NUREG/CR-6702

ORNL/TM-2000/72

Limited Burnup Credit 

in Criticality Safety Analysis: 

A Comparison of ISG-8

and Current International

Practice

Prepared by

I. C. Gauld, 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-6702

 ORNL/TM-2000/72

Limited Burnup Credit

in Criticality Safety Analyses:

A Comparison of ISG-8

and Current International

Practice

Manuscript Completed: March 2000

Date Published: January 2001

Prepared by

I. C. Gauld, ORNL

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6370

D. D. Ebert, NRC Project Manager

Prepared for

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code W6479

iii 

ABSTRACT

This report has been prepared to qualitatively assess the amount of burnup credit (reactivity margin) provided by

ISG-8 compared to that provided by the burnup credit methodology developed and currently applied in France. 

For the purposes of this study, the methods proposed in the DOE Topical Report have been applied to the ISG-8

framework since this methodology (or one similar to it) is likely to form the basis of initial cask licensing

applications employing limited burnup credit in the United States. This study limits the scope of the comparison

to several of the fundamental burnup credit parameters: the nuclides credited in the analysis, the axial-burnup

profile, and the cooling time. An investigation of other parameters, such as horizontal burnup effects and

isotopic correction factors to account for biases and uncertainties in calculated actinide compositions, were

beyond the scope of this review. This report compares the amount of burnup credit provided by the respective

methodologies for typical axial-burnup profiles derived from averaging actual PWR axial-burnup distributions. 

In addition, a limited assessment of several atypical axial-burnup distributions is also included.

 
 
v 

CONTENTS

Page

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

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

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

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

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

2 BURNUP CREDIT METHODS ......................................................... 3

2.1 ISG-8 APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 FRENCH APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

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

3.1 PWR ASSEMBLY AND TRANSPORT CASK MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 ASSEMBLY AXIAL-BURNUP PROFILES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.1 Characteristic Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2.2 Uncharacteristic Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 SPENT FUEL COMPOSITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1 CHARACTERISTIC AXIAL-BURNUP PROFILES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1.1 OECD Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1.2 GBC-32 Cask Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2 UNCHARACTERISTIC AXIAL-BURNUP PROFILES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

vii 

LIST OF FIGURES

Figure Page

1 Section view of 32-assembly GBC-32 cask model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Typical axial profiles based on PWR assembly database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Comparison of burnup credit for OECD cask model using French and ISG-8 methodologies . . . . . . . . . . 15

4 Comparison of burnup credit for GBC-32 cask using French and ISG-8 methodologies . . . . . . . . . . . . . . 16

5 Comparison of calculated k-effectives for GBC-32 cask model using various methodologies . . . . . . . . . . 17

6 Comparison of calculated k-effectives for uncharacteristic profiles and GBC-32 cask . . . . . . . . . . . . . . . 19
 
ix 

LIST OF TABLES

Table Page

1 Actinides considered for burnup credit in criticality safety evaluations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Typical axial-burnup profiles based on PWR assembly database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Parameters for burnup groups derived from PWR assembly database . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Data for assemblies with uncharacteristic axial-burnup profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Criticality results for characteristic PWR assembly axial-burnup profiles . . . . . . . . . . . . . . . . . . . . . . . . 14

6 Criticality results for uncharacteristic PWR assembly profiles in GBC-32 cask . . . . . . . . . . . . . . . . . . . . 18
 
xi 

ACKNOWLEDGMENTS

This work was supported by the U.S. Nuclear Regulatory Commission (NRC) under Project JCN W6479,

Development of Criticality Safety Technology for Licensing Review. The helpful review comments and

suggestions provided by M. D. DeHart and J. C. Wagner, and guidance provided by C. V. Parks are gratefully

acknowledged.
 
1 

1 INTRODUCTION

In August 1999, the Nuclear Regulatory Commission (NRC) issued Revision 1 of the Interim Staff Guidance 8

(ISG-8), "Limited Burnup Credit." The ISG-8 guidance accepts, in principle, the use of actinide-only burnup credit

in criticality safety analyses of pressurized water reactor (PWR) spent fuel in transport and storage casks. ISG-8

limits the amount of burnup credit to that available from actinide compositions associated with PWR irradiation of

UO2 fuel with an assembly-average burnup of 40 GWd/MTU or less, and initial uranium enrichments of no more

than 4.0-wt % 235U without a loading offset penalty, and up to 5.0-wt % 235U with a loading offset.

This study compares the subcritical margin associated with burnup credit provided using an implementation of 

ISG-8 with that obtained using an actinide-only burnup credit methodology currently applied in France. The

amount of burnup credit is defined as the relative difference in the calculated keff using burnup credit compared with

that obtained using unirradiated fuel compositions. At this time, France is the only other country with an approved

burnup credit methodology for PWR fuel transport. Consequently, this study has limited the comparison of ISG-8

to the methods currently approved by the French Safety Authority.

ISG-8 restricts the application of burnup credit to assemblies that have not used burnable absorbers. The French

methodology however has no such restriction. The assemblies used in the comparisons presented in this report do

not employ burnupable absorbers and therefore the results and conclusions from these comparisons are only

applicable to assembly types allowed within the constraints of ISG-8.

The ISG-8 guidance defines the limits of application and the key parameters which must be addressed by an

applicant employing actinide-only burnup credit for safety evaluations in licensing submissions, without endorsing

a specific methodology. For the purposes of this study, the Topical Report on actinide-only burnup credit, issued in

1998 by the U.S. Department of Energy (DOE) Office of Civilian Radioactive Waste Management,1

 has been used

to define the specific actinide set and the bounding axial profiles. While ISG-8 acknowledges the work in the DOE

Topical Report, it does not approve the use of, nor endorse, the specific methodologies proposed in it. The burnup

credit methodology proposed in the DOE Topical Report have been applied to ISG-8 because this methodology (or

one similar to it) is likely to form the basis of initial cask licensing applications employing limited burnup credit in

the United States. The amount of burnup credit provided by ISG-8 will depend on the cask design and the specific

burnup credit methodologies employed in the licensing-basis analysis, which may be different than those presented

in this study. Therefore, the results presented here are only intended to provide an approximate measure of the

amount of burnup credit provided by the ISG-8 guidance with respect to current French practice for the fuel types

currently permitted in ISG-8.

The burnup credit calculations performed using the ISG-8 and French methodologies have been compared for a

21-assembly OECD benchmark cask and a generic 32-assembly burnup credit cask which is prototypical of the

next generation of PWR fuel transport casks likely to be used in the United States.
 
3 

2 BURNUP CREDIT METHODS

2.1 ISG-8 APPROACH

The ISG-8 guidance allows for burnup credit for actinides only, but does not endorse the use of a particular subset

of actinides. Instead, the guidance states that "the particular set of nuclides used to determine the k-effective value

should be limited to that established in the validation process." For the purposes of this study, the subset of

actinides proposed in the DOE Topical Report1

 have been adopted for comparison with the French methodology.2

Although the NRC does not necessarily endorse this subset for a given application, the Topical Report reflects the

current status of burnup credit validation efforts, and the use of these actinides is supported by measured isotopic

data and criticality benchmarks. This set of actinides is very similar to that currently allowed in French practice. 

A comparison of burnup credit actinides is presented in Table 1. Actinide compositions for the ISG-8 calculations

were obtained for a cooling time of 5 years.

ISG-8 also does not make specific reference to the axial-burnup profiles that should be used for criticality safety

analyses, but states "The calculation of the k-effective value should be performed using cask models, appropriate

analysis assumptions, and code inputs that allow adequate representation of the physics. Of particular concern

should be the need to account for the axial and horizontal variation of burnup within a spent fuel assembly (e.g., the

assumed axial-burnup profiles)<," leaving the onus on the license proponent to justify and support the use of a

particular axial shape as being appropriate or bounding.

The axial-burnup profiles applied to the ISG-8 methodology for the purposes of this report are those presented in

the DOE Topical Report. These profiles were determined to be bounding for PWR assemblies included in a

database of calculated assembly profiles collected from a selection of utilities whose reactors represent the range of

commercial PWR fuel lattices. The assembly profiles are used for the qualitative purposes of this study, although

the bounding nature of these profiles is not independently verified here.

Other aspects of ISG-8, such as the need to account for biases and uncertainties in the calculation of actinide

compositions due to code and nuclear data biases, and uncertainties in reactor operating parameters and conditions,

are not addressed in this report. Correction factors applied to isotopic calculations will be dependent on the

particular physics codes and nuclear data used, and on the supporting experimental assay programs. For this study,

isotopic correction factors and conservative depletion analysis parameters were not considered in the calculation of

actinide inventories since the same codes were used to compare the different methodologies. In addition, the need to

account for the horizontal variation of the burnup within the assembly in ISG-8 is not addressed in the comparisons,

although the horizontal effect is believed to be a relatively minor effect for spent fuel storage casks. Since the

recommendations of ISG-8 have only been partially implemented in this study (specifically those recommendations

most likely to emphasize differences between the ISG-8 and French methodologies), the amount of burnup credit

provided by the ISG-8 methodology presented in this report should only be viewed as a qualitative measure for

the purposes of comparing the respective methodologies.

2.2 FRENCH APPROACH

The French Safety Authority has approved the use of burnup credit for the major actinides.2 Credit for fission

products is not currently allowed. For criticality safety studies, the assembly is assumed to have a uniform axial

burnup based on averaging the assembly burnup over the contiguous 50-cm length of the fuel assembly having the

least irradiation. No credit for reactivity reduction with cooling time is generally permitted. Since 1997 the decay
Burnup Credit Methods Section 2

4

of 241Pu and buildup of the 241Am progeny during the cooling time is accounted for in some criticality safety

assessments.3

 No decay time was assumed in the French methodology as applied in this study.

The burnup credit actinides proposed in the DOE Topical Report, and those allowed by the French Safety

Authority, are summarized in Table 1.

Table 1 Actinides considered for burnup credit in criticality

safety evaluations

Actinides DOE topical French practice

234U Y

235U YY

236U Y

238U YY

238Pu Y Y

239Pu Y Y

240Pu Y Y

241Pu Y Y

242Pu Y Y

241Am Y
5 

Figure 1 Section view of 32-assembly GBC-32 cask model

3 ANALYSIS

3.1 PWR ASSEMBLY AND TRANSPORT CASK MODELS

The criticality calculations were performed using two transport cask models: a 21-assembly stainless steel

transport cask design used in the OECD burnup credit criticality benchmark Phase II-B,4

 and a 32-assembly

generic burnup credit cask (GBC-32) model that incorporates design features that are anticipated to be

representative of the next generation of PWR fuel transport casks in the United States. The OECD and GBC-32

casks use a square assembly lattice arrangement (5 × 5 array, and 6 × 6 array, respectively, with the four corners

removed). The GBC-32 cask is illustrated in Figure 1.

The fuel assembly used in the comparisons was based on the Westinghouse 17 × 17 assembly design with an initial

enrichment of 3.5 wt % 235U. For the OECD cask studies, the assembly contained 289 fuel pins, with no guide

tubes % the same configuration used in the OECD benchmark specifications. For the GBC-32 cask calculations the

17 × 17 assembly model contained 25 instrument tubes, which is more representative of current PWR assemblies. 

No burnable absorbers were assumed to be present in the assemblies. The interior of the cask was assumed to be

flooded with water in all criticality calculations.
Analysis Section 3

6

3.2 ASSEMBLY AXIAL-BURNUP PROFILES

PWR fuel assembly axial-burnup profiles were required in this study in order to obtain an effective axial burnup

for the French burnup-credit approach (based on least irradiated 50 cm of the assembly), and also to obtain the

actual, or best-estimate k-effective for the system. For this study, assembly profiles taken from the PWR axialburnup profile database5

 were used as the starting point. The database contains axial-burnup profiles based on

reactor physics calculations of core operating cycles from a selection of utilities whose reactors represent the range

of commercial PWR fuel lattices. Assembly profiles from the database were averaged to obtain typical profiles

over a burnup range from 3 to 40 GWd/MTU. Assemblies with a burnup greater than 40 GWd/MTU, the

maximum allowed in ISG-8, were excluded.

A number of assemblies from the database were excluded in the profile averaging due to considerations such as

axial enrichment zoning of the assembly, and low-enriched or naturally enriched uranium assembly end regions. 

The assemblies rejected from the database were the same ones as those rejected in previous work to determine

bounding axial profiles.6

 The database contains enrichments from 1.24 to 4.75 wt %. Although ISG-8 limits the

enrichment level to no more than 4.0 wt % 235U without a loading offset penalty, assemblies with enrichments above

4.0 wt % were not excluded in this study. Burnup was assumed to be uniform hortizonally across the assemblies. 

An analysis of the horizontal-burnup effects was not included as part of this study, although this effect is likely

minor (< 1 %) for spent fuel storage casks.

3.2.1 Characteristic Profiles

The assemblies in the PWR axial-burnup profile database were grouped to determine representative axial shapes

for several burnup ranges. These selected ranges were 37%40 GWd/MTU, 20%25 GWd/MTU, 10%15 GWd/MTU

and 3%7 GWd/MTU. Assemblies having burnup values between these groups were not used. The characteristic,

or typical profiles, are the average of all of the assembly profiles in the corresponding burnup group. The averaged

burnup profiles derived from the selected assemblies in each group are listed in Table 2 and graphed in Figure 2. 

The average assembly parameters for each group are listed in Table 3. As expected, the average initial enrichment

increases with increased burnup. The burnup profiles within each burnup group were not further categorized by

enrichment (i.e., all enrichments in the database were used to obtain the average group profiles). In other words,

the axial-burnup profiles were based only on assembly burnup.

The characteristic axial profiles derived for these burnup groups are well-behaved, based on composite profiles for

a large number of assemblies covering a wide range of operating histories and assembly designs.

3.2.2 Uncharacteristic Profiles

Several calculations were also performed using axial-burnup profiles that were considered to be atypical of the

high-burnup Group 1 assemblies (37%40 GWd/MTU). The bounding axial-burnup profile as applied to the ISG-8

methodology in this study is designed to be conservative for both characteristic and uncharacteristic profiles. The

calculated keff is therefore independent of the actual axial profile. However the result using the French methodology

is sensitive to the profile near the ends of the assembly. Assemblies which tend to have a small burnup gradient at

the end of the assembly will have a higher average burnup in the criticality analysis using the French approach

compared with assemblies that have a large burnup gradient, and consequently a lower analysis burnup value. The

actual, or best-estimate value of the keff for the system is also impacted by the axial-burnup profile. Calculating the
Section 3 Analysis

7 

best-estimate keff then provides a measure of the safety margin, or "burnup penalty," imposed by the different

burnup credit methodologies.

The uncharacteristic assemblies selected from Ref. 5 for this comparison were H. B. Robinson Unit 2

Westinghouse (WE) 15 × 15 assembly D102, and Maine Yankee Combustion Engineering (CE) 14 × 14 assembly

N863. Assembly N863 had the smallest burnup gradient near the end region of the assembly out of all 193

assemblies considered in the high-burnup Group 1. The ratio of the burnup averaged over the least irradiated

50 cm of the assembly to that of the entire assembly is about 0.839. Assembly N863 used burnable poison rods

(BPRs) during part of the irradiation history. Although it is recognized that ISG-8 does not allow burnable

absorbers, the axial-burnup profile for this assembly was selected to provide an estimate of the bounding difference

(due to profiles) between the ISG-8 and French burnup credit methodologies. Only the axial profile for this

assembly was used in the analysis. The assembly design used to predict the isotopic compositions and for the

criticality analysis did not use burnable absorbers. Assembly D102 had the largest burnup gradient, with a burnup

ratio value of 0.664. Both assemblies achieved an exit burnup of about 38 GWd/MTU. The assembly data and

axial-burnup profiles for these assemblies are listed in Table 4. The initial fuel compositions and burnup used for

both assemblies were taken from H. B. Robinson assembly D102, with an initial enrichment of 3.73-wt % 235U. 

The criticality calculations using the axial profiles from assemblies D102 and N863 were only performed for the

GBC-32 cask model (Figure 1).

Table 2 Typical axial-burnup profiles based on PWR assembly database

Axial node Axial height, %

Group 1

37%40 GWd/MTU

Group 2

20%25 GWd/MTU

Group 3

10%15 GWd/MTU

Group 4

3%7 GWd/MTU

 1 2.78 0.66694 0.64611 0.58313 0.54324

 2 8.33 0.9405 0.9388 0.90303 0.88252

 3 13.89 1.0434 1.05293 1.04794 1.04417

 4 19.44 1.07189 1.08291 1.09345 1.10351

 5 25.00 1.08185 1.09043 1.11046 1.11937

 6 30.56 1.07909 1.08458 1.10824 1.11992

 7 36.11 1.07792 1.08291 1.11134 1.11637

 8 41.69 1.07505 1.08172 1.11283 1.11286

 9 47.22 1.07107 1.07958 1.11175 1.11078

10 57.80 1.07206 1.08271 1.11671 1.11008

11 58.33 1.06946 1.08133 1.11337 1.10988

12 63.89 1.06992 1.0818 1.11156 1.10889

13 69.44 1.06864 1.07927 1.10381 1.10473

14 75.00 1.06149 1.06918 1.08245 1.09192

15 80.56 1.04815 1.04882 1.0446 1.05779

16 86.11 1.00342 0.99051 0.95937 0.97614

17 91.67 0.88255 0.8508 0.78871 0.80163

18 97.22 0.6166 0.57559 0.49724 0.4862 
Analysis Section 3

8

Table 3 Parameters for burnup groups derived from PWR assembly database

Parameter Group 1 Group 2 Group 3 Group 4

Burnup Range (GWd/MTU) 37%40 20%25 10%15 3%7

Number of assemblies in group 193 457 296 64

Average burnup (MWd/MTU) 38595 22230 12757 5830

Average enrichment (wt % 235U) 3.52 3.28 2.93 2.61

Minimum 50-cm BU fraction 0.7971 0.7651 0.7023 0.7062

Minimum 50-cm BU (GWd/MTU) 30764.1 17008.2 8959.2 4117.2
Section 3 Analysis

9 

Table 4 Data for assemblies with uncharacteristic axial-burnup profiles

Reactor H.B. Robinson 2 Maine Yankee

Assembly ID D102 N863

Fuel Type W 15 × 15 CE 14 × 14

U-235 wt % 3.73 3.3

No. BP rods 0 8

BP Type B4C

Burnup 37814 37626

Axial height % Axial profile Axial profile

 2.78 0.31488 0.67053

 8.33 0.92825 0.93322

13.89 1.07846 1.02433

19.44 1.12253 1.05329

25.00 1.13896 1.06026

30.56 1.13669 1.06185

36.11 1.12818 1.06215

41.69 1.13176 1.06249

47.22 1.13029 1.06312

57.80 1.12513 1.06408

58.33 1.12194 1.06541

63.89 1.12587 1.06702

69.44 1.12096 1.06836

75.00 1.11259 1.0676 

80.56 1.09614 1.05918

86.11 1.02752 1.02515

91.67 0.86161 0.92262

97.22 0.29808 0.66935

French Burnup Factora 0.66387 0.83894

a

Defined as the ratio of the burnup averaged over the least irradiated 50 cm of the

assembly to that of the entire assembly.
Analysis Section 3

10

 Figure 2 Typical axial profiles based on PWR assembly database
Section 3 Analysis

11 

3.3 SPENT FUEL COMPOSITIONS

The fuel assembly isotopic compositions used as the basis for comparing burnup credit using ISG-8 and French

Safety Authority practices were calculated using the ORIGEN-ARP sequence of the SCALE code system.7

ORIGEN-ARP uses the ORIGEN-S isotope generation and depletion code and pre-calculated burnup- and

problem-dependent cross-section libraries. For this study the basic ARP cross-section library generated for a

17 × 17 Westinghouse PWR was used. The ARP library extends to initial 235U enrichments of 5.0 wt %, and a

maximum burnup of 60 GWd/MTU.

The irradiation times assumed for each burnup group were selected to maintain an average assembly power of

about 25 MW/MTU. For calculations involving axial-burnup profiles, the axial zone power was scaled

accordingly to the normalized axial burnup for that zone. Following a depletion calculation using ORIGEN-S for

an axial zone, the fuel inventories for the zone were read from the binary composition interface and converted to

units of atom density (atoms/barn-cm). The nuclides allowed in the burnup credit analysis (see Table 1) were then

written in a format suitable for execution using the CSASI control module8

 of SCALE. CSASI prepares selfshielded macroscopic cross sections for each mixture in the problem. The cross- section identifiers for each of the

fuel mixtures were subsequently renumbered according to the axial zone position, and used in a KENO V.a

criticality calculation for the cask models. The KENO V.a calculations used the cross sections available in the

44GROUPNDF5 library.

For comparison with the burnup credit results, calculations were performed using the initial fresh fuel

compositions. The fresh fuel results represent the reference used for comparison with the burnup credit results. 

In addition, "best-estimate" keff calculations were also performed. These calculations are useful in estimating the

subcritical margin for the system.

Both the ISG-8 and French methodologies require the use of conservative modeling of both the irradiation history

and burnup parameters (e.g., fuel temperature, moderator density, etc.) to predict the actinide compositions, and the

use of correction factors to the isotopic concentrations that account for biases and uncertainties in depletion

calculations (e.g., f-BUC factors recommended in the DOE Topical Report). For the purposes of this study the

spent fuel compositions applied to both burnup credit methodologies were taken directly from the depletion

calculations without any corrections. The isotopic correction factors are assumed to affect the amount of burnup

credit provided by both methodologies by a similar amount, because the ability of current codes to predict the major

actinides is well established. 

The isotopics for the ISG-8 calculations were obtained for a cooling time of 5 years, as recommended in the

guidance. The calculations using the French Safety Authority methodology applied the fuel isotopics at discharge

(no cooling time), with no credit for the decay of 241Pu to 241Am.
 
13

 

4 RESULTS AND DISCUSSION

The amount of burnup credit, defined here as the relative difference in the calculated keff using burnup credit

compared with that obtained using unirradiated fuel compositions, is assessed using the ISG-8 and French actinideonly burnup credit methodologies. Calculations were performed using characteristic axial PWR burnup profiles

obtained from averaging the profiles of many assemblies having a wide range of operating histories. The results for

two cask designs are presented. In addition, uncharacteristic axial-burnup profiles which represented the extremes

in terms of the burnup gradient in the assembly end regions were also evaluated for the high-burnup regime in this

study.

It is emphasized that the calculations using the burnup-credit methodologies do not apply conservative modeling

methods for calculating fuel inventories, nor do they apply isotopic correction factors to the calculated inventories. 

Additionally, consideration of the horizontal burnup distribution, required by ISG-8, is not included. Consequently,

the results should only be used qualitatively for the purposes of comparing the respective burnup credit

methodologies.

4.1 CHARACTERISTIC AXIAL-BURNUP PROFILES

4.1.1 OECD Cask Model

The KENO V.a results for the OECD cask model are listed in Table 5 for the four burnup groups using the

actinide-only burnup credit methodologies of the ISG-8 guidance and the current French practice. The bestestimate keff values were calculated using the averaged axial profiles determined for the PWR assemblies in each of

the groups (see Table 2) and taking credit for all actinides and fission products in the fuel that have associated

cross section data in the 44GROUPNDF5 library used in the KENO V.a analysis. A comparison of the different

methodologies is plotted in Figure 3 as the relative change in keff compared to the reference, or fresh fuel value (i.e.,

)k/k), defined as (kfresh % kcredit)/kfresh.

The results indicate that the current French approach to burnup credit is consistently more restrictive (i.e., more

penalizing) and provides less burnup credit than the ISG-8 approach for the assemblies and burnup ranges (up to

40 GWd/MTU) considered. For the PWR transport casks and configurations evaluated, ISG-8 provides about 2%

more burnup credit compared to the French approach.

4.1.2 GBC-32 Cask Model

The KENO V.a results for the GBC-32 cask model are given in Table 5. The results are similar to those for the

OECD cask model. ISG-8 provides about 2% more burnup credit than the French approach for the burnup range

and assembly types studied. The amount of burnup credit using the different methodologies is compared in

Figure 4.

The actual keff values calculated for the GBC-32 cask are compared in Figure 5 for uniform fresh fuel compositions,

and using the actinide-only ISG-8 and French burnup credit methodologies. In addition, best-estimate values based

on the characteristic (averaged) axial-burnup profiles (Table 2) and comprehensive representation of all fission

products and actinides with associated cross-section data are presented for comparison. The figure shows that the
Results and Discussion Section 4

14

keff values calculated using the burnup-credit methodologies are similar, and lie nearly midway between the fresh

fuel results and the best-estimate results, that is, the amount of burnup credit is nearly equal to the burnup penalty,

or subcritical margin, as established from the best-estimate values.

Several additional calculations were performed to evaluate the relative importance of 241Am as a burnup credit

actinide in the ISG-8 calculations (241Am is not included in the French methodology), and the differences in

decay time assumed by ISG-8 and French practice. The buildup of 241Am from the decay of 241Pu (14.4 y halflife) is a significant contributor to the decrease in keff during the initial 5 years of cooling time. The elimination

of 241Am as a burnup credit actinide in the ISG-8 calculations resulted in an increase in the calculated keff for the

transport casks of between 1 and 2% for the higher burnup assembly group. The increase in the ISG-8 keff results

caused by excluding 241Am significantly reduced the differences observed between the ISG-8 and French burnup

credit methodologies. ISG-8 calculations that included 241Am but assumed no cooling time yielded similar

results, confirming buildup of 241Am during the cooling time as the dominant contributor to the difference. 

Table 5 Criticality results for characteristic PWR assembly axial-burnup profiles

Burnup group Group 1 Group 2 Group 3 Group 4

Average burnup

(GWd/MTU) 38.6 22.2 12.8 5.8

Average BU/

Least 50-cm BU 0.797 0.765 0.702 0.706

21-Assembly OECD Benchmark Cask (keff ± 1 F)

Fresh fuel (3.5 wt %) k-effective = 1.0630 ± 0.0011

French 0.8938 ± 0.0009 0.9735 ± 0.0009 1.0192 ± 0.0010 1.0366 ± 0.0010

ISG-8 0.8711 ± 0.0009 0.9432 ± 0.0010 1.0043 ± 0.0012 1.0247 ± 0.0010

Best-estimate 0.7551 ± 0.0009 0.8618 ± 0.0010 0.9359 ± 0.0010 0.9746 ± 0.0010

32-Assembly GBC-32 Cask (keff ± 1 F)

Fresh fuel (3.5 wt %) k-effective = 1.1034 ± 0.0011

French 0.9451 ± 0.0009 1.0205 ± 0.0009 1.0590 ± 0.0010 1.0778 ± 0.0011

ISG-8 0.9049 ± 0.0011 0.9784 ± 0.0012 1.0406 ± 0.0010 1.0592 ± 0.0010

Best-estimate 0.7835 ± 0.0011 0.8968 ± 0.0011 0.9732 ± 0.0010 1.0139 ± 0.0010
Section 4 Results and Discussion

15 

 Figure 3 Comparison of burnup credit for OECD cask model using French and ISG-8 methodologies
Results and Discussion Section 4

16

 Figure 4 Comparison of burnup credit for GBC-32 cask using French and ISG-8 methodologies
Section 4 Results and Discussion

17 

 Figure 5 Comparison of calculated k-effectives for GBC-32 cask model using various methodologies
Results and Discussion Section 4

18

4.2 UNCHARACTERISTIC AXIAL-BURNUP PROFILES

The results for the uncharacteristic, high-burnup assemblies N863 and D102 are listed in Table 6 and are plotted in

Figure 6. The results for the two assembly profiles only change for the French methodology and the best-estimate

calculations, because the ISG-8 calculations have applied a bounding axial profile that is independent of the actual

assembly profile.

The results show that the ISG-8 approach still yields a larger amount of burnup credit than the French approach for

either of the two extreme burnup profiles assessed. The amount of credit provided by the two methods is very

similar for assembly N863 (with a relatively small gradient); the assembly D102 profile (with a large gradient)

resulted in significantly less credit using the French approach. If viewed from the perspective of subcritical margin

(i.e., comparison of the French and ISG-8 results with the best estimate results rather than fresh fuel results), the

amount of margin provided by both burnup credit methods is larger for assembly N863 than D102.

Table 6 Criticality results for uncharacteristic PWR assembly profiles in GBC-32 cask

keff ± 1 F keff ± 1 F

Burnup Credit

()k/k)a

Burnup Credit

()k/k) 

Assembly profile D102 N863 D102 N863

French burnup factorb 0.66387 0.83894

Fresh fuel (3.75-wt %) 1.1145 ± 0.0011 1.1145 ± 0.0011

French 0.9813 ± 0.0011 0.9423 ± 0.0010 0.1195 0.1545

ISG-8 0.9213 ± 0.0011 0.9213 ± 0.0011 0.1734 0.1734

Best-estimate 0.8479 ± 0.0011 0.7901 ± 0.0009

a

Defined as (kfresh % kcredit)/kfresh. b

Defined as the ratio of the burnup averaged over the least irradiated 50 cm of the assembly to that

of the entire assembly.
Section 4 Results and Discussion

19 

 

Figure 6 Comparison of calculated k-effectives for uncharacteristic profiles and GBC-32 cask.
 
21 

5 CONCLUSIONS

The methodologies for actinide-only burnup credit in ISG-8 and current French practice generally lead to similar

levels of burnup credit. For the assembly types allowed within the recommendations of ISG-8, the French approach

is slightly more restrictive for all burnups and axial profiles considered. The differences between the OECD and

GBC-32 cask designs did not have a significant impact on the predicted level of burnup credit. ISG-8 provides

typically 2% more burnup credit in terms of keff than the French approach for typical PWR axial-burnup profiles. 

A significant part of the difference between the two methodologies is attributed to 241Am buildup in the ISG-8

calculations, whereas 241Am is excluded as a burnup credit actinide in the French calculations. The buildup of

241Am from the decay of 241Pu (14.4 y half-life) is a significant contributor to the decrease in keff for actinide-only

calculations for spent fuel with a cooling time of 5 years. The elimination of 241Am as a burnup credit actinide in

the ISG-8 calculations resulted in an increase in the calculated keff of the transport casks of between 1 and 2% for

the higher burnup assembly groups, significantly reducing the differences between the two methodologies.

Analyses using two uncharacteristic or atypical axial profiles resulted in significantly less burnup credit being

provided by the French approach relative to ISG-8 for profiles having a large burnup gradient near the end of the

assembly. In all cases and assembly profiles considered, the ISG-8 approach afforded a larger degree of burnup

credit than the French methodology.

The burnup credit calculations based on the current French practice of using a uniform burnup to represent the fuel

assembly were significantly more straightforward than using the bounding 18-axial-zone profiles proposed in the

DOE Topical Report. The lack of any symmetry in the bounding profiles and explicit axial zoning in the central

region of the assembly (which can be accurately simulated with a uniform axial burnup) results in a significant

overhead in terms of complexity, model preparation, data management, and computational time. Note that the

French are currently investigating use of a more complex approach similar to ISG-82

 as a means to increase the

burnup credit provided.

The results presented here are only intended to provide an approximate measure of the amount of burnup credit

provided by the ISG-8 guidance with respect to current French practice. The results are based on an analysis of

averaged, well-behaved PWR assembly axial profiles, and provide a limited analysis of atypical profiles. The

amount of burnup credit and the subcritical margin provided by the respective methodologies will vary depending

on the degree of deviation from the typical profiles used in this study. Individual assemblies may exhibit different

subcritical margins than those presented here, particularly for assemblies with atypical end-region profiles which

have a significant effect on the amount of burnup credit and subcritical margin provided using the current French

approach.
 
23 

6 REFERENCES

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3. H. P. Dyck, J. C. Neuber, W. H. Lake, and A. Santamarina, "Overview of the Burnup Credit Activities at the

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Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as

CCC-545.
 
25 

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NUREG/CR-6702 

ORNL/TM-2000/72 2. TITLE AND SUBTITLE

Limited Burnup Credit in Criticality Safety Analyses: 

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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

D. D. Ebert, NRC Project Manager

11. ABSTRACT (200 words or less)

This report has been prepared to qualitatively assess the amount of burnup credit (reactivity margin) provided by

ISG-8 compared to that provided by the burnup credit methodology developed and currently applied in France. 

For the purposes of this study, the methods proposed in the DOE Topical Report have been applied to the ISG-8

framework since this methodology (or one similar to it) is likely to form the basis of initial cask licensing applications

employing limited burnup credit in the United States. This study limits the scope of the comparison to several of the

fundamental burnup credit parameters: the nuclides credited in the analysis, the axial-burnup profile, and the cooling

time. An investigation of other parameters, such as horizontal burnup effects and isotopic correction factors to account

for biases and uncertainties in calculated actinide compositions, were beyond the scope of this review. This report

compares the amount of burnup credit provided by the respective methodologies for typical axial-burnup profiles

derived from averaging actual PWR axial burnup distributions. In addition, a limited assessment of several atypical

axial burnup distributions is also included.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

 criticality safety, burnup credit, transportation, dry storage, ISG-8

13. AVAILABILITY STATEMENT

 unlimited

14. SECURITY CLASSIFICATION

(This Page) unclassified

(This Report) unclassified

15. NUMBER OF PAGES

16. PRICE

15&)250