An Approach for Validating 

Actinide and Fission Product 

Burnup Credit Criticality Safety 

Analyses—Isotopic 

Composition Predictions

Office of Nuclear Regulatory Research

NUREG/CR-7108 

ORNL/TM-2011/509
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An Approach for Validating 

Actinide and Fission Product 

Burnup Credit Criticality Safety 

Analyses—Isotopic 

Composition Predictions

Manuscript Completed: December 2011

Date Published: April 2012

Prepared by

G. Radulescu

I. C. Gauld

G. llas

J. C. Wagner

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6170

Don Algama, NRC Project Manager

Prepared for

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code V6005

Office of Nuclear Regulatory Research

 NUREG/CR-7108

ORNL/TM-2011/509

iii 

ABSTRACT 

Taking credit for the reduced reactivity of spent nuclear fuel in criticality analyses is referred to 

as burnup credit. Criticality safety evaluations employing burnup credit require validation of the 

depletion and criticality calculation methods and computer codes with available measurement 

data. To address the issues of burnup credit criticality validation, the U.S. Nuclear Regulatory 

Commission initiated a project with Oak Ridge National Laboratory to (1) develop and establish 

a validation approach for commercial spent nuclear fuel criticality safety evaluations based on 

best-available data and methods and (2) apply the approach on representative spent nuclear 

fuel storage and transport systems and conditions to demonstrate its usage and applicability, as 

well as to provide reference bias and bias uncertainty results. This report describes an approach 

for establishing depletion code bias and bias uncertainty in terms of a reactivity difference based 

on comparison of measured and calculated nuclide concentrations. 

v 

TABLE OF CONTENTS 

Section Page 

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

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

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

EXECUTIVE SUMMARY ............................................................................................................. xi

ACKNOWLEDGMENTS ............................................................................................................. xiii

LIST OF ACRONYMS AND UNITS ............................................................................................ xv

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

2. OVERVIEW OF BURNUP CREDIT ANALYSIS ....................................................................... 3

3. ISOTOPIC VALIDATION DATA ............................................................................................... 7

3.1 NUCLIDES IMPORTANT TO BURNUP CREDIT ............................................................. 7

3.2 PWR ISOTOPIC VALIDATION DATA ............................................................................... 9

3.3 BWR ISOTOPIC VALIDATION DATA ............................................................................. 12

4. COMPUTER CODES AND NUCLEAR DATA ........................................................................ 15

5. SAFETY ANALYSIS MODELS ............................................................................................... 17

5.1 PWR ASSEMBLY MODEL .............................................................................................. 17

5.2 PWR SFP STORAGE RACK MODELS .......................................................................... 17

5.3 PWR SNF CASK MODEL ............................................................................................... 18

5.4 LOADING CURVES FOR PWR SNF .............................................................................. 19

5.5 BWR ASSEMBLY MODEL .............................................................................................. 20

5.6 BWR SFP STORAGE RACK MODEL............................................................................. 21

6. CALCULATION OF BIAS AND BIAS UNCERTAINTY IN keff ................................................. 23

6.1 MONTE CARLO UNCERTAINTY SAMPLING METHOD ............................................... 23

6.1.1 Calculation of Bias and Bias Uncertainty in Calculated Nuclide Concentrations ... 24 

6.1.2 Statistical Analysis of the Measured-to-Calculated Concentration Ratio Values ... 25

6.1.2.1 Analysis of Trends .................................................................................. 26

6.1.2.2 Normality Test Results ........................................................................... 28

6.1.2.3 Correlations among Nuclide Concentration Uncertainties...................... 28

6.1.3 Isotopic Bias and Bias Uncertainty Values ............................................................ 29

6.1.4 Nuclide Concentrations for keff Calculations........................................................... 32

6.1.5 Validation of the Assumption for Data Normality ................................................... 33
vi 

TABLE OF CONTENTS 

(Continued) 

Section Page

6.1.6 Convergence of the Monte Carlo keff Bias Uncertainty Estimate ........................... 34

6.2 DIRECT-DIFFERENCE METHOD .................................................................................. 36

7. BIAS AND BIAS UNCERTAINTY IN keff RESULTS ............................................................... 43

7.1 PWR SNF ANALYSIS MODELS ..................................................................................... 43

7.2 BWR SFP STORAGE RACK MODEL............................................................................. 47

7.3 PARAMETRIC ANALYSIS .............................................................................................. 47

8. CONCLUSIONS ..................................................................................................................... 53

9. REFERENCES ....................................................................................................................... 55

APPENDIX A. keff UNCERTAINTY ANALYSIS USING CROSS-SECTION 

 SENSITIVITY/UNCERTAINTY ANALYSES .................................................... A-1

A.1 Relative Importance of Individual Nuclides to Fuel Reactivity ............... A-2

A.2 Non-normal Distributions for Measured-to-Calculated 

Concentration Ratio ............................................................................... A-3

A.3 Analysis of keff Bias and Bias Uncertainty Components ........................ A-7

A.4 Importance of Decay-Time Corrections for the 

Direct-Difference Method ..................................................................... A-11

APPENDIX B. ISOTOPIC VALIDATION DATA CORRELATIONS .......................................... B-1

APPENDIX C. REFERENCE SPENT FUEL NUCLIDE CONCENTRATIONS ........................ C-1
vii

LIST OF FIGURES 

Figure Page

Figure 2.1 Overview of the burnup credit validation process ............................................................ 5

Figure 3.1 Atom density as a function of decay time for burnup credit nuclides exhibiting 

density variations after fuel discharge. .............................................................................. 9

Figure 3.2 Enrichment and burnup values of the measured PWR fuel samples compared 

to loading curves for a representative PWR SFP storage rack model. ...................... 11

Figure 5.1 Horizontal cross section of the representative PWR SFP storage rack cell 

representation ...................................................................................................................... 18

Figure 5.2 Cutaway view of the GBC-32 cask model showing bottom half with a quarter 

of the model removed ......................................................................................................... 19

Figure 5.3 Loading curves for PWR SNF in cask and pool storage rack configurations. ........... 20

Figure 5.4 Horizontal cross section of the BWR SFP storage rack cell representation. ............. 21

Figure 6.1 Measured-to-calculated concentration ratio versus fuel sample burnup for 

(a) 235U; (b) 239Pu. ................................................................................................................ 27

Figure 6.2 Illustration of the Monte Carlo estimates. ........................................................................ 35

Figure 6.3 Linear regression analysis of the ∆keff results illustrating the bias and the margin 

for uncertainty represented by the one-sided tolerance limit at a 95% probability, 

95% confidence level [95% tolerance limit (TL)] for the unpoisoned SFP storage 

rack ........................................................................................................................................ 41

Figure 7.1 keff bias uncertainty for the representative PWR SFP storage rack model ................ 44

Figure 7.2 keff bias uncertainty for the PWR SNF cask model ........................................................ 46

Figure 7.3 Variation of bias uncertainty in keff with parameters important to criticality 

analyses for (a) 10-, (b) 25-, and (c) 40-GWd/MTU assembly average 

burnup ................................................................................................................................... 51

Figure A.1 Sensitivity coefficients (absolute values) shown on a logarithmic scale for 

burnup credit actinide and fission product nuclides in the representative 

PWR SFP rack model at 3-day cooling time ................................................................. A-2

Figure A.2 Sensitivity coefficients (absolute values) shown on a logarithmic scale for 

burnup credit actinide and fission product nuclides in the PWR SNF cask 

(GBC-32) model at 5-year cooling time ......................................................................... A-3

Figure A.3 Histogram of the M/C concentration ratio values for 235U within the burnup 

interval 15 to 40 GWd/MTU. ............................................................................................ A-4

Figure A.4 Histogram plot for 235  U

keff values based on actual M/C concentration ratio 

values for 235U within the burnup range 15 to 40 GWd/MTU ................................. A-6 

Figure A.5 Individual nuclide contributions to keff bias uncertainty for the representative 

PWR SFP storage rack model and 10-GWd/MTU assembly average burnup ........ A-7
viii

LIST OF FIGURES 

(Continued) 

Figure Page

Figure A.6 Individual nuclide contributions to keff bias uncertainty for the representative 

PWR SFP storage rack model and 40-GWd/MTU assembly average burnup. ... A-8

Figure A.7 Individual nuclide contributions to keff bias uncertainty for the PWR SNF cask 

model and 10-GWd/MTU assembly average burnup .......................................... A-8 

Figure A.8 Individual nuclide contributions to keff bias uncertainty for the PWR SNF cask 

model and 40-GWd/MTU assembly average burnup .......................................... A-8 

Figure A.9 Individual nuclide contributions to keff bias uncertainty for the unpoisoned 

PWR SFP storage rack model and 40-GWd/MTU assembly average burnup. .. A-9 

Figure A.10 Illustration of keff bias components using (a) ENDF/B-VII nuclear data; 

(b) ENDF/B-V nuclear data ........................................................................................ A-10
ix

LIST OF TABLES 

Table Page

Table 3.1 Actinide and fission product nuclides important to burnup credit criticality 

analyses ...................................................................................................................... 8 

Table 3.2 Initial enrichment and burnup values for the measured PWR fuel samples............... 11 

Table 3.3 Initial enrichment and burnup values for the measured BWR fuel samples............... 13 

Table 6.1 Isotopic bias and bias uncertainty values for PWR SNF compositions ...................... 30 

Table 6.2 Isotopic bias and bias uncertainty values for BWR SNF compositions ...................... 31 

Table 6.3 Unpoisoned PWR SFP storage rack Δkeff obtained with measured 

and calculated nuclide concentrations ...................................................................... 39 

Table 7.1 keff bias and keff bias uncertainty for the representative PWR SFP storage rack 

model ......................................................................................................................... 44 

Table 7.2 keff bias and keff bias uncertainty for the unpoisoned PWR SFP storage rack 

model using burnup credit actinide and fission product nuclides .............................. 45 

Table 7.3 keff bias and keff bias uncertainty for the representative PWR SNF cask model ........ 45 

Table 7.4 keff bias and keff bias uncertainty for the BWR SFP storage rack model ................... 47 

Table 7.5 Model parameters addressed in the sensitivity analysis ........................................... 48 

Table 7.6 keff bias and keff bias uncertainty as a function of sensitivity parameter .................... 50 

Table A.1 keff bias due to the bias in calculated 235U concentration based on measurement 

data from fuel samples within the burnup range 15 to 40 GWd/MTU ..................... A-5 

Table A.2 keff bias calculations using fuel sample and analysis model compositions ............ A-13 

Table B.1 Correlations at the 0.5 significance level for the isotopic validation data 

applicable to the burnup range 40 to 60 GWd/MTU ................................................ B-3

Table C.1 Reference nuclide concentrations (g/gU initial) ....................................................... C-2 

xi 

EXECUTIVE SUMMARY 

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

burnup credit is the validation of depletion and criticality computer codes used in the safety 

evaluation—in particular, the availability and use of applicable experimental data to support 

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

and bias uncertainty in the effective neutron multiplication factor (keff) that results from biases 

and bias uncertainties in the calculated nuclide concentrations. The validation approach 

described in this report is independent of the depletion and criticality computational methods 

being used and of the choice of the safety analysis models. 

The depletion validation approach has the following characteristics: (1) calculated nuclide 

concentrations are compared to available measurements of nuclide concentrations obtained by 

destructive radiochemical assay (RCA) to determine isotopic biases and bias uncertainties in 

the calculated nuclide concentrations, and (2) the isotopic biases and bias uncertainties are 

applied to the fuel compositions of representative safety analysis models to determine reference 

values for bias and bias uncertainty in keff by the use of the Monte Carlo uncertainty sampling 

method. The Monte Carlo uncertainty sampling method represents the effects of nuclide 

concentration uncertainty on keff values by sampling nuclide concentrations from uncertainty 

distributions developed from measurement data. The direct-difference method was used in a 

limited manner to provide a check of the validation results obtained from the Monte Carlo 

uncertainty sampling method. The direct-difference method applies measured nuclide 

concentrations directly in the safety analysis model to calculate a keff value, which then is 

compared with the keff value for the safety analysis model that uses calculated nuclide 

concentrations. 

The SCALE 6.1 code system and the ENDF/B-VII nuclear data were used to obtain reference 

keff bias and bias uncertainty results for representative safety analysis models, which include a 

pressurized water reactor (PWR) spent fuel pool (SFP) storage rack model, a boiling water 

reactor (BWR) SFP storage rack model, and a spent nuclear fuel (SNF) cask model. The fuel 

compositions for these models consist of 28 actinide and fission product nuclides that are 

important to fuel reactivity (i.e., nuclides with large neutron fission cross sections and nuclides 

with large neutron absorption cross sections) and have sufficient experimental data for use in 

depletion code validations. The RCA data for isotopic bias and bias uncertainty calculations 

include measured nuclide concentration values for 100 PWR fuel samples with initial 

enrichments varying from 2.453 to 4.657 wt % 235U and burnup varying from 7 to 60 GWd/MTU 

and 32 BWR fuel samples with initial enrichments varying from 2.54 to 3.91 wt % 235U and 

burnup varying from 14.4 to 44.0 GWd/MTU. Depletion validation results are provided for PWR 

fuel assembly average burnup values up to 60 GWd/MTU and for a BWR fuel assembly at peak 

reactivity. 

The calculated keff bias and bias uncertainty values are similar for the representative PWR SFP 

storage rack and SNF cask models. For the assembly average burnup range 5 to 40 GWd/MTU, 

the keff bias is approximately 0.004 and the keff bias uncertainty is approximately 0.016. For an 

assembly average burnup range of 40 to 60 GWd/MTU, the estimated keff bias and keff bias 

uncertainty values gradually increase to 0.010 and 0.030, respectively. The results show that 

the PWR nuclide concentrations calculated with the SCALE 6.1 code system and the ENDF/BVII nuclear cross-section data produce a small positive keff bias (i.e., slight overprediction of keff) 

with a significantly larger associated uncertainty value. The keff bias uncertainty is primarily due 
xii 

to bias uncertainties associated with actinide nuclide concentrations. The uncertainties in the 

calculated 235U and 239Pu concentrations contribute approximately 90 to 95% of the keff bias 

uncertainty. The keff bias uncertainty due to the bias uncertainties in the calculated fission 

product concentrations is small (<3% of the keff bias uncertainty). The calculated keff bias and keff

bias uncertainty values for BWR SNF are approximately 0.002 and 0.032, respectively. 

Sensitivity of bias and bias uncertainty in keff to parameters important to PWR SFP criticality 

safety analyses was evaluated considering variations in fuel assembly design, fuel irradiation 

conditions, rack design, soluble boron concentration, fuel cooling time, axial representation of 

fuel burnup in the safety analysis model, and nuclear data (ENDF/B-V only). The assembly 

average burnup values considered in the parametric study are 10, 25, and 40 GWd/MTU. The 

calculated keff bias uncertainty values exhibit a small variability as a function of the sensitivity 

parameter and assembly average burnup. Based on the ENDF/B-VII calculations, the average 

values of keff bias uncertainty are 0.015, 0.016, and 0.017 for the assembly average burnup 

values of 10, 25, and 40 GWd/MTU, respectively. The largest variations from the representative 

SFP safety analysis model were obtained for the unpoisoned (i.e., 0-g/cm2 10B areal density in 

the Boral panels) PWR SFP analysis model. For this analysis model, the keff bias uncertainty is 

approximately 0.019 for the burnup range 10 to 40 GWd/MTU. The keff bias for all the evaluated 

cases using the ENDF/B-VII nuclear data is approximately 0.004. The keff bias values in the 

case of the ENDF/B-V nuclear data are negative and vary with assembly average burnup from 

-0.0001 (10 GWd/MTU) to -0.004 (40 GWd/MTU). 

The bias and bias uncertainty values estimated from the direct-difference method for a single 

application model are comparable with, but smaller than, the values obtained by the Monte 

Carlo uncertainty sampling method. Although not definitive, the comparison provides increased 

confidence in the Monte Carlo approach for uncertainty propagation. For depletion code 

validations using the direct-difference method, recommendations are provided concerning use 

of surrogate (i.e., substitute) data for nuclides with very few measurement data and appropriate 

decay-time adjustments for measured nuclide concentrations. 
xiii 

ACKNOWLEDGMENTS 

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

U.S. Nuclear Regulatory Commission (NRC). The authors acknowledge useful review 

comments and suggestions provided by D. Algama, the NRC Project Manager; K. A. L. Wood of 

the Office of Nuclear Reactor Regulation; M. Aissa and R. Y. Lee of the Office of Nuclear 

Research; M. Rahimi, A. B. Barto, and Z. Li of the Office of Nuclear Material Safety and 

Safeguards; and C. N. Van Wert and A. Patel of the Office of New Reactors. The authors would 

like to thank J. M. Scaglione and W. J. Marshall for their peer review of this document and 

H. Turpin for her careful editing of the final report.

xv 

LIST OF ACRONYMS AND UNITS 

2-D two dimensional 

ANSI/ANS American National Standards Institute, Inc./American Nuclear Society 

ARIANE Actinide Research in a Nuclear Element 

B&W Babcock & Wilcox 

BWR boiling water reactor 

CFR Code of Federal Regulations 

ENDF Evaluated Nuclear Data File 

GBC generic burnup credit cask 

GE General Electric 

GKN II Gemeinschaftskernkraftwerk Unit II in Neckarwestheim/Neckar 

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

keff effective neutron multiplication factor 

ISG interim staff guidance 

LCE laboratory critical experiments 

M/C measured-to-calculated 

MALIBU radiochemical analysis of MOX and UOX LWR fuels irradiated to high burnup 

MOX mixed oxide 

MTU metric ton of uranium 

NRC U.S. Nuclear Regulatory Commission 

PWR pressurized water reactor 

OFA optimized fuel assembly 

RCA radiochemical assay 

REBUS Reactivity Tests for a Direct Evaluation of the Burnup Credit on Selected 

Irradiated LWR Fuel Bundles 

ROP range of parameters 

SFP spent fuel pool 

SNF spent nuclear fuel 

T1/2 half-life 

TL tolerance limit 

TMI Three Mile Island 

W Westinghouse 

WABA wet annular burnable absorber 
xvi 
1 

1. INTRODUCTION 

One of the most significant challenges associated with implementing burnup credit is the 

validation of the depletion and criticality computer codes used in the safety evaluation—in 

particular, the availability and application of experimental data to support computer code 

validation. The expanded use of burnup credit in the United States for dry storage casks and 

transportation packages, hereafter referred to as casks, has been constrained by the availability 

of experimental fission product data to support computer code validation (Ref. 1). Historically, 

uncertainty in the fuel depletion calculation for burnup credit in spent fuel pools has been based 

on engineering judgment (Ref. 2) in lieu of validation with experimental data. To address the 

issues of burnup credit criticality validation, the U.S. Nuclear Regulatory Commission (NRC) 

initiated a project with Oak Ridge National Laboratory to (1) develop and establish a validation 

approach for burnup credit commercial spent nuclear fuel (SNF) system criticality safety 

evaluations based on best-available data and methods and (2) apply the approach on 

representative SNF storage and transport configurations and conditions to demonstrate its 

usage and applicability, as well as to provide reference keff bias and bias uncertainty results. 

The purpose of this report is to describe an approach for establishing depletion code bias and 

bias uncertainty in terms of a reactivity difference (i.e., Δkeff). Validation of criticality calculations 

is addressed in a companion report (Ref. 3). The main characteristics of the depletion validation 

approach are as follows: (1) calculated nuclide concentrations are compared to available 

measurements of nuclide concentrations from destructive radiochemical assay (RCA) to 

determine isotopic biases and bias uncertainties in the calculated nuclide concentrations, and 

(2) the isotopic biases and bias uncertainties are applied to the fuel compositions of 

representative safety analysis models to determine reference values for bias and bias 

uncertainty in keff by the use of the Monte Carlo uncertainty sampling method. 

Several methods for isotopic depletion code validation have been previously developed, as 

detailed in NUREG/CR-6811 (Ref. 4). The current validation study expands on two of these 

methods, the Monte Carlo uncertainty sampling method and the direct-difference method, in 

great detail. The Monte Carlo uncertainty sampling method represents the effects of nuclide 

concentration uncertainty on keff values by sampling isotopic concentrations from uncertainty 

distributions developed from experimental data. This method is used in this depletion validation 

study to calculate reference results of keff bias and bias uncertainty for representative safety 

analysis models. The direct-difference method applies measured nuclide concentrations directly 

in the safety analysis model to calculate a keff value, which then is compared with the keff value 

for the safety analysis model with calculated nuclide concentrations. This method is primarily 

used in this validation study to analyze the importance of establishing surrogate (i.e., substitute) 

data for nuclides with very few measurement data and performing decay-time adjustments for 

measured nuclide concentrations. 

The depletion validation approach described in this report is independent of the depletion and 

criticality computational methods being used and of the choice of the safety analysis models. 

Application of the depletion validation approach is demonstrated for representative SNF storage 

pool and cask configurations/conditions. Reference results for bias and bias uncertainty in keff

due to biases and bias uncertainties in calculated nuclide concentrations are obtained with 

SCALE 6.1 (Ref. 5) and the Evaluated Nuclear Data File/B Version VII.0 (ENDF/B-VII) nuclear 

cross-section data (Ref. 6). 
2 

This document is organized as follows: Section 2 presents an overview of a generic burnup 

credit analysis methodology identifying the main components of the depletion and criticality 

validation methodologies documented in this report and in the companion report (Ref. 3), 

respectively. The RCA data used in the depletion validation are presented in Sect. 3. Section 4 

describes the computational methods and nuclear data used to demonstrate application of the 

depletion validation approach. Representative analysis models for pressurized water reactor 

(PWR) and boiling water reactor (BWR) SNF burnup credit applications are described in Sect. 5. 

Implementation details for the Monte Carlo uncertainty sampling and direct-difference methods 

are provided in Sect. 6. Section 7 presents keff bias and bias uncertainty results based on 

SCALE 6.1. Results are provided for representative analysis models as well as for variants of 

those models. Conclusions are provided in Sect. 8. The appendices of this document describe 

various calculations in support of the depletion validation approach. 

 
3 

2. OVERVIEW OF BURNUP CREDIT ANALYSIS 

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

transport configuration meets the applicable requirements of Title 10, Code of Federal 

Regulations (CFR), Parts 50, 52, 70, 71, and 72 (Ref. 7). A general overview of the process for 

implementing burnup credit for SNF criticality safety analyses is outlined in Figure 2.1. The 

process includes development of safety analysis models considering a range of parameters 

important to criticality safety and isotopic and criticality validation analyses to demonstrate that 

the proposed configuration will meet the maximum keff limits specified in the applicable 

requirements and guidance. The methods of analysis used to determine the burnup credit 

nuclide compositions are validated through comparisons to measurement data. The depletion 

validation provided in this report addresses items (5) through (7) in Figure 2.1. The criticality 

validation (Ref. 3) addresses items (8) through (15) in Figure 2.1. For the sake of facilitating this 

discussion with a common terminology, the terms from ANSI/ANS-8.27 (Ref. 8) are being used 

in a slightly modified format as presented in Eq. (1). 

The depletion validation approach consists of two consecutive calculation steps: (1) calculated 

and measured nuclide concentrations for fuel samples are compared to determine biases and 

bias uncertainties associated with calculated nuclide concentrations, and (2) depletion code bias 

and bias uncertainty are established in terms of a reactivity difference (i.e., Δkeff). This latter step 

is referred to as “propagation” of isotopic composition uncertainties to keff in Figure 2.1, item 6. 

Throughout this document, the average change in keff from biases in the calculated nuclide 

concentrations is referred to as “keff bias,” and the variance of the change in keff at a 95% 

probability, 95% confidence level, resulting from bias uncertainties in calculated nuclide 

concentrations is referred to as “keff bias uncertainty.” Consistent with the approach in 

NUREG/CR-6698 (Ref. 9), a bias that reduces the calculated value of keff is not considered in 

Eq. (1). 

The criteria for establishing subcriticality with credit for the reactivity decrease due to fuel 

burnup is that the calculated multiplication factor kp plus allowances for biases and uncertainties 

shall be equal to or less than an established, allowable neutron multiplication factor; that is, 

kp + kp + βi + ki + β + kβ + Δkx + km ≤ klimit, (1)

where 

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

kp is an allowance for 

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

 material and fabrication tolerances, 

 uncertainties due to geometric or material representation limitations of the 

models used in the determination of kp; 

βi is the bias in kp due to depletion code bias in the calculated nuclide concentrations; 

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

nuclide concentrations; 

 
4 

β is the bias that results from using a particular calculation method and nuclear crosssection data to calculate the benchmark criticality experiments; 

 

kβ is the criticality bias uncertainty, which includes 

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

 uncertainties in the benchmark criticality experiments, 

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

technique to the critical experiment results, 

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

confidence level; 

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

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

accounted for in the benchmark criticality experiments used for calculating β; 

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

subcriticality of the physical system being modeled (this term is typically referred to 

as an administrative margin); 

klimit is the upper limit on the keff value for which the system is considered. 
5 

Figure 2.1 Overview of the burnup credit validation process 

Safety Analysis Isotopic Validation Criticality Validation Licensing

7 

3. ISOTOPIC VALIDATION DATA 

An approach accepted by the international nuclear engineering community for use in depletion 

code validations is based on comparing calculated nuclide concentrations with measured 

nuclide concentrations from destructive radiochemical assay of fuel samples (Refs. 8, 10, 11, 

12, 13). A fuel sample is a small portion of an irradiated fuel rod (e.g., a pellet segment or a few 

adjacent pellets cut from a fuel rod). A small number of assembly-average measurements also 

exist (e.g., measurements for five Obrigheim full-length reprocessed fuel assemblies as 

described in Ref. 14). To obtain measurements of nuclide concentrations, SNF samples are 

destructively examined with radiochemical analysis methods that involve a series of complex 

analytical techniques for sample preparation and isotopic and elemental measurements. 

Measurement error is dependent on the measurement instruments and radiochemical 

procedures, and can range from <1% for the major uranium and plutonium isotopes when using 

state-of-the-art radiochemical analysis methods (Ref. 15), to more than 5% when using less 

precise methods (Ref. 16). Measurement data for uranium and plutonium nuclides exist for each 

measured fuel sample. However, measurement data for additional burnup credit nuclides vary 

depending on the experimental programs. Modern measurement programs, such as ARIANE, 

MALIBU, REBUS, and ENUSA (Refs. 17, 18, 19), dedicated to radiochemical analysis of highburnup PWR and BWR fuel samples, provide thorough isotopic characterization and include 

multi-laboratory cross checks. 

Inherent components of the biases and bias uncertainties associated with the calculated nuclide 

concentrations determined from comparisons to RCA data include biases and uncertainties 

related to the radiochemical assay data, the measurement techniques, the ability to model the 

sample depletion environments, the nuclear cross-section data used, and the intrinsic 

uncertainties and approximations used in the numerical solutions. The objective of depletion 

code validation is to establish a predictable relationship between calculated nuclide 

concentrations and reality. For depletion code validations, local depletion conditions for a 

measured fuel sample or assembly-average depletion conditions for a measured fuel assembly 

must be modeled as accurately as possible to avoid introducing additional inaccuracy in the 

validation result. 

The RCA data evaluations described in Refs. 20 and 21 are based on a review of primary 

experimental references; hence, these references provide a database that can be used for 

validating computational predictions of SNF isotopic compositions. Burnup credit nuclides with 

available RCA data are described in Sect. 3.1. The PWR and BWR RCA data used in this report 

to determine biases and bias uncertainties in the calculated nuclide concentrations are 

presented in Sects. 3.2 and 3.3, respectively. 

3.1 NUCLIDES IMPORTANT TO BURNUP CREDIT 

Nuclide concentrations in commercial SNF and corresponding fuel reactivity vary depending on 

fuel design, depletion parameters, and cooling time. The reactivity of a discharged commercial 

SNF assembly reaches a maximum value at approximately 3 days after fuel discharge, when 

short-lived fission product nuclides with significant neutron absorption cross sections (e.g., 

135Xe) and their precursors are mostly decayed. The reactivity then decreases with increasing 

cooling time until approximately 100 years after fuel discharge, primarily a result of the decay of 

the fissile nuclide 241Pu (T1/2 = 14.4 years) to 241Am (neutron absorber) and of the formation of 

155Gd (a strong neutron absorber) from the beta decay of 155Eu (T1/2 = 4.75 years) (Ref. 22). 
8 

The depletion validation presented in this report considers SNF compositions consisting of 

12 actinide and 16 fission product nuclides selected on the basis of their importance to fuel 

reactivity (i.e., nuclides with large neutron fission cross sections and nuclides with large neutron 

absorption cross sections) and on the basis of availability of sufficient experimental data for use 

in depletion code validations. The 28 nuclides, referred to hereafter as burnup credit nuclides, 

are presented in Table 3.1. The burnup credit nuclides have been identified in previous studies 

(Refs. 23 and 24) as the nuclides with the most significant effects on keff for SNF cask burnup 

credit applications. The 28 nuclides or subsets of those nuclides are the ones commonly 

considered in fuel compositions for burnup credit criticality safety analyses that base validation 

of calculated nuclide concentrations on comparisons to available RCA data (Refs. 13, 25, 26). 

Except for 151Sm (T1/2 = 90 years), 238Pu (T1/2 = 87.7 years), 241Pu (T1/2 = 14.4 years), and 241Am 

(T1/2 = 432.7 years), the burnup credit nuclides are either very long-lived or stable. The 

concentrations of nuclides such as 147Sm, 149Sm, 151Eu, 155Gd, 234U, 239Pu, 237Np, and 241Am 

increase after fuel discharge as a result of the decay of their precursors. Figure 3.1 shows atom 

density variation as a function of decay time for nuclides exhibiting density variations after fuel 

discharge. Concentration values for 147Sm, 151Eu, 155Gd, and 241Am, typically measured at 

cooling times greater than 5 years, contain significant contributions from the radioactive decay 

of precursors 147Pm, 151Sm, 155Eu, and 241Pu, respectively. Note that 239Pu atom density slightly 

increases a short time after fuel discharge as a result of 239Np (T1/2 = 2.355 day) decay; 

however, 239Pu is not shown in the graph as a nuclide with varying atom density after fuel 

discharge. 

Table 3.1 Actinide and fission product nuclides important to burnup credit criticality 

analyses 

234U 235U 236U 238U 237Np 238Pu

239Pu 240Pu 241Pu 242Pu 241Am 243Am

95Mo 99Tc 101Ru 103Rh 109Ag 133Cs

143Nd 145Nd 147Sm 149Sm 150Sm 151Sm

152Sm 151Eu 153Eu 155Gd _ _ 
9 

 

Figure 3.1 Atom density as a function of decay time for burnup credit nuclides 

exhibiting density variations after fuel discharge. Atom density 

values are shown for a Westinghouse 17×17 optimized fuel assembly 

of 4.7 wt % 235U initial enrichment and 40 GWd/MTU burnup. 

3.2 PWR ISOTOPIC VALIDATION DATA 

The isotopic validation data used in this report for PWR SNF include RCA data for 100 PWR 

fuel samples with initial enrichments varying from 2.453 to 4.657 wt % 235U and burnup varying 

from 7 to 60 GWd/MTU obtained from low-, moderate-, and high-burnup fuel assemblies 

irradiated in the following nine PWRs: Trino Vercellese, Kernkraftwerk Obrigheim, Turkey Point 

Unit 3, H. B. Robinson Unit 2, Calvert Cliffs Unit 1, Three Mile Island (TMI) Unit 1, Takahama 

Unit 3, Gösgen, and GKN II. The 100 PWR fuel samples were selected from the 118 PWR fuel 

samples evaluated in Ref. 20 as explained further in this section. 

Three Gösgen fuel samples with burnup values ranging from 47.2 to 70.4 GWd/MTU from the 

MALIBU program were excluded from the isotopic validation data set because the results of the 

MALIBU program are proprietary information (Ref. 18) and therefore not publicly available at 

this time. Twelve measured PWR fuel samples obtained from the peripheral rods of Obrigheim 

assemblies BE124 and BE210 were irradiated in a core containing both UO2 and mixed oxide 

(MOX) assembly types (Ref. 27). Information concerning the locations and the characteristics of 

the MOX assemblies was unavailable (Ref. 20); therefore, significant uncertainty exists 

regarding the type of fuel assembly adjacent to the measured rods. Hence, the Obrigheim 

samples from assembly peripheral rods were not used in this evaluation. Takahama fuel 

samples SF95-1, SF96-1, and SF97-1 were excluded because of their proximity to the end of 

the active fuel region. These samples were obtained from locations near the extreme ends of 

the fuel rods (<20 cm) where the neutron flux gradient varies significantly over short lengths. 

The depletion calculation method used to demonstrate the validation approach (see Sect. 4) 

uses a two-dimensional representation of the depletion environment, so the effects of the strong 

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

0 50 100 150 200 250 300

Atom Density (atom/barn·cm)

Decay Time (years)

Pu-241

Np-237

Pu-238

Sm-147

U-234

Am-241

Sm-151

Sm-149

Gd-155

Eu-151
10 

gradient would not be accounted for accurately in the depletion calculations. Therefore, these 

samples were omitted for the purpose of this study. 

The number of samples and the ranges of initial enrichment and final burnup of the PWR fuel 

samples providing measurement data for each burnup credit nuclide are presented in Table 3.2. 

Measured concentrations for the 235U, 238U, 239Pu, 240Pu, and 241Pu nuclides are available for all 

PWR fuel samples. However, there are significantly fewer fuel samples providing RCA data for 

fission product nuclides. A comparison of the enrichment and burnup values of the 100 PWR 

fuel samples to loading curves developed for a representative spent fuel pool (SFP) storage 

rack model (see Sect. 5.2) is shown in Figure 3.2. The graph identifies the initial enrichment and 

final burnup of the fuel samples providing measurement data for actinide sets, partial fission 

product sets, and for the full set of actinide and fission product (28) nuclides considered in fuel 

compositions for this depletion validation (see Table 3.1). Only two Gösgen fuel samples 

provide measured concentrations for all 28 burnup credit nuclides. The TMI, Takahama, and 

some of the Calvert Cliffs fuel samples provide measurement data for most of the 16 burnup 

credit fission product nuclides. 

The range of applicability of the initial enrichments and final burnups of the measured PWR fuel 

samples is presented in Table 3.2. For measured actinide concentrations, fuel sample initial 

enrichment ranges from approximately 2.5 to 4.7 wt % 235U, and final burnup ranges from 

approximately 10 to 60 GWd/MTU. For most of the measured fission product nuclides, fuel 

sample initial enrichment ranges from approximately 2.5 to 4.7 wt % 235U, and final burnup 

ranges from approximately 20 to 60 GWd/MTU. Measurement data for fission product nuclides 

such as 95Mo, 101Ru, 103Rh, and 133Cs have a burnup range of applicability from approximately 

30 to 60 GWd/MTU; the 109Ag measurement data has a burnup range of applicability from 

approximately 45 to 60 GWd/MTU. In this depletion validation, the PWR RCA data is used to 

calculate bias and bias uncertainty in keff for fuel assemblies with an axial burnup profile 

(see Sect. 5.1) and average burnup up to 60 GWd/MTU (see Sect. 7.1). 

For a PWR application model (see Sect. 5) with the 60 GWd/MTU assembly average burnup 

value, the applied axial burnup profile resulted in a maximum burnup value of approximately 

66.5 GWd/MTU. Therefore, for this assembly average burnup value, the area of applicability of 

the RCA data was expanded to burnup values up to 66.5 GWd/MTU. The impact on keff bias 

uncertainty of extending the area of applicability of the RCA data to higher burnup values was 

evaluated with PWR RCA data that includes the MALIBU proprietary data for three Gösgen fuel 

samples having burnup values from 47.2 to 70.4 GWd/MTU. This validation data set was used 

to calculate the keff bias uncertainty value for a SFP storage rack model (see Sect. 5.2) with an 

assembly average burnup of 60 GWd/MTU, which was then compared to the keff bias 

uncertainty value for this model obtained from applying isotopic bias uncertainties based on the 

measurement data for the 100 PWR fuel samples with burnup values up to 60 GWd/MTU. The 

two keff bias uncertainty values differed by approximately 1%. Therefore, expanding the area of 

applicability of the RCA data to higher burnup values is justified because the impact on keff bias 

uncertainty is small. 

Measured nuclide concentrations for burnup credit nuclides have been reported either at the 

time of fuel discharge or at the actual measurement time depending on the measurement 

program (see Ref. 20). The measurement data reported for discharged compositions include 

decay time corrections for nuclides exhibiting concentration variation as a function of the decay 

time (see Figure 3.1) that have been performed by the experimental programs. Note that 239Pu 

measurement data reported for discharged compositions includes a very small contribution from 

239Np (T1/2 = 2.355 day) decay (Ref. 28). Applicability of measured data for nuclides with varying 
11 

concentrations as a function of decay time is limited to the reported time relative to fuel 

discharge. For the direct-difference method, which uses measurement nuclide concentrations 

directly in keff calculations, decay-time corrections may be necessary to extend the area of 

applicability of the measurement data for nuclides exhibiting variation with cooling time to the 

cooling time of the criticality safety analysis (see Sect. 6.2). 

Table 3.2 Initial enrichment and burnup values for the measured PWR fuel samples 

Nuclide 

No. of 

samples

Enrichment 

range

 (wt % 235U)

Burnup range 

(GWd/MTU) Nuclide

No. of 

samples

Enrichment 

range 

(wt % 235U)

Burnup 

range 

(GWd/MTU)

234U 63 2.453–4.657 7.2–59.7 101Ru 15 3.5–4.1 31.1–59.7 

235U 100 2.453–4.657 7.2–59.7 103Rh 16 2.453–4.1 31.1–59.7 

236U 85 2.453–4.657 12.9–59.7 109Ag 14 3.5–4.1 44.8–59.7 

238U 100 2.453–4.657 7.2–59.7 133Cs 7 3.038– 4.1 27.4–59.7 

237Np 44 2.453–4.657 16.0–59.7 143Nd 44 2.453–4.657 16.0–59.7 

238Pu 85 2.453–4.657 12.9–59.7 145Nd 44 2.453–4.657 16.0–59.7 

239Pu 100 2.453–4.657 7.2–59.7 147Sm 32 2.453–4.657 23.7–59.7 

240Pu 100 2.453–4.657 7.2–59.7 149Sm 28 3.5–4.657 23.7–59.7 

241Pu 100 2.453–4.657 7.2–59.7 150Sm 32 2.453–4.657 23.7–59.7 

242Pu 99 2.453–4.657 7.2–59.7 151Sm 32 2.453–4.657 23.7–59.7 

241Am 47 2.453–4.657 17.1–59.7 152Sm 32 2.453–4.657 23.7–59.7 

243Am 48 2.63–4.657 17.1–59.7 151Eu 21 3.5–4.657 23.7–59.7 

95Mo 15 3.5–4.1 31.1–59.7 153Eu 27 2.453–4.657 23.7–59.7 

99Tc 25 2.453–4.1 16.0–59.7 155Gd 27 2.453–4.657 23.7–59.7 

Figure 3.2 Enrichment and burnup values of the measured PWR fuel samples compared 

to loading curves for a representative PWR SFP storage rack model 
12 

3.3 BWR ISOTOPIC VALIDATION DATA 

The biases and bias uncertainties associated with calculated nuclide concentrations in BWR 

SNF were based on comparisons to measured nuclide concentrations for 32 BWR fuel samples 

obtained from fuel assemblies consisting of 8×8, 7×7, and 6×6 pin lattices from the Fukushima 

Daini Unit 2, Cooper, and Gundremmingen-A reactors, respectively. Therefore, the BWR assay 

data is limited in its range of applicability since modern BWR assembly designs are significantly 

more complex. More extensive BWR isotopic assay data from modern assembly designs 

(i.e., 10×10 lattice) exists but was not available for inclusion in this analysis. The initial fuel 

enrichment for the measured samples varies from 2.54 to 3.91 wt % 235U, and the burnup varies 

from 14.4 to 44.0 GWd/MTU. 

Measurement data for the 12 burnup credit actinide nuclides and for eight of the 16 burnup 

credit fission product nuclides were available for use in the depletion validation. The number of 

samples and the ranges of initial enrichment and final burnup values of the BWR fuel samples 

providing measurement data for each burnup credit nuclide are presented in Table 3.3. 

As described in Ref. 21, void fraction values corresponding to the fuel sample locations were 

unavailable for some of the measured BWR fuel samples considered in this validation study. For 

those BWR fuel samples, representative void fraction values were derived based on actual 

reported void fraction distributions from other similar assemblies at different average assembly 

powers. Consequently, the calculated nuclide concentrations for the BWR fuel samples include 

an uncertainty component due to approximate moderator density values used in the depletion 

calculations. 

 
13 

Table 3.3 Initial enrichment and burnup values for the measured BWR fuel samples 

Nuclide 

No. of 

samples 

Enrichment 

range 

 (wt % 235U) 

Burnup 

range 

(GWd/MTU) Nuclide

No. of 

samples

Enrichment 

range 

(wt % 235U) 

Burnup 

range 

(GWd/MTU) 

234U 21 2.93–3.91 16.7–44 99Tc 6 2.93 17.8–33.9 

235U 32 2.54–3.91 14.4–44 143Nd 14 3.41–3.91 16.7–44 

236U 32 2.54–3.91 14.4–44 145Nd 14 3.41–3.91 16.7–44 

238U 32 2.54–3.91 14.4–44 147Sm 11 3.41–3.91 16.7–44 

237Np 20 2.93–3.91 16.7–44 149Sm 11 3.41–3.91 16.7–44 

238Pu 32 2.54–3.91 14.4–44 150Sm 11 3.41–3.91 16.7–44 

239Pu 32 2.54–3.91 14.4–44 151Sm 11 3.41–3.91 16.7–44 

240Pu 32 2.54–3.91 14.4–44 152Sm 11 3.41–3.91 16.7–44 

241Pu 32 2.54–3.91 14.4–44 _ _ _ _

242Pu 32 2.54–3.91 14.4–44 _ _ _ _

241Am 20 2.93–3.91 16.7–44 _ _ _ _

243Am 14 3.41–3.91 27.2–44 _ _ _ _

15 

4. COMPUTER CODES AND NUCLEAR DATA 

This section describes the various computer codes and nuclear data used to perform the 

calculations described throughout this report. 

SCALE 6.1 (Ref. 5) and the ENDF/B-VII nuclear data were selected in this study to obtain 

reference keff bias and bias uncertainty values for representative SFP storage rack and SNF 

cask configurations. SCALE 6.1 is the most recent release version of the SCALE code system 

developed at Oak Ridge National Laboratory. This computer code has been distributed for more 

than 30 years through the Radiation Safety Information Computational Center and the Nuclear 

Energy Agency Data Bank under license agreement. SCALE has been used for safety analysis 

and design by regulators, licensees, and research institutions around the world. This code is 

accepted by the NRC for criticality safety applications (Ref. 29). SCALE 6.1 was selected 

because it has multiple unique capabilities (Ref. 30) relevant to depletion and criticality code 

validations as briefly described in this section. SCALE 6.1 provides both depletion and criticality 

analysis capabilities within a common system. 

SCALE 6.1 contains improved capabilities relevant to the current burnup credit calculations, 

including improved resonance self-shielding methodologies for cross-section processing and an 

improved ENDF/B-VII nuclear cross-section library for transport calculations. The ENDF/B-VII 

cross-section data yield significantly more accurate calculated eigenvalues than those obtained 

with the previous nuclear data version for a wide range of critical experiments, including 

moderated, low-enriched uranium fuel rod lattice configurations, and for unmoderated, bare or 

reflected, critical benchmark assemblies (Refs. 31 and 32). Improvements have also been 

observed in isotopic predictions using SCALE and the ENDF/B-VII cross-section data (Ref. 33). 

The SCALE 6.1 capabilities used in the report include automated sequences to produce 

problem-dependent multigroup cross-section data (Ref. 34) and analysis sequences for Monte 

Carlo neutron transport (CSAS5 and CSAS6) (Ref. 35), fuel depletion (TRITON) (Ref. 36), 

isotopic decay (ORIGEN-S) (Ref. 37), burnup-credit criticality safety (STARBUCS) (Ref. 38), 

and cross-section sensitivity and uncertainty (TSUNAMI) (Ref. 39) calculations. Unless 

otherwise noted, the 238-group cross-section library based on the ENDF/B-VII.0 nuclear data 

and the resonance cross-section methodology employing CENTRM (Ref. 34) were used in the 

various SCALE 6.1 calculations in support of this depletion validation study. 

The TRITON two-dimensional (2-D) depletion sequence (Ref. 5, Sect. T01) was used to perform 

depletion calculations. TRITON has the capability of simulating the depletion of multiple 

mixtures in a fuel assembly model, which allows a detailed representation of the local flux 

distribution for a specific fuel rod in the assembly. Within the TRITON 2-D depletion calculation 

sequence, ORIGEN-S (Ref. 5, Sect. F07) is used to perform depletion and decay calculations, 

and NEWT (Ref. 5, Sect. F21) is used to perform 2-D discrete ordinates transport calculations. 

The STARBUCS sequence was used to determine burnup-dependent nuclide concentrations for 

PWR criticality calculations (see Sect. 5.1) and to generate loading curves for the PWR safety 

analysis models (see Sect. 5.4). STARBUCS enables modeling of the phenomena important to 

burnup credit and allows analysts to investigate the impact on criticality safety of various 

assumptions related to the burnup credit calculation methodology. The STARBUCS sequence 

provides a burnup credit loading curve search capability in addition to its initial capability of 

performing criticality safety analyses employing burnup credit. This capability may be used to 

determine the combination of assembly initial enrichment and burnup values that result in a 
16 

user-specified keff value. STARBUCS uses the ORIGEN-ARP method, described in Section D01 

of Ref. 5, to rapidly generate fuel compositions as a function of fuel mixture initial enrichment 

and burnup. ORIGEN-ARP libraries for the STARBUCS calculations were obtained by 

performing TRITON depletion calculations for the PWR assembly types used in the safety 

analysis models and for a range of fuel initial enrichment (e.g., 1 to 5 wt % 235U) and assembly 

average burnup (e.g., 0 to 80 GWd/MTU) values. 

TSUNAMI-3D was used to determine sensitivity coefficients for individual burnup credit nuclides 

in support of the sensitivity/uncertainty analyses presented in this report. TSUNAMI-3D is the 

SCALE analysis sequence dedicated to computing the sensitivity of keff to energy-dependent 

cross-section data for each reaction of each nuclide in a system model using linear perturbation 

theory as described in Sections C09 and F22 of Ref. 5. The sensitivity of keff to total cross 

section, integrated over energy, is referred to as the sensitivity coefficient. Sensitivity coefficient 

values may also be obtained by performing direct perturbation calculations that employ 

variations of nuclide atom density resulting in small keff variations that are consistent with the 

linear-perturbation approximation. 

KENO V.a (Ref. 5, Sect. F11) is the Monte Carlo transport criticality code used within the 

CSAS5 (Ref. 5, Sect. C05), STARBUCS, and TSUNAMI sequences to calculate the keff values 

of the PWR safety analysis models. KENO VI is the Monte Carlo transport criticality code used 

within the CSAS6 (Ref. 5, Sect. C06) sequence to calculate keff values for the BWR safety 

analysis model. 
17 

5. SAFETY ANALYSIS MODELS 

To assess the impact of nuclide concentration uncertainties on keff for realistic storage 

configurations and to provide reference keff bias and bias uncertainty values, representative 

safety analysis models were developed for SFP storage rack and SNF cask configurations. The 

characteristics of a PWR SFP storage rack model, a PWR SNF cask model, and a BWR SFP 

storage rack model are described in this section. The sensitivity of bias and bias uncertainty in 

keff to a range of parameters important to criticality safety analysis (e.g., SFP storage rack 

design, fuel assembly type, burnup, cooling time, axial burnup representation, boron 

concentration, and nuclear data) was also evaluated (see Sect. 7.3). 

5.1 PWR ASSEMBLY MODEL 

The fuel assembly type selected for use in the PWR SFP storage rack and SNF cask models 

was the Westinghouse (W) 17×17 optimized fuel assembly (OFA). This assembly type is one of 

the assembly types used in previous burnup credit studies (Ref. 40) performed in support of 

ISG-8 Rev. 2 (Ref. 1). The fuel rods were represented in the model with 18 axial zones; the 

burnup values for the axial zones were based on burnup-dependent axial burnup profiles, which 

have been demonstrated to be conservative with respect to criticality (Refs. 41 and 42). Axially 

varying burnup-dependent nuclide concentrations were generated with reactor operating 

parameters for depletion calculations that increase discharge reactivity (Ref. 23), including the 

use of (1) wet annular burnable absorber (WABA) rod insertion in each of the 24 guide tube 

locations throughout the irradiation time period; (2) higher fuel and moderator temperatures 

(1100 K and 610 K, respectively) than typical values; (3) decreased moderator density 

(0.63 g/cm3

); and (4) a constant soluble boron concentration of 1000 ppm throughout the 

irradiation time period. 

5.2 PWR SFP STORAGE RACK MODELS 

The PWR SFP storage rack model is represented as a laterally infinite array of loaded fuel 

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

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

0.292 cm (0.115 in.). One 0.203-cm-thick (0.080-in.-thick) Boral® panel with a 10B areal density 

of 0.020 g/cm2

 was modeled between each storage cell. The center-to-center spacing for this 

model is 23.139 cm (9.110 in.). The poison panels were modeled to the same axial length as 

the active fuel. The PWR fuel used in the safety analysis model is the W 17×17 OFA described 

in Sect. 5.1. The PWR fuel assembly was modeled as centered in the storage cell. A horizontal 

cross-section view of the PWR SFP storage rack cell model is shown in Figure 5.1. This PWR 

SFP storage rack configuration is referred to as the “representative” SFP storage rack model. 

As shown in Sect. 5.4, the representative SFP storage rack configuration uses fuel assemblies 

with high initial enrichment relative to burnup so that the maximum burnup value corresponding 

to 5 wt % 235U initial enrichment is 44.33 GWd/MTU. To obtain keff bias and bias uncertainty 

results for assemblies of higher burnup values, a second PWR SFP storage rack configuration 

was considered. This configuration differs from the representative SFP storage rack model in 

that it utilizes unpoisoned panels; this configuration is referred to as the “unpoisoned” SFP 

storage rack model. 
18 

The cooling time used to generate burnup-dependent nuclide concentrations for the PWR SFP 

storage rack models was 3 days. This cooling time approximately corresponds to maximum 

SNF reactivity, which results from the decay of short-lived fission product nuclides with 

significant neutron absorption cross sections. The burnup-dependent nuclide concentrations 

were determined so that the keff value of the PWR SFP storage rack models without soluble 

boron is 0.99. This value was based on the requirements of 10 CFR 50.68[b](4) (if credit is 

taken for soluble boron and the system is flooded with unborated water) and an assumed 

allowance for biases and uncertainties of 1%. 

Figure 5.1 Horizontal cross section of the representative PWR SFP storage rack cell 

representation 

5.3 PWR SNF CASK MODEL 

The representative safety analysis model for a PWR SNF cask is a generic high-capacity cask 

design, referred to as a GBC-32 cask, which has been developed in Ref. 43 as a reference 

configuration for burnup credit studies. The generic cask, which can accommodate 32 PWR 

assemblies, uses Boral panels containing 10B as a fixed neutron poison dispersed uniformly with 

a 10B areal density of 0.0225 g/cm2

. The PWR fuel used in the safety analysis model is the 

W 17×17 OFA described in Sect. 5.1. A cutaway view of the GBC-32 cask model showing the 

bottom half with a quarter of the model removed is illustrated in Figure 5.2. The cooling time 

used to generate burnup-dependent nuclide concentrations for the representative PWR SNF 

cask was 5 years. The burnup-dependent nuclide concentrations for the GBC-32 cask model 

were determined so that the keff value was 0.94. The model keff value was determined by 

applying an assumed allowance for biases and uncertainties of 0.01 to the recommended keff

value of 0.95 for cask criticality safety analyses (Refs. 29, 44, 45). 

Neutron absorber panel 

Fuel rod location 

Guide tube location 

Stainless steel can 

Moderator 

Neutron absorber panel 

Stainless steel can 

Fuel rod location 
19 

Figure 5.2 Cutaway view of the GBC-32 cask model showing bottom half with a quarter 

of the model removed. The different colors in the fuel region represent 

varying axial burnup zones.

5.4 LOADING CURVES FOR PWR SNF 

For validation purposes only, loading curves were developed for the PWR SFP storage rack and 

SNF cask models with the keff values of 0.99 and 0.94, respectively, for fuel compositions 

consisting of the 12 burnup credit actinide nuclides and for the 28 burnup credit actinide and 

fission product nuclides (see Table 3.1). The effects of including the 16 fission product nuclides 

in actinide-only compositions on loading curves for the representative SNF configurations are 

illustrated in Figure 5.3, where the loading curves are shown superimposed over the 2002 PWR 

SNF assembly inventory (Ref. 46). 
20 

Figure 5.3 Loading curves for PWR SNF in cask and pool storage rack 

configurations. Loading curves developed for the representative 

PWR SFP storage rack and SNF cask models correspond to the keff

values of 0.99 and 0.94, respectively. The horizontal segments of the 

loading curves were caused by changes in the fuel axial burnup 

profiles at 18 and 30 GWd/MTU. The color-coded numbers shown on 

the graph represent the numbers of PWR assemblies with certain 

initial enrichment and final burnup; yellow, burnt orange, and pink 

identify a number of assemblies in the range 20 to 99, 100 to 299, 

and greater than 300, respectively. 

5.5 BWR ASSEMBLY MODEL 

A BWR assembly model was developed using the approach commonly employed in criticality 

safety evaluations for the wet storage of BWR SNF in a high-density fuel storage rack (Ref. 47). 

The model for a BWR fuel assembly was a generic 10×10-8 assembly design with eight fuel 

rods containing gadolinium oxide (Gd2O3) and two water rods that displaced eight fuel rods. 

Unlike the approach employed for the PWR burnup credit criticality analysis, which uses a range 

of enrichment and burnup values based on the loading curve, the BWR analysis uses fuel 

compositions corresponding to the assembly peak reactivity. A 5 wt % 235U initial enrichment of 

the UO2 fuel was used to account for the highest anticipated fuel enrichment. The Gd2O3

content in UO2 was 3 wt %. The BWR SFP application assumed a 3 day post-irradiation decay 

period. 
21 

The reactivity of a fuel assembly in the BWR reactor core initially increases with burnup as a 

result of the depletion of gadolinium (burnable poison) until it reaches a peak value. The peak 

reactivity value is reached when the burnable poison is mostly depleted. Then the reactivity of 

the fuel assembly decreases with burnup until the fuel assembly is removed from the reactor. 

For the representative model, the assembly peak reactivity occurred at approximately 

11 GWd/MTU. 

5.6 BWR SFP STORAGE RACK MODEL 

The BWR SFP storage rack was modeled as an infinite array of loaded fuel storage cells. Each 

storage cell is a stainless steel box having an internal dimension of 15.063 cm (5.93 in.) and a 

wall thickness of 0.18 cm (0.070 in.). One 0.203-cm-thick (0.080-in.-thick) Boral plate with a 10B 

areal density of 0.020 g/cm2 was modeled between each storage cell. The center-to-center 

spacing for this model is 17.063 cm (6.72 in.). The BWR fuel assembly was modeled as 

centered in the storage cell with reflective boundary conditions used axially and radially. The 

assembly axial burnup representation is uniform. A horizontal cross section of the unit cell of the 

BWR SFP rack model is illustrated in Figure 5.4. The kinf value of the BWR SFP storage rack 

model is 0.94. This value was based on the requirements of 10 CFR 50.68[b](4) (if no credit is 

taken for soluble boron and the system is flooded with unborated water) and an assumed 

allowance for biases and uncertainties of 0.01. 

Figure 5.4 Horizontal cross section of the BWR SFP storage rack cell representation 

Neutron absorber panel 

Stainless steel can 

Moderator 

Gd2O3 rod location 

UO2 rod location 

Water rod location 

23 

6. CALCULATION OF BIAS AND BIAS UNCERTAINTY IN keff 

Two different methods are used in this validation study: the Monte Carlo uncertainty sampling 

method (Sect. 6.1) and the direct-difference method (Sect. 6.2). These methods were selected 

on the basis of an evaluation of existing depletion validation methods (Refs. 4, 25, 48). The 

characteristics of the methods and their implementation for the current validation study are 

described in this section.

6.1 MONTE CARLO UNCERTAINTY SAMPLING METHOD 

The Monte Carlo uncertainty sampling method is often used in simulating uncertainties in 

physical systems with many coupled degrees of freedom as well as in modeling phenomena 

with significant uncertainty in inputs (Refs. 49, 50, 51). In this depletion validation study, the 

method is used to represent the effects of nuclide concentration uncertainty on keff values by 

sampling isotopic concentrations from uncertainty distributions developed from experimental 

data. The Monte Carlo uncertainty sampling method requires determination of biases and bias 

uncertainties in the calculated nuclide concentrations. Implementation of the Monte Carlo 

uncertainty sampling method uses a normal or a uniform probability distribution (Sect. 6.1.1), 

depending on the number of available measurements for each burnup credit nuclide, as the 

mathematical model for expected isotopic concentration uncertainty variation, and independent 

sampling from the uncertainty distributions of individual nuclides. This implementation of the 

method requires analysis of the assumptions concerning normality and independence of the 

isotopic uncertainty data to determine the impact of those assumptions on the depletion 

validation results. 

The following calculations and analyses were performed: 

 calculation of bias and bias uncertainty in calculated nuclide concentrations (Sects. 6.1.1 

and 6.1.3); 

 statistical analysis of the measured-to-calculated (M/C) concentration ratio values 

(Sect. 6.1.2), including 

– analysis of trends, 

– normality tests, and 

– correlation coefficient calculations; 

 calculation of isotopic bias and bias uncertainty (Sect. 6.1.3); 

 calculation of nuclide concentration values for use in keff calculations (Sect. 6.1.4); 

 validation of the normality assumption for bias uncertainty in calculated nuclide 

concentrations (Sect. 6.1.5); and 

 convergence of the Monte Carlo keff bias uncertainty estimate (Sect. 6.1.6). 

 
24 

6.1.1 Calculation of Bias and Bias Uncertainty in Calculated Nuclide 

Concentrations 

The measured-to-calculated nuclide concentration ratio, j Xn , is calculated with Eq. (2), 

j jj X MC n nn / , (2)

where 

 n = a burnup credit nuclide, 

 j = the index of a measured fuel sample in the series of Nn evaluated fuel samples, 

j Mn = the measured concentration of nuclide n in the evaluated fuel sample j, j Cn = the calculated concentration of nuclide n in the evaluated fuel sample j.

The sample mean X n and sample standard deviation n s of the j Xn values are calculated with 

Eqs. (3) and (4), respectively, 

1

 

Nn

j

n nn

j

X X N/ , (3)

2

1

1   

Nn

j

n nn n

j

s XX N ( )( ) , (4)

where 

j Xn = M/C concentration ratio defined by Eq. (2); 

Nn = the number of evaluated fuel samples. 

A normal distribution is characterized by the mean value and the standard deviation. Sample 

mean and sample standard deviation calculated with Eqs. (3) and (4), respectively, are only 

approximations of the true mean and standard deviation of nuclide concentration uncertainties 

because the calculations use a limited number of fuel samples. To bound the uncertainty in a 

sample standard deviation value because a limited number of measurement data was used, 

tolerance intervals are used in place of confidence intervals in the sampling procedure. 

Tolerance intervals have been introduced as a means to account for uncertainty due to sample 

size (Ref. 52). A statistical tolerance interval defines the limits within which a stated proportion 

of a population is expected to lie, based on a sample that was measured from this population. In 

this analysis, a tolerance interval is determined with tolerance limit factors for the normal 

distribution, which depend on the sample size, the specified proportion of the population within 

the bounds, and the specified certainty. Note that the magnitude of a tolerance-limit factor 

increases as the sample size decreases and that a tolerance interval for isotopic uncertainty 

determined as described further in this section is significantly larger than a confidence interval 

for nuclides with a small number of measurements. 

The Monte Carlo uncertainty sampling method uses a normal or a uniform probability 

distribution, depending on the number of available measurements for each burnup credit 

nuclide, as the mathematical model for expected isotopic concentration uncertainty variation 

(Sect. 6.1.4). A normal distribution is used if more than 10 measurement data are available for a 

nuclide. For nuclides with fewer than 10 measured concentration values (i.e., 133Cs and 99Tc for 

PWR and BWR fuel, respectively), it is not appropriate to represent the uncertainty with a 
25 

normal distribution. Therefore, a uniform distribution model is used because this model enables 

conservative sampling of a larger uncertainty range than a normal distribution. 

The two-sided tolerance-limit factor, denoted as 2

n tf , for the normal distribution corresponding to 

the sample size, 95% certainty, and 68.3% of the population, is applied as an adjustment factor 

as shown in Eq. (5) to determine a bounding value for one-sigma isotopic uncertainty based on 

more than 10 measurement data. This adjustment is made to account for uncertainty due to 

limited sample size. For example, the two-sided tolerance-limit factor values applied vary from 

1.174 (69 samples) to 1.664 (11 samples) (Ref. 53). The 68.3% probability level is used 

because the tolerance-limit factor is applied as an adjustment factor to the one-sigma sample 

standard deviation. The adjusted one-sigma sample standard deviation is then used to define 

the sampling distribution. Hence, a normal distribution of mean X n and variance σn

determined as shown in Eqs. (3) and (5), respectively, is used as the mathematical model of 

uncertainty in the calculated nuclide concentrations for a nuclide n with more than 10 

measurement data. If fewer than 10 measurement data are available to determine sample mean 

and standard deviation values, the one-sided tolerance-limit factor for the normal distribution 

corresponding to the sample size, 95% certainty, and 95% of the population, denoted as 1

n tf , is 

used as an adjustment factor as shown in Eq. (5) to determine a uniform sampling interval. For 

example, the one-sided tolerance limit factor values applied for six and seven samples are 

3.711 and 3.399 (Ref. 54), respectively. A uniform distribution is characterized by the lower and 

upper limits within which a random variable falls. Hence, a uniform distribution of parameters 

σn and σn is used as the mathematical model of uncertainty in the calculated nuclide 

concentrations for nuclides with fewer than 10 measurement data, 

2

1

, 10 ,

,

    

  

n

n n

n n

n

s tf N

σ

s tf

 if 

 otherwise .

(5)

The sample mean, X n , and sample standard deviation adjusted to account for uncertainties 

related to sample size, σn , determined as shown in Eqs. (3) and (5), respectively, are hereafter 

referred to as isotopic bias and isotopic bias uncertainty, respectively. 

6.1.2 Statistical Analysis of the Measured-to-Calculated Concentration 

Ratio Values 

Prior to developing probability distribution functions for nuclide concentration uncertainties, a 

statistical evaluation of the M/C concentration ratio values is required. A trending analysis 

(Sect. 6.1.2.1) was performed to identify M/C concentration ratio values exhibiting variations 

with sample burnup. The trending analysis was performed by applying the test described in 

Ref. 55, which is designed to evaluate the statistical significance of the slope resulting from a 

linear regression model. The Shapiro-Wilk normality test was applied to the M/C concentration 

ratio values for individual burnup credit nuclides to identify non-normal data sets (Sect. 6.1.2.2). 

The degree of correlation (dependence) among nuclide composition uncertainties was 

determined on the basis of correlation coefficient calculations (Sect. 6.1.2.3). 
26 

6.1.2.1 Analysis of Trends 

For the PWR isotopic composition evaluations, a trending analysis identified a dependence of 

the M/C concentration ratio values on sample burnup for the major actinide nuclides 235U, 236U, 

238U, 239Pu, 240Pu, and 241Pu. The isotopic bias for these nuclides varies as a function of sample 

burnup. In addition, the variance of the M/C concentration ratio values within the burnup range 

40 to 60 GWd/MTU is significantly larger than that of the M/C concentration ratio values within 

the burnup range 5 to 40 GWd/MTU. Dependence of the M/C concentration ratio values on the 

initial enrichment of the PWR fuel samples was not identified for any of the burnup credit 

nuclides. The observed dependencies on sample burnup were considered in calculating isotopic 

bias and bias uncertainty values for burnup intervals, as explained further in this section. 

A stepwise function was used to define constant isotopic bias and constant isotopic bias 

uncertainty within defined burnup intervals and to avoid a regression analysis. The burnup 

interval 5 to 60 GWd/MTU was divided into two or three subintervals so that the isotopic bias as 

well as the isotopic bias uncertainty are constant (i.e., do not exhibit a dependence on burnup) 

within each individual burnup subinterval. For nuclides with a large number of measurements 

that cover a wide range of fuel burnup values, including major actinide nuclides 235U, 238U, 239Pu, 

240Pu, 241Pu, and 242Pu, isotopic bias and bias uncertainty values were determined for three 

burnup subintervals: 5 to 15 GWd/MTU, 15 to 40 GWd/MTU, and 40 to 60 GWd/MTU. Two 

different sets of isotopic bias and bias uncertainty values applicable to burnup values below and 

above 40 GWd/MTU were determined for the actinide nuclides 234U, 236U, 237Np, 238Pu, 241Am, 

and 243Am. A single set of isotopic bias and bias uncertainty values was determined for each 

burnup credit fission product nuclide since a smaller number of measurement data were 

available (e.g., from 7 for 133Cs and up to 44 for 143Nd and 145Nd). The M/C concentration ratio 

values for 235U and 239Pu are shown in Figure 6.1(a) and Figure 6.1(b), respectively. The figures 

illustrate the approach of subdividing the burnup interval 5 to 60 GWd/MTU to calculate isotopic 

bias and bias uncertainty values. 

In the case of the BWR isotopic data evaluations, the isotopic bias and bias uncertainty values 

were based on the entire set of available BWR RCA data since dependencies on fuel sample 

initial enrichment and final burnup were not identified for any of the burnup credit nuclides with 

measured concentrations. 

 
27 

 (a) 

(b) 

Figure 6.1 Measured-to-calculated concentration ratio versus fuel sample burnup for 

(a) 235U; (b) 239Pu. The error bars in the graph represent the reported one 

sigma measurement errors; very small measurement errors (0.1%) are not 

visible on the graph. 

 

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

5 10 15 20 25 30 35 40 45 50 55 60 65

M/C Concentration Ratio

Fuel Sample Burnup (GWd/MTU)

235U

Trino Vercellese

Obrigheim

Turkey Point-3

H. B. Robinson-2

Calvert Cliffs-1

Takahama-3

TMI-1

Gosgen

GKN II

0.60

0.70

0.80

0.90

1.00

1.10

1.20

5 10 15 20 25 30 35 40 45 50 55 60 65

M/C Concentration Ratio

Fuel Sample Burnup (GWd/MTU)

239Pu

Trino Vercellese

Obrigheim

Turkey Point-3

H. B. Robinson-2

Calvert Cliffs-1

Takahama-3

TMI-1

Gosgen

GKN II
28 

6.1.2.2 Normality Test Results 

Data normality was assessed with the Shapiro-Wilk normality test at the 0.05 significance level 

(Ref. 56). The PWR M/C concentration ratio values for 235U within the burnup interval 15 to 40 

GWd/MTU did not approach a normal distribution. Other nuclides with non-normal PWR M/C 

concentration ratio values are 238U, 237Np, 241Am, 147Sm, 150Sm, 151Sm, 151Eu, and 155Gd. 

In the case of the BWR isotopic composition data evaluations, the M/C concentration ratio 

values for nuclides with minor importance to fuel reactivity such as 236U, 143Nd, and 147Sm were 

identified as non-normal data sets. 

The impact on keff bias uncertainty of using a normal distribution probability function to sample 

nuclide concentration uncertainties for these nuclides is analyzed in Sect. 6.1.5. 

6.1.2.3 Correlations among Nuclide Concentration Uncertainties 

The independence of variables is an assumption used in the current implementation of the 

Monte Carlo uncertainty sampling method. Complex multivariate statistical analyses (Refs. 57 

and 58), which attempt to establish mathematical relationships between variables considered 

relevant to the problem being studied, require detailed understanding of both the calculational 

and experimental uncertainties and correlations. This analysis evaluated the degree of 

correlations (dependence) based on Pearson correlation coefficient (Ref. 53) calculations. An 

example of correlation coefficient values for the burnup range 40 to 60 GWd/MTU is presented 

in Appendix B. 

Correlations between the M/C concentration ratio values for 235U and 239Pu were evaluated 

because these two nuclides are the main contributors to keff bias uncertainty. The uncertainties 

in the calculated 235U and 239Pu concentrations contribute approximately 90% to 95% of the keff

bias uncertainty [see Eq. (8)] for the SFP storage rack and SNF cask models analyzed in this 

report, as demonstrated in Sect. A.3. A negative correlation between the 235U and 239Pu M/C 

concentration ratio values may exist because of biases associated with measured fuel sample 

burnup values or because of depletion code biases. Correlations between the isotopic validation 

data for 235U and 239Pu were determined to be insignificant at the 0.05 significance level 

throughout the burnup range 5 to 60 GWd/MTU based on correlation coefficient calculations. 

Statistically significant correlations were identified for the Pu isotopes; the effects of positive 

239Pu and 241Pu correlations need to be considered for fuel assemblies with high burnup and 

relatively low initial enrichment for the burnup (refer to the fuel initial enrichment and burnup 

values in Table 7.2), such as the nuclide concentrations in the unpoisoned SFP storage rack 

model (see Sect. 5.2). For these assemblies, the uncertainties in the calculated Pu 

concentrations dominate keff bias uncertainty (see Sect. A.3, Figure A.9 ). The contribution of the 

bias uncertainty in the calculated 241Pu concentration to keff bias uncertainty is <1% and ~5% for 

the representative models and for the unpoisoned rack model, respectively. In this analysis, as 

described in Appendix B, to account for additional uncertainty due to neglected positive 

correlations in the validation data for 239Pu and 241Pu, the contribution to keff bias uncertainty of 

the bias uncertainty in the prediction of 241Pu was doubled in the calculation of total keff bias 

uncertainty. For the unpoisoned SFP storage rack model with 40-GWd/MTU assembly average 

burnup, this resulted in a 0.001 ∆keff effect, which is small compared to the keff bias uncertainty 

value of 0.018 (~5%). For the representative SFP and cask analysis models, existing 

correlations are considered to have negligible impact on the calculated keff bias uncertainty 

values because the keff bias uncertainty is dominated by 235U and 239Pu concentration prediction 
29 

uncertainties; all other nuclides have a relatively small (<1.3%) or negligible contributions to keff

bias uncertainty. 

6.1.3 Isotopic Bias and Bias Uncertainty Values 

Isotopic bias and bias uncertainty values for PWR and BWR SNF, along with their 

corresponding burnup range of applicability, are presented in Table 6.1 and Table 6.2, 

respectively. The isotopic bias and bias uncertainty values were determined with 

Eqs. (3) and (5), respectively, where the nuclide concentration values for measured nuclides in 

fuel samples were calculated with SCALE 6.1 and the ENDF/B-VII nuclear data (see Sect. 4). 

The isotopic bias and bias uncertainty values were used as parameters for the distribution 

models in the Monte Carlo uncertainty sampling procedure (see Sect. 6.1.4). 

 

The area of applicability of the isotopic bias and bias uncertainty values is based on fuel 

samples with the enrichment and burnup values as shown in Table 3.2 and Table 3.3 for the 

PWR and BWR fuel samples, respectively. The area of applicability of the isotopic bias and bias 

uncertainty values for fission products, typically measured for mid- and high-burnup samples, is 

extended to low burnup values. This extension of the area of applicability has insignificant 

impact on the accuracy of the calculated keff bias uncertainty values because (1) the relative 

importance of fission products to fuel reactivity for low-burnup assemblies is small 

(see Sect. A.1); and (2) the total contribution to keff bias uncertainty of the bias uncertainties 

associated with the calculated fission product concentrations is very small (e.g., <3%, as 

demonstrated in Sect. A.3) for the analysis models. 

 
30 

Table 6.1 Isotopic bias and bias uncertainty values for PWR SNF compositions 

Burnup 

range 5 < Burnup a ≤ 15 GWd/MTU 15 < Burnup ≤ 40 GWd/MTU 40 < Burnup ≤ 60 GWd/MTU 

Nuclide 

No. of 

samples

Isotopic 

bias

Isotopic bias 

uncertainty b No. of samples 

Isotopic 

bias

Isotopic bias

uncertainty 

No. of 

samples 

Isotopic 

bias

Isotopic bias

uncertainty 235U 11 0.9814 0.0284 69 0.9907 0.0416 20 0.9459 0.1096 

238U 11 0.9990 0.0063 69 1.0017 0.0042 20 1.0020 0.0021 

239Pu 11 0.9906 0.0453 69 0.9587 0.0375 20 0.8984 0.0727 

240Pu 11 1.0155 0.0700 69 0.9801 0.0317 20 0.8981 0.0810 

241Pu 11 1.0648 0.1103 69 1.0108 0.0514 20 0.9833 0.0839 

242Pu 10 1.1029 0.1905 69 1.0647 0.0783 20 1.0636 0.0852 

Burnup 

range 5 < Burnup ≤ 40 GWd/MTU 40 < Burnup ≤ 60 GWd/MTU 

Nuclide 

No. of 

samples 

Isotopic 

bias

Isotopic bias 

uncertainty 

No. of 

samples 

Isotopic 

bias

Isotopic bias 

uncertainty 

234U 43 0.9119 0.1749 20 0.9114 0.1077 

236U 65 1.0249 0.0445 20 0.9862 0.0303 

237Np 25 0.9905 0.2429 19 1.0011 0.1072 

238Pu 65 1.1500 0.0923 20 1.1375 0.2331 

241Am 27 0.9312 0.2077 20 0.9947 0.3224 

243Am 30 0.9998 0.2269 18 0.9216 0.2124 

Burnup 

range 5 < Burnup ≤ 60 GWd/MTU 

Nuclide 

No. of 

samples 

Isotopic 

bias

Isotopic bias 

uncertainty 

95Mo 15 1.0002 0.0745 

99Tc 25 0.9400 0.2030 

101Ru 15 0.9726 0.1152 

103Rh 16 0.9021 0.0894 

109Ag 14 0.5546 0.2694 

133Cs c 7 0.9810 0.0680 

143Nd 44 0.9779 0.0526 

145Nd 44 0.9978 0.0291 

147Sm 32 0.9379 0.0967 

149Sm 28 0.9634 0.0995 

150Sm 32 0.9656 0.0663 

151Sm 32 0.9961 0.0782 

152Sm 32 0.9736 0.0427 

151Eu 21 1.4721 0.7644 

153Eu 27 0.9967 0.0480 

155Gd 27 1.2556 0.3391 

a

Either axial zone burnup or assembly average burnup. 

b

One-sigma uncertainty value. 

c

Uniform distribution within the interval defined by bias ± bias uncertainty (i.e., 0.9130 to 

1.0410) was assumed. 
31 

Table 6.2 Isotopic bias and bias uncertainty values for BWR SNF compositions 

Nuclide 

No. of 

samples 

Isotopic 

bias

Isotopic 

bias 

uncertainty a

 234U 20 0.9648 0.0508 

235U 32 1.0027 0.0726 

236U 32 1.0315 0.0295 

238U 32 1.0046 0.0096 

237Np 20 1.0334 0.1596 

238Pu 32 1.0866 0.1121 

239Pu 32 0.9768 0.0561 

240Pu 32 0.9944 0.0394 

241Pu 32 1.0042 0.0613 

242Pu 32 1.0342 0.0796 

241Am 20 0.8985 0.1244 

243Am 14 0.9506 0.1056 

99Tc b 6 0.8761 0.1013

143Nd 14 1.0012 0.0353 

145Nd 14 1.0102 0.0364 

147Sm 11 1.0494 0.0541 

149Sm 11 1.0607 0.2255 

150Sm 11 1.0355 0.0397 

151Sm 11 1.0687 0.0858 

152Sm 11 1.0389 0.0524 

a

One-sigma uncertainty value. 

b

Uniform distribution within 0.7748 to 0.9774 was assumed for 99Tc.
32 

6.1.4 Nuclide Concentrations for keff Calculations 

In the Monte Carlo uncertainty sampling procedure, a normal distribution model is used to 

determine isotopic bias and bias uncertainty values if more than 10 measured concentration 

values are available for a nuclide. For nuclides with fewer than 10 measured concentration 

values (i.e., 133Cs and 99Tc for PWR and BWR fuel, respectively), it is not appropriate to use a 

normal distribution to represent the uncertainty. Therefore, a uniform distribution model is used 

because this model enables conservative sampling of a larger uncertainty range than a normal 

distribution. 

The calculated nuclide concentrations in each burnup-dependent fuel mixture of the safety 

analysis model are adjusted as shown in Eq. (6) for burnup-dependent isotopic bias and bias 

uncertainty. Random numbers drawn from either the standard normal distribution (i.e., the 

normal distribution with the distribution mean of zero and standard deviation of unity) or from the 

uniform distribution of parameters –1 and +1 are used as shown in Eq. (6) to simulate nuclide 

concentration variations within the range of uncertainty, 

      

   

b bk

nb n n n n k normal

n b b bk

nb n n n uniform

c X σ R N

c

c X σ R

,

,

,

( ), if 10

( ), otherwise , (6)

where 

n = credited nuclide in SNF compositions; 

k = the index of a criticality calculation; 

k

n b c , = concentration of nuclide n in a fuel mixture of burnup b for criticality calculation k

adjusted for isotopic bias and bias uncertainty; 

n b c , = calculated concentration of nuclide n in a fuel mixture of burnup b; 

b Xn = isotopic bias (see Sect. 6.1.3) corresponding to the burnup b of the fuel mixture; 

b σn = isotopic bias uncertainty (see Sect. 6.1.3) corresponding to the burnup b of the 

fuel mixture; k

n normal

R = random number sampled from the standard normal distribution (i.e., the normal 

distribution with the distribution mean of zero and standard deviation of unity). 

Random numbers from the standard normal distribution have the following 

characteristics: 68.3% of the population falls between ±1, 95.5% of the 

population falls between ±2, and 99.7% of the population falls between ±3 

(Ref. 53); k

n uniform

R = random number sampled from the uniform distribution ranging from -1 to 1. 

Sampling from the standard normal distribution was performed by the method described in 

Ref. 59. Note that Eq. (6) may result in negative nuclide concentration values for nuclides with 

very large isotopic bias uncertainty values, as in the case of the isotopic bias uncertainty for 

151Eu (see Table 6.1). In the implementation of the Monte Carlo uncertainty sampling method, 

negative nuclide concentration values resulting from application of Eq. (6) were set to zero. 
33 

The keff values from a statistically significant number (Sect. 6.1.6) of Monte Carlo calculations 

approach a normal distribution with the mean and standard deviation given by Eqs. (7) and (8), 

respectively, 

1

NC

i

eff eff C

i

k kN  , (7)

2

1

( ) ( 1)

C

eff

N

i

k eff eff C

i

σ kk N    , (8)

where 

eff k = sample mean of the keff values from the Monte Carlo calculations; 

NC = number of calculated keff values; 

i

eff k = keff value for criticality calculation i in the series of NC criticality calculations; 

eff σk = sample standard deviation of the keff values from the Monte Carlo 

simulations. 

The series shown in Eq. (7) converges to the keff value obtained by adjusting the calculated 

nuclide concentrations for isotopic bias only. The difference between the reference value, 

keff-REF, (i.e., keff for the calculated nuclide concentrations with no adjustments) and eff k

represents the bias in the application keff resulting from isotopic bias, 

. eff eff REF eff k kk    bias (9)

Bias uncertainty in keff at a 95% probability, 95% confidence level is calculated with Eq. (10), 

1 C

eff

N

eff k k bias uncertainty   σ tf , (10)

where eff σk is determined with Eq. (8) and 1

NC tf is the one-sided tolerance-limit factor for the 

normal distribution corresponding to the number of calculated keff values (Nc), at a 95% 

probability, 95% confidence level. 

The bias and bias uncertainty in keff resulting from biases and bias uncertainties in the 

calculated nuclide concentrations, i.e., βi + ∆ki in Eq. (1), is determined with Eq. (11), 

1

1

( ) C

eff

C

eff

N

eff eff REF k eff eff REF

i i N

k

k k σ tf k k

β k

σ tf

         

  

 if , 

, otherwise.

(11)

6.1.5 Validation of the Assumption for Data Normality 

As indicated in Sect. 6.1.2.2, the PWR M/C concentration ratio values for 235U within the burnup 

interval 15 to 40 GWd/MTU did not pass the normality test. Since 235U is a very important 

nuclide to fuel reactivity, a sensitivity/uncertainty analysis using the actual M/C concentration 
34 

ratio values for 235U in place of the normal distribution model was performed in Sect. A.2 to 

evaluate the impact of assuming a normal distribution. The analysis determined the keff bias 

uncertainty, including all burnup credit nuclides, to be 0.0152, which is slightly less than 0.0168, 

calculated on the basis of a normal distribution with mean and standard deviation of 0.9907 and 

0.0416, respectively (see Table 6.1), for this burnup range. For this case, a normal distribution 

can be used because the keff bias uncertainty value obtained from the normal distribution in 

place of the actual distribution is slightly conservative (i.e., larger uncertainty). 

Other nuclides for which PWR M/C concentration ratio values did not pass a normality test, such 

as 238U, 237Np, 241Am, 147Sm, 150Sm, 151Sm, 151Eu, and 155Gd, have either negligible or relatively 

small individual contributions (<0.5%) to keff bias uncertainty (see Section A.3). The individual 

contributions to keff bias uncertainty of the nuclides with non-normal BWR M/C concentration 

ratio values (i.e., 236U, 143Nd, and 147Sm) were evaluated and found to be negligible. Therefore, 

the impact of the sampling distribution model on the keff bias uncertainty values is negligible for 

these nuclides. Hence, sampling from a normal distribution is adequate. 

6.1.6 Convergence of the Monte Carlo keff Bias Uncertainty Estimate 

The Monte Carlo uncertainty sampling method is computationally intensive because a 

significant number of fuel composition simulations are necessary to ensure that the underlying 

probability distributions are adequately sampled and that the Monte Carlo estimates of eff k [see 

Eq. (7)] and eff σk [see Eq. (8)] have reached convergence. Convergence is considered achieved 

when eff k and eff σk values change insignificantly (e.g., within ±0.0005) with additional 

simulation. 

The impact of the statistical estimates on the accuracy of using 250 simulations was further 

analyzed for the representative PWR SFP rack model and the 40-GWd/MTU assembly average 

burnup using a total of 2500 keff simulations. The sample standard deviation of the keff values 

was 0.0083 based on 2500 simulations, varied from 0.0078 to 0.0086 based on five batches of 

500 simulations, and varied from 0.0078 to 0.0088 based on 10 batches of 250 simulations. 

Based on this study, the sample standard deviation of the keff values based on 250 keff

calculations is determined within ±0.0005. For the Monte Carlo uncertainty sampling method, 

250 criticality calculations are considered sufficient to ensure that the keff bias uncertainty 

estimate is determined with significant accuracy. 

The results for keff bias uncertainty were obtained from the use of either 250 or 500 keff

calculations. The graph in Figure 6.2 shows the keff values from a Monte Carlo simulation for 

500 keff calculations, the sample mean, eff k , the upper limit of the 95%/95% tolerance interval, 

and the bias and bias uncertainty in keff, βi i  k [see Eq. (11)], for the representative PWR SFP 

storage rack model with a 40-GWd/MTU assembly average burnup. The simulated keff values 

passed the Shapiro-Wilk normality test at the 0.05 level. 

 
35 

Figure 6.2 Illustration of the Monte Carlo estimates 

bias and bias uncertainty in keff

at a 95% probability, 95% 

confidence level [i.e., βi+Δki in 

Eq. (11)]

eff REF  k , the keff value obtained 

from the use of nuclide 

concentrations with no 

adjustments 

keff bias [see Eq. (9)]; positive 

bias in keff is typically not 

credited in criticality safety 

analyses 

eff k [see Eq. (7)] 

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0.96

0.97

0.98

0.99

1.00

1.01

1.02

0 100 200 300 400 500

keff

Case No.

keff

upper limit of the 95%/95% tolerance interval

average keff value
36 

6.2 DIRECT-DIFFERENCE METHOD 

The bias and bias uncertainty in criticality calculations resulting from the bias and bias 

uncertainty in the computed nuclide concentrations may be assessed by a method that 

compares keff values obtained with calculated nuclide concentrations, c

eff k , to keff values 

obtained with measured nuclide concentrations, m

eff k . The difference in the values, 

  , c m

eff eff eff kkk (12)

is a direct measure of the keff bias associated with the calculated SNF concentrations. Given a 

sufficient set of measurements for fuel compositions that are representative of the application, 

multiple keff calculations can be performed to generate a distribution of eff k values that can 

then be statistically evaluated to determine average keff bias and bias uncertainty associated 

with the calculated nuclide concentrations. This method is sometimes referred to as the “direct 

difference” uncertainty analysis method. The method has the advantage of not requiring an 

evaluation of uncertainties associated with individual nuclide concentrations. Nuclide 

concentration uncertainties are propagated directly to the keff value, without a requirement to 

quantify individual nuclide uncertainties, trends, or correlations between different nuclides (i.e., 

covariance). The direct-difference approach used in this report is similar to that described in 

Ref. 4 except for the use of surrogate (i.e., substitute) data in place of missing measurement 

data and decay-time corrections for measurement data. 

The experimental data evaluated for this analysis included the 100 PWR SNF samples listed in 

Table 6.3. Depletion calculations were performed with the best available information on fuel 

design and reactor operating conditions for the SNF samples to obtain the calculated nuclide 

concentrations. An immediate challenge for the direct-difference method is that measurements 

are generally available for only a subset of the 28 actinide and fission product nuclides used in 

the burnup credit analysis. Measurement data for major uranium and plutonium nuclides exist 

for each measured fuel sample. However, measurement data for additional burnup credit 

nuclides vary depending on the experimental programs. Surrogate data were developed for 

nuclides without measurements to avoid introducing potential bias in the  eff k results caused by 

using samples with different credited nuclides (corresponding to the measured nuclides) and to 

provide a consistent basis for comparing the results for different SNF samples. These surrogate 

data are presented in Appendix C, Table C.1. 

The surrogate data were based on measurement results from other samples for which nuclide 

measurements were available. Calculated nuclide concentrations adjusted for the mean 

measured-to-calculated concentration ratio obtained from other similar samples (see Table 6.1) 

were used as surrogate data for nuclides without measurements. For example, measurements 

of 103Rh were available for only 16 of the evaluated samples. Based on these samples, the 

calculation bias was determined to be 0.9021 (see Table 6.1); that is, 103Rh is overpredicted, on 

average, by about 10%. Surrogate data for samples without 103Rh measurements were 

therefore derived by multiplying the calculated 103Rh concentration by the bias, effectively 

reducing the calculated content by about 10% and correcting for known computational bias. This 

procedure ensures that the bias attributed to each nuclide is accounted for in the keff

calculations, but it does not include the uncertainties (variance) associated with the surrogate 

data (i.e., the uncertainty in the nuclide bias). An analysis of uncertainties in Sect. A.3 of this 

report demonstrated that keff bias uncertainty is dominated by the major uranium and plutonium 
37 

isotopes for which measurement data are available in all samples considered. Hence, the 

approach of using average bias values to derive surrogate measurement data is justified. 

The impact on m

eff k of applying the calculated fission product bias values to lower burnup values, 

particularly for nuclides with relatively few available measurements, are further analyzed with 

sensitivity coefficients that represent the relative change in keff caused by a change in the 

nuclide concentration [see Appendix A, Eq. (A-1)]. Additional uncertainties in the nuclide M/C 

concentration ratio values may be introduced by extrapolating the results beyond the range of 

the measurement data. For example, measurements for the fission product nuclides 95Mo, 

101Ru, 103Rh, and 133Cs were not available in samples with a burnup less than approximately 30 

GWd/MTU, and 109Ag measurements were not available below approximately 45 GWd/MTU. 

The error in the calculated nuclide concentrations attributed to nuclear cross section data has 

been evaluated previously as a function of burnup of the fuel (Ref. 60). The results in Ref. 60 

show that the relative error in the calculated nuclide contents increases as a function of burnup 

for the fission products listed above. Therefore, the bias (i.e., over prediction or under prediction 

by a code) derived using measurements for high burnup fuels are expected to be bounding for 

applications at lower burnup values. The maximum standard error in the keff bias caused by 

extrapolation of data, estimated with sensitivity coefficients [Eq. (A-1)] for these five fission 

products without extensive measurements for low burnup fuels, is determined to be less than 

0.04%. 

The relative error in the average M/C concentration ratio value is represented by the confidence 

interval of the mean, calculated using the standard deviation of the M/C concentration ratio 

distributions and the number of samples (obtained from Table 6.1). The impact on m

eff k caused 

by uncertainties in the average M/C concentration ratio values was estimated using sensitivity 

coefficients [Eq. (A-1)]. The maximum standard error in the keff values for the representative 

SFP storage rack model was found to be approximately 0.06%. This value is derived assuming 

surrogate data are applied for all 16 fission product nuclides and the actinide nuclides 234U, 236U, 

237Np, 238Pu, 241Am, and 243Am, considered in the burnup credit analysis. Therefore, it is 

concluded that the potential bias associated with the use of surrogate data in this analysis is 

minor. 

Another consideration in the application of measured data is the decay time of the 

measurements. Several burnup credit nuclides have time-dependent concentrations due to 

decay and in-growth from decay precursors. Burnup credit nuclides exhibiting the largest 

changes include 241Pu, 241Am, 147Sm, 151Eu, and 155Gd (see Sect. 3.1). Note that the 

measurement laboratories commonly use the decay schemes and nuclide half-lives to 

analytically adjust the measurement results to a common reference date for convenience. The 

measurement nuclide concentrations must correspond to the decay time considered for the 

application model to ensure that representative keff bias uncertainty values are obtained. For 

example, an application model involving SNF with a cooling time of 3 days will include relatively 

low concentrations of 241Am, 155Gd, and 151Eu, as these nuclides are generated predominantly 

by the decay of parent nuclides after discharge (i.e., 241Pu, 155Eu, and 151Sm, respectively). 

Therefore, these nuclides will not contribute significantly to the keff bias uncertainty for this 

model. However, SNF compositions measured several years after discharge will include larger 

concentrations of these nuclides than would be present at 3 days. It is important to consider the 

effect of decay time between the application model and measurement data to ensure that 

representative keff bias uncertainty values are obtained (see Sect. A.4). 
38 

Measured concentrations for nuclides that vary with the decay time must be adjusted according 

to analytical decay equations, to account for differences between the time of measurement and 

a reference time corresponding to the application. Nuclides that vary with time according to their 

half-lives, such as 151Sm, can be adjusted with only their decay constant. The adjustment of 

nuclides that are produced by the decay of other nuclides, such as 151Eu, must account for both 

decay of the nuclide and decay of precursor nuclides; in this case, the production of 151Eu from 

the decay of 151Sm. For a general case of radionuclide B with a decay precursor A, e.g., A → B 

→ C, the content of nuclide B at the measurement time t is: 

  0 0     

A B B A λ t λ t λ t

BA B

B A

λ N N e e Ne

λ λ , (13)

where NB is the content of nuclide B at the measurement time t, 0 NA is the content of precursor 

nuclide A in the discharged fuel composition (i.e., zero time), 0 NB is the content of nuclide B in 

the discharged fuel composition (i.e., at zero time), and λA and λB are the decay constants for 

nuclides A and B, respectively. In experiments where measurements of a decay precursor are 

not reported, precluding the adjustment of the measured nuclide concentrations, the 

calculations should consider the effect on the derived bias and uncertainties of differences 

between the nuclide concentrations at the time of measurement and the application. 

As an illustrative example of the approach, the SNF samples listed in Table 6.3 were applied to 

an uncertainty analysis for the unpoisoned SFP storage rack model evaluated for a cooling time 

of 3 days after the fuel was discharged from the reactor. The nuclides 241Am, 155Gd, and 151Eu 

were excluded from the keff calculations (measured and calculated nuclide contents) because of 

their low concentrations at the time of interest. Other nuclides are either stable or exhibit 

relatively small changes in their concentration between the time of measurement and the time of 

application (see Sect. 3.1) and therefore do not require corrections. 

The keff values for the application model using the measured nuclide concentrations and the 

calculated nuclide concentrations as well as the  eff k values are listed in Table 6.3. Statistical 

analysis of the  eff k values for all samples with a burnup less than 45 GWd/MTU was 

performed with a linear regression model to calculate the fit and the one-sided 95% upper 

prediction limit (tolerance limit). The analysis was performed with the linear regression model in 

the OriginPro 8.1 software (copyright OriginLab Corporation). Statistical analysis of the data 

yields a small burnup-dependent bias (~ 0.002) in keff and a one-sided tolerance limit 

(uncertainty) of 0.013 at a 95% probability, 95% confidence level, when burnup is used as the 

trending parameter (Figure 6.3). The bias and bias uncertainty values estimated from the directdifference calculations for this single application model are comparable with, but smaller than, 

the values obtained by the Monte Carlo uncertainty sampling method presented in Sect. 7 

(Table 7.2). This comparison provides some limited evidence that the two different methods can 

produce similar results, thereby providing limited reassurance in the Monte Carlo approach for 

uncertainty propagation. However, further work with the direct-difference method, including 

additional comparisons and fully addressing the considerations described below, is needed prior 

to drawing firm conclusions. 
39 

Table 6.3 Unpoisoned PWR SFP storage rack ∆keff obtained with measured 

and calculated nuclide concentrations 

Reactor Assembly Sample ID 

Enrichment 

 (wt % 235U) 

Burnup 

(GWd/MTU) c

eff k a meff k b  eff k c

Calvert Cliffs BT03 NBD107-GG 2.453 37.27 0.8027 0.8178 -0.0150 

Calvert Cliffs BT03 NBD107-MM 2.453 31.40 0.8495 0.8661 -0.0166 

Calvert Cliffs BT03 NBD107-Q 2.453 46.46 0.7574 0.7629 -0.0056 

Calvert Cliffs D047 MKP109-CC 3.038 37.12 0.9207 0.9174 0.0033 

Calvert Cliffs D047 MKP109-LL 3.038 27.35 1.0047 1.0037 0.0010 

Calvert Cliffs D047 MKP109-P 3.038 44.34 0.8782 0.8647 0.0135 

Calvert Cliffs D101 MLA098-BB 2.72 26.62 0.9719 0.9700 0.0019 

Calvert Cliffs D101 MLA098-JJ 2.72 18.68 1.0477 1.0469 0.0008 

Calvert Cliffs D101 MLA098-P 2.72 33.17 0.9227 0.9033 0.0195 

H.B. Robinson B05 N9BN 2.561 23.81 0.9632 0.9638 -0.0006 

H.B. Robinson B05 N9BS 2.561 16.02 1.0465 1.0470 -0.0005 

H.B. Robinson B05 N9CD 2.561 31.66 0.9053 0.8994 0.0059 

H.B. Robinson B05 N9CJ 2.561 28.47 0.9333 0.9569 -0.0236 

Obrigheim BE124 E3P1 3.0 20.18 1.0612 1.0608 0.0004 

Obrigheim BE124 E3P2 3.0 29.35 0.9782 0.9809 -0.0027 

Obrigheim BE124 E3P3 3.0 36.26 0.9341 0.9276 0.0065 

Obrigheim BE124 E3P4 3.0 30.92 0.9794 0.9736 0.0058 

Obrigheim BE124 E3P5 3.0 22.86 1.0451 1.0518 -0.0067 

Obrigheim BE124 G7P1 3.0 17.13 1.1005 1.1050 -0.0045 

Obrigheim BE124 G7P2 3.0 25.83 1.0233 1.0291 -0.0058 

Obrigheim BE124 G7P3 3.0 31.32 0.9872 0.9724 0.0148 

Obrigheim BE124 G7P4 3.0 27.71 1.0193 1.0251 -0.0058 

Obrigheim BE124 G7P5 3.0 25.81 1.0341 1.0294 0.0047 

Obrigheim BE168 - 3.13 29.35 1.0032 1.0124 -0.0092 

Obrigheim BE170 - 3.13 27.01 1.0231 1.0301 -0.0070 

Obrigheim BE171 - 3.13 28.74 1.0087 1.0164 -0.0077 

Obrigheim BE172 - 3.13 27.89 1.0147 1.0160 -0.0013 

Obrigheim BE176 - 3.13 28.78 1.0076 1.0140 -0.0064 

Takahama NT3G23 SF95-2 4.11 24.46 1.1705 1.1596 0.0109 

Takahama NT3G23 SF95-3 4.11 35.68 1.0987 1.0853 0.0134 

Takahama NT3G23 SF95-4 4.11 37.01 1.0824 1.0682 0.0142 

Takahama NT3G23 SF95-5 4.11 30.45 1.1197 1.1087 0.0110 

Takahama NT3G23 SF96-2 2.63 17.43 1.1259 1.1205 0.0054 

Takahama NT3G23 SF96-3 2.63 29.69 1.0301 1.0391 -0.0090 

Takahama NT3G23 SF96-4 2.63 30.41 1.0147 1.0239 -0.0092 

Takahama NT3G23 SF96-5 2.63 25.42 1.0478 1.0515 -0.0037 

Takahama NT3G24 SF97-2 4.11 30.48 1.1161 1.1105 0.0056 

Takahama NT3G24 SF97-3 4.11 42.10 1.0369 1.0301 0.0068 

Takahama NT3G24 SF97-4 4.11 47.07 0.9948 0.9876 0.0072 

Takahama NT3G24 SF97-5 4.11 47.26 0.9839 0.9825 0.0014 

Takahama NT3G24 SF97-6 4.11 40.85 1.0280 1.0170 0.0110 

TMI-1 NJ05YU A1B 4.013 44.80 0.9878 0.9676 0.0202 

TMI-1 NJ05YU A2 4.013 50.60 0.9577 0.9294 0.0283 

TMI-1 NJ05YU B1B 4.013 54.50 0.9353 0.9199 0.0154 

TMI-1 NJ05YU B2 4.013 50.10 0.9644 0.9295 0.0349 

TMI-1 NJ05YU B3J 4.013 53.00 0.9375 0.9149 0.0226 

TMI-1 NJ05YU C1 4.013 50.20 0.9729 0.9430 0.0299 

TMI-1 NJ05YU C2B 4.013 52.60 0.9497 0.9160 0.0337 

TMI-1 NJ05YU C3 4.013 51.30 0.9599 0.9432 0.0167 

TMI-1 NJ05YU D1A2 4.013 55.70 0.9363 0.9446 -0.0083 

TMI-1 NJ05YU D1A4 4.013 50.50 0.9695 0.9551 0.0144 

TMI-1 NJ05YU D2 4.013 44.80 1.0109 0.9639 0.0470 

TMI-1 NJ070G O12S4 4.657 23.54 1.1975 1.1906 0.0069 

TMI-1 NJ070G O12S5 4.657 26.26 1.1824 1.1752 0.0072 

TMI-1 NJ070G O12S6 4.657 24.09 1.1997 1.1996 0.0001 

TMI-1 NJ070G O13S7 4.657 23.21 1.1998 1.1930 0.0068 

TMI-1 NJ070G O13S8 4.657 26.10 1.1837 1.1748 0.0089 

TMI-1 NJ070G O1S1 4.657 25.53 1.1817 1.1729 0.0088 

TMI-1 NJ070G O1S2 4.657 29.92 1.1554 1.1359 0.0195 

TMI-1 NJ070G O1S3 4.657 26.84 1.1798 1.1725 0.0073 
40 

Table 6.3 Unpoisoned PWR SFP storage rack keff obtained with measured 

and calculated nuclide concentrations (continued) 

Reactor Assembly Sample ID 

Enrichment 

 (wt % 235U) 

Burnup 

(GWd/MTU) c

eff k a meff k b  eff k c

Trino Vercellese 032 E11P1 3.13 7.24 1.2240 1.2204 0.0036 

Trino Vercellese 032 E11P4 3.13 15.38 1.1616 1.1581 0.0035 

Trino Vercellese 032 E11P7 3.13 15.90 1.1560 1.1492 0.0068 

Trino Vercellese 032 E11P9 3.13 11.53 1.1875 1.1871 0.0004 

Trino Vercellese 032 H9P4 3.13 16.56 1.1468 1.1478 -0.0010 

Trino Vercellese 032 H9P7 3.13 17.45 1.1393 1.1420 -0.0027 

Trino Vercellese 032 H9P9 3.13 12.37 1.1766 1.1744 0.0022 

Trino Vercellese 049 J8P1 2.719 8.71 1.1696 1.1654 0.0042 

Trino Vercellese 049 J8P4 2.719 14.77 1.1205 1.1094 0.0111 

Trino Vercellese 049 J8P7 2.719 15.49 1.1147 1.1115 0.0032 

Trino Vercellese 049 J8P9 2.719 11.13 1.1465 1.1427 0.0038 

Trino Vercellese 049 L5P1 2.719 14.16 1.1799 1.1826 -0.0027 

Trino Vercellese 049 L5P4 2.719 14.49 1.1307 1.1306 0.0001 

Trino Vercellese 049 L5P9 2.719 10.18 1.1588 1.1559 0.0029 

Trino Vercellese 104 M11P7 3.897 12.04 1.2452 1.2452 0.0000 

Trino Vercellese 069 E11P1 3.13 12.86 1.1816 1.1785 0.0031 

Trino Vercellese 069 E11P2 3.13 20.60 1.1295 1.1215 0.0080 

Trino Vercellese 069 E11P4 3.13 23.72 1.1087 1.0938 0.0149 

Trino Vercellese 069 E11P5 3.13 24.52 1.1024 1.0914 0.0110 

Trino Vercellese 069 E11P7 3.13 24.30 1.1014 1.0947 0.0067 

Trino Vercellese 069 E11P8 3.13 23.41 1.1062 1.0979 0.0083 

Trino Vercellese 069 E11P9 3.13 19.25 1.1325 1.1298 0.0027 

Trino Vercellese 069 E5P4 3.13 23.87 1.1074 1.1004 0.0070 

Trino Vercellese 069 E5P7 3.13 24.68 1.0997 1.0914 0.0083 

Trino Vercellese 069 E5P9 3.13 19.21 1.1325 1.1249 0.0076 

Trino Vercellese 069 J9P4 3.13 24.85 1.0948 1.0845 0.0103 

Trino Vercellese 069 J9P7 3.13 25.26 1.0884 1.0805 0.0079 

Trino Vercellese 069 L11P4 3.13 23.93 1.1069 1.1011 0.0058 

Trino Vercellese 069 L11P7 3.13 24.36 1.1008 1.0926 0.0082 

Trino Vercellese 069 L5P4 3.13 24.33 1.1045 1.1031 0.0014 

Trino Vercellese 069 L5P7 3.13 24.31 1.1008 1.1008 0.0000 

Turkey Point D01 G10 2.556 30.51 0.9309 0.9283 0.0026 

Turkey Point D01 G9 2.556 30.72 0.9294 0.9321 -0.0027 

Turkey Point D01 H9 2.556 31.56 0.9215 0.9303 -0.0089 

Turkey Point D04 G10 2.556 31.31 0.9247 0.9254 -0.0007 

Turkey Point D04 G9 2.556 31.26 0.9254 0.9304 -0.0050 

GKN-II 419 M11 3.8 54.00 0.9244 0.9076 0.0168 

Gösgen 1240 GU1 3.5 60.70 0.8269 0.8098 0.0171 

Gösgen 1701 GU3 4.1 53.20 0.9385 0.9533 -0.0148 

Gösgen 1701 GU4 4.1 31.10 1.0894 1.0813 0.0081 

a

keff value obtained with calculated nuclide concentrations. 

b

keff value obtained with measured nuclide concentrations. c

The difference between the keff values obtained with calculated and measured nuclide 

concentrations. 

 
41 

Figure 6.3 Linear regression analysis of the ∆keff results illustrating the bias and the 

margin for uncertainty represented by the one-sided tolerance limit at a 

95% probability, 95% confidence level [95% tolerance limit (TL)] for the 

unpoisoned SFP storage rack 

 
42 

The following points summarize the main considerations when using the direct-difference 

analysis approach: 

1. The analysis should account for the effect of nuclides not measured in samples either 

through the use of appropriate surrogate data or some other means to demonstrate that 

potential bias in code calculations for nuclides without extensive measurements has 

been taken into account. 

2. Surrogate data for nuclides with very few measurements may require additional margins 

of uncertainty. In cases where extrapolation beyond the range of the measured data is 

required, the surrogate data should include additional uncertainty associated with the 

extrapolation to the criticality safety application. The use of sensitivity and uncertainty 

methods in the analysis of nuclide uncertainty trends provides a means to technically 

support extrapolating data to the range of the application. 

3. Statistical analysis of the ∆keff distribution should consider the similarity between the 

nuclide concentrations of the measured fuel samples and the nuclide concentration of 

the application model. For example, uncertainties derived from measured fuel samples 

with a high burnup (e.g., low keff) may not be appropriate for an application model using 

fuel assemblies with low burnup (e.g., keff = 0.99). Applicability may be established with 

an appropriately determined trending parameter (e.g., fuel burnup or burnup divided by 

enrichment). 

4. Measured and calculated nuclide concentrations used in the application model should 

have a consistent decay time. The relative worth of the different nuclides changes as a 

function of the decay time and must be accounted for to provide an accurate estimate of 

the keff bias and bias uncertainty. Adjusting measured nuclide concentrations to the time 

of application may be performed accurately through use of the nuclide decay half-lives. 

For nuclides with decay precursors, the production from decay parents must be 

evaluated or, in cases where a decay precursor was not measured, accounted for with 

conservative methods. 
43

7. BIAS AND BIAS UNCERTAINTY IN keff RESULTS 

This section presents reference values of estimated bias and bias uncertainty in keff associated 

with bias and bias uncertainty in the calculated nuclide concentrations for representative safety 

analysis models (see Sect. 5). The values presented are specific to SCALE 6.1 and the 

ENDF/B-VII nuclear data (see Sect. 4). The results were obtained with the Monte Carlo 

uncertainty sampling method described in Sect. 6.1 and the PWR and BWR isotopic bias and 

bias uncertainty values presented in Table 6.1 and Table 6.2, respectively. The keff bias [i.e., the 

term βi in Eq. (1)] and keff bias uncertainty [i.e., the term ∆ki in Eq. (1)] were determined as a 

function of assembly average burnup. The keff bias uncertainty values correspond to a 95% 

probability, 95% confidence level. Depletion validation results for the representative PWR and 

BWR safety analysis models are presented in Sects. 7.1 and 7.2, respectively. Results based 

on parametric variations for the representative PWR SFP storage rack model are presented in 

Sect. 7.3. 

7.1 PWR SNF ANALYSIS MODELS 

Table 7.1 presents the keff bias and keff bias uncertainty values as a function of assembly 

average burnup for the representative PWR SFP storage rack model (see Sect. 5.2) using 

either actinide or actinide and fission product nuclides (refer to Table 3.1 for the list of burnup 

credit nuclides). The keff bias uncertainty values are illustrated as a function of assembly 

average burnup in the bar graph shown in Figure 7.1. For the actinide and fission product 

compositions, the assembly average burnup corresponding to a maximum fuel initial enrichment 

of 5 wt % 235U was 44.33 GWd/MTU; hence, the graph shows keff bias uncertainty values for 

actinide and fission product compositions up to an assembly average burnup of 

44.33 GWd/MTU. Table 7.2 presents the keff bias and keff bias uncertainty values for the 

unpoisoned PWR storage rack model (see Sect. 5.2) using actinide and fission product nuclide 

compositions. The unpoisoned rack model was used to determine keff bias and bias uncertainty 

values for assembly average burnup values greater than 44.33 GWd/MTU because this model 

is more reactive than the representative rack model (e.g., the 235U-to-239Pu atom density ratio 

values for the reference and the unpoisoned rack models with a 40-GWd/MTU average 

assembly burnup are 2.37 and 0.90, respectively). The PWR SFP storage rack models include 

an 18-zone axial burnup profile. Nuclide compositions for PWR SFP storage rack calculations 

were determined for a 3-day cooling time and for selected assembly average burnup values 

within the burnup range 5 to 60 GWd/MTU so that the keff value is 0.99. 

Table 7.3 presents the keff bias and keff bias uncertainty values as a function of assembly 

average burnup for the representative PWR SNF cask model (see Sect. 5.3) using either 

actinide or actinide and fission product nuclide compositions. The keff bias uncertainty values are 

illustrated as a function of assembly average burnup in the bar graph shown in Figure 7.2. The 

cask models include an 18-zone axial burnup profile. Nuclide compositions for cask calculations 

were determined for a 5-year cooling time and for selected assembly average burnup values 

within the burnup range 5 to 60 GWd/MTU so that the keff value is 0.94. For the actinide and 

fission product compositions, the assembly average burnup corresponding to a maximum fuel 

initial enrichment of 5 wt % 235U was 45 GWd/MTU; hence, the graph shows keff bias uncertainty 

values for actinide and fission product compositions up to an assembly average burnup of 

45 GWd/MTU. 
44

The relative importance of the burnup credit nuclides to fuel reactivity is similar for the 

representative SFP storage rack and SNF cask models, as shown in Figures A.1 and A.2, 

respectively. The neutronic similarity of the two different nuclear systems leads to similar results 

for keff bias and keff bias uncertainty, as shown in Table 7.1 and Table 7.2. Based on the 

demonstration of neutronic similarity of the two systems, the keff bias and bias uncertainty values 

obtained for the unpoisoned rack model (see Table 7.2) are aplicable to cask configurations 

using assembly average burnup values within the range 45 to 60 GWd/MTU. 

Table 7.1 keff bias and keff bias uncertainty for the representative PWR SFP 

storage rack model 

 Actinide nuclides Actinide and fission product nuclides 

Burnup a

(GWd/MTU) 

Initial wt % 

235U b keff bias c

 

keff bias 

uncertainty d

Initial wt % 

235U b keff bias c

 

keff bias 

uncertainty d

5 2.08 0.0043 0.0154 2.28 0.0038 0.0148 

10 2.23 0.0040 0.0152 2.49 0.0034 0.0150 

18 2.63 0.0050 0.0150 3.12 0.0031 0.0145 

25 2.93 0.0050 0.0145 3.55 0.0034 0.0154 

30 3.21 0.0052 0.0145 4.00 0.0028 0.0148 

40 3.68 0.0064 0.0167 4.70 0.0034 0.0168 

44.33 _ _ _ 5.00 0.0045 0.0189 

50 4.14 0.0083 0.0194 _ _ _

60 4.65 0.0109 0.0251 _ _ _

a

Assembly average burnup. 

b

Fuel initial enrichment value is so that the keff value for the assembly average burnup is 

0.99. 

c

Positive keff bias values are typically not credited in criticality safety analyses. d

Uncertainty in keff at a 95% probability, 95% confidence level. 

Figure 7.1 keff bias uncertainty for the representative PWR SFP storage rack model. 

Uncertainty in keff is at a 95% probability, 95% confidence level. 

0.0154

0.0152

0.0150

0.0145

0.0145

0.0167

0.0194

0.0251

0.0148

0.0150

0.0145

0.0154

0.0148

0.0168 0.0189

0.000

0.005

0.010

0.015

0.020

0.025

0.030

keff Bias Uncertainty

Burnup (GWd/MTU)

12 actinide nuclides

28 actinide and fission

product nuclides
45

Table 7.2 keff bias and keff bias uncertainty for the unpoisoned PWR SFP storage rack 

model using burnup credit actinide and fission product nuclides 

Burnup a

(GWd/MTU) Initial wt % 235U b keff bias c keff bias uncertainty d

25 1.95 0.0046 0.0190 

40 2.69 0.0034 0.0188 

50 3.14 0.0061 0.0219 

60 3.62 0.0105 0.0300 

a

Assembly average burnup. 

b

Fuel initial enrichment value is so that the keff value for the assembly average burnup is 

0.99. 

c

Positive keff bias values are typically not credited in criticality safety analyses. d

Uncertainty in keff at a 95% probability, 95% confidence level. 

Table 7.3 keff bias and keff bias uncertainty for the representative PWR SNF cask model 

 Actinide nuclides Actinide and fission product nuclides 

Burnup a

(GWd/MTU) 

Initial wt % 

235U b keff bias c

 

keff bias 

uncertainty d

Initial wt % 

235U b keff bias c

keff bias 

uncertainty d

5 1.90 0.0042 0.0145 2.12 0.0040 0.0150 

10 2.05 0.0040 0.0143 2.33 0.0039 0.0148 

18 2.48 0.0036 0.0150 3.00 0.0037 0.0157 

25 2.78 0.0047 0.0150 3.44 0.0023 0.0154 

30 3.10 0.0052 0.0154 3.92 0.0031 0.0161 

40 3.58 0.0059 0.0170 4.64 0.0035 0.0163 

45 _ _ _ 5.00 0.0050 0.0205 

50 4.05 0.0073 0.0192 _ _ _

60 4.55 0.0112 0.0260 _ _ _

a

Assembly average burnup. 

b

Fuel initial enrichment value is so that the keff value for the assembly average burnup is 

0.94. 

c

Positive keff bias values are typically not credited in criticality safety analyses. d

Uncertainty in keff at a 95% probability, 95% confidence level. 
46

Figure 7.2 keff bias uncertainty for the PWR SNF cask model. Uncertainty in keff is at a 

95% probability, 95% confidence level. 

The calculation results for SCALE 6.1 and the ENDF/B-VII nuclear data indicate: 

1. The calculated nuclide concentrations result in a slight overprediction of keff. The positive 

bias is significantly smaller than the uncertainty in the bias. 

2. The keff bias uncertainty values for actinide compositions and the keff bias uncertainty 

values for actinide and fission product compositions are similar. 

3. The keff bias and keff bias uncertainty values are fairly constant for the burnup range 5 to 

30 GWd/MTU and gradually increase with increasing assembly average burnup values 

above 30 GWd/MTU. 

4. For the representative SFP storage rack model, the values of estimated bias and bias 

uncertainty in keff due to biases and bias uncertainties in the calculated concentrations 

for the 28 burnup credit nuclides are approximately 0.016 and 0.019 for the assembly 

average burnup range 5 to 40 GWd/MTU and for a 44.33-GWd/MTU assembly average 

burnup, respectively. 

5. For the representative PWR SNF cask model, the values of estimated bias and bias 

uncertainty in keff due to biases and bias uncertainties in the calculated concentrations 

for the 28 burnup credit nuclides are approximately 0.016 and 0.021 for the assembly 

average burnup range 5 to 40 GWd/MTU and for a 45-GWd/MTU assembly average 

burnup, respectively. 

6. For the unpoisoned PWR SFP storage rack model, the values of estimated bias and bias 

uncertainty in keff due to biases and bias uncertainties in the calculated concentrations 

for the 28 burnup credit nuclides are approximately 0.019, 0.022, and 0.030 for the 

assembly average burnup range 25 to 40 GWd/MTU, for a 50-GWd/MTU assembly 

average burnup, and for a 60-GWd/MTU average assembly burnup, respectively. Based 

on demonstrated neutronic similarity between the fuel cask and storage rack models, 

these calculation results are also applicable to the cask configurations that use assembly 

average burnup values up to 60 GWd/MTU. 

0.0145

0.0143

0.0150

0.0150

0.0154

0.0170

0.0192

0.0260

0.0150

0.0148

0.0157

0.0154

0.0161

0.0163

0.0205

‐0.003

0.002

0.007

0.012

0.017

0.022

0.027

5 10 18 25 30 40 45 50 60

keff Bias Uncertainty

Burnup (GWd/MTU)

12 actinide nuclides

28 actinide and fission

product nuclides
47

7.2 BWR SFP STORAGE RACK MODEL 

The keff bias and keff bias uncertainty values for the BWR SFP storage rack model 

(see Sect. 5.6) are presented in Table 7.4. The nuclide concentrations in the model correspond 

to the fuel assembly at peak reactivity achieved at a burnup value of approximately 

11 GWd/MTU. The calculated keff bias values for the actinide-only composition and for the 

actinide and fission product nuclide composition were 0.001 and 0.002, respectively. Typically, 

positive keff bias values are not credited in criticality safety analyses. The calculated keff bias 

uncertainty values were 0.029 and 0.032 for the actinide-only composition and for the actinide 

and fission product nuclide composition, respectively. 

The BWR keff bias uncertainty is significantly larger than the keff bias uncertainty for PWR burnup 

credit applications and similar assembly average burnup because of the large variance of the 

M/C concentration ratio values in the small sample set of available BWR RCA data 

(see Sect. 3.3). For example, the bias uncertainty values associated with the calculated 235U 

and 239Pu concentrations are 0.0726 and 0.0561, respectively, based on the BWR fuel samples, 

and 0.0284 and 0.0453, respectively, based on the PWR fuel samples with burnup from 5 to 15 

GWd/MTU. The large bias uncertainty values for the calculated 235U and 239Pu concentrations 

for BWR SNF are primarily the result of approximate moderator density values used in the 

depletion calculations for measured fuel samples with unavailable void fraction data. 

Table 7.4 keff bias and keff bias uncertainty for the BWR SFP storage rack model 

Fuel compositions a keff bias b

keff bias 

uncertainty c

Actinide nuclides 0.0010 0.0287 

Actinide and fission product nuclides 0.0017 0.0316 

a

Nuclide concentrations correspond to fuel peak reactivity achieved during irradiation. 

b

Positive keff bias is typically not credited in criticality safety analyses. c

Uncertainty in keff at a 95% probability, 95% confidence level. 

7.3 PARAMETRIC ANALYSIS 

An analysis was performed to determine the sensitivity of bias and bias uncertainty in keff to 

parameters important to PWR SFP criticality safety analyses, including fuel assembly design, 

fuel irradiation conditions, rack design, soluble boron concentration, fuel cooling time, axial 

representation of fuel burnup in the safety analysis model, and nuclear data. The reference case 

for the parametric analysis is the representative PWR SFP storage rack model loaded with the 

W 17×17 OFA described in Sect. 5.2. The parametric variations considered in the analysis are 

summarized in Table 7.5. Note that the reference case was developed with reactor operating 

parameters that increase fuel discharge reactivity (e.g., higher fuel and moderator temperatures, 

lower moderator density, and burnable absorber exposure) as described in Sect. 5.1. The SNF 

compositions used in the analysis include the burnup credit nuclides presented in Table 3.1. 

The sensitivity of bias and bias uncertainty in keff was evaluated as a function of assembly 

average burnup for the burnup values 10, 25, and 40 GWd/MTU. 

For the soluble boron concentration cases, the reference case was modified to include the 

soluble boron concentration values shown in the table. The 1000 ppm soluble concentration 

case resulted in keff values much lower than 0.99 (i.e., 0.8425, 0.8617, and 0.8744 for assembly 
48

average burnup values of 10, 25, and 40 GWd/MTU, respectively); the other soluble boron 

concentration variations resulted in a keff value of 0.94. For the other parametric variation cases, 

new nuclide concentrations were determined by STARBUCS (see Sect. 4) to yield a keff value of 

0.99 for the burnup values of 10, 25, and 40 GWd/MTU. For the case using the Babcock and 

Wilcox (B&W) 15×15 fuel assembly in place of the W 17×17 assembly, conservative depletion 

parameters with respect to criticality, which are documented in Ref. 61, were used to develop 

ORGEN-ARP libraries for STARBUCS. 

The calculated values for keff bias and keff bias uncertainty for the reference case and for the 

parametric variations considered are presented in Table 7.6 as a function of assembly average 

burnup. The keff bias uncertainty values are illustrated in the bar graphs shown in Figure 7.3 (a), 

(b), and (c) for the assembly average burnup values of 10, 25, and 40 GWd/MTU, respectively. 

Table 7.5 Model parameters addressed in the sensitivity analysis 

Model parameters Reference case Parameter varied a

Depletion condition WABA rods No WABA rods 

Assembly type W 17×17 OFA B&W 15×15

Burnup axial 

representation 18-zone axial profile Uniform 

Cooling time 3 days 

5 years 

20 years 

40 years 

10B areal density of 

the Boral panels 0.020 g/cm2 

0.022 g/cm2 (10% increase from the reference value) 

0.018 g/cm2 (10% decrease from the reference value) 

0 g/cm2 

Pitch size of rack cell 9.110 in. (23.1394 cm) Reference value + 0.5 in. (1.27 cm) 

Soluble boron 

concentration in pool 

water 

0 ppm 

1000 ppm (10, 25, and 40 GWd/MTU assembly 

burnup) 

Soluble boron concentrations yielding a target keff

value of 0.94 (303, 348, and 393 ppm for assembly 

average burnup values of 10, 25, and 40 GWd/MTU, 

respectively) 

Cross-section data ENDF/B-VII, 238 

energy groups ENDF/B-V, 44 energy groups 

a

An individual calculation was performed for each parameter. 

All the evaluated cases using the ENDF/B-VII nuclear data produced similar positive keff bias 

values. The average keff bias was approximately 0.0035, and the associated standard deviation 

was approximately 0.0007 (see Table 7.6), regardless of the assembly average burnup value. 

Positive keff bias is typically not credited in criticality safety analyses. The keff bias values in the 

case of the ENDF/B-V nuclear data were negative and varied with assembly average burnup 

from -0.0001 (10 GWd/MTU) to -0.0040 (40 GWd/MTU). Therefore, there are significant 

differences between the keff bias values based on the ENDF/B-VII and on the ENDF/B-V nuclear 

cross-section data libraries. As demonstrated in Sect. A.3 for the reference SFP storage rack 

model using a 40-GWd/MTU assembly average burnup, the nuclides with significantly different 

effects on keff bias between the ENDF/B-VII and ENDF/B-V nuclear data are 235U, 239Pu, 149Sm, 

and 151Sm. The calculated 235U and 239Pu concentrations for that application model using either 
49

the ENDF/B-V or the ENDF/B-VII nuclear data result in an overprediction of keff. However, the 

keff overprediction based on the ENDF/B-VII nuclear data is larger. The calculated 149Sm and 

151Sm concentrations based on the ENDF/B-V nuclear data result in an underprediction of keff; 

the calculated 149Sm and 151Sm concentrations based on the ENDF/B-VII nuclear data have a 

negligible effect on the keff bias. Therefore, the net keff bias resulting from the biases in the 

calculated concentrations for these nuclides varies depending on the nuclear data. 

Overall, the keff bias uncertainty values exhibit a small variability as a function of sensitivity 

parameter and assembly average burnup throughout the burnup range 10 to 40 GWd/MTU. 

Based on the ENDF/B-VII calculations, the average values of keff bias uncertainty are 0.0152, 

0.0160, and 0.0171 for the assembly average burnup values of 10, 25, and 40 GWd/MTU, 

respectively. The largest variations from the reference case were obtained for the unpoisoned 

(i.e., 0-g/cm2 10B areal density in the Boral panels) PWR SFP analysis model. 
50 

Table 7.6 keff bias and keff bias uncertainty as a function of sensitivity parameter 

Assembly burnup (GWd/MTU) 10 25 40 cSensitivity parameter keff bias a

keff bias 

uncertainty b keff bias a

keff bias 

uncertainty b keff bias a

keff bias 

uncertainty b

Reference 0.0034 0.0150 0.0034 0.0154 0.0034 0.0168 W 17×17: depletion w/o WABA 0.0043 0.0146 0.0028 0.0159 0.0027 0.0178 B&W 15×15 0.0037 0.0135 0.0028 0.0143 0.0031 0.0168 Axially uniform burnup 0.0029 0.0154 0.0029 0.0168 0.0022 0.0170 Cooling time: 5 years 0.0033 0.0152 0.0035 0.0152 0.0040 0.0167 Cooling time: 20 years 0.0043 0.0148 0.0034 0.0168 0.0032 0.0165 Cooling time: 40 years 0.0046 0.0152 0.0038 0.0161 0.0035 0.0174 10B loading: +10% 0.0036 0.0159 0.0031 0.0161 0.0031 0.0170 10B loading: -10% 0.0034 0.0154 0.0031 0.0150 0.0036 0.0168 10B loading: 0% d 0.0030 0.0196 0.0046 0.0190 0.0053 0.0188 Rack cell pitch: +0.5 in. 0.0032 0.0139 0.0027 0.0148 0.0030 0.0168 Soluble boron: 1000 ppm 0.0042 0.0148 0.0042 0.0167 0.0044 0.0181 Soluble boron: 303, 348, 393 ppm 0.0041 0.0148 0.0035 0.0154 0.0036 0.0161 Average value e 0.0037 0.0152 0.0034 0.0160 0.0035 0.0171 Standard deviation e 0.0006 0.0014 0.0006 0.0012 0.0008 0.0007 Maximum value e 0.0046 0.0196 0.0046 0.0190 0.0053 0.0188 Minimum value e 0.0029 0.0135 0.0027 0.0143 0.0022 0.0161 ENDF/B-V f -0.0001 0.0135 -0.0029 0.0139 -0.0040 0.0165 

aPositive keff bias values are typically not credited in criticality safety analyses. 

bkeff bias uncertainty at a 95% probability, 95% confidence level. cThe burnup values corresponding to the 5 wt % 235U initial enrichment limit were 39, 35, 33, 38, and 39.8 GWd/MTU for the 

5-, 20-, and 40-year decay time, cell pitch, and uniform burnup profile cases, respectively. 

dThe initial enrichment for this case and a 10-GWd/MTU assembly average burnup was 1.34 wt % 235U, which is an atypical 

fuel enrichment (see Figure 5.3). 

eBias and bias uncertainty values based on the results of all calculations using the ENDF/B-VII nuclear data. fThe values of bias and bias uncertainty in keff [(i.e., βi + Δki in Eq. (1)] are 0.0136, 0.0168, and 0.0205 for the assembly 

average burnup values of 10, 25, and 40 GWd/MTU, respectively. 
51 

(a) 

(b) 

 (c) 

Figure 7.3 Variation of bias uncertainty in keff with parameters important to criticality 

analyses for (a) 10-, (b) 25-, and (c) 40-GWd/MTU assembly average 

burnup. Uncertainty in keff is at a 95% probability, 95% confidence level. 

0.0150

0.0146

0.0135

0.0154

0.0152

0.0148

0.0152

0.0159

0.0154

0.0196

0.0139

0.0148

0.0135

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

keff Bias Uncertainty

Reference case

W 17x17 (no WABA)

B&W 15x15

Axially uniform burnup

Cooling time (5 years)

Cooling time (20 years)

Cooling time (40 years)

B‐10 loading (+10%)

B‐10 loading (‐10%)

B‐10 loading (0%)

Cell pitch (+ 1.27 cm)

Soluble B (1000 ppm)

Soluble B (303 ppm)

ENDF/B‐V

0.0154

0.0159

0.0143

0.0168

0.0152

0.0161

0.0150

0.0190

0.0148

0.0167

0.0154

0.0139

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

keff Bias Uncertainty

Reference case

W 17x17 (no WABA)

B&W 15x15

Axially uniform burnup

Cooling time (5 years)

Cooling time (20 years)

Cooling time (40 years)

B‐10 loading (+10%)

B‐10 loading (‐10%)

B‐10 loading (0%)

Cell pitch (+ 1.27 cm)

Soluble B (1000 ppm)

Soluble B (348 ppm)

ENDF/B‐V

0.0168

0.0178

0.0168

0.0170

0.0167

0.0165

0.0174

0.0170

0.0168

0.0188

0.0168

0.0181

0.0161

0.0165

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

keff Bias Uncertainty

Reference case

W 17x17 (no WABA)

B&W 15x15

Axially uniform burnup

Cooling time (5 years)

Cooling time (20 years)

Cooling time (40 years)

B‐10 loading (+10%)

B‐10 loading (‐10%)

B‐10 loading (0%)

Cell pitch (+ 1.27 cm)

Soluble B (1000ppm)

Soluble B (393 ppm)

ENDF/B‐V

53 

8. CONCLUSIONS 

This report describes an approach for establishing depletion code bias and bias uncertainty in 

terms of a reactivity difference (i.e., ∆keff) for burnup credit criticality safety analyses. The 

depletion validation approach is demonstrated with the SCALE 6.1 code system and the 238-

group ENDF/B-VII cross-section library for representative SNF storage pool and cask 

configurations/conditions. A total of 28 actinide and fission product nuclides are considered in 

the fuel compositions. Depletion validation results are provided for PWR fuel assembly average 

burnup values up to 60 GWd/MTU and for a BWR fuel assembly at peak reactivity. 

The validation approach described in this report is independent of the depletion and criticality 

computational methods being used and of the choice of the safety analysis models. The main 

characteristics of the depletion validation approach are as follows: (1) calculated nuclide 

concentrations are compared to available measurements of nuclide concentrations from 

destructive radiochemical assay to determine isotopic biases and bias uncertainties in the 

calculated nuclide concentrations, and (2) the isotopic biases and bias uncertainties are applied 

to the fuel compositions of representative safety analysis models to determine reference values 

for bias and bias uncertainty in keff by the use of the Monte Carlo uncertainty sampling method. 

The Monte Carlo uncertainty sampling method represents the effects of nuclide concentration 

uncertainty on keff values by sampling isotopic concentrations from uncertainty distributions 

developed from experimental data. The direct-difference method was used in a limited manner 

to provide a check of the validation results obtained from the Monte Carlo uncertainty sampling 

method. The direct-difference method applies measured nuclide concentrations directly in the 

safety analysis model to calculate a keff value, which then is compared with the keff value for the 

safety analysis model with calculated nuclide concentrations. 

The validation results for the PWR safety analysis models obtained with SCALE 6.1 and the 

ENDF/B-VII nuclear data indicate that: 

1. The calculated nuclide concentrations result in a slight overprediction of keff. The positive 

bias, which typically is not credited in criticality safety analyses, is significantly smaller 

than the uncertainty in the bias. 

2. The keff bias and keff bias uncertainty values are fairly constant for the burnup range 5 to 

40 GWd/MTU and gradually increase with increasing assembly average burnup values 

above 40 GWd/MTU. 

3. For a representative SFP storage rack model, the values of estimated bias and bias 

uncertainty in keff due to biases and bias uncertainties in the calculated nuclide 

concentrations are approximately 0.016 and 0.019 for the assembly average burnup 

range 5 to 40 GWd/MTU and for a 44.33-GWd/MTU assembly average burnup, 

respectively. 

4. Parametric variations from the representative SFP storage rack model have a relatively 

small impact on bias and bias uncertainty in keff for the burnup range 10 to 40 GWd/MTU. 

The estimated average value for keff bias is approximately 0.004 for this burnup range; 

the estimated average values for keff bias uncertainty are 0.015, 0.016, and 0.017 for the 

assembly average burnup values of 10, 25, and 40 GWd/MTU, respectively. The largest 
54 

keff bias uncertainty value was obtained for the unpoisoned SFP storage rack model (i.e., 

0-g/cm2 10B areal density in the Boral panels). 

5. For the unpoisoned SFP storage rack model, the values of estimated bias and bias 

uncertainty in keff due to biases and bias uncertainties in the calculated nuclide 

concentrations are approximately 0.019, 0.022, and 0.030 for the assembly average 

burnup range 25 to 40 GWd/MTU, for a 50-GWd/MTU assembly average burnup, and for 

a 60-GWd/MTU average assembly burnup, respectively. 

6. For a representative SNF cask model, the values of estimated bias and bias uncertainty 

in keff due to biases and bias uncertainties in the calculated nuclide concentrations are 

approximately 0.016 and 0.021 for the assembly average burnup range 5 to 40 

GWd/MTU and for a 45-GWd/MTU assembly average burnup, respectively. 

7. The uncertainties in the calculated 235U and 239Pu concentrations contribute 

approximately 90% to 95% of the keff bias uncertainty. 

8. The keff bias uncertainty due to the depletion uncertainties in the calculated fission 

product concentrations is small (<3% of the keff bias uncertainty). 

Bias and bias uncertainty in keff for the representative SFP storage rack model using 10-, 25-, 

and 40-GWd/MTU assembly average burnup values was also calculated with the SCALE 44-

group library based on the ENDF/B-V nuclear data. The keff bias values obtained with the 

ENDF/B-V nuclear data are negative and vary with assembly average burnup from -0.0001 

(10 GWd/MTU) to -0.004 (40 GWd/MTU). These values differ significantly from the keff bias 

value (~ 0.004) obtained with the ENDF/B-VII nuclear data primarily because different biases in 

the calculated 235U, 239Pu, 149Sm, and 151Sm concentrations were obtained from use of the two 

nuclear data libraries. The keff bias uncertainty values obtained with the ENDF/B-V nuclear data 

are approximately 0.014, 0.014, and 0.017 for the 10-, 25-, and 40-GWd/MTU assembly 

average burnup values, respectively, which are similar to the keff bias uncertainty values 

obtained with the ENDF/B-VII nuclear data. 

 

The calculated keff bias and keff bias uncertainty values for BWR SNF are approximately 0.002 

and 0.032, respectively. The BWR depletion validation was conducted for an assembly at peak 

reactivity with available RCA data for 32 BWR fuel samples obtained from discharged fuel of 

relatively old fuel designs and higher burnup. As additional RCA data for BWR SNF becomes 

available in the future, depletion code validations for BWR SNF should be performed to verify 

the validity of the keff bias and keff bias uncertainty values developed in this depletion validation 

study. 

The bias and bias uncertainty values estimated from the direct-difference method for a single 

application model are comparable with, but smaller than, the values obtained by the Monte 

Carlo uncertainty sampling method. Although not definitive, the comparison provides increased 

confidence in the Monte Carlo approach for uncertainty propagation. For depletion code 

validations using the direct-difference method, recommendations are provided concerning use 

of surrogate (i.e., substitute) data for nuclides with very few measurement data and appropriate 

decay-time adjustments for measured nuclide concentrations. 
55 

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57 

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58 

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59 

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A-1 

APPENDIX A. keff UNCERTAINTY ANALYSIS USING CROSS-SECTION 

SENSITIVITY/UNCERTAINTY ANALYSES 

Sensitivity/uncertainty analysis is used to determine contributions made by individual nuclide 

concentration uncertainties to bias and bias uncertainty in keff. The cross-section 

sensitivity/uncertainty analysis uses first-order linear perturbation approximations to determine 

the effects of small perturbations (uncertainties) in nuclide concentrations on keff. 

A sensitivity coefficient, defined as shown in Eq. (A-1) (Ref. 39), is a measure of the first-order 

effect of perturbations in the macroscopic cross sectionn

tot of a nuclide n upon keff, 

/ . /   

eff eff

n n n

tot tot

δk k S

δ (A-1)

Sensitivity coefficients specific to a nuclear system may be used to establish the relative 

importance of individual nuclides to fuel reactivity for that system. Uncertainties in calculated 

nuclide concentrations can be propagated to keff values through the use of sensitivity 

coefficients (Ref. 39). Equations (A-2) through (A-5) for keff bias and bias uncertainty 

calculations were derived from first-order (linear) approximation, 

  (1 ),  n

j

eff eff n n k kS X (A-2)

1 (1 ),

N

eff eff n n

j k k S Xn       (A-3)

1 bias (1 ) N

n n eff eff n k k S X       , (A-4)

2

1 bias uncertainty N n

eff eff n n n

σ k kS

X 

         . (A-5)

where 

 effn k = keff bias due to the bias in the calculated nuclide concentration for nuclide n

based on measurement data for fuel sample j; 

keff = keff value using predicted nuclide concentrations; 

Sn = sensitivity coefficient (see Eq. (A-1); 

j Xn = measured-to-calculated concentration ratio for nuclide n and fuel sample j; 

∆keff = keff bias due to biases in the calculated nuclide concentrations based on 

measurement data for fuel sample j; 

N = the number of burnup credit nuclides in fuel compositions (28 in this 

validation study); 

X n = isotopic bias [see Eq. (3)]; 

σn = isotopic bias uncertainty [see Eq. (5)]; 

keff bias = keff bias due to biases in the calculated nuclide concentrations;

keff bias 

uncertainty = one-sigma keff bias uncertainty due to bias uncertainties in the calculated 

nuclide concentrations. 

Eqs. (A-2) through (A-4) show that keff bias is a function of the sensitivity coefficients and biases 

in calculated nuclide concentrations; Eq. (A-5) shows that keff bias uncertainty is a function of 
A-2 

the square of the sensitivity coefficients and of the square of the uncertainties in calculated 

nuclide concentrations. Equations (A-1) through (A-5) were used to perform various analyses as 

described in Sections A.1 through A.4. Section A.1 illustrates the relative importance of 

individual burnup credit nuclides to fuel reactivity for the analysis models using sensitivity 

coefficients [see Eq. (A-1)], which were calculated with the TSUNAMI-3D sequence 

(see Sect. 4). Section A.2 presents an analysis in support of the data normality assumption 

used in the Monte Carlo uncertainty sampling method implementation (see Sect. 6.1). Individual 

nuclide contributions to keff bias and bias uncertainty for the representative analysis models are 

shown in Sect. A.3. An analysis illustrating the importance of decay time corrections for directdifference calculations is presented in Sect. A.4. 

A.1 Relative Importance of Individual Nuclides to Fuel Reactivity 

The relative importance of the burnup credit nuclides to fuel reactivity for the representative 

PWR SFP storage rack and SNF cask analysis models is illustrated on a logarithmic scale in 

Figures A.1 and A.2, respectively, which use the absolute values of sensitivity coefficients 

[see Eq. (A-1)]. The absolute values of the sensitivity coefficients are shown for the 10- and 40-

GWd/MTU assembly average burnup values. The nuclides are shown in order of decreasing 

nuclide importance to fuel reactivity for the 40-GWd/MTU burnup value. Sensitivity coefficients, 

which are illustrated in this section, were used to evaluate the contributions of individual 

nuclides to keff bias and bias uncertainty (see Sects. A.2 through A.4). 

Figure A.1 Sensitivity coefficients (absolute values) shown on a logarithmic scale for 

burnup credit actinide and fission product nuclides in the representative 

PWR SFP rack model at 3-day cooling time 

1.E‐06

1.E‐05

1.E‐04

1.E‐03

1.E‐02

1.E‐01

1.E+00

U‐235

U‐238

Pu‐239Pu‐240Pu‐241

Sm‐149

Nd‐143

Rh‐103

Sm‐151

U‐236

Cs‐133

Np‐237

Tc‐99

Sm‐152

Nd‐145

Eu‐153

Pu‐242

Sm‐150

Mo‐95

Ru‐101

Pu‐238

Ag‐109

Am‐241Am‐243

Sm‐147

Gd‐155

U‐234

Eu‐151

|Sn|

SFP; 40 GWd/MTU

SFP; 10 GWd/MTU
A-3 

Figure A.2 Sensitivity coefficients (absolute values) shown on a logarithmic scale for 

burnup credit actinide and fission product nuclides in the PWR SNF cask 

(GBC-32) model at 5-year cooling time 

A.2 Non-normal Distributions for Measured-to-Calculated 

Concentration Ratio 

The M/C concentration ratio values for 235U based on the PWR fuel samples within the burnup 

interval 15 to 40 GWd/MTU formed a skewed unimodal frequency distribution, as illustrated by 

the histogram shown in Figure A.3. In the Monte Carlo uncertainty sampling procedure, 

uncertainties in calculated 235U concentrations were represented as a normal distribution with 

mean and standard deviation of 0.9907 and 0.0416, respectively. The impact on keff bias 

uncertainty of using the normal distribution in place of the actual distribution is evaluated on the 

basis of a sensitivity/uncertainty analysis for the representative SFP storage rack configuration 

and the 40-GWd/MTU assembly average burnup. 

1.E‐06

1.E‐05

1.E‐04

1.E‐03

1.E‐02

1.E‐01

1.E+00

U‐235

Pu‐239

U‐238

Pu‐240Pu‐241

Sm‐149

Nd‐143

Rh‐103

Am‐241

Sm‐151

Gd‐155

U‐236

Cs‐133

Np‐237

Tc‐99

Sm‐152

Nd‐145

Eu‐153

Sm‐147

Pu‐242

Mo‐95

Sm‐150

Ru‐101

Pu‐238

Ag‐109

Am‐243

Eu‐151

U‐234

|Sn|

GBC‐32; 40 GWd/MTU

GBC‐32; 10 GWd/MTU
A-4 

 

Figure A.3 Histogram of the M/C concentration ratio values for 235U within the burnup 

interval 15 to 40 GWd/MTU 

Table A.1 shows the M/C concentration ratio values for 235U and the individual keff changes from 

the reference value of 0.99, 235  U

keff [see Eq. (A-2)], resulting from the bias in the calculated 

235U concentration, which were determined from measurement data within the burnup range 15 

to 40 GWd/MTU. The 235  U

keff values did not approach a normal distribution, as illustrated in the 

histogram shown in Figure A.4. The 95/95 distribution-free tolerance limit for the 235  U

keff values 

was calculated as being 0.0125. Therefore, the keff bias uncertainty component due to the 

uncertainty in the predicted 235U concentration is 0.0125. The total keff bias uncertainty can be 

calculated with all keff bias uncertainty components from individual nuclides, as shown in Eq. (A5), where the 235  U eff k component is 0.0125. The keff bias uncertainty value thus calculated is 

0.0152 compared to 0.0168 (see Table 7.1) based on calculations using the normal distribution 

model with mean and standard deviation of 0.9907 and 0.0416, respectively, for 235U within the 

burnup range 15 to 40 GWd/MTU. For this case, a normal distribution can be used because the 

keff bias uncertainty value obtained with the normal distribution in place of the actual distribution 

is slightly conservative (i.e., it causes larger keff bias uncertainty). 

 

0.92 0.94 0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10

0

5

10

15

20

Counts

M/C Concentration Ratio

 235U

15 GWd/MTU < Burnup <= 40 GWd/MTU
A-5 

Table A.1 keff bias due to the bias in calculated 235U concentration based on 

measurement data from fuel samples within the burnup range 

15 to 40 GWd/MTU 

Reactor Sample ID 235U X a

235  U eff k b

Reactor Sample ID 235U X a

235  U eff k b

Trino Vercellese 509-032-E11-4 0.9702 0.0045 Turkey Point D01.G10 0.9381 0.0094 

Trino Vercellese 509-032-E11-7 0.9549 0.0068 Turkey Point D01.G9 0.9826 0.0026 

Trino Vercellese 509-032-H9-4 0.9920 0.0012 Turkey Point D01.H9 0.9856 0.0022 

Trino Vercellese 509-032-H9-7 1.0060 -0.0009 Turkey Point D04.G10 0.9757 0.0037 

Trino Vercellese 509-049-J8-7 0.9685 0.0048 Turkey Point D04.G9 0.9497 0.0076 

Trino Vercellese 509-069-E11-2 0.9758 0.0037 H.B. Robinson B-05.N-9B-N 0.9994 0.0001 

Trino Vercellese 509-069-E11-4 0.9561 0.0067 H.B. Robinson B-05.N-9B-S 0.9946 0.0008 

Trino Vercellese 509-069-E11-5 0.9926 0.0011 H.B. Robinson B-05.N-9C-D 0.9773 0.0034 

Trino Vercellese 509-069-E11-7 0.9778 0.0034 H.B. Robinson B-05.N-9C-J 1.0567 -0.0086 

Trino Vercellese 509-069-E11-8 0.9679 0.0049 Calvert Cliffs BT03.NBD107-GG 1.0829 -0.0125 

Trino Vercellese 509-069-E11-9 0.9815 0.0028 Calvert Cliffs BT03.NBD107-MM 1.0409 -0.0062 

Trino Vercellese 509-069-E5-4 0.9950 0.0008 Calvert Cliffs D047.MKP109-CC 0.9976 0.0004 

Trino Vercellese 509-069-E5-7 0.9761 0.0036 Calvert Cliffs D047.MKP109-LL 1.0018 -0.0003 

Trino Vercellese 509-069-E5-9 0.9913 0.0013 Calvert Cliffs MLA098-BB 1.0005 -0.0001 

Trino Vercellese 509-069-J9-4 0.9745 0.0039 Calvert Cliffs MLA098-JJ 0.9943 0.0009 

Trino Vercellese 509-069-J9-7 0.9803 0.0030 Calvert Cliffs MLA098-P 0.9508 0.0075 

Trino Vercellese 509-069-L5-4 1.0174 -0.0026 Takahama-3 NT3G23.SF95-2 0.9713 0.0044 

Trino Vercellese 509-069-L5-7 0.9754 0.0037 Takahama-3 NT3G23.SF95-3 0.9643 0.0054 

Trino Vercellese 509-069-L11-4 0.9903 0.0015 Takahama-3 NT3G23.SF95-4 0.9572 0.0065 

Trino Vercellese 509-069-L11-7 0.9724 0.0042 Takahama-3 NT3G23.SF95-5 0.9759 0.0037 

Obrigheim BE124.E3P1 1.0148 -0.0022 Takahama-3 NT3G23.SF96-2 0.9728 0.0041 

Obrigheim BE124.E3P2 1.0601 -0.0091 Takahama-3 NT3G23.SF96-3 0.9535 0.0071 

Obrigheim BE124.E3P3 1.0693 -0.0105 Takahama-3 NT3G23.SF96-4 0.9433 0.0086 

Obrigheim BE124.E3P4 0.9954 0.0007 Takahama-3 NT3G23.SF96-5 0.9676 0.0049 

Obrigheim BE124.E3P5 1.0442 -0.0067 Takahama-3 NT3G24.SF97-2 0.9766 0.0035 

Obrigheim BE124.G7P1 1.0325 -0.0049 TMI-1 NJ070G.O12S4 0.9613 0.0059 

Obrigheim BE124.G7P2 1.0883 -0.0134 TMI-1 NJ070G.O12S5 0.9551 0.0068 

Obrigheim BE124.G7P3 0.9745 0.0039 TMI-1 NJ070G.O12S6 0.9804 0.0030 

Obrigheim BE124.G7P4 1.0779 -0.0118 TMI-1 NJ070G.O13S7 0.9599 0.0061 

Obrigheim BE124.G7P5 0.9876 0.0019 TMI-1 NJ070G.O13S8 0.9547 0.0069 

Obrigheim BE168 1.0331 -0.0050 TMI-1 NJ070G.O1S1 0.9560 0.0067 

Obrigheim BE170 1.0297 -0.0045 TMI-1 NJ070G.O1S2 0.9364 0.0096 

Obrigheim BE171 1.0324 -0.0049 TMI-1 NJ070G.O1S3 0.9647 0.0054 

Obrigheim BE172 1.0145 -0.0022 Gösgen 1701.GU4 0.9877 0.0019 

Obrigheim BE176 1.0215 -0.0033 

a

Measured-to-calculated concentration ratio for 235U in a fuel sample. 

b

keff bias due to bias in the calculated 235U nuclide concentration based on 235U 

measurement data for a fuel sample.
A-6 

Figure A.4 Histogram plot for 235  U

keff values based on actual M/C concentration ratio 

values for 235U within the burnup range 15 to 40 GWd/MTU. The 235  U

keff

values used in the histogram were calculated with Eq. (A-2). 

-0.015 -0.012 -0.009 -0.006 -0.003 0.000 0.003 0.006 0.009 0.012

0

2

4

6

8

10

12

14

16

18

20

22

24

Count

keff
A-7 

A.3 Analysis of keff Bias and Bias Uncertainty Components 

The contributions of individual burnup credit nuclides to keff bias and bias uncertainty were 

evaluated through sensitivity/uncertainty analyses. Figure A.5 through Figure A.8 show 

individual nuclide contributions to keff bias uncertainty for the reference PWR SFP storage rack 

and SNF cask models using 10- and 40- GWd/MTU assembly average burnup values. For 

these analysis models, the bias uncertainties in the calculated 235U concentrations have a 

dominating effect on the keff bias uncertainty (~90%). The combined contributions from the bias 

uncertainties associated with the calculated 235U and 239Pu concentrations account for 

approximately 95%; the total contribution of bias uncertainties in calculated fission product 

concentrations is relatively small (<2%) for these representative analysis models. 

Individual nuclide contributions to keff bias uncertainty for the unpoisoned SFP storage rack 

model and the 40-GWd/MTU assembly average burnup are illustrated in Figure A.9. For this 

model, 239Pu has the largest contribution to keff bias uncertainty (~70%), 235U contributes ~20% 

of keff bias uncertainty, and 241Pu and 240Pu contribute approximately 7% of the total keff bias 

uncertainty; the total contribution of bias uncertainties in the calculated fission product 

concentrations is relatively small (~3%). 

In Figures A.5 through A.9, the 235U and 239Pu percentage values are shown on the left-hand 

side Y axis, whereas the percentage values for the other burnup credit nuclides are shown on 

the right-hand side Y axis. 

Figure A.5 Individual nuclide contributions to keff bias uncertainty for the 

representative PWR SFP storage rack model and 10-GWd/MTU 

assembly average burnup 

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Contribution to keff Bias Uncertainty

Contribution to keff Bias Uncertainty

Percentage values on the left‐hand side Y axis

Percentage values on the right‐hand side Y axis
A-8 

Figure A.6 Individual nuclide contributions to keff bias uncertainty for the representative 

PWR SFP storage rack model and 40-GWd/MTU assembly average burnup 

Figure A.7 Individual nuclide contributions to keff bias uncertainty for the PWR 

SNF cask model and 10-GWd/MTU assembly average burnup 

Figure A.8 Individual nuclide contributions to keff bias uncertainty for the PWR 

SNF cask model and 40-GWd/MTU assembly average burnup 

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

0.9%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Contribution to keff Bias Uncertainty

Contribution to keff Bias Uncertainty

Percentage values on the left‐hand side Y axis

Percentage values on the right‐hand side Y axis

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Contribution to keff Bias Uncertainty

Contribution to keff Bias Uncertainty

Percentage values on the left‐hand side Y axis

Percentage values on the right‐hand side Y axis

0.0%

0.1%

0.2%

0.3%

0.4%

0.5%

0.6%

0.7%

0.8%

0.9%

1.0%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Contribution to keff Bias Uncertainty

Contribution to keff Bias Uncertainty

Percentage values on the left‐hand side Y axis

Percentage values on the right‐hand side Y axis
A-9 

Figure A.9 Individual nuclide contributions to keff bias uncertainty for the 

unpoisoned PWR SFP storage rack model and 40-GWd/MTU 

assembly average burnup 

The keff bias values obtained with the ENDF/B-VII and ENDF/B-V nuclear cross-section data 

were significantly different (see Sect. 7.3). For example, over the burnup range 10 to 40 

GWd/MTU, the keff bias value based on the ENDF/B-VII nuclear data is approximately 0.0035, 

whereas keff bias values based the ENDF/B-V nuclear data vary from -0.0001 (10 GWd/MTU) to 

-0.0040 (40 GWd/MTU). 

Individual nuclide keff bias components based on ENDF/B-VII and ENDF/B-V nuclear data are 

illustrated in Figure A.10 (a) and (b), respectively, for the reference SFP storage rack model and 

40-GWd/MTU assembly average burnup. Nuclides with significantly different biases between 

the ENDF/B-VII and ENDF/B-V nuclear data are 235U, 149Sm, and 151Sm. Both ENDF/B-V and 

ENDF/B-VII nuclear data overpredict 235U and 239Pu concentrations; however, the bias values 

based on the ENDF/B-VII data are greater than the bias values based on the ENDF/B-V data for 

these nuclides. 

 

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Contribution to keff Bias Uncertainty

Contribution to keff Bias Uncertainty

Percentage values on the left‐hand side Y axis

Percentage values on the right‐hand side Y axis
A-10 

(a) 

(b) 

Figure A.10 Illustration of keff bias components using (a) ENDF/B-VII nuclear data; 

(b) ENDF/B-V nuclear data

‐2.0E‐03

‐1.0E‐03

0.0E+00

1.0E‐03

2.0E‐03

3.0E‐03

4.0E‐03

keff Bias Components

Nuclide

SFP; 40GWd/MTU; ENDF/B‐VII

‐2.0E‐03

‐1.0E‐03

0.0E+00

1.0E‐03

2.0E‐03

3.0E‐03

4.0E‐03

keff Bias Components

Nuclide

SFP; 40GWd/MTU; ENDF/B‐V
A-11 

A.4 Importance of Decay-Time Corrections for the Direct-Difference 

 Method 

The direct-difference method applies measured nuclide concentrations from representative fuel 

samples directly in safety application models for criticality calculations. Measured nuclide 

concentrations for burnup credit nuclides have been reported either at the time of fuel discharge 

or at the actual measurement time depending on the experimental programs (see Ref. 20). The 

measurement data reported for discharged compositions include decay time corrections for 

nuclides exhibiting concentration variation as a function of decay time (see Ref. 20). Therefore, 

a review of the measurement data and reported decay times should be performed to identify 

nuclides that require decay-time corrections because fuel sample nuclide concentrations for 

criticality calculations must correspond to the fuel cooling time considered in the safety analysis 

models. 

The importance for direct-difference calculations to use fuel sample nuclide compositions 

corresponding to the cooling time considered in the safety analysis is discussed in the following 

sensitivity/uncertainty analysis example. 

Measured and corresponding calculated nuclide concentrations for the Calvert Cliffs MKP109-P 

fuel sample were directly applied in the unpoisoned SFP storage rack model considering 

uniform axial burnup. The measured and calculated nuclide concentration values for the fuel 

sample correspond to the reported measurement time (e.g., 4,656 days after fuel discharge for 

155Gd). The purpose of these calculations is to determine the difference between the keff values 

using measured and calculated nuclide concentrations corresponding to the reported 

measurement time. 

Nuclide concentration values were determined for the representative fuel assembly, W 17×17 

(see Sect. 5.1), with a 50-GWd/MTU assembly average burnup, a uniform burnup profile, a 3-

day cooling time, and a keff value of 0.99 in the unpoisoned SFP storage rack configuration. 

Measured-to-calculated concentration ratio values (i.e., isotopic uncertainties) based on Calvert 

Cliffs MKP109-P fuel sample measurements were applied as adjustment factors to the nuclide 

concentration values. The purpose of the calculations is to determine the effects of the isotopic 

uncertainty based on Calvert Cliffs MKP109-P fuel sample measurements on the keff for the 

analysis model. Note that the nuclide concentrations for the fuel sample and for the application 

model have very similar burnup-to-enrichment and 235U-to-239Pu atom density ratios, as seen in 

Table A.2. 

Sensitivity coefficients, the  effn k bias due to individual isotopic biases [see Eq. (A-2)], and 

 eff k bias due to all isotopic biases [see Eq. (A-3)] were calculated for the unpoisoned SFP 

storage rack model using (1) fuel sample nuclide concentrations corresponding to the reported 

measurement time and (2) nuclide concentrations for the analysis model corresponding to the 3-

day cooling time. Table A.2 presents the calculated values for those quantities as well as the 

M/C concentration ratio values based on the Calvert Cliffs MKP109-P fuel sample 

measurements. The  eff k value obtained with the direct-difference method for the Calvert Cliffs 

MKP109-P fuel sample was 0.0221 versus 0.0217 from Eq. (A-3), demonstrating the 

applicability of this equation for sensitivity/uncertainty analyses. The keff bias value obtained by 

applying Calvert Cliffs MKP109-P measurement uncertainty data for the application model is 
A-12 

only 0.009, which is significantly smaller than the keff bias value of ~0.022 from the directdifference method using measurement-time nuclide compositions. 

Table A.2 shows that the  effn k values due to individual isotopic biases for the fuel sample and 

for the analysis model are in fairly good agreement for all nuclides except for 155Gd and 241Am. 

For example, the bias associated with 155Gd concentration causes a 0.0086 change in keff, if 

155Gd concentration corresponds to the reported measurement time, versus a 0.0001 change in 

keff, if this bias is applied to a 3-day cooling time nuclide concentration. This is because the 

155Gd is only present in negligible concentrations after 3 days of cooling, which demonstrates 

the impact of different nuclide worth effects if cooling time is not considered. 

 
A-13 

Table A.2 keff bias calculations using fuel sample and analysis model compositions 

Calvert Cliffs MKP109-P fuel sample

Unpoisoned SFP storage rack 

model 

Burnup 

(GWd/MTU) 44.3 50 

Initial wt % 235U 3.04 3.56 

Burnup-to-initial 

enrichment ratio 14.6 14 235U-to-239Pu atom 

density ratio 0.83 0.87 

keff 0.85 0.99 

Nuclide Sn

 a Xnb

  effn k c Sn

a Xnb  effn k c

95Mo -2.35E-03 1.0002 0.0000 -2.03E-03 1.0002 0.0000 99Tc -5.07E-03 0.8901 -0.0005 -5.24E-03 0.8901 -0.0006 101Ru -1.87E-03 0.9726 0.0000 -2.05E-03 0.9726 -0.0001 103Rh -1.40E-02 0.9021 -0.0012 -1.29E-02 0.9021 -0.0013 109Ag -2.49E-03 0.5546 -0.0009 -2.70E-03 0.5546 -0.0012 133Cs -6.62E-03 0.9914 0.0000 -6.65E-03 0.9914 -0.0001 143Nd -1.92E-02 0.9827 -0.0003 -1.85E-02 0.9827 -0.0003 145Nd -4.15E-03 1.0310 0.0001 -4.10E-03 1.0310 0.0001 147Sm -2.57E-03 1.1947 0.0004 -7.05E-04 1.1947 0.0001 149Sm -1.09E-02 0.9634 -0.0003 -1.70E-02 0.9634 -0.0006 150Sm -2.77E-03 0.9691 -0.0001 -2.83E-03 0.9691 -0.0001 151Sm -8.56E-03 0.9907 -0.0001 -1.09E-02 0.9907 -0.0001 152Sm -3.99E-03 1.0179 0.0001 -3.77E-03 1.0179 0.0001 151Eu -2.59E-04 1.4721 0.0001 -5.92E-06 1.4721 0.0000 153Eu -4.75E-03 1.0142 0.0001 -4.76E-03 1.0142 0.0001 155Gd -1.74E-02 1.5827 0.0086 -2.15E-04 1.5827 0.0001 234U -9.10E-04 0.9610 0.0000 -2.03E-05 0.9610 0.0000 235U 1.09E-01 0.9673 0.0030 8.55E-02 0.9673 0.0028 236U -4.02E-03 0.9831 -0.0001 -4.39E-03 0.9831 -0.0001 238U -1.36E-01 1.0014 0.0002 -1.24E-01 1.0014 0.0002 237Np -5.80E-03 0.9737 -0.0001 -6.57E-03 0.9737 -0.0002 238Pu -5.10E-03 1.1155 0.0005 -4.93E-03 1.1155 0.0006 239Pu 2.52E-01 0.9407 0.0126 1.81E-01 0.9407 0.0107 240Pu -5.96E-02 0.9712 -0.0015 -5.63E-02 0.9712 -0.0016 241Pu 7.71E-02 1.0000 0.0000 8.08E-02 1.0000 0.0000 242Pu -4.47E-03 1.0826 0.0003 -4.86E-03 1.0826 0.0004 241Am -1.43E-02 1.0793 0.0010 -1.50E-03 1.0793 0.0001 243Am -2.44E-03 0.9216 -0.0002 -3.14E-03 0.9216 -0.0002 

∆keff 0.0217 0.0089 

a

First-order effect of perturbations in the macroscopic cross section of a nuclide upon 

keff [see Eq. (A-1)]. 

b

M/C concentration ratio for a nuclide based on measured data for the fuel sample. 

c

keff bias due to bias in the calculated nuclide concentration based on measured data for 

the fuel sample [Eq. (A-2)]. 

B-1 

APPENDIX B. ISOTOPIC VALIDATION DATA CORRELATIONS 

It was assumed that correlations (relationships) between validation data could be neglected in 

the implementation of the Monte Carlo uncertainty method so that sampling from probability 

distributions for nuclide composition uncertainties could be performed independently. To 

evaluate the potential impact of this assumption, an analysis was conducted to identify existing 

correlations that may impact the accuracy of the results obtained with the Monte Carlo 

uncertainty method. The degree of correlations (dependence) among nuclide composition 

uncertainties was determined on the basis of Pearson correlation coefficient (Ref. 53) 

calculations. Pearson correlation coefficient values closer to zero indicate that the variables are 

uncorrelated; values closer to either +1 or -1 indicate a strong linear dependence between 

variables. Positive values indicate positive correlations; negative values indicate negative 

correlation. A critical value, which depends on the degrees of freedom and statistical 

significance level, is used to identify statistically significant relationships between any pair of 

variables. A Pearson correlation coefficient greater than the critical value indicates a statistically 

significant relationship between the variables. For 26 degrees of freedom (2 less than the 

number of burnup credit nuclides considered) and 0.05 significance level, the critical value is 

approximately 0.36 (Ref. 53). 

An example correlation matrix is shown in Table B.1 for the measured-to-calculated 

concentration ratio values used for depletion validation within the burnup range 40 to 60 

GWd/MTU. This table shows the Pearson coefficients greater than the critical value of 0.36 

above the main diagonal. 

For the SFP storage rack and SNF cask models analyzed in this report, the uncertainties in the 

calculated 235U and 239Pu nuclide concentrations contribute approximately 90 to 95% of the keff

bias uncertainty (see Sect. A.3). Based on correlation calculations, correlations between the 

isotopic validation data for 235U and 239Pu are insignificant at the 0.05 significance level 

throughout the burnup range 5 to 60 GWd/MTU. Statistically significant correlations were 

identified for the Pu isotopes; these correlations need to be considered in the uncertainty 

calculations for fuel assemblies with high burnup and relatively low initial enrichment for the 

burnup, such as the nuclide concentrations in the unpoisoned SFP storage rack model (see 

Sect. 5.2). For this SFP storage rack model and the 40-GWd/MTU burnup, the uncertainties in 

calculated 239Pu, 241Pu, and 240Pu concentrations contribute approximately 70%, 5%, and 1.5%, 

respectively, to the keff bias uncertainty value (see Sect. A.3, Figure A.9). For this case, the total 

keff bias uncertainty is approximately 0.018; the keff bias uncertainty due to bias uncertainty in 

the calculated 241Pu concentrations is approximately 0.001. Therefore, positive correlations 

between the isotopic validation data for 239Pu and 241Pu, if considered in the sampling 

procedure, would increase the small contribution (0.001) made by 241Pu to keff bias uncertainty, 

and the net effect would be a relatively small contribution to the calculated keff bias uncertainty 

values based on independent sampling. Other neglected positive correlations would decrease 

the keff bias uncertainty if considered in the sampling procedure, such as the observed positive 

correlation between 239Pu (fissile) and 240Pu (absorber) uncertainties. Overall, the neglected 

correlations in the Monte Carlo uncertainty sampling would have the effect of a small increase in 

the calculated keff bias uncertainty comparable to the 241Pu contribution to keff bias uncertainty. In 

this analysis, to account for additional uncertainty due to neglected positive correlations in the 

validation data for 239Pu and 241Pu, the contribution of 241Pu concentration uncertainty to keff bias 

uncertainty (e.g., <1% and ~5% in the case of the representative models and the unpoisoned 

rack model, respectively) is doubled in the calculation of total keff bias uncertainty. For the 

reference PWR SFP and cask analysis models, existing correlations are considered to have 

negligible impact on the calculated keff bias uncertainty values because the keff bias uncertainty 
B-2 

is dominated by 235U or 239Pu concentration prediction uncertainties; all other nuclides have 

relatively small (<1.3%) or negligible contributions to keff bias uncertainty. 
B-3 

Table B.1 Correlations at the 0.5 significance level for the isotopic validation data applicable to the 

burnup range 40 to 60 GWd/MTU 

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

234U 1 -0.63 -0.46 -0.64 -0.82 -0.54 -0.53 235U 1 0.58 -0.71 0.76 0.57 0.50 0.51 0.69 -0.76236U 1 0.67 0.74 0.63 0.46 0.49 -0.54 0.51 0.51 0.47 238U 1 -0.46 -0.54 -0.49238Pu 1 0.56 0.52 239Pu 1 0.84 0.70 -0.79 0.46 0.49 0.68 -0.53 240Pu 1 0.58 0.51 -0.71 0.77 241Pu 1 0.87 0.79 0.74 0.38 0.72 0.61 242Pu 1 0.64 237Np 1 0.57 0.55 0.62 0.62 241Am 1 -0.68 -0.50 -0.51 -0.58243Am 1 -0.48 0.85 95Mo 1 0.75 0.59 99Tc 1 101Ru 1 0.79 103Rh 1 0.54 109Ag 1 133Cs 1 143Nd 1 0.76 0.44 0.53 0.36 0.42 -0.74145Nd 1 0.40 0.37 147Sm 1 0.86 0.53 0.65 -0.78 0.72 -0.54 149Sm 1 150Sm 1 0.56 0.66 -0.84 0.79 151Sm 1 0.44 -0.48 0.62 152Sm 1 -0.48 0.58 151Eu 1 -0.71153Eu 1 -0.41 155Gd 1 

Note: Matrix correlation identifying correlations that are significant at the 0.05 level; Pearson coefficient values and statistical significance obtained with OriginPro 8.1 (copyright OriginLab Corporation). 

 C-1 

APPENDIX C. REFERENCE SPENT FUEL NUCLIDE 

CONCENTRATIONS

This appendix documents reference spent fuel nuclide concentrations that can be used in 

burnup credit calculations. These data are compiled from measurements of 100 PWR spent fuel 

samples that have been used in this report. The nuclide concentrations have been converted to 

a consistent format in units of mg/gU initial at the time of measurements (or the time reported by 

the laboratory). When laboratories have reported the results at the time of discharge, it is 

important to note that the results for 239Pu include the contribution from short lived 239Np. In 

several experiments the reported measurement dates vary for the different nuclides in the 

sample. This is the case for samples obtained from the GKN-II, Gösgen, Takahama (Sm 

isotopes), Calvert Cliffs (lanthanides), and Trino Vercellese (241Am) reactors. The reference 

nuclide concentrations listed in this appendix have been adjusted by the authors to a common 

reference date for each sample using the analytical equations in Sect. 6.2 given for decay time 

corrections. 

To enable users to derive nuclide concentrations for other decay times, the appendix includes 

the reference inventories for both the burnup credit nuclides (Table 3.1) and the major precursor 

nuclides. The additional precursor nuclides include 242Cm, 244Cm, 147Pm, and 155Eu. Any 

adjustments of the data to other decay times must be done within the time range where the 

given parent and daughter relationship remains valid. 

For samples that did not include measurements of all burnup credit nuclides (and precursors), 

surrogate data based on calculated nuclide concentrations are provided. As discussed in Sect. 

6.2, the surrogate data attempt to correct for bias in the calculated nuclide concentrations as 

based on measured nuclide contents obtained from other samples. The surrogate data 

therefore represent best-estimate calculated values and are largely independent of the code 

and nuclear data. 

The reference data for the SNF compositions are listed in Table C.1. The table includes all 28 

burnup credit nuclides plus four addition decay precursor nuclides that are not considered in 

burnup credit. Each sample is identified by the reactor, the assembly, and the sample 

identification. Also provided is the reference decay time for the nuclide concentration data. The 

concentrations of surrogate data developed from computations are identified with a negative 

sign. 

 
C-2 

Table C.1 Reference nuclide compositions (g/gU initial) 

Nuclide 

Calvert Cliffs 

BT03 

NBD107-GG 

(5658 days)a

Calvert Cliffs 

BT03 

NBD107-MM 

(2447 days) 

Calvert Cliffs

BT03 

NBD107-Q 

(2447 days)

Calvert Cliffs

D047 

MKP109-CC

(4653 days)

Calvert Cliffs

D047 

MKP109-LL(4171 days)

Calvert Cliffs

D047 

MKP109-P 

(4653 days)

Calvert Cliffs 

D101 

MLA098-BB 

(2374 days) 

Calvert Cliffs

D101 

MLA098-JJ 

(2374 days)

Calvert Cliffs

D101 

MLA098-P 

(2374 days)

GKN-II 

419 

M11 

(2735 days)

Gösgen 

1240 

GU1 

(1054 days)

U-234 1.590E-04 1.736E-04 8.497E-05 1.714E-04 1.871E-04 1.540E-04 1.373E-04 1.588E-04 1.361E-04 1.496E-04 1.201E-04U-235 3.074E-03 4.379E-03 1.595E-03 5.865E-03 9.609E-03 4.016E-03 7.873E-03 1.163E-02 5.423E-03 5.130E-03 2.110E-03U-236 3.437E-03 3.244E-03 3.449E-03 4.005E-03 3.562E-03 4.186E-03 3.392E-03 2.836E-03 3.698E-03 5.360E-03 4.830E-03U-238 9.572E-01 9.581E-01 9.384E-01 9.446E-01 9.558E-01 9.358E-01 9.686E-01 9.700E-01 9.554E-01 9.220E-01 9.200E-01

Np-237 3.758E-04 2.967E-04 4.290E-04 4.134E-04 3.097E-04 5.434E-04 3.403E-04 1.984E-04 3.887E-04 6.090E-04 -7.229E-04

Pu-238 2.060E-04 1.618E-04 3.224E-04 2.022E-04 1.090E-04 2.871E-04 1.099E-04 5.502E-05 1.682E-04 4.281E-04 4.540E-04Pu-239 4.349E-03 4.327E-03 4.272E-03 4.942E-03 4.836E-03 4.942E-03 4.824E-03 4.486E-03 4.750E-03 5.770E-03 4.890E-03Pu-240 2.631E-03 2.345E-03 2.948E-03 2.538E-03 1.949E-03 2.883E-03 2.003E-03 1.410E-03 2.395E-03 3.220E-03 3.180E-03Pu-241 6.008E-04 8.236E-04 1.005E-03 7.074E-04 5.691E-04 7.993E-04 7.739E-04 5.154E-04 9.217E-04 1.283E-03 1.440E-03Pu-242 8.795E-04 6.197E-04 1.326E-03 6.535E-04 3.278E-04 9.530E-04 3.745E-04 1.581E-04 6.210E-04 1.170E-03 1.550E-03

Am-241 7.949E-04 3.901E-04 7.207E-04 7.000E-04 4.825E-04 7.833E-04 3.276E-04 2.205E-04 3.967E-04 5.218E-04 2.507E-04Am-243 -1.790E-04 -1.076E-04 -2.958E-04 -1.328E-04 -4.993E-05 -2.054E-04 -5.854E-05 -1.676E-05 -1.199E-04 2.490E-04 4.030E-04

Cm-242b -2.755E-09 -3.423E-09 -3.893E-09 -2.815E-09 -2.290E-09 -3.092E-09 -2.367E-09 -1.442E-09 -3.037E-09 4.608E-09 3.695E-07Cm-244b -3.609E-05 -2.405E-05 -1.235E-04 -2.794E-05 -7.425E-06 -6.010E-05 -1.102E-05 -2.019E-06 -3.054E-05 1.311E-04 2.451E-04

Mo-95 -8.066E-04 -7.035E-04 -9.541E-04 -8.192E-04 -6.339E-04 -9.421E-04 -6.184E-04 -4.536E-04 -7.424E-04 1.040E-03 1.230E-03

Tc-99 5.936E-04 5.101E-04 7.221E-04 8.149E-04 6.353E-04 8.944E-04 6.208E-04 4.684E-04 7.486E-04 1.250E-03 1.250E-03

Ru-101 -8.570E-04 -7.268E-04 -1.054E-03 -8.387E-04 -6.231E-04 -9.927E-04 -6.169E-04 -4.350E-04 -7.639E-04 9.680E-04 1.290E-03Rh-103 6.800E-04 -4.164E-04 -5.462E-04 -4.703E-04 -3.658E-04 -5.367E-04 -3.703E-04 -2.675E-04 -4.465E-04 5.810E-04 6.130E-04

Ag-109 -5.789E-05 -4.590E-05 -7.609E-05 -5.065E-05 -3.260E-05 -6.461E-05 -3.495E-05 -2.057E-05 -4.798E-05 1.070E-04 7.510E-05Cs-133 -1.214E-03 -1.059E-03 -1.429E-03 1.237E-03 9.643E-04 1.407E-03 -9.241E-04 -6.755E-04 -1.110E-03 1.600E-03 1.720E-03

Nd-143 7.189E-04 -6.561E-04 -7.367E-04 8.123E-04 6.954E-04 8.656E-04 -6.527E-04 -5.171E-04 -7.392E-04 1.070E-03 9.330E-04Nd-145 7.246E-04 -6.202E-04 -8.170E-04 7.408E-04 5.786E-04 8.440E-04 -5.507E-04 -4.094E-04 -6.538E-04 9.970E-04 1.040E-03

Pm-147b -2.545E-06 -2.413E-05 -2.804E-05 -6.208E-06 -7.653E-06 -6.583E-06 -3.058E-05 -2.470E-05 -3.390E-05 -2.974E-05 -1.077E-04

Sm-147 2.659E-04 -2.253E-04 -2.492E-04 2.704E-04 2.303E-04 3.081E-04 -1.984E-04 -1.619E-04 -2.173E-04 2.990E-04 2.220E-04Sm-149 2.174E-06 -1.435E-06 -1.719E-06 -2.077E-06 -1.943E-06 -2.268E-06 -2.069E-06 -1.843E-06 -2.328E-06 2.390E-06 3.280E-06Sm-150 3.000E-04 -2.485E-04 -3.726E-04 2.896E-04 2.089E-04 3.638E-04 -2.173E-04 -1.463E-04 -2.783E-04 4.780E-04 5.080E-04Sm-151 7.970E-06 -7.261E-06 -8.883E-06 9.408E-06 7.521E-06 1.072E-05 -8.442E-06 -7.541E-06 -9.498E-06 1.430E-05 1.300E-05Sm-152 1.210E-04 -1.087E-04 -1.377E-04 1.096E-04 8.968E-05 1.325E-04 -9.294E-05 -7.042E-05 -1.074E-04 1.470E-04 1.660E-04

Eu-151 -1.379E-06 -5.908E-07 -7.122E-07 -1.415E-06 -1.172E-06 -1.572E-06 -6.624E-07 -6.022E-07 -7.396E-07 -1.307E-06 -4.410E-07Eu-153 1.483E-04 -1.131E-04 -1.721E-04 1.300E-04 8.516E-05 1.622E-04 -9.138E-05 -5.643E-05 -1.204E-04 1.920E-04 2.100E-04

Eu-155b 1.138E-06 -4.088E-06 -6.854E-06 1.385E-06 1.041E-06 1.815E-06 -3.316E-06 -1.861E-06 -4.670E-06 5.856E-06 1.130E-05

Gd-155 7.028E-06 -6.055E-06 -1.010E-05 7.408E-06 6.248E-06 9.959E-06 -4.678E-06 -2.644E-06 -6.570E-06 1.010E-05 5.644E-06

aTime after discharge. bDecay precursor.
C-3 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Gösgen 

1701 

GU3 

(919 days)a 

Gösgen 

1701 

GU4 

(846 days) 

HB Robinson 

B05 

N9BN 

(3936 days) 

HB Robinson 

B05 

N9BS 

(3631 days) 

HB Robinson 

B05 

N9CD 

(3631 days) 

HB Robinson 

B05 

N9CJ 

(3631 days) 

Obrigheim 

BE124 

E3P1 

(10 days) 

Obrigheim 

BE124 

E3P2 

(10 days) 

Obrigheim 

BE124 

E3P3 

(10 days) 

Obrigheim 

BE124 

E3P4 

(10 days) 

Obrigheim 

BE124 

E3P5 

(10 days) 

U-234 1.435E-04 1.953E-04 1.556E-04 1.755E-04 1.253E-04 1.339E-04 -1.812E-04 -1.545E-04 -1.356E-04 -1.492E-04 -1.720E-04U-235 6.050E-03 1.450E-02 8.181E-03 1.209E-02 5.514E-03 7.010E-03 1.275E-02 8.440E-03 6.090E-03 7.660E-03 1.185E-02U-236 5.650E-03 4.590E-03 3.103E-03 2.487E-03 3.403E-03 3.204E-03 2.820E-03 3.770E-03 4.120E-03 3.870E-03 3.620E-03U-238 9.270E-01 9.440E-01 9.613E-01 9.605E-01 9.549E-01 9.460E-01 9.571E-01 9.422E-01 9.430E-01 9.470E-01 9.534E-01

Np-237 8.110E-04 5.250E-04 2.953E-04 1.753E-04 3.778E-04 3.445E-04 -1.994E-04 -3.279E-04 -4.300E-04 -3.626E-04 -2.466E-04

Pu-238 3.715E-04 1.109E-04 7.894E-05 3.208E-05 1.479E-04 1.293E-04 4.100E-05 1.040E-04 1.650E-04 1.140E-04 6.200E-05Pu-239 5.810E-03 5.160E-03 4.557E-03 4.132E-03 4.765E-03 5.162E-03 4.280E-03 4.620E-03 4.770E-03 4.925E-03 4.650E-03Pu-240 2.840E-03 1.840E-03 1.890E-03 1.241E-03 2.404E-03 2.236E-03 1.360E-03 1.990E-03 2.410E-03 2.230E-03 1.620E-03Pu-241 1.805E-03 9.811E-04 5.722E-04 3.447E-04 7.847E-04 7.733E-04 6.200E-04 1.020E-03 1.260E-03 1.185E-03 8.400E-04Pu-242 1.020E-03 3.100E-04 3.208E-04 1.155E-04 6.001E-04 4.682E-04 1.390E-04 3.800E-04 6.290E-04 4.760E-04 2.110E-04

Am-241 2.261E-04 1.610E-04 -3.750E-04 -2.266E-04 -4.859E-04 -4.456E-04 -1.534E-05 -2.195E-05 -2.499E-05 -2.416E-05 -1.893E-05Am-243 2.380E-04 4.380E-05 -4.432E-05 -1.061E-05 -1.155E-04 -8.332E-05 -1.719E-05 -6.743E-05 -1.381E-04 -8.561E-05 -3.026E-05

Cm-242b 1.367E-05 -2.858E-07 -1.019E-09 -6.030E-10 -1.557E-09 -1.489E-09 4.500E-06 -1.116E-05 1.479E-05 1.501E-05 7.100E-06Cm-244b 1.386E-04 1.226E-05 -6.175E-06 -9.084E-07 -2.462E-05 -1.550E-05 2.040E-06 -1.675E-05 4.162E-05 2.349E-05 5.130E-06

Mo-95 1.180E-03 7.580E-04 -5.580E-04 -3.923E-04 -7.086E-04 -6.475E-04 -3.992E-04 -5.547E-04 -6.603E-04 -5.765E-04 -4.436E-04

Tc-99 1.120E-03 5.990E-04 5.360E-04 3.604E-04 6.691E-04 5.930E-04 -4.864E-04 -6.808E-04 -8.162E-04 -7.099E-04 -5.434E-04

Ru-101 1.210E-03 7.490E-04 -5.540E-04 -3.741E-04 -7.317E-04 -6.593E-04 -4.690E-04 -6.783E-04 -8.326E-04 -7.129E-04 -5.302E-04Rh-103 5.400E-04 4.540E-04 -3.443E-04 -2.366E-04 -4.430E-04 -4.048E-04 -2.561E-04 -3.574E-04 -4.255E-04 -3.753E-04 -2.887E-04

Ag-109 1.190E-04 -3.224E-05 -3.153E-05 -1.750E-05 -4.760E-05 -4.114E-05 -2.088E-05 -3.722E-05 -5.110E-05 -4.091E-05 -2.603E-05Cs-133 1.630E-03 1.080E-03 -8.375E-04 -5.862E-04 -1.064E-03 -9.738E-04 -7.272E-04 -1.010E-03 -1.200E-03 -1.051E-03 -8.099E-04

Nd-143 1.070E-03 8.620E-04 5.711E-04 4.429E-04 6.550E-04 6.592E-04 -5.477E-04 -6.922E-04 -7.723E-04 -7.200E-04 -5.988E-04Nd-145 9.890E-04 6.760E-04 4.819E-04 3.445E-04 5.853E-04 5.573E-04 -4.451E-04 -6.070E-04 -7.131E-04 -6.297E-04 -4.923E-04

Pm-147b -1.348E-04 -1.183E-04 -1.062E-05 -8.323E-06 -1.473E-05 -1.399E-05 -1.711E-04 -2.100E-04 -2.276E-04 -2.132E-04 -1.827E-04

Sm-147 1.960E-04 1.610E-04 -1.981E-04 -1.551E-04 -2.227E-04 -2.128E-04 -4.812E-05 -5.796E-05 -6.118E-05 -5.808E-05 -5.086E-05Sm-149 3.360E-06 3.020E-06 -2.514E-06 -2.127E-06 -2.793E-06 -2.572E-06 -2.672E-06 -3.312E-06 -3.898E-06 -3.575E-06 -2.988E-06Sm-150 4.460E-04 2.430E-04 -1.959E-04 -1.259E-04 -2.695E-04 -2.393E-04 -1.605E-04 -2.443E-04 -3.102E-04 -2.605E-04 -1.855E-04Sm-151 1.470E-05 1.130E-05 -7.510E-06 -6.634E-06 -8.962E-06 -8.530E-06 -8.181E-06 -9.296E-06 -1.073E-05 -1.028E-05 -9.183E-06Sm-152 1.340E-04 9.460E-05 -8.817E-05 -6.354E-05 -1.069E-04 -9.928E-05 -7.537E-05 -1.006E-04 -1.147E-04 -1.023E-04 -8.195E-05

Eu-151 -4.348E-07 -3.422E-07 -9.726E-07 -8.654E-07 -1.067E-06 -1.018E-06 -1.554E-08 -1.200E-08 -1.145E-08 -1.311E-08 -1.580E-08Eu-153 1.840E-04 9.390E-05 -7.932E-05 -4.571E-05 -1.149E-04 -1.009E-04 -5.972E-05 -9.958E-05 -1.297E-04 -1.075E-04 -7.221E-05

Eu-155b 1.432E-05 4.405E-06 -1.536E-06 -8.306E-07 -2.680E-06 -2.288E-06 -5.164E-06 -9.433E-06 -1.300E-05 -1.031E-05 -6.392E-06

Gd-155 3.999E-06 2.635E-06 -5.186E-06 -2.812E-06 -7.737E-06 -6.613E-06 -4.599E-08 -6.728E-08 -8.600E-08 -7.579E-08 -5.582E-08

aTime after discharge. bDecay precursor. 
C-4 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Obrigheim 

BE124 

G7P1 

(10 days)a 

Obrigheim 

BE124 

G7P2 

(10 days) 

Obrigheim 

BE124 

G7P3 

(10 days) 

Obrigheim 

BE124 

G7P4 

(10 days) 

Obrigheim 

BE124 

G7P5 

(10 days) 

Obrigheim 

BE168 

(10 days) 

Obrigheim 

BE170 

(10 days) 

Obrigheim 

BE171 

(10 days) 

Obrigheim 

BE172 

(10 days) 

Obrigheim 

BE176 

(10 days) 

Takahama 

NT3G23 

SF95-2 

(10 days) 

U-234 -1.894E-04 -1.635E-04 -1.479E-04 -1.571E-04 -1.623E-04 -1.617E-04 -1.683E-04 -1.636E-04 -1.657E-04 -1.633E-04 2.850E-04U-235 1.521E-02 1.076E-02 7.555E-03 1.009E-02 1.009E-02 9.346E-03 1.043E-02 9.657E-03 9.830E-03 9.504E-03 1.927E-02U-236 2.920E-03 3.850E-03 3.960E-03 4.050E-03 3.600E-03 3.785E-03 3.651E-03 3.738E-03 3.680E-03 3.751E-03 4.024E-03U-238 9.580E-01 9.508E-01 9.464E-01 9.484E-01 9.502E-01 9.474E-01 9.494E-01 9.481E-01 9.491E-01 9.481E-01 9.424E-01

Np-237 -1.682E-04 -2.914E-04 -3.765E-04 -3.299E-04 -3.023E-04 -3.387E-04 -3.048E-04 -3.287E-04 -3.174E-04 -3.300E-04 -3.035E-04

Pu-238 3.100E-05 7.900E-05 1.415E-04 1.060E-04 7.900E-05 1.192E-04 8.875E-05 1.028E-04 9.392E-05 1.069E-04 7.102E-05Pu-239 4.260E-03 4.700E-03 5.015E-03 5.080E-03 5.080E-03 5.008E-03 4.876E-03 4.923E-03 4.793E-03 4.928E-03 5.655E-03Pu-240 1.160E-03 1.810E-03 2.280E-03 2.040E-03 1.950E-03 2.046E-03 1.881E-03 1.961E-03 1.895E-03 1.982E-03 1.539E-03Pu-241 5.500E-04 9.400E-04 1.205E-03 1.110E-03 1.050E-03 1.123E-03 1.026E-03 1.076E-03 1.031E-03 1.093E-03 9.578E-04Pu-242 9.900E-05 2.790E-04 4.890E-04 3.660E-04 3.200E-04 4.290E-04 3.445E-04 3.880E-04 3.720E-04 4.035E-04 1.844E-04

Am-241 -1.313E-05 -2.124E-05 -2.518E-05 -2.387E-05 -2.255E-05 -4.213E-05 -3.688E-05 -4.176E-05 -3.847E-05 -4.161E-05 2.344E-05Am-243 -9.930E-06 -4.535E-05 -8.923E-05 -6.167E-05 -4.874E-05 -6.469E-05 -4.871E-05 -5.962E-05 -5.428E-05 -6.031E-05 2.289E-05

Cm-242b 2.940E-06 8.580E-06 1.479E-05 1.188E-05 -9.287E-06 2.135E-05 1.880E-05 2.010E-05 2.180E-05 2.020E-05 7.672E-06Cm-244b 1.040E-06 9.490E-06 2.823E-05 1.652E-05 1.068E-05 1.755E-05 1.245E-05 1.590E-05 1.420E-05 1.675E-05 5.042E-06

Mo-95 -3.422E-04 -4.938E-04 -5.810E-04 -5.218E-04 -4.906E-04 -5.900E-04 -5.425E-04 -5.788E-04 -5.550E-04 -5.790E-04 -5.015E-04

Tc-99 -4.170E-04 -6.068E-04 -7.175E-04 -6.436E-04 -6.043E-04 -6.784E-04 -6.305E-04 -6.643E-04 -6.488E-04 -6.663E-04 -5.791E-04

Ru-101 -3.985E-04 -5.979E-04 -7.215E-04 -6.399E-04 -5.969E-04 -6.752E-04 -6.224E-04 -6.596E-04 -6.423E-04 -6.618E-04 -5.612E-04Rh-103 -2.207E-04 -3.221E-04 -3.809E-04 -3.440E-04 -3.233E-04 -3.635E-04 -3.370E-04 -3.564E-04 -3.442E-04 -3.566E-04 -3.099E-04

Ag-109 -1.657E-05 -3.123E-05 -4.193E-05 -3.533E-05 -3.183E-05 -3.629E-05 -3.207E-05 -3.501E-05 -3.359E-05 -3.518E-05 -2.453E-05Cs-133 -6.245E-04 -9.023E-04 -1.062E-03 -9.552E-04 -8.982E-04 -1.009E-03 -9.388E-04 -9.881E-04 -9.651E-04 -9.910E-04 -8.625E-04

Nd-143 -4.869E-04 -6.485E-04 -7.299E-04 -6.822E-04 -6.523E-04 -7.102E-04 -6.755E-04 -7.004E-04 -6.877E-04 -7.015E-04 7.149E-04Nd-145 -3.841E-04 -5.450E-04 -6.350E-04 -5.745E-04 -5.420E-04 -6.074E-04 -5.678E-04 -5.959E-04 -5.830E-04 -5.975E-04 5.384E-04

Pm-147b -1.524E-04 -1.961E-04 -2.146E-04 -2.016E-04 -1.942E-04 -1.822E-04 -1.780E-04 -1.796E-04 -1.776E-04 -1.797E-04 -1.937E-04

Sm-147 -4.281E-05 -5.405E-05 -5.789E-05 -5.485E-05 -5.315E-05 -8.641E-05 -7.990E-05 -8.582E-05 -8.487E-05 -8.636E-05 -5.667E-05Sm-149 -2.586E-06 -3.194E-06 -3.675E-06 -3.483E-06 -3.346E-06 -2.931E-06 -2.915E-06 -2.884E-06 -2.980E-06 -2.907E-06 -3.863E-06Sm-150 -1.342E-04 -2.127E-04 -2.648E-04 -2.313E-04 -2.136E-04 -2.395E-04 -2.187E-04 -2.332E-04 -2.248E-04 -2.336E-04 -1.969E-04Sm-151 -8.274E-06 -9.466E-06 -1.063E-05 -1.049E-05 -1.023E-05 -9.853E-06 -9.614E-06 -9.765E-06 -9.670E-06 -9.771E-06 -1.361E-05Sm-152 -6.463E-05 -8.995E-05 -1.022E-04 -9.290E-05 -8.819E-05 -9.930E-05 -9.342E-05 -9.762E-05 -9.555E-05 -9.785E-05 -8.020E-05

Eu-151 -1.918E-08 -1.448E-08 -1.374E-08 -1.550E-08 -1.619E-08 -1.724E-08 -1.742E-08 -1.774E-08 -1.634E-08 -1.740E-08 -3.832E-08Eu-153 -4.812E-05 -8.514E-05 -1.095E-04 -9.429E-05 -8.603E-05 -9.929E-05 -8.906E-05 -9.624E-05 -9.277E-05 -9.668E-05 -7.489E-05

Eu-155b -4.051E-06 -7.821E-06 -1.062E-05 -8.820E-06 -7.885E-06 -9.173E-06 -8.041E-06 -8.819E-06 -8.469E-06 -8.876E-06 -6.331E-06

Gd-155 -4.219E-08 -6.291E-08 -7.931E-08 -7.239E-08 -6.750E-08 -8.308E-08 -7.353E-08 -8.142E-08 -7.517E-08 -8.115E-08 -9.205E-08

aTime after discharge. bDecay precursor. 
C-5 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Takahama 

NT3G23 

SF95-3 

(10 days)a 

Takahama 

NT3G23 

SF95-4 

(10 days) 

Takahama 

NT3G23 

SF95-5 

(10 days) 

Takahama 

NT3G23 

SF96-2 

(10 days) 

Takahama 

NT3G23 

SF96-3 

(10 days) 

Takahama 

NT3G23 

SF96-4 

(10 days) 

Takahama 

NT3G23 

SF96-5 

(10 days) 

Takahama 

NT3G24 

SF97-2 

(1446 days)

Takahama 

NT3G24 

SF97-3 

(1446 days) 

Takahama 

NT3G24 

SF97-4 

(1446 days) 

Takahama 

NT3G24 

SF97-5 

(1446 days) 

U-234 1.873E-04 1.870E-04 2.829E-04 1.522E-04 1.251E-04 1.250E-04 1.354E-04 2.386E-04 2.089E-04 1.971E-04 1.963E-04U-235 1.326E-02 1.230E-02 1.544E-02 1.408E-02 8.638E-03 8.064E-03 9.937E-03 1.571E-02 1.030E-02 8.179E-03 7.932E-03U-236 4.911E-03 4.999E-03 4.566E-03 2.411E-03 3.244E-03 3.302E-03 3.013E-03 4.560E-03 5.312E-03 5.528E-03 5.532E-03U-238 9.338E-01 9.335E-01 9.388E-01 9.580E-01 9.476E-01 9.475E-01 9.522E-01 9.377E-01 9.282E-01 9.246E-01 9.247E-01

Np-237 -4.913E-04 -4.989E-04 -3.858E-04 1.323E-04 2.168E-04 2.252E-04 1.875E-04 4.037E-04 5.848E-04 6.607E-04 6.704E-04

Pu-238 1.539E-04 1.588E-04 1.020E-04 4.172E-05 1.206E-04 1.248E-04 7.978E-05 1.313E-04 2.680E-04 3.299E-04 3.275E-04Pu-239 6.194E-03 6.005E-03 5.635E-03 5.459E-03 6.001E-03 5.819E-03 5.519E-03 5.927E-03 6.216E-03 6.036E-03 5.975E-03Pu-240 2.186E-03 2.207E-03 1.821E-03 1.494E-03 2.303E-03 2.327E-03 1.964E-03 1.872E-03 2.478E-03 2.679E-03 2.659E-03Pu-241 1.486E-03 1.466E-03 1.153E-03 8.684E-04 1.498E-03 1.480E-03 1.203E-03 1.019E-03 1.394E-03 1.461E-03 1.448E-03Pu-242 4.516E-04 4.803E-04 2.976E-04 1.615E-04 5.103E-04 5.411E-04 3.551E-04 3.152E-04 6.517E-04 8.246E-04 8.341E-04

Am-241 3.310E-05 2.351E-05 2.840E-05 1.735E-05 2.845E-05 3.094E-05 2.149E-05 2.550E-04 3.429E-04 3.611E-04 3.584E-04Am-243 8.047E-05 8.472E-05 4.400E-05 1.728E-05 8.872E-05 9.598E-05 5.078E-05 5.130E-05 1.409E-04 1.923E-04 1.934E-04

Cm-242b 1.964E-05 2.328E-05 1.006E-05 5.781E-06 1.628E-05 1.679E-05 1.115E-05 2.496E-08 4.260E-08 4.711E-08 4.403E-08Cm-244b 2.562E-05 2.837E-05 1.064E-05 3.092E-06 2.862E-05 3.128E-05 1.280E-05 1.189E-05 4.895E-05 7.570E-05 7.582E-05

Mo-95 -6.978E-04 -7.226E-04 -6.159E-04 -3.065E-04 -5.085E-04 -5.214E-04 -4.447E-04 -7.203E-04 -9.467E-04 -1.040E-03 -1.046E-03

Tc-99 -8.081E-04 -8.356E-04 -7.105E-04 -3.930E-04 -6.511E-04 -6.664E-04 -5.679E-04 -7.067E-04 -9.319E-04 -1.023E-03 -1.028E-03

Ru-101 -8.084E-04 -8.373E-04 -6.983E-04 -3.854E-04 -6.635E-04 -6.793E-04 -5.691E-04 -6.953E-04 -9.472E-04 -1.053E-03 -1.058E-03Rh-103 -4.289E-04 -4.402E-04 -3.753E-04 -2.363E-04 -3.831E-04 -3.890E-04 -3.337E-04 -4.046E-04 -5.286E-04 -5.731E-04 -5.731E-04

Ag-109 -4.250E-05 -4.411E-05 -3.310E-05 -2.225E-05 -4.411E-05 -4.499E-05 -3.572E-05 -3.327E-05 -5.278E-05 -6.090E-05 -6.073E-05Cs-133 -1.193E-03 -1.233E-03 -1.054E-03 -5.911E-04 -9.716E-04 -9.942E-04 -8.501E-04 -1.051E-03 -1.373E-03 -1.501E-03 -1.510E-03

Nd-143 9.299E-04 9.373E-04 8.303E-04 4.778E-04 7.158E-04 7.184E-04 6.433E-04 8.307E-04 1.008E-03 1.048E-03 1.049E-03Nd-145 7.392E-04 7.598E-04 6.518E-04 3.575E-04 5.766E-04 5.880E-04 5.095E-04 6.480E-04 8.387E-04 9.118E-04 9.179E-04

Pm-147b -2.374E-04 -2.432E-04 -2.235E-04 -1.441E-04 -2.029E-04 -2.068E-04 -1.886E-04 -7.132E-05 -8.337E-05 -8.735E-05 -8.786E-05

Sm-147 -6.690E-05 -6.869E-05 -6.472E-05 -3.403E-05 -4.702E-05 -4.811E-05 -4.442E-05 2.050E-04 2.355E-04 2.468E-04 2.479E-04Sm-149 -4.482E-06 -4.343E-06 -3.883E-06 -3.000E-06 -3.869E-06 -3.749E-06 -3.312E-06 3.976E-06 4.259E-06 3.943E-06 3.799E-06Sm-150 -3.016E-04 -3.129E-04 -2.522E-04 -1.321E-04 -2.448E-04 -2.504E-04 -2.039E-04 2.499E-04 3.599E-04 4.074E-04 4.113E-04Sm-151 -1.540E-05 -1.464E-05 -1.318E-05 -1.044E-05 -1.235E-05 -1.165E-05 -1.048E-05 1.351E-05 1.503E-05 1.491E-05 1.465E-05Sm-152 -1.050E-04 -1.094E-04 -9.723E-05 -6.394E-05 -9.722E-05 -1.003E-04 -8.923E-05 9.546E-05 1.191E-04 1.298E-04 1.319E-04

Eu-151 -2.960E-08 -2.641E-08 -2.852E-08 -2.808E-08 -1.970E-08 -1.762E-08 -1.846E-08 -6.467E-07 -7.017E-07 -6.819E-07 -6.460E-07Eu-153 -1.210E-04 -1.257E-04 -9.904E-05 -6.290E-05 -1.131E-04 -1.150E-04 -9.399E-05 -9.922E-05 -1.460E-04 -1.642E-04 -1.645E-04

Eu-155b -1.168E-05 -1.225E-05 -8.994E-06 -5.351E-06 -1.098E-05 -1.123E-05 -8.767E-06 -4.979E-06 -8.301E-06 -9.682E-06 -9.696E-06

Gd-155 -1.293E-07 -1.246E-07 -1.003E-07 -8.541E-06 -7.718E-06 -7.085E-06 -6.989E-06 -3.528E-06 -5.830E-06 -6.771E-06 -6.771E-06

aTime after discharge. bDecay precursor. 
C-6 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Takahama 

NT3G24 

SF97-6 

(1446 days)a 

TMI-1 

NJ05YU 

A1B 

(1711 days) 

TMI-1 

NJ05YU 

A2 

(1103 days) 

TMI-1 

NJ05YU 

B1B 

(1711 days) 

TMI-1 

NJ05YU 

B2 

(1103 days) 

TMI-1 

NJ05YU 

B3J 

(1711 days) 

TMI-1 

NJ05YU 

C1 

(1103 days) 

TMI-1 

NJ05YU 

C2B 

(1711 days) 

TMI-1 

NJ05YU 

C3 

(1103 days) 

TMI-1 

NJ05YU 

D1A2 

(1711 days) 

TMI-1 

NJ05YU 

D1A4 

(1711 days) 

U-234 2.124E-04 2.054E-04 1.912E-04 1.877E-04 1.868E-04 1.834E-04 1.977E-04 1.808E-04 1.847E-04 1.927E-04 1.975E-04U-235 1.016E-02 8.604E-03 6.319E-03 6.386E-03 6.205E-03 6.111E-03 6.588E-03 6.228E-03 6.251E-03 6.966E-03 7.485E-03U-236 5.272E-03 5.111E-03 5.497E-03 5.402E-03 5.400E-03 5.456E-03 5.470E-03 5.185E-03 5.327E-03 5.452E-03 5.362E-03U-238 9.310E-01 9.292E-01 9.239E-01 9.202E-01 9.247E-01 9.217E-01 9.240E-01 9.226E-01 9.233E-01 9.178E-01 9.229E-01

Np-237 5.573E-04 6.040E-04 6.938E-04 7.012E-04 6.917E-04 7.060E-04 7.041E-04 6.864E-04 6.823E-04 7.058E-04 6.848E-04

Pu-238 2.265E-04 4.033E-04 3.538E-04 4.316E-04 3.144E-04 3.982E-04 3.299E-04 4.585E-04 2.511E-04 3.809E-04 3.747E-04Pu-239 5.676E-03 5.064E-03 5.340E-03 5.107E-03 5.289E-03 5.088E-03 5.405E-03 4.991E-03 5.512E-03 5.452E-03 5.399E-03Pu-240 2.331E-03 2.342E-03 2.781E-03 2.632E-03 2.728E-03 2.654E-03 2.753E-03 2.546E-03 2.844E-03 2.708E-03 2.621E-03Pu-241 1.233E-03 1.208E-03 1.358E-03 1.362E-03 1.387E-03 1.364E-03 1.423E-03 1.329E-03 1.403E-03 1.469E-03 1.430E-03Pu-242 5.977E-04 6.792E-04 9.229E-04 9.570E-04 9.145E-04 1.106E-03 9.000E-04 9.318E-04 9.233E-04 9.637E-04 9.414E-04

Am-241 3.029E-04 3.466E-04 3.021E-04 2.880E-04 3.412E-04 5.060E-04 3.770E-04 5.074E-04 3.028E-04 3.350E-04 5.261E-04Am-243 1.170E-04 1.245E-04 2.541E-04 2.043E-04 2.552E-04 2.111E-04 2.458E-04 1.956E-04 2.465E-04 2.056E-04 1.846E-04

Cm-242b 3.725E-08 -2.117E-08 -2.954E-07 -2.741E-08 -2.884E-07 -2.641E-08 -2.933E-07 -2.641E-08 -2.993E-07 -2.870E-08 -2.594E-08Cm-244b 3.627E-05 -5.288E-05 -9.473E-05 -1.205E-04 -9.143E-05 -1.064E-04 -9.367E-05 -1.056E-04 -1.011E-04 -1.329E-04 -9.068E-05

Mo-95 -9.266E-04 1.041E-03 1.118E-03 1.150E-03 1.128E-03 1.124E-03 1.100E-03 1.098E-03 1.006E-03 1.111E-03 1.089E-03

Tc-99 -9.095E-04 1.422E-03 1.081E-03 1.316E-03 1.091E-03 1.244E-03 1.081E-03 1.356E-03 1.034E-03 1.138E-03 1.191E-03

Ru-101 -9.175E-04 1.115E-03 1.155E-03 1.187E-03 1.202E-03 1.171E-03 1.164E-03 1.172E-03 1.025E-03 1.129E-03 1.098E-03Rh-103 -5.108E-04 5.956E-04 6.190E-04 6.267E-04 6.288E-04 6.203E-04 6.181E-04 6.145E-04 5.475E-04 6.168E-04 6.027E-04

Ag-109 -4.905E-05 5.111E-05 5.968E-05 4.399E-05 5.280E-05 7.788E-05 5.359E-05 6.532E-05 9.233E-05 4.607E-05 8.463E-05Cs-133 -1.343E-03 -1.426E-03 -1.567E-03 -1.654E-03 -1.554E-03 -1.621E-03 -1.553E-03 -1.610E-03 -1.581E-03 -1.679E-03 -1.558E-03

Nd-143 9.736E-04 9.850E-04 9.516E-04 1.086E-03 9.987E-04 1.060E-03 9.794E-04 1.033E-03 9.510E-04 1.111E-03 1.080E-03Nd-145 8.247E-04 8.521E-04 8.777E-04 9.847E-04 9.062E-04 9.770E-04 8.972E-04 9.411E-04 8.965E-04 1.000E-03 9.598E-04

Pm-147b -8.329E-05 -6.966E-05 -1.113E-04 -7.263E-05 -1.104E-04 -7.257E-05 -1.102E-04 -7.191E-05 -1.109E-04 -7.312E-05 -7.135E-05

Sm-147 2.371E-04 2.258E-04 1.968E-04 2.549E-04 1.859E-04 2.479E-04 1.866E-04 2.288E-04 1.819E-04 2.515E-04 2.353E-04Sm-149 3.843E-06 3.113E-06 3.816E-06 3.423E-06 3.264E-06 3.189E-06 3.188E-06 3.358E-06 2.899E-06 3.855E-06 3.599E-06Sm-150 3.409E-04 3.577E-04 3.742E-04 4.675E-04 3.754E-04 4.525E-04 3.835E-04 4.189E-04 3.619E-04 4.525E-04 4.125E-04Sm-151 1.294E-05 1.292E-05 1.256E-05 1.500E-05 1.341E-05 1.475E-05 1.247E-05 1.329E-05 1.256E-05 1.551E-05 1.412E-05Sm-152 1.207E-04 1.217E-04 1.321E-04 1.436E-04 1.295E-04 1.419E-04 1.266E-04 1.301E-04 1.256E-04 1.423E-04 1.338E-04

Eu-151 -6.130E-07 -7.296E-07 -5.071E-07 -8.054E-07 -5.119E-07 -7.798E-07 -5.285E-07 -8.042E-07 -5.208E-07 -8.334E-07 -8.116E-07Eu-153 -1.392E-04 1.468E-04 1.709E-04 1.859E-04 1.674E-04 1.834E-04 1.672E-04 1.725E-04 1.606E-04 1.891E-04 1.744E-04

Eu-155b -7.776E-06 1.004E-05 1.284E-05 1.546E-05 1.313E-05 1.032E-05 1.432E-05 9.964E-06 1.274E-05 9.821E-06 1.264E-05

Gd-155 -5.444E-06 8.223E-06 6.060E-06 1.003E-05 6.547E-06 1.041E-05 6.357E-06 9.411E-06 6.666E-06 1.019E-05 1.394E-05

aTime after discharge. bDecay precursor. 
C-7 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

TMI-1 

NJ05YU 

D2 

(1103 days)a 

TMI-1 

NJ070G 

O12S4 

(1298 days) 

TMI-1 

NJ070G 

O12S5 

(1529 days) 

TMI-1 

NJ070G 

O12S6 

(1298 days) 

TMI-1 

NJ070G 

O13S7 

(1529 days) 

TMI-1 

NJ070G 

O13S8 

(1529 days) 

TMI-1 

NJ070G 

O1S1 

(1298 days) 

TMI-1 

NJ070G 

O1S2 

(1529 days) 

TMI-1 

NJ070G 

O1S3 

(1298 days) 

Trino I 

509-032 

E11P1 

(10 days) 

Trino I 

509-032 

E11P4 

(10 days) 

U-234 1.923E-04 3.332E-04 3.126E-04 3.260E-04 3.427E-04 3.184E-04 3.263E-04 3.037E-04 3.134E-04 2.110E-04 2.312E-04U-235 7.378E-03 2.356E-02 2.181E-02 2.388E-02 2.376E-02 2.191E-02 2.203E-02 1.916E-02 2.170E-02 2.329E-02 1.728E-02U-236 5.334E-03 4.299E-03 4.615E-03 4.384E-03 4.216E-03 4.579E-03 4.529E-03 4.990E-03 4.668E-03 -1.554E-03 -2.676E-03U-238 9.292E-01 9.386E-01 9.361E-01 9.367E-01 9.389E-01 9.363E-01 9.376E-01 9.345E-01 9.354E-01 9.624E-01 9.558E-01

Np-237 6.755E-04 3.032E-04 3.482E-04 3.278E-04 2.826E-04 3.474E-04 3.038E-04 3.953E-04 3.639E-04 -6.298E-05 -1.757E-04

Pu-238 3.252E-04 6.270E-05 8.799E-05 7.765E-05 6.019E-05 8.699E-05 7.192E-05 1.084E-04 9.354E-05 -5.814E-06 -3.304E-05Pu-239 5.427E-03 5.435E-03 6.000E-03 6.182E-03 5.418E-03 5.880E-03 5.448E-03 5.588E-03 6.024E-03 3.483E-03 5.266E-03Pu-240 2.667E-03 1.389E-03 1.647E-03 1.508E-03 1.371E-03 1.620E-03 1.519E-03 1.850E-03 1.712E-03 4.420E-04 1.118E-03Pu-241 1.366E-03 6.890E-04 8.397E-04 7.999E-04 6.610E-04 8.230E-04 7.539E-04 9.149E-04 8.942E-04 1.710E-04 6.140E-04Pu-242 7.945E-04 1.483E-04 2.059E-04 1.649E-04 1.446E-04 2.022E-04 1.800E-04 2.841E-04 2.208E-04 1.170E-05 8.425E-05

Am-241 3.457E-04 1.521E-04 2.078E-04 1.377E-04 1.624E-04 2.022E-04 1.144E-04 1.981E-04 1.712E-04 -3.545E-06 -1.446E-05Am-243 1.923E-04 1.690E-05 2.771E-05 1.649E-05 1.606E-05 2.669E-05 1.500E-05 3.504E-05 2.563E-05 -3.999E-07 -8.362E-06

Cm-242b -2.557E-07 1.849E-08 1.123E-08 1.873E-08 6.995E-09 1.170E-08 1.772E-08 1.635E-08 2.713E-08 -3.050E-07 -2.830E-06Cm-244b -6.015E-05 2.713E-06 5.158E-06 3.016E-06 2.460E-06 4.897E-06 2.494E-06 7.177E-06 4.976E-06 -2.337E-08 -1.141E-06

Mo-95 9.199E-04 -5.840E-04 -6.423E-04 -5.936E-04 -5.766E-04 -6.386E-04 -6.288E-04 -7.211E-04 -6.538E-04 -1.506E-04 -3.051E-04

Tc-99 9.757E-04 -5.642E-04 -6.219E-04 -5.746E-04 -5.571E-04 -6.184E-04 -6.075E-04 -6.986E-04 -6.332E-04 -1.815E-04 -3.722E-04

Ru-101 9.478E-04 -5.388E-04 -5.994E-04 -5.510E-04 -5.317E-04 -5.959E-04 -5.828E-04 -6.793E-04 -6.112E-04 -1.688E-04 -3.576E-04Rh-103 5.157E-04 -3.211E-04 -3.569E-04 -3.296E-04 -3.171E-04 -3.551E-04 -3.466E-04 -4.024E-04 -3.647E-04 -9.609E-05 -2.032E-04

Ag-109 4.655E-05 -2.012E-05 -2.430E-05 -2.144E-05 -1.974E-05 -2.412E-05 -2.265E-05 -2.943E-05 -2.514E-05 -4.739E-06 -1.519E-05Cs-133 -1.421E-03 -8.441E-04 -9.286E-04 -8.590E-04 -8.337E-04 -9.234E-04 -9.080E-04 -1.041E-03 -9.449E-04 -2.743E-04 -5.597E-04

Nd-143 9.134E-04 7.049E-04 7.638E-04 7.175E-04 6.958E-04 7.594E-04 7.454E-04 8.336E-04 7.745E-04 -2.353E-04 -4.516E-04Nd-145 8.288E-04 5.247E-04 5.719E-04 5.283E-04 5.174E-04 5.693E-04 5.626E-04 6.420E-04 5.809E-04 -1.725E-04 -3.442E-04

Pm-147b -1.071E-04 -8.540E-05 -7.556E-05 -8.473E-05 -7.164E-05 -7.528E-05 -9.014E-05 -8.168E-05 -9.072E-05 -7.746E-05 -1.399E-04

Sm-147 1.821E-04 1.699E-04 1.881E-04 1.677E-04 1.746E-04 1.863E-04 1.791E-04 2.056E-04 1.815E-04 -1.987E-05 -3.536E-05Sm-149 3.094E-06 4.055E-06 4.156E-06 4.430E-06 3.972E-06 4.139E-06 4.051E-06 4.074E-06 4.415E-06 -2.248E-06 -2.907E-06Sm-150 3.485E-04 1.981E-04 2.256E-04 2.033E-04 1.934E-04 2.228E-04 2.157E-04 2.598E-04 2.310E-04 -5.279E-05 -1.215E-04Sm-151 1.264E-05 1.295E-05 1.413E-05 1.480E-05 1.268E-05 1.414E-05 1.275E-05 1.374E-05 1.431E-05 -7.796E-06 -1.016E-05Sm-152 1.208E-04 8.091E-05 8.677E-05 7.877E-05 7.953E-05 8.605E-05 8.654E-05 9.999E-05 8.924E-05 -2.671E-05 -5.593E-05

Eu-151 -5.209E-07 4.027E-07 4.699E-07 4.580E-07 4.206E-07 4.672E-07 3.891E-07 4.430E-07 4.312E-07 -4.310E-08 -2.966E-08Eu-153 1.561E-04 6.918E-05 8.097E-05 7.203E-05 6.695E-05 8.062E-05 7.548E-05 9.438E-05 8.231E-05 -1.478E-05 -4.351E-05

Eu-155b 1.227E-05 -3.267E-06 -3.590E-06 -3.440E-06 -2.915E-06 -3.555E-06 -3.721E-06 -4.443E-06 -4.100E-06 -1.425E-06 -3.597E-06

Gd-155 5.594E-06 1.905E-06 2.509E-06 2.182E-06 1.972E-06 2.528E-06 2.307E-06 2.888E-06 2.638E-06 -3.476E-08 -5.043E-08

aTime after discharge. bDecay precursor. 
C-8 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Trino I 

509-032 

E11P7 

(10 days)a 

Trino I 

509-032 

E11P9 

(10 days) 

Trino I 

509-032 

H9P4 

(10 days) 

Trino I 

509-032 

H9P7 

(10 days) 

Trino I 

509-032 

H9P9 

(10 days) 

Trino I 

509-049 

J8P1 

(10 days) 

Trino I 

509-049 

J8P4 

(10 days) 

Trino I 

509-049 

J8P7 

(10 days) 

Trino I 

509-049 

J8P9 

(10 days) 

Trino I 

509-049 

L5P1 

(10 days) 

Trino I 

509-049 

L5P4 

(10 days) 

U-234 1.410E-04 -2.121E-04 -1.955E-04 1.502E-04 1.676E-04 1.367E-04 1.312E-04 -1.685E-04 -1.812E-04 1.291E-04 1.435E-04U-235 1.661E-02 2.017E-02 1.672E-02 1.631E-02 1.889E-02 1.854E-02 1.390E-02 1.386E-02 1.663E-02 1.972E-02 1.503E-02U-236 -2.734E-03 -2.190E-03 -2.807E-03 -2.904E-03 -2.298E-03 -1.680E-03 -2.416E-03 -2.461E-03 -1.999E-03 -1.555E-03 -2.366E-03U-238 9.558E-01 9.595E-01 9.551E-01 9.548E-01 9.471E-01 9.654E-01 9.603E-01 9.595E-01 9.635E-01 9.658E-01 9.601E-01

Np-237 -1.802E-04 -1.153E-04 -1.845E-04 -1.961E-04 -1.198E-04 -7.793E-05 -1.583E-04 -1.615E-04 -1.048E-04 -7.101E-05 -1.592E-04

Pu-238 -3.455E-05 -1.611E-05 -3.601E-05 -3.982E-05 -1.727E-05 -8.971E-06 -2.989E-05 -3.088E-05 -1.478E-05 -7.622E-06 -3.005E-05Pu-239 5.234E-03 4.418E-03 5.172E-03 5.234E-03 4.446E-03 3.606E-03 4.769E-03 4.926E-03 4.134E-03 3.608E-03 5.016E-03Pu-240 1.137E-03 7.750E-04 1.211E-03 1.247E-03 8.340E-04 5.600E-04 1.160E-03 1.196E-03 8.020E-04 5.150E-04 1.121E-03Pu-241 6.180E-04 3.690E-04 6.760E-04 6.940E-04 4.090E-04 2.280E-04 6.150E-04 6.370E-04 3.710E-04 2.040E-04 6.025E-04Pu-242 9.252E-05 3.709E-05 1.047E-04 1.080E-04 -4.313E-05 1.887E-05 9.938E-05 1.036E-04 4.205E-05 1.532E-05 8.493E-05

Am-241 -1.486E-05 -8.487E-06 -1.545E-05 -1.632E-05 -9.102E-06 -5.749E-06 -1.430E-05 -1.449E-05 -8.535E-06 -4.868E-06 -1.418E-05Am-243 -9.124E-06 -2.521E-06 -1.033E-05 -1.214E-05 -3.049E-06 -1.118E-06 -8.889E-06 -9.454E-06 -2.726E-06 -7.782E-07 -8.375E-06

Cm-242b -3.009E-06 -1.187E-06 -3.296E-06 -3.674E-06 -1.369E-06 -6.598E-07 -2.952E-06 -3.073E-06 -1.261E-06 -5.015E-07 -2.816E-06Cm-244b -1.270E-06 -2.387E-07 -1.451E-06 -1.790E-06 -2.945E-07 -8.143E-08 -1.175E-06 -1.264E-06 -2.508E-07 -5.307E-08 -1.125E-06

Mo-95 -3.153E-04 -2.345E-04 -3.282E-04 -3.449E-04 -2.516E-04 -1.784E-04 -2.916E-04 -3.000E-04 -2.253E-04 -1.605E-04 -2.816E-04

Tc-99 -3.844E-04 -2.841E-04 -3.997E-04 -4.201E-04 -3.044E-04 -2.165E-04 -3.573E-04 -3.673E-04 -2.741E-04 -1.948E-04 -3.458E-04

Ru-101 -3.697E-04 -2.686E-04 -3.850E-04 -4.056E-04 -2.880E-04 -2.034E-04 -3.444E-04 -3.542E-04 -2.597E-04 -1.826E-04 -3.334E-04Rh-103 -2.094E-04 -1.526E-04 -2.174E-04 -2.280E-04 -1.628E-04 -1.173E-04 -1.982E-04 -2.031E-04 -1.492E-04 -1.056E-04 -1.927E-04

Ag-109 -1.581E-05 -9.540E-06 -1.669E-05 -1.787E-05 -1.038E-05 -6.975E-06 -1.565E-05 -1.612E-05 -9.904E-06 -6.022E-06 -1.515E-05Cs-133 -5.779E-04 -4.284E-04 -6.008E-04 -6.310E-04 -4.589E-04 -3.270E-04 -5.378E-04 -5.528E-04 -4.135E-04 -2.944E-04 -5.206E-04

Nd-143 -4.640E-04 -3.551E-04 -4.794E-04 -4.999E-04 -3.774E-04 -2.730E-04 -4.254E-04 -4.351E-04 -3.373E-04 -2.478E-04 -4.145E-04Nd-145 -3.553E-04 -2.663E-04 -3.691E-04 -3.873E-04 -2.851E-04 -2.035E-04 -3.286E-04 -3.377E-04 -2.556E-04 -1.835E-04 -3.181E-04

Pm-147b -1.438E-04 -1.137E-04 -1.484E-04 -1.542E-04 -1.208E-04 -8.941E-05 -1.338E-04 -1.370E-04 -1.092E-04 -8.146E-05 -1.300E-04

Sm-147 -3.633E-05 -2.900E-05 -3.756E-05 -3.898E-05 -3.086E-05 -2.294E-05 -3.399E-05 -3.482E-05 -2.797E-05 -2.089E-05 -3.286E-05Sm-149 -2.876E-06 -2.502E-06 -2.850E-06 -2.877E-06 -2.440E-06 -2.056E-06 -2.514E-06 -2.488E-06 -2.153E-06 -2.073E-06 -2.603E-06Sm-150 -1.260E-04 -8.787E-05 -1.317E-04 -1.396E-04 -9.471E-05 -6.517E-05 -1.171E-04 -1.207E-04 -8.515E-05 -5.803E-05 -1.133E-04Sm-151 -9.959E-06 -8.767E-06 -9.869E-06 -9.813E-06 -8.522E-06 -7.362E-06 -8.788E-06 -8.601E-06 -7.581E-06 -7.377E-06 -9.156E-06Sm-152 -5.799E-05 -4.336E-05 -6.053E-05 -6.351E-05 -4.693E-05 -3.369E-05 -5.573E-05 -5.748E-05 -4.334E-05 -2.987E-05 -5.343E-05

Eu-151 -2.799E-08 -3.299E-08 -2.638E-08 -2.479E-08 -2.967E-08 -3.211E-08 -2.381E-08 -2.248E-08 -2.637E-08 -3.538E-08 -2.603E-08Eu-153 -4.535E-05 -2.845E-05 -4.760E-05 -5.108E-05 -3.091E-05 -1.983E-05 -4.236E-05 -4.380E-05 -2.783E-05 -1.726E-05 -4.105E-05

Eu-155b -3.761E-06 -2.387E-06 -3.972E-06 -4.290E-06 -2.589E-06 -1.790E-06 -3.579E-06 -3.712E-06 -2.388E-06 -1.600E-06 -3.449E-06

Gd-155 -4.998E-08 -3.898E-08 -5.028E-08 -5.128E-08 -3.823E-08 -3.250E-08 -4.474E-08 -4.425E-08 -3.450E-08 -3.283E-08 -4.624E-08

aTime after discharge. bDecay precursor. 
C-9 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Trino I 

509-049 

L5P9 

(10 days)a 

Trino I 

509-104 

M11P7 

(10 days) 

Trino II 

509-069 

E11P1 

(10 days) 

Trino II 

509-069 

E11P2 

(10 days) 

Trino II 

509-069 

E11P4 

(10 days) 

Trino II 

509-069 

E11P5 

(10 days) 

Trino II 

509-069 

E11P7 

(10 days) 

Trino II 

509-069 

E11P8 

(10 days) 

Trino II 

509-069 

E11P9 

(10 days) 

Trino II 

509-069 

E5P4 

(10 days) 

Trino II 

509-069 

E5P7 

(10 days) 

U-234 1.545E-04 -2.687E-04 -2.064E-04 -1.811E-04 -1.720E-04 -1.699E-04 -1.709E-04 -1.737E-04 -1.864E-04 -1.717E-04 -1.703E-04U-235 1.745E-02 2.663E-02 1.946E-02 1.436E-02 1.248E-02 1.227E-02 1.235E-02 1.262E-02 1.497E-02 1.291E-02 1.221E-02U-236 -1.879E-03 -2.503E-03 2.450E-03 3.315E-03 3.615E-03 3.620E-03 3.640E-03 3.590E-03 3.240E-03 3.530E-03 3.545E-03U-238 9.639E-01 9.513E-01 9.591E-01 9.522E-01 9.498E-01 9.491E-01 9.496E-01 9.502E-01 9.542E-01 9.496E-01 9.487E-01

Np-237 -9.819E-05 -1.234E-04 -1.408E-04 -2.657E-04 -3.159E-04 -3.276E-04 -3.208E-04 -3.047E-04 -2.352E-04 -3.181E-04 -3.245E-04

Pu-238 -1.314E-05 -1.600E-05 2.500E-05 8.050E-05 1.090E-04 1.170E-04 1.170E-04 1.190E-04 6.800E-05 1.170E-04 1.155E-04Pu-239 4.116E-03 4.586E-03 4.580E-03 5.755E-03 5.895E-03 6.010E-03 6.070E-03 5.910E-03 5.630E-03 5.950E-03 5.980E-03Pu-240 7.325E-04 7.165E-04 8.400E-04 1.520E-03 1.755E-03 1.790E-03 1.825E-03 1.720E-03 1.410E-03 1.760E-03 1.785E-03Pu-241 3.375E-04 3.475E-04 4.000E-04 8.850E-04 1.030E-03 1.040E-03 1.060E-03 1.030E-03 7.800E-04 1.050E-03 1.055E-03Pu-242 3.373E-05 3.057E-05 4.600E-05 1.720E-04 2.435E-04 2.400E-04 2.575E-04 2.320E-04 1.470E-04 2.400E-04 2.540E-04

Am-241 -7.653E-06 -7.615E-06 3.053E-05 5.569E-05 7.018E-05 1.693E-04 1.588E-04 -7.372E-05 -5.837E-05 8.093E-05 1.025E-04Am-243 -2.077E-06 -1.832E-06 -4.327E-06 2.395E-05 4.535E-05 5.495E-05 4.586E-05 4.372E-05 3.013E-05 -4.012E-05 4.617E-05

Cm-242b -1.032E-06 -9.494E-07 5.188E-06 1.770E-05 2.436E-05 2.574E-05 2.665E-05 2.452E-05 1.739E-05 2.319E-05 2.513E-05Cm-244b -1.834E-07 -1.631E-07 -4.852E-07 4.677E-06 9.021E-06 9.918E-06 9.908E-06 7.590E-06 3.641E-06 8.964E-06 9.426E-06

Mo-95 -2.066E-04 -2.479E-04 -2.859E-04 -4.386E-04 -4.974E-04 -5.126E-04 -5.096E-04 -4.933E-04 -4.149E-04 -5.002E-04 -5.141E-04

Tc-99 -2.515E-04 -2.944E-04 -3.136E-04 -4.856E-04 -5.520E-04 -5.690E-04 -5.651E-04 -5.465E-04 -4.577E-04 -5.552E-04 -5.703E-04

Ru-101 -2.378E-04 -2.801E-04 -2.993E-04 -4.774E-04 -5.483E-04 -5.665E-04 -5.619E-04 -5.415E-04 -4.467E-04 -5.517E-04 -5.674E-04Rh-103 -1.373E-04 -1.565E-04 -1.767E-04 -2.771E-04 -3.147E-04 -3.240E-04 -3.211E-04 -3.103E-04 -2.591E-04 -3.165E-04 -3.240E-04

Ag-109 -8.831E-06 -8.596E-06 -1.151E-05 -2.339E-05 -2.859E-05 -2.990E-05 -2.935E-05 -2.773E-05 -2.072E-05 -2.884E-05 -2.977E-05Cs-133 -3.795E-04 -4.494E-04 -4.742E-04 -7.303E-04 -8.280E-04 -8.530E-04 -8.475E-04 -8.203E-04 -6.893E-04 -8.328E-04 -8.551E-04

Nd-143 -3.125E-04 -3.806E-04 -3.924E-04 -5.739E-04 -6.372E-04 -6.524E-04 -6.476E-04 -6.300E-04 -5.441E-04 -6.401E-04 -6.522E-04Nd-145 -2.349E-04 -2.821E-04 -2.931E-04 -4.441E-04 -5.012E-04 -5.158E-04 -5.128E-04 -4.971E-04 -4.208E-04 -5.039E-04 -5.172E-04

Pm-147b -1.013E-04 -1.211E-04 -7.947E-05 -1.134E-04 -1.251E-04 -1.280E-04 -1.276E-04 -1.245E-04 -1.087E-04 -1.257E-04 -1.285E-04

Sm-147 -2.590E-05 -3.084E-05 -7.251E-05 -9.869E-05 -1.068E-04 -1.089E-04 -1.089E-04 -1.070E-04 -9.602E-05 -1.072E-04 -1.095E-04Sm-149 -2.180E-06 -3.019E-06 -2.352E-06 -2.719E-06 -2.821E-06 -2.826E-06 -2.762E-06 -2.704E-06 -2.511E-06 -2.822E-06 -2.766E-06Sm-150 -7.712E-05 -9.085E-05 -9.584E-05 -1.605E-04 -1.874E-04 -1.944E-04 -1.923E-04 -1.843E-04 -1.485E-04 -1.887E-04 -1.944E-04Sm-151 -7.750E-06 -1.044E-05 -9.552E-06 -1.148E-05 -1.198E-05 -1.199E-05 -1.167E-05 -1.139E-05 -1.047E-05 -1.199E-05 -1.170E-05Sm-152 -4.015E-05 -4.372E-05 -4.705E-05 -6.994E-05 -7.799E-05 -8.012E-05 -8.007E-05 -7.806E-05 -6.734E-05 -7.843E-05 -8.072E-05

Eu-151 -2.969E-08 -4.447E-08 -8.589E-08 -5.323E-08 -4.530E-08 -4.308E-08 -4.189E-08 -4.283E-08 -5.178E-08 -4.493E-08 -4.141E-08Eu-153 -2.453E-05 -2.826E-05 -3.396E-05 -6.597E-05 -7.941E-05 -8.279E-05 -8.164E-05 -7.762E-05 -5.950E-05 -8.004E-05 -8.269E-05

Eu-155b -2.139E-06 -2.343E-06 -2.585E-06 -5.379E-06 -6.770E-06 -7.140E-06 -7.017E-06 -6.585E-06 -4.763E-06 -6.836E-06 -7.130E-06

Gd-155 -3.432E-08 -4.490E-08 -7.138E-08 -1.093E-07 -1.243E-07 -1.268E-07 -1.219E-07 -1.158E-07 -9.345E-08 -1.248E-07 -1.229E-07

aTime after discharge. bDecay precursor. 
C-10 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Trino II 

509-069 

E5P9 

(10 days)a

Trino II 

509-069 

J9P4 

(10 days) 

Trino II 

509-069 

J9P7 

(10 days) 

Trino II 

509-069 

L11P4 

(10 days) 

Trino II 

509-069 

L11P7 

(10 days) 

Trino II 

509-069 

L5P4 

(10 days) 

Trino II 

509-069 

L5P7 

(10 days) 

Turkey Point 

D01 

G10 

(927 days)

Turkey Point 

D01 

G9 

(927 days) 

Turkey Point 

D01 

H9 

(927 days) 

U-234 -1.866E-04 -1.694E-04 -1.689E-04 -1.715E-04 -1.708E-04 -1.703E-04 -1.710E-04 1.299E-04 1.299E-04 1.205E-04U-235 1.514E-02 1.201E-02 1.175E-02 1.282E-02 1.225E-02 1.297E-02 1.231E-02 5.607E-03 5.793E-03 5.515E-03U-236 3.270E-03 3.640E-03 3.690E-03 3.760E-03 3.465E-03 3.480E-03 3.570E-03 3.229E-03 3.228E-03 3.149E-03U-238 9.536E-01 9.483E-01 9.489E-01 9.489E-01 9.486E-01 9.491E-01 9.476E-01 9.510E-01 9.506E-01 9.499E-01

Np-237 -2.344E-04 -3.266E-04 -3.281E-04 -3.191E-04 -3.214E-04 -3.256E-04 -3.203E-04 -3.557E-04 -3.574E-04 -3.665E-04

Pu-238 6.300E-05 1.200E-04 1.340E-04 1.060E-04 1.160E-04 1.100E-04 1.140E-04 1.370E-04 1.365E-04 1.436E-04Pu-239 5.270E-03 5.820E-03 5.830E-03 6.060E-03 5.995E-03 6.060E-03 5.970E-03 4.875E-03 4.860E-03 4.966E-03Pu-240 1.330E-03 1.810E-03 1.840E-03 1.790E-03 1.810E-03 1.770E-03 1.790E-03 2.311E-03 2.286E-03 2.312E-03Pu-241 7.300E-04 1.070E-03 1.080E-03 1.050E-03 1.055E-03 1.060E-03 1.060E-03 1.076E-03 1.075E-03 1.113E-03Pu-242 1.350E-04 2.700E-04 2.820E-04 2.470E-04 2.590E-04 2.440E-04 2.500E-04 5.286E-04 5.107E-04 5.517E-04

Am-241 5.431E-05 6.787E-05 -7.725E-05 -7.769E-05 6.116E-05 1.006E-04 1.565E-04 -1.643E-04 -1.658E-04 -1.688E-04Am-243 -1.800E-05 -4.494E-05 5.015E-05 4.454E-05 4.249E-05 -4.271E-05 -4.137E-05 -1.029E-04 -1.056E-04 -1.141E-04

Cm-242b 1.394E-05 2.553E-05 2.848E-05 2.797E-05 2.467E-05 2.523E-05 2.482E-05 -3.371E-07 -3.430E-07 -3.594E-07Cm-244b 2.544E-06 1.070E-05 9.672E-06 9.159E-06 9.739E-06 9.528E-06 8.790E-06 -2.852E-05 -2.951E-05 -3.252E-05

Mo-95 -4.142E-04 -5.199E-04 -5.288E-04 -5.014E-04 -5.107E-04 -5.088E-04 -5.099E-04 -6.872E-04 -6.911E-04 -7.074E-04

Tc-99 -4.569E-04 -5.766E-04 -5.860E-04 -5.565E-04 -5.664E-04 -5.649E-04 -5.654E-04 -6.919E-04 -6.956E-04 -7.119E-04

Ru-101 -4.458E-04 -5.742E-04 -5.838E-04 -5.531E-04 -5.632E-04 -5.622E-04 -5.621E-04 -7.047E-04 -7.093E-04 -7.285E-04Rh-103 -2.586E-04 -3.274E-04 -3.314E-04 -3.173E-04 -3.218E-04 -3.220E-04 -3.212E-04 -4.207E-04 -4.230E-04 -4.327E-04

Ag-109 -2.065E-05 -3.033E-05 -3.077E-05 -2.894E-05 -2.944E-05 -2.965E-05 -2.935E-05 -4.425E-05 -4.474E-05 -4.637E-05Cs-133 -6.880E-04 -8.644E-04 -8.784E-04 -8.347E-04 -8.494E-04 -8.470E-04 -8.480E-04 -1.031E-03 -1.036E-03 -1.060E-03

Nd-143 -5.432E-04 -6.573E-04 -6.636E-04 -6.413E-04 -6.486E-04 -6.491E-04 -6.476E-04 -6.911E-04 -6.932E-04 -7.014E-04Nd-145 -4.201E-04 -5.226E-04 -5.310E-04 -5.050E-04 -5.139E-04 -5.121E-04 -5.131E-04 -6.065E-04 -6.094E-04 -6.230E-04

Pm-147b -1.086E-04 -1.295E-04 -1.313E-04 -1.259E-04 -1.278E-04 -1.273E-04 -1.277E-04 -1.002E-04 -1.003E-04 -1.016E-04

Sm-147 -9.595E-05 -1.103E-04 -1.120E-04 -1.074E-04 -1.091E-04 -1.083E-04 -1.090E-04 -1.464E-04 -1.465E-04 -1.483E-04Sm-149 -2.505E-06 -2.756E-06 -2.690E-06 -2.824E-06 -2.757E-06 -2.840E-06 -2.753E-06 -2.820E-06 -2.830E-06 -2.858E-06Sm-150 -1.481E-04 -1.970E-04 -2.003E-04 -1.893E-04 -1.928E-04 -1.928E-04 -1.923E-04 -2.568E-04 -2.587E-04 -2.662E-04Sm-151 -1.045E-05 -1.174E-05 -1.139E-05 -1.200E-05 -1.166E-05 -1.208E-05 -1.164E-05 -9.447E-06 -9.464E-06 -9.477E-06Sm-152 -6.728E-05 -8.156E-05 -8.324E-05 -7.858E-05 -8.029E-05 -7.955E-05 -8.020E-05 -1.012E-04 -1.017E-04 -1.043E-04

Eu-151 -5.182E-08 -4.057E-08 -3.774E-08 -4.481E-08 -4.168E-08 -4.410E-08 -4.174E-08 -2.885E-07 -2.889E-07 -2.888E-07Eu-153 -5.930E-05 -8.392E-05 -8.535E-05 -8.030E-05 -8.186E-05 -8.205E-05 -8.164E-05 -1.105E-04 -1.115E-04 -1.151E-04

Eu-155b -2.139E-06 -2.343E-06 -2.585E-06 -5.379E-06 -6.770E-06 -7.140E-06 -7.017E-06 -6.585E-06 -4.763E-06 -6.836E-06

Gd-155 -9.305E-08 -1.241E-07 -1.206E-07 -1.251E-07 -1.218E-07 -1.273E-07 -1.215E-07 -3.005E-06 -3.037E-06 -3.149E-06

aTime after discharge. bDecay precursor. 
C-11 

Table C.1 Reference nuclide concentrations (g/gU initial) (continued) 

Nuclide 

Turkey Point 

D04 

G10 

(927 days)a 

Turkey Point 

D04 

G9 

(927 days) 

U-234 1.298E-04 1.113E-04 U-235 5.593E-03 5.442E-03 U-236 3.226E-03 3.131E-03 U-238 9.502E-01 9.503E-01 

Np-237 -3.662E-04 -3.645E-04 

Pu-238 1.382E-04 1.392E-04 Pu-239 4.823E-03 4.977E-03 Pu-240 2.294E-03 2.337E-03 Pu-241 1.080E-03 1.132E-03 Pu-242 5.273E-04 5.467E-04 

Am-241 -1.674E-04 -1.679E-04 Am-243 -1.112E-04 -1.113E-04 

Cm-242b -3.528E-07 -3.536E-07 Cm-244b -3.189E-05 -3.181E-05 

Mo-95 -7.022E-04 -7.012E-04 

Tc-99 -7.073E-04 -7.060E-04 

Ru-101 -7.227E-04 -7.214E-04 Rh-103 -4.298E-04 -4.291E-04 

Ag-109 -4.584E-05 -4.582E-05 Cs-133 -1.053E-03 -1.051E-03 

Nd-143 -7.002E-04 -6.993E-04 Nd-145 -6.187E-04 -6.177E-04 

Pm-147b -1.013E-04 -1.011E-04 

Sm-147 -1.478E-04 -1.474E-04 Sm-149 -2.861E-06 -2.858E-06 Sm-150 -2.643E-04 -2.637E-04 Sm-151 -9.549E-06 -9.533E-06 Sm-152 -1.030E-04 -1.029E-04 

Eu-151 -2.912E-07 -2.907E-07 Eu-153 -1.140E-04 -1.138E-04 

Eu-155b -7.130E-06 -7.770E-06 

Gd-155 -3.121E-06 -3.115E-06 

aTime after discharge. bDecay precursor. 




UNITED STATES 

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

--------------------

OFFICIAL BUSINESS
NUREG/CR-7108 An Approach for Validating Actinide and Fission Product Burnup Credit 

Criticality Safety Analyses—Isotopic Composition Predictions