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).
67

APPENDIX D

DISCUSSION OF REFERENCE RESULTS
68
69

APPENDIX D

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, which corresponds to the cooling time addressed in ISG8. Figures D.1–D.4 plot the keff

values in the GBC-32 cask for the two nuclide sets (refer to Tables D1 and D2 for specification of nuclide sets) as

a function of burnup and 5-year cooling time 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 enrichments of 2 and 3 wt % 235U are below 40 GWd/MTU.

Similarly, for enrichments of 4 and 5 wt % 235U, typical discharge burnups are greater than 30 GWd/MTU. Thus,

one should be cognizant of this fact 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 are available in Ref. D.1.

The reactivity reductions due to the major actinides (set 1 in Table D.1), additional nuclides (set 3 Table D.2),

and all of the nuclides considered (set 2 in Table D.1) are plotted in Figures D.5–D.8 as a function of burnup and

5-year cooling time 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–D.12. The relative reactivity reduction 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 examine the effect of initial enrichment, Figures D.13 and D.14 show the reactivity reductions (in terms of ∆k

values) as a function of burnup, for initial enrichments of 3, 4, and 5 wt % 235U, for (a) the major actinides and

(b) the additional nuclides, respectively. The effect of initial enrichment on these contributions to the reactivity

reduction is shown to be relatively minor. However, these figures do reveal that, for a given burnup, an increase

in the initial enrichment results in a decrease in the contribution from the major actinides and a simultaneous

increase in the contribution from the additional nuclides. Consequently, the relative contribution from the

additional nuclides to the total reactivity reduction increases with enrichment. The individual contributions to the

total reactivity reduction from (a) the major actinides and (b) the additional nuclides, for the various initial

enrichments are shown in Figures D.15 and D.16.

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 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 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.
Discussion of Reference Results Appendix D

70

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, except for the extremely unrealistic case at 2 wt % initial enrichment

burned to 60 GWd/MTU, the minimum values correspond to zero cooling time.

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

set 1: Major actinides (10 total)

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

set 2: Actinides and major fission products (29 total)

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

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

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

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

 calculations.

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)

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

Sm-149 Sm-150 Sm-151 Sm-152 Nd-143 Nd-145 Eu-151 Eu-153 Gd-155
Appendix D Discussion of Reference Results

71

Figure D.1 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide

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

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel

Major Actinides

(set 1)

Actinides & Major

Fission Products

(set 2)
Discussion of Reference Results Appendix D

72

Figure D.2 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide

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

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel

Major Actinides

(set 1)

Actinides & Major

Fission Products

(set 2)
Appendix D Discussion of Reference Results

73

Figure D.3 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide

sets and 5-year cooling time for fuel of 4 wt % 235U initial enrichment

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel

Major Actinides

(set 1)

Actinides & Major

Fission Products

(set 2)
Discussion of Reference Results Appendix D

74

Figure D.4 Values of keff in the GBC-32 cask as a function of burnup using the different nuclide sets

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

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

0 10 20 30 40 50 60

Burnup (GWd/MTU)

keff in GBC-32 Cask

Fresh Fuel

Major Actinides

(set 1)

Actinides & Major

Fission Products

(set 2)
Appendix D Discussion of Reference Results

75

Figure D.5 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

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

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆k in GBC-32 Cask

Total (set 2)

Major Actinides (set 1)

Additional Nuclides (set 3)
Discussion of Reference Results Appendix D

76

Figure D.6 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

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

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆k in GBC-32 Cask

Total (set 2)

Major Actinides (set 1)

Additional Nuclides (set 3)
Appendix D Discussion of Reference Results

77

Figure D.7 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

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

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆k in GBC-32 Cask

Total (set 2)

Major Actinides (set 1)

Additional Nuclides (set 3)
Discussion of Reference Results Appendix D

78

Figure D.8 ∆k values (relative to fresh fuel) in the GBC-32 cask as a function of burnup using the

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

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆k in GBC-32 Cask

Total (set 2)

Major Actinides (set 1)

Additional Nuclides (set 3)
Appendix D Discussion of Reference Results

79

Figure D.9 Individual contributions to the total reduction in keff for the different nuclide sets as a

function of burnup and 5-year cooling time for fuel of 2 wt % 235U initial enrichment

0%

10%

20%

30%

40%

50%

60%

70%

80%

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction 

Major Actinides (set 1) Additional Nuclides (set 3)
Discussion of Reference Results Appendix D

80

Figure D.10 Individual contributions to the total reduction in keff for the different nuclide sets as a

function of burnup and 5-year cooling time for fuel of 3 wt % 235U initial enrichment

0%

10%

20%

30%

40%

50%

60%

70%

80%

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction 

Major Actinides (set 1) Additional Nuclides (set 3)
Appendix D Discussion of Reference Results

81

Figure D.11 Individual contributions to the total reduction in keff for the different nuclide sets as a

function of burnup and 5-year cooling time for fuel of 4 wt % 235U initial enrichment

0%

10%

20%

30%

40%

50%

60%

70%

80%

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction 

Major Actinides (set 1) Additional Nuclides (set 3)
Discussion of Reference Results Appendix D

82

Figure D.12 Individual contributions to the total reduction in keff for the different nuclide sets as a

function of burnup and 5-year cooling time for fuel of 5 wt % 235U initial enrichment

0%

10%

20%

30%

40%

50%

60%

70%

80%

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction 

Major Actinides (set 1) Additional Nuclides (set 3)
Appendix D Discussion of Reference Results

83

Figure D.13 ∆k (relative to fresh fuel) in GBC-32 cask due to the major actinides (set 1) as a

function of burnup for various initial enrichments and 5-year cooling time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

10 20 30 40 50 60

Burnup (GWd/MTU)

∆

k

5.0 wt%

4.0 wt%

3.0 wt%
Discussion of Reference Results Appendix D

84

Figure D.14 ∆k in GBC-32 cask due to the additional nuclides (set 3) as a function of burnup for

various initial enrichments and 5-year cooling time

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

10 20 30 40 50 60

Burnup (GWd/MTU)

∆

k

5.0 wt%

4.0 wt%

3.0 wt%
Appendix D Discussion of Reference Results

85

Figure D.15 Effect of initial enrichment on the contribution to total reduction in keff due to the

major actinides (set 1) as a function of burnup for 5-year cooling time

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction

5.0 wt% 4.0 wt% 3.0 wt%
Discussion of Reference Results Appendix D

86

Figure D.16 Effect of initial enrichment on the contribution to total reduction in keff due to the

additional nuclides (set 3) as a function of burnup for 5-year cooling time

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

10 20 30 40 50 60

Burnup (GWd/MTU)

Contribution to total reactivity reduction

5.0 wt% 4.0 wt% 3.0 wt%
Appendix D Discussion of Reference Results

87

Figure D.17 ∆k (relative to fresh fuel) in the GBC-32 cask due to the major actinides (set 1) as a

function of burnup for various cooling times and 4 wt % 235U initial enrichment

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆

k

0-yrs

5-yrs

10-yrs

20-yrs

40-yrs
Discussion of Reference Results Appendix D

88

Figure D.18 ∆k in the GBC-32 cask due to the additional nuclides (set 3) as a function of burnup

for various cooling times and 4 wt % 235U initial enrichment

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0 10 20 30 40 50 60

Burnup (GWd/MTU)

∆

k

0-yrs

5-yrs

10-yrs

20-yrs

40-yrs
Appendix D Discussion of Reference Results

89

Figure D.19 Range of ∆k values in the GBC-32 cask due to the additional nuclides (set 3) as a

function of burnup for all cooling times and initial enrichments considered

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

10 20 30 40 50 60

Burnup (GWd/MTU)

∆k due to Additional Nuclides

maximum

minimum
Discussion of Reference Results Appendix D

90

REFERENCES

D.1 Spent Nuclear Fuel Discharges from U.S. Reactors – 1994, SR/CNEAF/96-01, Energy Information

Administration, U.S. Department of Energy, February 1996.

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 LongTerm 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).
91

APPENDIX E

LIMITED NUCLIDE COMPOSITION DATA
92
Appendix E Limited Nuclide Composition Data

93

Table E.1 Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt % 235

U,

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

U-234 7.25E-06 6.30E-06 5.41E-06 4.61E-06 3.88E-06 3.24E-06

U-235 6.99E-04 5.05E-04 3.55E-04 2.41E-04 1.58E-04 9.97E-05

U-236 5.07E-05 8.42E-05 1.08E-04 1.23E-04 1.32E-04 1.35E-04

U-238 2.24E-02 2.22E-02 2.20E-02 2.18E-02 2.16E-02 2.14E-02

Np-237 1.81E-06 5.14E-06 9.13E-06 1.32E-05 1.69E-05 2.01E-05

Pu-238 1.42E-07 8.27E-07 2.26E-06 4.48E-06 7.33E-06 1.05E-05

Pu-239 8.03E-05 1.17E-04 1.34E-04 1.40E-04 1.41E-04 1.41E-04

Pu-240 1.15E-05 2.89E-05 4.51E-05 5.85E-05 6.86E-05 7.58E-05

Pu-241 4.34E-06 1.56E-05 2.70E-05 3.59E-05 4.19E-05 4.55E-05

Pu-242 3.13E-07 2.55E-06 7.32E-06 1.42E-05 2.23E-05 3.10E-05

Am-241 2.47E-08 1.76E-07 4.27E-07 6.80E-07 8.70E-07 9.82E-07

Am-243 1.53E-08 2.77E-07 1.24E-06 3.19E-06 6.11E-06 9.75E-06

Mo-95 5.16E-06 1.76E-05 3.09E-05 4.33E-05 5.46E-05 6.48E-05

Tc-99 1.49E-05 2.92E-05 4.23E-05 5.44E-05 6.53E-05 7.52E-05

Ru-101 1.30E-05 2.59E-05 3.86E-05 5.10E-05 6.32E-05 7.49E-05

Rh-103 5.58E-06 1.34E-05 2.07E-05 2.68E-05 3.18E-05 3.57E-05

Ag-109 6.27E-07 1.89E-06 3.47E-06 5.22E-06 7.01E-06 8.77E-06

Cs-133 1.53E-05 3.03E-05 4.40E-05 5.64E-05 6.73E-05 7.70E-05

Nd-143 1.16E-05 2.23E-05 3.07E-05 3.68E-05 4.09E-05 4.33E-05

Nd-145 9.21E-06 1.74E-05 2.47E-05 3.12E-05 3.68E-05 4.17E-05

Sm-147 2.28E-07 7.98E-07 1.47E-06 2.09E-06 2.60E-06 2.95E-06

Sm-149 1.02E-07 1.16E-07 1.19E-07 1.16E-07 1.12E-07 1.07E-07

Sm-150 2.90E-06 6.51E-06 1.04E-05 1.42E-05 1.78E-05 2.12E-05

Sm-151 4.13E-07 5.39E-07 6.37E-07 7.20E-07 7.91E-07 8.55E-07

Eu-151 3.12E-10 4.27E-10 4.76E-10 4.98E-10 5.06E-10 5.11E-10

Sm-152 1.41E-06 2.95E-06 4.33E-06 5.55E-06 6.63E-06 7.59E-06

Eu-153 6.80E-07 1.89E-06 3.44E-06 5.13E-06 6.81E-06 8.38E-06

Gd-155 1.77E-10 4.27E-10 8.17E-10 1.29E-09 1.81E-09 2.33E-09

O-16 4.70E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
Limited Nuclide Composition Data Appendix E

94

Table E.2 Nuclide atom densities (atoms/b-cm) for fuel with initial enrichment of 4 wt % 235

U,

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

U-234 7.26E-06 6.33E-06 5.51E-06 4.79E-06 4.18E-06 3.67E-06

U-235 6.99E-04 5.05E-04 3.55E-04 2.41E-04 1.58E-04 9.97E-05

U-236 5.07E-05 8.43E-05 1.08E-04 1.23E-04 1.32E-04 1.35E-04

U-238 2.24E-02 2.22E-02 2.20E-02 2.18E-02 2.16E-02 2.14E-02

Np-237 1.99E-06 5.45E-06 9.54E-06 1.37E-05 1.75E-05 2.06E-05

Pu-238 1.45E-07 8.49E-07 2.34E-06 4.64E-06 7.58E-06 1.08E-05

Pu-239 8.31E-05 1.20E-04 1.37E-04 1.43E-04 1.45E-04 1.45E-04

Pu-240 1.15E-05 2.89E-05 4.51E-05 5.86E-05 6.90E-05 7.67E-05

Pu-241 3.41E-06 1.23E-05 2.12E-05 2.82E-05 3.29E-05 3.58E-05

Pu-242 3.13E-07 2.55E-06 7.32E-06 1.42E-05 2.23E-05 3.10E-05

Am-241 9.52E-07 3.51E-06 6.20E-06 8.34E-06 9.81E-06 1.07E-05

Am-243 1.54E-08 2.78E-07 1.24E-06 3.20E-06 6.12E-06 9.76E-06

Mo-95 1.55E-05 2.97E-05 4.27E-05 5.46E-05 6.53E-05 7.51E-05

Tc-99 1.53E-05 2.96E-05 4.27E-05 5.48E-05 6.57E-05 7.55E-05

Ru-101 1.30E-05 2.59E-05 3.86E-05 5.10E-05 6.32E-05 7.49E-05

Rh-103 8.68E-06 1.72E-05 2.48E-05 3.12E-05 3.64E-05 4.05E-05

Ag-109 6.33E-07 1.90E-06 3.49E-06 5.23E-06 7.03E-06 8.79E-06

Cs-133 1.62E-05 3.12E-05 4.49E-05 5.72E-05 6.82E-05 7.78E-05

Nd-143 1.33E-05 2.40E-05 3.23E-05 3.84E-05 4.24E-05 4.47E-05

Nd-145 9.23E-06 1.74E-05 2.47E-05 3.12E-05 3.69E-05 4.18E-05

Sm-147 3.56E-06 6.01E-06 7.64E-06 8.64E-06 9.18E-06 9.39E-06

Sm-149 1.72E-07 2.00E-07 2.14E-07 2.19E-07 2.20E-07 2.19E-07

Sm-150 2.90E-06 6.51E-06 1.04E-05 1.42E-05 1.78E-05 2.12E-05

Sm-151 4.10E-07 5.33E-07 6.28E-07 7.09E-07 7.79E-07 8.41E-07

Eu-151 1.64E-08 2.13E-08 2.51E-08 2.83E-08 3.11E-08 3.35E-08

Sm-152 1.41E-06 2.95E-06 4.33E-06 5.55E-06 6.63E-06 7.59E-06

Eu-153 7.00E-07 1.93E-06 3.49E-06 5.19E-06 6.89E-06 8.48E-06

Gd-155 1.74E-08 4.15E-08 7.96E-08 1.27E-07 1.79E-07 2.29E-07

O-16 4.70E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
Appendix E Limited Nuclide Composition Data

95

Table E.3 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

U-234 7.28E-06 6.43E-06 5.77E-06 5.31E-06 5.03E-06 4.89E-06

U-235 6.99E-04 5.05E-04 3.55E-04 2.41E-04 1.58E-04 9.98E-05

U-236 5.07E-05 8.43E-05 1.08E-04 1.24E-04 1.32E-04 1.35E-04

U-238 2.24E-02 2.22E-02 2.20E-02 2.18E-02 2.16E-02 2.14E-02

Np-237 2.04E-06 5.62E-06 9.83E-06 1.41E-05 1.79E-05 2.11E-05

Pu-238 1.29E-07 7.54E-07 2.08E-06 4.12E-06 6.73E-06 9.63E-06

Pu-239 8.30E-05 1.20E-04 1.37E-04 1.43E-04 1.45E-04 1.45E-04

Pu-240 1.15E-05 2.89E-05 4.52E-05 5.89E-05 6.98E-05 7.84E-05

Pu-241 1.65E-06 5.94E-06 1.03E-05 1.37E-05 1.59E-05 1.73E-05

Pu-242 3.13E-07 2.55E-06 7.32E-06 1.42E-05 2.23E-05 3.10E-05

Am-241 2.66E-06 9.66E-06 1.68E-05 2.25E-05 2.63E-05 2.86E-05

Am-243 1.54E-08 2.78E-07 1.24E-06 3.19E-06 6.11E-06 9.75E-06

Mo-95 1.55E-05 2.97E-05 4.27E-05 5.46E-05 6.53E-05 7.51E-05

Tc-99 1.53E-05 2.96E-05 4.27E-05 5.48E-05 6.57E-05 7.55E-05

Ru-101 1.30E-05 2.59E-05 3.86E-05 5.10E-05 6.32E-05 7.49E-05

Rh-103 8.68E-06 1.72E-05 2.48E-05 3.12E-05 3.64E-05 4.05E-05

Ag-109 6.33E-07 1.90E-06 3.49E-06 5.23E-06 7.03E-06 8.79E-06

Cs-133 1.62E-05 3.12E-05 4.49E-05 5.72E-05 6.82E-05 7.78E-05

Nd-143 1.33E-05 2.40E-05 3.23E-05 3.84E-05 4.24E-05 4.47E-05

Nd-145 9.23E-06 1.74E-05 2.47E-05 3.12E-05 3.69E-05 4.18E-05

Sm-147 4.75E-06 7.87E-06 9.84E-06 1.10E-05 1.15E-05 1.17E-05

Sm-149 1.72E-07 2.00E-07 2.14E-07 2.19E-07 2.20E-07 2.19E-07

Sm-150 2.90E-06 6.51E-06 1.04E-05 1.42E-05 1.78E-05 2.12E-05

Sm-151 3.66E-07 4.75E-07 5.60E-07 6.32E-07 6.94E-07 7.49E-07

Eu-151 6.12E-08 7.95E-08 9.37E-08 1.06E-07 1.16E-07 1.25E-07

Sm-152 1.41E-06 2.95E-06 4.33E-06 5.55E-06 6.63E-06 7.59E-06

Eu-153 7.00E-07 1.93E-06 3.49E-06 5.19E-06 6.89E-06 8.48E-06

Gd-155 3.14E-08 7.49E-08 1.44E-07 2.30E-07 3.23E-07 4.14E-07

O-16 4.70E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02 4.69E-02
96
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Safeguards, MS O13-D13, Washington, DC 20555-0001

112. T. Parish, Department of Nuclear Engineering, Texas A & M University, College Station, TX 

77843-3313

113. V. A. Perin, U.S. Nuclear Regulatory Commission, NMSS/DWM/HLWB, MS T7-F3,

Washington, DC 20555-0001

114. B. Petrovic, Westinghouse Electric Company, Science and Technology Department, 1344 Beulah

Road, Pittsburgh, PA 15235

115. J. S. Philbin, Sandia National Laboratory, PO Box 5800, Mail Stop 1143, Albuquerque,

New Mexico 87185-1143
100

116. M. Rahimi, U.S. Nuclear Regulatory Commission, NMSS/DWM/HLWB, MS T7-F3,

Washington, DC 20555-0001

117. E. L. Redmond II, Holtec International, 555 Lincoln Drive West, Marlton, NJ 08053

118. C. Rombough, CTR Technical Services, Inc., 5619 Misty Crest Dr., Arlington, TX 76017-4147

119. J. E. Rosenthal, U.S. Nuclear Regulatory Commission, RES/DSARE/REAHFB, MS T10-E46,

Washington, DC 20555-0001

120. D. Salmon, Bechtel SAIC Company, LLC, 1261 Town Center Drive, Las Vegas, Nevada 89134

121. A. Santamarina, Commissariat A L’Energie Atomique, Nuclear Reactor Division, Reactor

Studies Department, Reactor and Cycle Physics Service,

CEA/CADARACHE/DRN/DER/SPRC Bat. 230, 13108 Saint-Paul-Lez-Durance, Cedex,

France

122. E. Sartori, OECD/NEA Data Bank, Le Seine-Saint Germain, 12 Boulevard des Iles, F-92130

Issy-les-Moulineaux, France

123. J. J. Sapyta, Framatome Cogema Fuels, 3315 Old Forest Road, P.O. Box 10935, Lynchburg,

Virginia 24506-0935 

124. H. H. Schweer, Bundesamt fuer Strahlenschutz, Willi Brandt Str. 5, D-38226 SALZGITTER,

Germany

125. M. Smith, Virginia Power Co., P.O. Box 2666, Richmond, VA 23261

126. N. R. Smith, AEA Technology, A32 Winfrith, Dorchester, Dorset DT2 8DH, United Kingdom

127. J. T. Stewart, Department of Environment, Transport, and Re, RMTD, 4/18, GMH, 76

Marsham Street, London SW1P 4DR, United Kingdom

128. T. Suto, Power Reactor and Nuclear Fuel Development Corporation, Technical Service Division,

Tokai Reprocessing Plant, Tokai Works, Tokai-Mura, Naka-gun, Ibaraki-ken, Japan

129. H. Taniuchi, Kobe Steel, Ltd., 2-3-1 Shinhama, Arai-Cho, Takasago, 676 Japan

130. D. A. Thomas, Bechtel SAIC Company, LLC, 1261 Town Center Drive, Las Vegas, Nevada

89134

131. P. R. Thorne, British Nuclear Fuels plc (BNFL), Nuclear and Radiological Safety,

R101 Rutherford House, Risley Warrington WA3 6AS, United Kingdom

132. J. R. Thornton, Duke Engineering & Services, 230 S. Tyron St., P.O. Box 1004, Charlotte, NC

28201-1004

133. S. E. Turner, Holtec International, 230 Normandy Circle East, Palm Harbor, FL 34683

134. A. P. Ulses, U.S. Nuclear Regulatory Commission, NRR/DSSA/SRXB, MS O10-B3,

Washington, DC 20555-0001

135. M. E. Wangler, U.S. Department of Energy, EH-33.2, Washington, DC 20585-0002

136. M. D. Waters, U.S. Nuclear Regulatory Commission, NMSS/SFPO/SLID, MS O13-D13,

Washington, DC 20555-0001

137. A. Wells, 2846 Peachtree Walk, Duluth, GA 30136

138. S. A. Whaley, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001

139. B. H. White, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001

140. Robert Wilson, Rocky Flats Field Office, USDOE, 10808 Highway 93, Golden, CO 80403-8200

141. C. J. Withee, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION

(2-89)

NRCM 1102 BIBLIOGRAPHIC DATA SHEET

3201, 3202 ( See instructions on the reverse)

1. REPORT NUMBER

(Assigned by NRC, Add Vol., Supp.,

Rev., and Addendum Numbers,

 if any.)

NUREG/CR-6747

ORNL/TM-2000/306 2. TITLE AND SUBTITLE

Computational Benchmark for Estimation of Reactivity Margin

from Fission Products and Minor Actinides in PWR Burnup Credit 3. DATE REPORT PUBLISHED

MONTH

 October 

YEAR

 2001

4. FIN OR GRANT NUMBER

W6479

5. AUTHOR(S)

 J. C. Wagner

 

6. TYPE OF REPORT

Technical

7. PERIOD COVERED (Inclusive Dates)

8. PERFORMING ORGANIZATION — NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing

address; if contractor, provide name and mailing address.)

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6370

9. SPONSORING ORGANIZATION — NAME AND ADDRESS (If NRC, type “Same as above”; if contractor, provide NRC Division, Office or Region, U.S. Regulatory

Commission, and mailing address.)

Division of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

10. SUPPLEMENTARY NOTES

R. Y. Lee, NRC Project Manager

11. ABSTRACT (200 words or less)

This report proposes and documents a computational benchmark problem 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 burnup credit cask designed to hold 32 pressurized-water-reactor (PWR) 

assemblies. The purpose of this computational benchmark is to provide a reference configuration for the estimation of

the additional reactivity margin, which is encouraged in the U.S. Nuclear Regulatory Commission (NRC) guidance for 

partial burnup credit (ISG8), and document reference estimations of the additional reactivity margin as a function of 

initial enrichment, burnup, and cooling time. Consequently, the geometry and material specifications are provided in 

sufficient detail to enable independent evaluations. The reference solutions were generated with the SAS2Hdepletion and CSAS25-criticality sequences of the SCALE 4.4a package. Although the SAS2H and CSAS25 

sequences have been extensively validated elsewhere, the reference solutions are not directly or indirectly based on 

experimental results. Consequently, this computational benchmark cannot be used to satisfy the ANS 8.1 

requirements for validation of calculational methods and is not intended to be used to establish biases for burnup 

credit analyses. 

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

 

 burnup credit, criticality safety, spent fuel, storage, transportation

13. AVAILABILITY STATEMENT

 unlimited

14. SECURITY CLASSIFICATION

(This Page) unclassified

(This Report) unclassified

15. NUMBER OF PAGES

16. PRICE

15&)250