NUREG/CR-7108

113 Pages·2012·2.47 MB·English

NUREG/CR-7108
ORNL/TM-2011/509
An Approach for Validating
Actinide and Fission Product
Burnup Credit Criticality Safety
Analyses—Isotopic
Composition Predictions

Office of Nuclear Regulatory Research
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NUREG/CR-7108
ORNL/TM-2011/509
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

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.

iii

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 k ................................................. 23 
eff
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 k Calculations........................................................... 32 
eff
6.1.5 Validation of the Assumption for Data Normality ................................................... 33 
v
TABLE OF CONTENTS
(Continued)

Section Page
6.1.6 Convergence of the Monte Carlo k Bias Uncertainty Estimate ........................... 34 
eff
6.2  DIRECT-DIFFERENCE METHOD .................................................................................. 36 
7. BIAS AND BIAS UNCERTAINTY IN k RESULTS ............................................................... 43 
eff
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. k UNCERTAINTY ANALYSIS USING CROSS-SECTION
eff
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 k Bias and Bias Uncertainty Components ........................ A-7 
eff
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 
vi
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 ∆k results illustrating the bias and the margin
eff
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 k bias uncertainty for the representative PWR SFP storage rack model ................ 44 
eff
Figure 7.2 k bias uncertainty for the PWR SNF cask model ........................................................ 46 
eff
Figure 7.3 Variation of bias uncertainty in k with parameters important to criticality
eff
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 k values based on actual M/C concentration ratio
eff
235U
values for 235U within the burnup range 15 to 40 GWd/MTU ................................. A-6
Figure A.5 Individual nuclide contributions to k bias uncertainty for the representative
eff
PWR SFP storage rack model and 10-GWd/MTU assembly average burnup ........ A-7 

vii
LIST OF FIGURES
(Continued)

Figure Page
Figure A.6 Individual nuclide contributions to k bias uncertainty for the representative
eff
PWR SFP storage rack model and 40-GWd/MTU assembly average burnup. ... A-8 
Figure A.7 Individual nuclide contributions to k bias uncertainty for the PWR SNF cask
eff
model and 10-GWd/MTU assembly average burnup .......................................... A-8
Figure A.8 Individual nuclide contributions to k bias uncertainty for the PWR SNF cask
eff
model and 40-GWd/MTU assembly average burnup .......................................... A-8
Figure A.9 Individual nuclide contributions to k bias uncertainty for the unpoisoned
eff
PWR SFP storage rack model and 40-GWd/MTU assembly average burnup. .. A-9
Figure A.10 Illustration of k bias components using (a) ENDF/B-VII nuclear data;
eff
(b) ENDF/B-V nuclear data ........................................................................................ A-10 

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