ML20063C757
| ML20063C757 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear, Waterford  |
| Issue date: | 12/31/1993 |
| From: | Lang R, Ober T, Shacter K ENTERGY OPERATIONS, INC. |
| To: | |
| Shared Package | |
| ML20063C739 | List: |
| References | |
| ENEAD-01-NP, ENEAD-01-NP-R00, ENEAD-1-NP, ENEAD-1-NP-R, NUDOCS 9402070165 | |
| Download: ML20063C757 (176) | |
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ENTERGY QUALIFICATION OF REACTOR PHYSICS METHODS FOR THE PRESSURIZED WATER REACTORS OF THE ENTERGY SYSTEM 1
ENEAD-01-NP REV 0 EDC FILE QR-038-45 AUTHORS R. B. LANG T. G. OBER K.B.SHACTER CENTRAL DESIGN ENGINEERING ENTERGY OPERATIONS, INC.
DECEMBER 1993 9402070165 DR 940123 ADOCK 05000313
I ACKNOWLEDGMENTS The authors gratefully acknowledge calculations done by Mr. A. Bencheikh, Mr.
R. E. Griffith, Mr. B. A. Hawes, Mr. R. E. Machado, and Mr. K. B. Megehee that provide the technical basis for this report. Mr. S. G. Shue and Ms. A. B. Smith's assistance in the review of this report is also recognized. The authors also acknowledge the efforts of Mr. R. A. Thompson for his help with the undocumented design features of Microsoft WORD, and the assistance in implementing the Studsvik CMS provided by the employees of Studsvik of America.
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l IMPORTANT NOTICE FOR NON-PROPRIETARY VERSION l
This document is the property of Entergy Corporation. Proprietary information developed and owned by Entergy Corporation or others has been removed from this non-proprietary (NP) version of the report. Proprietary information is indicated by a vertical bar in the right margin. ;
This document was prepared by Entergy Corporation for the use of the United States Nuclear Regulatory Commission in matters regarding the operating - l licenses of Arkansas Nuclear One - Unit 1, Arkansas Nuclear One - Unit 2 and .
the Waterford Steam Electric Station - Unit 3. To the best of the issuer's - !
L knowledge, this document contains work performed in accordance wi'.h sound .j engineering practice and is a true and accurate representation of the facts. 3 Any usage other than as described above is prohibited. Other than for the intended usage, neither Entergy Corporation, nor any of its employees or officers, nor any other person acting on its behalf:
. Makes any warranty or representation, express or implied, with respect to :
the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed herein would not infringe privately owned rights; or ,
. Assumes any liabilities with respect to the use of, or for damages !
resulting from the use of, any information, apparatus, method, or process i disclosed in this report.
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TABLE OF CONTENTS 1.0 I ntrod u ctio n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2.0 Description of Entergy Reactors.. .. . . . . . . . .. . . . . ... .13 2.1 ANO-1. .. . . . . . . . . . . . . . . . . . . . . . . . . .... .. ..................13 2.2 ANO-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .......13 .
2.3 WSES-3. . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . 14 3.0 Overview of the Calculational Model..... . . . . . ..................32 3.1 Lattice Physics Model .. ... .... .. ... ... . ..... .. . ... . .. . . . . . ..... 34 3.1.1 IN T E R PI N . .. . . . . . . . . . . . . . . . .....................34 3.1.2 CASMO..... . . . . . . ... ...................34 3.1.3 MICBURN .. ...... ... . ..... . . . .. . . . . . . . . . . . ... . 36 3.2 Nodal Model . . . ... . ..... ... . . . . . ..............39 3.2.1 SIMULATE ..... ... . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 39 3.2.2 TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 41 3.3 Rhodium In-core Instrument Model.. . .. . . . . . . . . . . . ... .. . .. 4 2 3.3.1 RHOBURN... .... ..................................42 3.3.2 Instrument Data For the Core Monitoring Codes... . . ... 45 4.0 Model Verification and Reliability.. ...... . . . . . . . . . . . . . . . . ...............49 4.1 Overview.. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . ...49 4.2 Estimated Critical States......... ... .. . . . .. ..... .. . . .. ....... ..... .53 4.2.1 Hot Zero Power Critical Boron. . . .........................53-4.2.2 Target Eigenvalue at Power Conditions....... . .. ....... ........ 57 4.3 inverse Boron Worth.. ... . .... ..... . . .. . .. ....... . . . . . . . . . . . . . . . . . 63 4.4 Rod Worth . ... . .. . .. ..... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.4.1 Rod Worth by Dilution.. .... ..... . .. ... .......... .. .. ...... . 68 4.4.2 Rod Worth by Swap. .... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.5 Isothermal Temperature Coefficients.. . .. .. . . . . . . . . . . . . . . 74 4.6 lsotopics . .. . ... .. ..... . . .. .... ... . . . . . ... .................79 4.7 Doppler Coefficient.... . ..... ... .. ...... .................89 4.8 Delayed Neutron Parameters... . . . . . . . ......................92 4.9 Power Distributions.. . . ...'. .. ... . . . . . . . . . . . . . . . 97 4.9.1 Nodal Peaking Uncertainty . . .. . . . . . .. . 97 ENEAD-01-NP REV O Page 4
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i 4.9.1.1 3-D Peaking Factor, Fq ..... . . ... .... . . . .. . .. . . 100 '
i 4.9.1.2 Integrated Radial Peaking Factor, Fr..... .. ...109 4.9.1.3 Planar Peaking Factor, Fxy . ... ... .... ..... .. .. .114 4.9.2 Local Peaking Uncertainty . . .. . ., ... ..... ... ... ........ . . .. 118 4.9.3 Combined Nodal and Local Peaking Tolerance Limit.. . .134 4.9.4 Reliability Factors ... . . ... .. .. . . . . ... ... . . . . . . . . . . . . . . 1 36 5.0 References .... . . . . . . . . . . . . . . . . ...................................137 Appendix A: Benchmarking Statepoints. .. .. .. ... . . . . . . . . . .. . .. ... . 139 Appendix B: ANO-1 Representative Cycle Comparisons.. .. . .. . . . . . . . . . 150 [
Appendix C: ANO-2 Representative Cycle Comparisons . . .. . . . . ...... ...157 ' -
Appendix D: WSES-3 Representative Cycle Comparisons . . . ....... .... .164 Appendix E: Representative Measurement Uncertainties.. . . . . . . . . . .... . . . 172 .
Appendix F: Representative Model Uncertainties.. ... . . . . . . . . . ... 174 !
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LIST OF FIGURES 1
1 Figure 2.3-1. ANO-1 Assembly Numbers. . . . . . . . . . . . . .. . . . .. . .16 ],
Figure 2.3-2. ANO-1 Self Powered Neutron Detector Map. . .. . .. .. . . 17 1 Figure 2.3-3. ANO-1 Axial Location of in-core Detectors.. . .. . . . . . ..... 18 Figure 2.3-4. ANO-1 Fuel Assembly Layout... . . ... ................19 Figure 2.3-5. ANO-1 CEA Bank identification Map for Cycle 7. . . . . . . .20 !
Figure 2.3-6: ANO-1 CEA Bank identification Map for Cycle 8. . . . . . . . . . . 21 Figure 2.3-7. ANO-1 CEA Bank identification Map for Cycles 9-11.. .. .. ... 22 Figure 2.3-8. ANO-2 Assembly Numbers ..... ... ..... . . . . . . . . . . . . . . . . . . . . . 23 Figure 2.3-9. ANO-2 Self Powered Neutron Detector Map . . . . .. ... ... . 24 [
Figure 2.3-10. ANO-2 Axial Location of In-core Detectors. ...................25 Figure 2.3-11. ANO-2/WSES-3 Fuel Assembly Layout. . . . . .. .. . 26 Figure 2.3-12. ANO-2 CEA Bank identification... . . .... ...... . . . . . .'.27 ;
Figure 2.3-13. WSES-3 Assembly Numbers . .. . ... .. . . . . . . . .. 28 Figure 2.3-14. WSES-3 Self Powered Neutron Detector Map.. . . . . . . .. . 29 !
Figure 2.3-15. WSES-3 Axial Location of n-core Detectors. . . . . . . . . . .30 Figure 2.3-16. WSES-3 CEA Bank identification . . . . . . . . . . . . . . . . . . . 31 Figure 3.0-1. Calculational Flow.... ... . .. . .. ..... .. . .. . . . . . . . . . . . . . . ..33 Figure 3.3-1. RHOBURN Program Data Flow.. .
.........................48 Figure 4.2-1. HZP Critical Boron Histogram (Observed). .. .. .........55 i
Figure 4.2-2. HZP Critical Boron Differences (Observed) vs. CBC............... . 55 j Figure 4.2-3. SIMULATE Eigenvalue (Observed) vs. Cycle Bumup. ..... .. .... 58 Figure 4.3-1. Inverse Boron Worth (Observed) Histogram.. .. . . ........ .. .. . . 65 Figure 4.3-2. Inverse Boron Worth Differences (Observed) vs. IBW. .. ... ... 65 .
Figure 4.4-1. Observed Rod Worth (Dilution) Histogram . . ...... . . . .......... . 69 Figure 4.4-2. Observed Rod Worth (Dilution) Differences vs Rod Worth... .69 i Figure 4.4-3. Observed Rod Worth (Swap) Histogram . . . . . . . . . ... . 72 -
t Figure 4.4-4. Observed Rod Worth (Swap) Differences vs. Rod Worth.. . ... 72 ;
Figure 4.5-1. HZP ARO ITC (Observed) Histogram. . . . . . . . . . . . . . . . . . . . . ... 76 Figure 4.5-2. HZP ARO ITC Differences (Observed) vs. Boron Conc... . .... . 76 :
Figure 4.6-1. Zion Assemblies C63 and C64 Measured Pin Layout.. . . . . 82 Figure 4.6-2. CASMO 1/8 Zion Assembly Model.. . . . . . . . . . . . ..... . 83 i
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i Figure 4.6-3. Zion isotopics for Pins #616,642 and 614, Part 1.. . ... . ..... . 84 Figure 4.6-4. Zion isotopics for Pins #616,642 and 614, Part 2...... . ..... ... 84 :
Figure 4.6-5. Zion Isotopics for Pins #616,642, and 614, Part 3.............. . ... 85 !
Figure 4.6-6. Zion isotopics for Pins #616,642,699 and 624. .. .. ... .... ...... 85 Pgure 4.9-1. ANO-1 Fq Normal Distribution ... ... ............ ..............105 Figure 4.9-2. ANO-2 Fq Normal Distribution .. ... . ... . .. . . .. ... .... ....... .105 .
Figure 4.9-3. WSES-3 Fq Normal Distribution .. ........ . .. .. .. .. ... .106 !
Figure 4.9-4. WSES-3 Cycle 6 ASI Context of Snapshot W7746DF.. . ... ...107 Figure 4.9-5. Error Component Reliability Factor Calc. Flowchart. .. ... ... 108 '
Figure 4.9-6. ANO-1 Fr Normal Distribution.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1 1 Figure 4.9-7. ANO-2 Fr Normal Distribution... . .... . .... .. .... . .. 112 i Figure 4.9-8. WSES-3 Fr Normal Distribution. .. ... . . .. . . . . . . . . . . . . . . . 1 12 ;
Figure 4.9-9. ANO-1 Fxy Normal Distribution..... . ....... . . . . . . .. .. ..116 4 Figure 4.9-10. ANO-2 Fxy Normal Distribution... . ... . . .. ... . . . .. ... ... 116 Figure 4.9-11. WSES-3 Fxy Normal Distribution. ... .. .... . .. . . . . . . . .117- i Figure 4.9-12. B&W Core Design 1. ..... .... . ..............................120 ,
Figure 4.9-13. B&W Core Design 5.. . .. .. ... ..... . ..... . ... . . . . . . . . . . . .121- ;
Figure 4.9-14. B&W Core Design 12. ...... . ..... .... .. . . . . . . . . . . . . . . . . . . . . . 1 22 Figure 4.9-15. B&W Core Design 14... ... .. ... .. . .. ......... .. .. . .. . ..............123 r
Figure 4.9-16. B&W Core Design 18... . .. . ........ ...... ......... ... ..... .. . ........124 >
Figure 4.9-17. B&W Core Design 20.. . . .. ... ..... . . . .... . . .. . . . .. . . . . . . 125 'i i
Figure 4.9-18. CE Core Design 1.. .... .. . ....... .... ............................126 Figure 4.9-19. CE Core Design 2.... ... ... . .... . . . ... . ..127 Figure 4.9-20. CE Core Design 3... ...................................................128
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Figure 4.9-21. CE Core Design 4..... .......... . . .... ..... . .. ..... .... .. .... 12 9 !
Figure B.0-1. ANO-1 Cycle 9 Radial Map, BOC ...... .. .. .. .. ... . ........ .. .....151 jl Figure B.0-2. ANO-1 Cycle 9 R.adial Map, MOC.. . . . . . . . . . . . . . . . . . . . . . . . . . 1 52 i Figure B.0-3. A NO-1 Cycle 9 Ra Ja! Map, EOC . ... ... .. . .... . ... ...... .. ... 153 Figure B.0-4. J40 1 Cycle 9 Otring 18, BOC . ...... . .. .. . ..... . ... .. ... .. 154 Figure B.0-5. ANO-1 Cycle 9 String 36, BOC... .... . . ...... . . . . . . . . . . . . . . . . 1 54 Figure B.0-6. ANO-1 Cycle 9 String 18, MOC . .... . .. . . . . . ... . . ..... ....155 Cigure B.0-7. ANO-1 Cycle 9 String 36, MOC ... .. .. ........ . ......., . .. .. ...155 1 1
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Figure B.0-8. ANO-1 Cycle 9 String 18, EOC. .. . . ..156 i Figure B.0-9. ANO-1 Cycle 9 String 36, EOC. . . . . . . ... . . . . 156 :
Figure C.0-1. ANO-2 Cycle 2 Radial Map, BOC.. . . . . . .. .158 i Figure C.0-2. ANO-2 Cycle 2 Radial Map, MOC.. . . . . . . . .. . .... . 159 .
Figure C.0-3. ANO-2 Cycle 2 Radial Map, EOC... ... . .. ... ..160 ,
Figure C.0-4. ANO-2 Cycle 2 String 6, BOC. . . . . . . . . . . .... .161 Figure C.0-5. ANO-2 Cycle 2 String 18, BOC.... . . . . . .. .. ..... . 161 Figure C.0-6. ANO-2 Cycle 2 String 6, MOC . . . . . . . . . . . . . .. 162 :
Figure C.0-7. ANO-2 Cycle 2 String 18, MOC . .... . . . . .. . . 162 Figure C.0-8. ANO-2 Cycle 2 String 6, EOC. . . . . . . . . . . . . . . . 163 Figure C.0-9. ANO-2 Cycle 2 String 18, EOC. .. . .. . . . . . . . . ...163 :
Figure D.0-1. WSES-3 Cycle 3 Radial Map, BOC . . . . .. ....... 165 Figure D.0-2. WSES-3 Cycle 3 Radial Map, MOC.. ... . . . ... .. . .. .166 Figure D.0-3. WSES-3 Cycle 3 Radial Map, EOC . . ... . . .. .. 167 Figure D.0-4. WSES-3 Cycle 3 String 4, BOC. . .. . . . . . . .... ..... . 1 6 8 Figure D.0-5. WSES-3 Cycle 3 String 8, BOC.. . . . . . . .. ... . 1 6 9 Figure D.0-6. WSES-3 Cycle 3 String 4, MOC . . ... .. .. . . . . . . . .... 169 Figure D.0-7. WSES-3 Cycle 3 String 8, MOC . . . . . . . . . . .... ..170 i Figure D.0-8. WSES-3 Cycle 3 String 4, EOC.. .... . . . . . . . . . . . .. ... . 170 Figure D.0-9. WSES-3 Cycle 3 String 8, EOC. .. . . . . . . . . ... .171 i
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L LIST OF TABLES r i
Table 3.3-1. Detector Depletion Laws.. .. . . .. . . . . . . . . . . . . . . . . . .. . 4 7 !
Table 4.1-1. Reliability Factors for Entergy PWRs.. ...... ..... . . . . . . . . . . . . .. 52 Table 4.2-1. Observed HZP Critical Boron Differences... . ... . .. ... .. . .. . 56 Table 4.2-2. Thompson's Outlier Test for WSES3 Cycle 6 HZP CBC Data.56 Table 4.2-3. SIMULATE Eigenvalues (Observed)... . . . ...... .. .. . .. 59 Table 4.3-1. Observed IBW Differences.. . . . . . . . .. . . . . .. . . . 66 ,
Table 4.3-2. Thompson's Outlier Test for ANO-2 Cycle 3 HZP IBW Data .. 66 Table 4.4-1. Observed Rod Worth (Dilution) Differences.. ...........70 ,
Table 4.4-2. Observed Rod Worth (Swap) Differences. . . . . . . . . ... 73 ;
Table 4.5-1. Observed HZP ARO ITC Differences. . . ... . .............77 Table 4.5-2. Observed ITC Repeatability. . . . . ... . .. . . . . .78 Table 4.6-1. Zion isotopic Comparisons. . . . . . . ...................86 ,
Table 4.6-2. Isotopic Statistics .. . .. . . . . . . . . . . . . . . . . . . 88 Table 4.7-1. Calculated k-inf and Doppler Coefficients... .. .. . . . . . .. 91 Table 4.7-2. Calc. vs Meas. Resonance Integrals and Doppler Coef.. ....... 91 Table 4.8-1. Delayed Neutron Fraction Comparisons. . .. . ... .. . . . . . . . 96 Table 4.9-1. Overall Nodal Fq Uncertainties. .. ... .. ....... . . . . . . . . ..107 1 Table 4.9-2. Overall Nodal Fr Uncertainties. .... ... . .... . ... . . ... . ... 113 Table 4.9-3. Overall Nodal Fxy Uncertainties..... . ..... .. .... ... .. ..... . ..117 ,
Table 4.9-4. Gadolinia Core Information ..... . .......... . . . . . .. .130 ,
Table 4.9-5. Erbium Core information ..... . . ..... ..... ........ .... .... .. . ........ 131 '
Table 4.9-6. Summary of Core Designs Analyzed., .. . . . . .. .. . ........ . 131 Table 4.9-7. LPF Statistical Model Error Summary: All Cores.... . .. ... .. .132 {
Table 4.9-8. LPF Statistical Model Error Summary: B&W No-Gd Cores. .132 Table 4.9-9. LPF Statistical Model Error Summary: B&W Gd Cores..... ..132 l Table 4.9-10. LPF Statistical Model Error Summary: CE Cores. .. . . . . . . 133 Table 4.9-11. Pin Power Distribution Results. .. ...... . ...... ... . . .. . ...... . 133 l Table 4.9-12. Overall Local Peaking Uncertainty.... . ........... . ..... . . ...133 ;
Table 4.9-13. Power Reliability Factors Based on Signals.. .... . . . . .. . 1 3 5 Table 4.9-14. Power Reliability Factors Based on Powers.. . . . . . . . . .135 Table 4.9-15. Power Distribution Reliability Factors . . . . . . . . ..136 j i
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Table A.0-1. ANO-1 Cycle 7 Statepoints ........ .. ... . ... .. . .. . . . . . .. 139 Table A.0-2. ANO-1 Cycle 8 Statepoints . . .. . , . .. . . . . .. .. . . ....139 Table A.0-3. ANO-1 Cycle 9 Statepoints . .. . .. . .... .. . . ... . . . . . . .140 Table A 0-4. ANO-1 Cycle 10 Statepoints ..... .... . . . . . . .. ....140 Table A.0-5. ANO-1 Cycle 11 Statepoints . . . . . . . . . . . . . . . . , . . . . ...141 Table A.0-6. ANO-2 Cycle 1 Statepoints .. . . . . . . . . . . . . .. . ...... . 141 Table A.0-7. ANO-2 Cycle 2 Statepoints . . . . . . ... ... 142 Table A.0-8. ANO-2 Cycle 3 Statepoints . . .. . ... .. . .. .. . . . .... . 142 Table A.0-9. ANO-2 Cycle 4 Statepoints .. . . . . . . . . .. .. .143 Table A.0-10. ANO-2 Cycle 5 Statepoints .. .. . . . . . . . . . . . . ...... .143 .
Table A.0-11. ANO-2 Cycle 6 Statepoints .. . .. . . .... .. . . . . . . . . . 144 ,
Table A.0-12. ANO-2 Cycle 7 Statepoints . ..... ...........................144 I
. Table A.0-13. ANO-2 Cycle 8 Statepoints .. .... . . . . . . . . . . . . . . . . . . . . . . . 1 44 -l Table A.0-14. ANO-2 Cycle 9 Statepoints . . . . ... . . ..................145 Table A.0-15. ANO-2 Cycle 10 Statepoints .... ... . .... ... .. .... . . . . .. .. .. 145 Table A.0-16. WSES-3 Cycle 1 Statepoints ... . . .. .. . . . . . ...... .146 ;
Table A.0-17. WSES-3 Cycle 2 Statepoints .. . . .. . . . ... .. ..... . 146 q Table A.0-18. WSES-3 Cycle 3 Statepoints . . .. . . . . . . . . . . . . . . . . . . . ... ..147 Table' A.0-19. WSES-3 Cycle 4 Statepoints .. .. ... . . . . . . . . . . . . . .. .147 !
Table A.0-20. WSES-3 Cycle 5 Statepoints ... . ..... ........ . . . . . . . . . . . . . .14 8 l
- Table A.0-21. WSES-3 Cycle 6 Statepoints .. . .. . .. .... . . . . . . . . . . . .149 j Table E.0-1. ANO-1 Cycle 9 inferred Measurement Uncertainties..... . ....172 Table E.0-2. ANO-2 Cycle 2 Inferred Measurement Uncertainties.. . .. ..172 j Table E.0-3. WSES-3 Cycle 3 Inferred Measurement Uncertainties.. . . .173 Table F.0-1. ANO-1 Cycle 9 Model Uncertainties.... .... . ..... .... ... ....... .174 j Table F.0-2. ANO-2 Cycle 2 Model Uncertainties.. . . . . . . . . . . . . . . . . . ..174 i Table F.0-3. WSES-3 Cycle 3 Model Uncertainties.... . .... ...... . . ... ..175 2
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1.0 INTRODUCTION
This report describes the methodology used at Entergy Corporation to determine ,
the uncertainties and the resultant " reliability factors" associated with the .
Entergy CASMO/ SIMULATE reactor physics models. The results contained in ;
I this document were derived from extensive benchmarking efforts performed by Entergy personnel on the three Entergy pressurized water reactors: Arkansas l Nuclear One - Unit 1 (ANO-1), Arkansas Nuclear One - Unit 2 (ANO-2), and the j Waterford Steam Electric Station - Unit 3 (WSES-3). Comparisons to critical !
experiments and isotopic measurements are also included. This report is intended to replace the existing NRC approved Entergy PWR Physics Topical ]
Report, MSS-NA1-P [ Reference 1] which was based on the PDQ/NODEP {
computer codes. -
l CASMO/ SIMULATE calculations were performed and comparisons .of the :
important physics parameters were made to the appropriate measured data.
Whenever possible, the uncertainties are based on comparisons to directly l
observable parameters, such as boron concentration and incore detector '
reaction rates. Data was taken from cycles 6-11 of ANO-1, cycles 1-10 of ANO- !
2, and cycles 1-6 of WSES-3, for a total of twenty-two cycles. No measured data.
l was rejected based on comparisons to calculations unless supported by independent calculational methods. In order to be objective in the choice of data :
to be used for the power distribution comparisons, all incore detector !
measurements were reviewed and qualified by comparing to symmetric readings j or by trending data. q A self-consistent statistical approach was used to derive the physics model uncertainties and reliability factors for each physics parameter. The comparisons of measured and calculated physics parameters demonstrate the CASMO/ SIMULATE model's ability to predict core physics parameters over a wide range of core design and operating conditions, including the use of advanced poisons. The degree of accuracy to which each parameter can be ENEAD-01-NP REV 0 Page 11
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predicted with the Entergy physics methodology is' quantitatively given in- !,
Table 4.1-1.
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2.0 DESCRIPTION
OF ENTERGY REACTORS i
2.1 ANO-1 Arkansas Nuclear One, Unit 1 is a 2568 MWth Pressurized water reactor designed by Babcock and Wilcox. The core contains 177 fuel assemblies and ,
52 strings of seven 4.75 inch long fixed self-powered neutron detectors. The fuel assembly numbering system is shown in Figure 2.3-1. The radial layout of the rhodium in-core detectors in the ANO-1 reactor core is shown in Figure 2.3-2 while the axial layout is shown in Figure 2.3-3. ;
The ANO-1 fuel assembly is a 15X15 matrix of fuel pins with the center pin replaced with a guide tube containing either moderator or a rhodium detector
- assembly, in addition, sixteen other lattice locations contain either a guide tube, a burnable poison assembly, or a control element assembly (CEA) as shown in Figure 2.3-4. The burnablo poison assemblies at ANO-1 are generally removed :
after one cycle of operation, however they can be reinserted in later cycles.
k ANO-1 began operation with 69 control rod assemblies of 16 poison rods arranged in four safety banks, three control banks and one bank of eight part length CEAs. Before Cycle 8 the center CEA was removed, leaving 68 CEAs in use from Cycle 8 - 11. CEA groups for Cycles 7 - 11 are shown in Figures 2.3-5 through 2.3-7. ANO-1 operates with axial power shaping part length CEAs near the core midplane for most of the cycle. They are withdrawn near the end of i cycle.
2.2 ANO-2 Arkansas Nuclear One, Unit 2 is a 2815 MWth Pressurized water reactor designed by Combustion Engineering. It contains 177 fuel assemblies and 44 strings of five 15.75 inch long fixed self-powered neutron detectors. The fuel j assembly numbering system is shown in Figure 2.3-8. The radial layout of the ENEAD-01-NP REV 0 Page 13
f rhodium incore detectors in the ANO-2 reactor core is shown in Figure 2.3-9 while the axial layout is shown in Figure 2.3-10.
The ANO-2 fuel assembly is a 16X16 matrix of fuel pins with five large " water" holes replacing four fuel pins each. The center water hole contains a guide tube with either moderator, a rhodium detector assembly, or a control element assembly (CEA) finger. The other four water holes contain guide tubes with or without CEA fingers. Bumable poison pins can replace fuel pins in the matrix.
As an alternative, integral fuel and burnable shim rods can be employed. The assembly layout is shown in Figure 2.3-11.
ANO-2 has 81 CEAs with five poison fingers each arranged in two shutdown banks, six regulating banks and one bank of 8 part-length CEAs. CEA groups are shown in Figure 2.3-12.
2.3 WSES-3 Waterford Steam Electric Station, Unit 3 is a 3390 MWth Pressurized water reactor designed by Combustion Engineering. It contains 217 fuel assemblies and 56 strings of five 15.75 inch long fixed self-powered neutron detectors. The fuel assembly numbering system is shown in Figure 2.3-13. The radial layout of :
the rhodium incere detectors in the WSES-3 reactor core is shown in Figure 2.3-14 while the axial layout of the rhodium detectors is shown in Figure 2.3-15.
The WSES-3 fuel assembly is essentially identical to the ANO-2 fuel assembly described above. The 16X16 matrix of fuel pins is shown in Figure 2.3-11.
WSES-3 has 91 CEAs arranged in two shutdown banks, six regulating banks, and two banks of 4 part-length CEAs. Eighty-seven (87) of the CEAs have five fingers each; four of the CEAs have four fingers. These four-finger CEAs are the bank "A" shutdown CEAs located in the offset assemblies at the core periphery.
ENEAD-01-NP REV 0 Page 14 5
~. _ . . - - -
a
+ t
-i
.c 1
Each four-finger CEA spans two assemblies. Control rod groups are shown in l
Figure 2.3-16.' '
.. l z
1 i
f b
(
f I
i k
t i,
i i
i I
-I l
1 i
i i
ENEAD-01-NP REV 0 Page 15 .
i
.. . i Figure 2.3-1. ANO-1 Assembly Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 I
ASSEMBLY NUMBER i
1 i
l I
ENEAD-01-NP REV 0 Page 16 1
L i
Figure 2.3-2. ANO-1 Self Powered Neutron Detector Map 31 30 32 29 28 52 33 27 51 i 34 7 5 26 35 6 4 24 23 r
36 9 8 3 25 22 ;
37 10 1 2 21 11 19 20 38 39 12 18 50 ,
40 13 16 17 49 41 14 15 :
42 43 47 48 44 45 46 i DETECTOR STRING NUMBER X i
l I
ENEAD-01-NP REV 0 Page 17 l
1
'I l
Figure 2.3-3. ANO-1 Axial Location ofin-core Detectors j 1
h 7O 6O Active Fuel 5C :
Height
~20.6 inches
,g
. 1T inches 4g 30 20 :
y f ~10.3 inches .
ENEAD-01-NP REV O Page 18
l:
l.
Figure 2.3-4. ANO-1 Fuel Assembly Layout g4 , 0 ,,
s
..~. I ov >
i
^
4p s M! gp;.
n Fuel Pin -
Control Rod Guide Tube Instrumentation Tube l
l ENEAD-01-NP REV O Page 19 l
l
i I
. .. i l
Figure 2.3-5. ANO-1 CEA Bank identification Map for Cycle 7-4 7 4 2 6 6 2 7 8 5 8 7 2 5 1 1 5 2 ,
4 8 3 7 3 8 4 i
6 1 3 3 1 6 !
7 5 7 2 7 5 7 ,
6 1 3 3 1 6 ,
4 8 3 7 3 8 4 2 5 1 1 5 2 7 8 5 8 7 l 2 6 6 2 4 7 4
)
i l
l 4
l BANK NUMBER -
SAFETY BK 1 8 SAFETY BK 2 9 SAFETY BK 3 8 .
SAFETY BK 4 8 l CONTROL BK 5 8 4 CONTROL BK 6 8 CEA BANK X i CONTROL BK 7 12 '
PLR BK 8 8 -l TOTAL 69 )
I ENEAD-01-NP REV 0 Page 20 l
4
t
'I i
Figure 2.3-6. ANO-1 CEA Bank identification Map for Cycle 8 i
i i
4 7 4 l 2 6 6 2 !
i 7 8 5 8 7 2 5 1 1 5 2 1
4 8 3 7 3 8 4 6 1 3 3 1 6 7 5 7 7 5 7 i 6 1 3 3 1 6 4 8 3 7 3 8 4 i 2 5 1 1 5 2 ,
7 8 5 8 7 2 6 6 2 i 4 7 4 i i
BANK NUMBER SAFETY BK 1 8 SAFETY BK 2 8 l SAFETY BK 3 8 i SAFETY BK 4 8 4 .
CONTROL BK 5 8 ' '
CONTROL BK 6 8 CEA BANK X )
CONTROL BK 7 12 )
PLR BK 8 8 ,
)
TOTAL 68 l
i 1
1 I
ENEAD-01-NP REV O Page 21 l l
I
.A - + 4 h A 4 an _
l l
1 1
Figure 2.3-7. ANO-1 CEA Bank identification Map for Cycles 9-11 t
1 6 1 3 5 5 3 7 8 7 8 7 3 5 4 4 5 3 ;
1 8 6 2 6 8 1 5 4 2 2 4 5 6 7 2 2 7 6 l 5 4 2 2 4 5 1 8 6 2 6 8 1 ,
3 5 4 4 5 3 f
7 8 7 8 7 3- 5 5 3 1 6 1 BANK NUMBER [
SAFETY BK 1 8 SAFETY BK 2 8 +
SAFETY BK 3 8 ,
SAFETY BK 4 8 ,
CONTROL BK 5 12 ,
CONTROL DK 6 8 CEA BANK X CONTROL BK 7 8 PLR BK 8 8 TOTAL 68 n
ENEAD-01-NP REV O Page 22 i
Figure 2.3-8. ANO-2 Assembly Numbers ;
i 1 2 3 4 5 !
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 !
1 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 ASSEMBLY NUMBER
- I ENEAD-01-NP REV 0 Page 23
-1 l
1 i
i Figure 2.3-9. ANO-2 Self Powered Neutron Detector Map f
1 2 3 4 P
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ;
'20 21 22 23 24 25 26 27 1 28 29 30 31 32 33 34 35 36 37 38 39 40 __
41 42 43 44 l
DETECTOR STRING NUMBER X l
ENEAD-01-NP REV O Page 24
4 4 Figure 2.3-10. ANO-2 Axial Location of In-core Detectors .
AL _ .
5 4
)L Active _ .
Fuel
~30.0 inches Height
~150
, y inches 3 2
7 1
y y ~14.3 inches ENEAD-01-NP REV 0 Page 25
i
~l i
i Figure 2.3-11. ANO-2/WSES-3 Fuel Assembly Layout l l l l l l l l l l A, - - '
- l l l 's i fg
~lw' ~ l l l yg l l l )
l l
i
)
l l l l
. w,-
O~~ %ye
.o l l l w :
l l l l l l l l l Fuel Pin j9:" Control Rod Guide Tube i as -
gia ' :!g.
i 5
Control Rod Guide Tubelinstrument Tube ENEAD-01-NP REV 0 Page 26
Figure 2.3-12. ANO-2 CEA Bank identification A A I 3 5 3 2 A 1 1 A 2 6 B P B 6 A P B B P A 3 8 4 2 4 8 3 A 1 B B B B 1 A 5 P 2 6 2 P 5 A 1 B B B B 1 A 3 8 4 2 4 8 3 A P B B P A 6 B P B 6 2 A 1 1 A 2 3 5 3 j BANK NUMBER A A I
SD BK A 16 SD BK B 20 REG BK 1 8 REG BK 2 8 REG BK 3 8 REG BK 4 4 l REG BK 5 4 REG BK 6 5
-PLR 8 CEA BANK X TOTAL 81 l
ENEAD-01-NP REV 0 Page 27
l Figure 2.3-13. WSES-3 Assembly Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 130 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 -
j205 206 207 2L8 209 210 211 212 213 I 3- i 216 217
!.21_.L.. !
.i
-l i
1 ASSEMBLY NUMBER ENEAD-01-NP REV O Page 28
Figure 2.3-14. WSES-3 Self Powered Neutron Detector Map 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 DETECTOR STRING NUMBER X Y
ENEAD-01-NP REV 0 Page 29 e
Figure 2.3-15. WSES-3 Axial Location ofin-core Detectors Ak _.
5 4
AL Active _.
Fuel
~30.0 inches Height
~150 q
inches 3 2
1 AL y V ~14.3 inches ENEAD-01-NP REV 0 Page 30
Figure 2.3-16. WSES-3 CEA Bank identification A
2 2 8 3 4 3 B 1 A B B A 1 B 5 P 6 P 5 B A A B B A A 3 P 4 1 4 P 3 2 B B A B B 2
-A- 4 6 1 2 1 6 4 t 2 B B A B B 2 3 P 4 1 4 P 3 A A B B A A l B 5 P 6 P 5 B l
i 1 A B B A 1 B 3 4 3 8 BANK NUMBER 2 2 SDBKA- 18 SD BK B- 24 _
^
REG BK 1 8 l REG BK 2 9 REG BK 3 8 REG BK 4 8 l REG BK 5 4 l REG BK 6 4 CEA BANK X PLR 8 TOTAL 91 ENEAD-01-NP REV 0 Page 31
l 3.0 OVERVIEW OF THE CALCULATIONAL MODEL The calculational model is based on the CASMO/ SIMULATE computer code l package developed by Studsvik of America. The basic methodology is described in detail in References 2 through Reference 6. The methodology is widely used in the industry and has been extensively benchmarked by several utilities [ References 7 through 9). Entergy's application is consistent with the earlier work, but Entergy's qualification of the methods for use on the Entergy PWRs has been independently developed. An overview of the computer codes used at Entergy for PWR design and the code interrelationships are shown schematically in Figure 3.0-1.
i J
l 1
i ENEAD-01-NP REV O Page 32 l l
e a Figure 3.0-1. Calculational Flow MICBURN INTERPIN Fuel Temperature Cross Sections for Highly Shielded Data Bumable Absorbers
-l 4 ,.
8r CASMO Assembly Homogenized !
Constants and Pin Peaking Data sr TABLES Functionalization of Assembly and Pin Peaking Data t
b 1Y SIMULATE 3-D Nodal Reactor Core Model 3
I t
i i
ENEAD-01-NP REV 0 Page 33
4 t
3.1 Lattice Physics Model The lattice physics model provides cross sections, reaction rates, and other i nodal information on a pin and assembly basis. The INTERPIN, CASMO, and ,
MICBURN computer programs are used in the Entergy lattice physics model.
3.1.1 INTERPIN ,
l
^
INTERPIN [ Reference 2) predicts the steady-state thermal performance of UO2 zircaloy-clad fuel operating in light water reactor cores. The program is designed to produce the fuel temperature data for the CASMO and SIMULATE computer programs.
INTERPIN models a single fuel rod and its surrounding coolant. The system is-represented by discrete axial nodes to allow for variations in power and coolant temperature and is analyzed in cylindrical coordinates. The fuel pellet 'is l modeled with ten radial mesh points and the volumetric heat generation is modeled as a radially dependent function.
The code calcu!ates cladding surface temperatures for all exposure intervals and defines exposure step sizes to be used within each exposure interval. The-i results of the cladding surface temperature calculations serve as the boundary condition for the fuel performance calculation. The fuel performance model l includes sub-models for fuel thermal, mechanical, and restructuring effects.
Finally INTERPIN produces fuel temperature input for the CASMO and SIMULATE computer programs.
3.1.2 CASMO ;
I CASMO [ Reference 3] is a multigroup two-dimensional transport theory code for -
bumup calculations on fuel assemblies. The geometry consists of cylindrical fuel rods of varying composition in a square pitch array with allowance for fuel rods mixed with a burnable poison such as erbium or gadolinium, burnable l
ENEAD-01-NP REV O Page 34
absorber rods, cluster control rods, in-core instrument assemblies and water gaps. CASMO provides effective cross sections, local pin power form factors, flux discontinuity factors and other nuclear data used by the SIMULATE 3-D 4 nodal code. CASMO has a model for generation of baffle and reflector data which is consistent with the nodal model contained in the SIMULATE code.
Some characteristics of CASMO which are used in the Entergy PWR models are listed below:
. Nuclear data are collected in a library containing microscopic cross sections in 70 energy groups. Neutron energies cover the range O to 10 MeV. A library containing data in 40 energy groups is also available and is usually used in production.
. Effective microscopic cross sections generated by the MICBURN code are -
used for highly self-shielded pins such as gadolinium bearing fuel.
. CASMO can accommodate non-symmetric fuel bundles containing up to 19X19 rods. Most bundles are, however, symmetric, and half, quadrant or ,
octant symmetry (mirror symmetry) can be utilized in the calculations.
. Absorber rods or water holes covering 1X1 (B&W), or 2X2 (CE) pin cell positions are allowed in the assembly.
i
. Effective resonance cross sections are calculated individually for each fuel pin.
t
. The calculational sequence is initiated in a simplified geometry. Energy groups are collapsed as spatial detail is increased. ;
. Up to 12 energy groups are allowed in the two-dimensional assernbly ,
transport theory calculation.
ENEAD-01-NP REV 0 Page 35
. A fundamental mode calculation is performed to account for axial leakage effects.
. The microscopic depletion is calculated in each fuel and burnable absorber pin.
. A predictor-corrector approach is used in the depletion calculation which greatly reduces the number of bumup steps necessary for a given accuracy.-
This is particularly important when bumable poison rods are involved.
. The output is flexible and gives few-group cross sections and reaction rates for any region of the assembly for use in overall reactor calculations.
. Flux discontinuity factors are calculated at the boundary between bundles and for reflector regions for use in the nodal codes.
. Critical information may be saved on a restart file at each bumup step to be used later for coefficient calculations at different exposures. A card image j file for linking to other programs is also created.
CASMO is run for each fuel segment witF unique mechanical or nuclear design. Cases are run considering variations in physics parameters such as fuel ,
bumup, boron concentration, moderator density, fuel temperature and control i rod presence. Cases which evaluate both instantaneous and history effects are j included. The specific CASMO cases run depend upon the fuel design and the j core operating strategy. .
1
'3.1.3 MICBURN MICBURN [ Reference 4] calculates the microscopic bumup in any highly self-shielded absorber rod containing an initially homogeneously distributed bumable ENEAD-01-NP REV O Page 36
absorber. It generates effective microscopic cross sections as a function of the absorber number density to be used in CASMO. In the case of an integral fuel and shim rod, effective microscopic cross sections are also generated for U235, Pu239, Pu240 and Pu241 ,
?
The input required for MICBURN are data for geometry and material composition, and instructions for the choice of options in the calculations.
Nuclear data are read from the CASMO data library.
The radial depletion of the gadolinia in the integral bumable absorber pin varies ,
strongly with time. Initially the pin is black for thermal neutrons and the bumup of the gadolinium isotopes is concentrated on the pin surface. It then moves inwards as the bumup proceeds. Further, natural gadolinium consists of several isotopes of which Gd155 and Gd157 have much larger cross sections than the remaining ones and these two isotopes entirely determine the thermal neutron absorption. The initial number densities of Gd155 and Gd157 are approximately the same but the cross section of Gd157 is about four times that of Gd155. This means that Gd157 is depleted faster than Gd155 and the effective cross section for each of the isotopes averaged over the pin varies considerably with bumup.
The effective cross sections for Gd155 and Gd157 taken together varies more slowly with burnup, and it is therefore advantageous to calculate this total absorption cross section of the bumable absorber for use in the CASMO program. At high irradiation when the number densities of Gd155 and Gd157 become small, the remaining Gd isotopes are of great importance for the residual Gd reactivity penalty. The contribution to the total absorption from these f
isotopes is therefore included.
A realistic spectrum for the bumup calculation is generated by surrounding the absorber pin with a buffer region. This region consists of homogenized fuel pin cells from the remainder of the lattice. MICBURN edits micro-group (40 or 70
- groups) cross sections averaged over the absorber region for use in CASMO.
These cross sections are relatively insensitive to the choice of buffer zone !
ENEAD-01-NP REV 0 Page 37
-I I
composition and size as well as to such parameters as void, temperature, boron i concentration or U235 enrichment in the absorber pin cell.
The MICBURN calculation includes: l
. Burnup of the gadolinium (or erbium, rhodium or other absorber) and fuel nuclides and the build-up of fission products in a large number of annular micro regions
. Burnup of the surrounding buffer zone +
. The following transition chain for gadolinium:
Gd154
- Gd155
- Gd156
- Gd157-+ Gd158
. Nonuniform build-up of Pu within the absorber pin
. A transport calculation in 40 or 70 energy groups and in a number of radial macro regions, each comprising a number of micro regions
.b l
ENEAD-01-NP REV O Page 38
3.2 Nodal Model l-The nodal model. provides core power distribution, criticality, reactivity coefficient, and rod worth calculations. The SIMULATE and TABLES computer j programs are used for the nodal model.
3.2.1 SIMULATE SIMULATE [ Reference 5] is an advanced two-group nodal code. The program is based on the QPANDA neutronics model which employs fourth order polynomial representations of the intranodal flux distributions in both the fast and thermal groups. Key features of SIMULATE are:
. Non-linear nodal expansion methodology (NEM) with assembly discontinuity factors
. Pin power reconstruction
. No normalization required against higher order calculations
. No adjustable parameters required in the nodal model
. Explicit representation of the reflector region
. Free format input
. Binary cross section library 1
. - Flexible cross section modeling capabilities
. Automatic geometry expansion from quarter to full radial core fraction l
ENEAD-01-NP REV O Page 39
SIMULATE can be used for the full range of fuel management, core follow, and reload physics calculations. Typical types of calculations performed by the code are:
. Cycle depletion in two or three dimensions, 1/8,1/4,1/2 or full radial core fraction
. Reload shuffling including reinsertion of discharged fuel and shutdown cooling
. Reactivity coefficient calculations
. Rod worths, including shutdown margin, dropped and ejected rod in 2 or 3 dimensions
. Core follow support for plant operations
. Start-up predictions
. Criticality searches SIMULATE cross-section input is provided by the CASMO program with linkage through the TABLES program. SIMULATE creates a run time library from the master TABLES library based upon the cross sections being requested via the input. This capability allows the user to maintain one master library that contains all cross-section information.
ENEAD-01-NP REV 0 Page 40
3.2.2 TABLES TABLES-[ Reference 6] is a data linkage code that allows definition of cross-section and other nuclear data libraries to meet user requirements for input into SIMULATE. The user can choose to create cross-section libraries that are designed for fuel management, core follow, reload analysis, or special picjects.
TABLES creates a master binary library consisting of cross sections for use by SIMULATE. The cross sections are constructed from parameterized table sets, called partial cross section tables. The partial cross sections can each be a function of up to three variables (e.g., exposure and fuel temperature, moderator temperature, control rod, enrichment, etc.).
SIMULATE reconstructs the i-th macroscopic or microscopic cross sections, discontinuity factors, fission product data, pin powers, and kinetics data from the TABLES-developed partial differences as the summation of several of these partials:
I,={AI, (3.2-1)
The dependencies of the partials are defined by the user. TABLES produces one , two- and throa dimensional tables of partials for each of the types of data:
AI, = F,(a,b,c) (3.2-2)
The only exception is that pin power re onstruction data is expressed as the summation of a base one-dimensional table (in exposure) and additional one-dimensional tables containing derivatives.
i ENEAD-01-NP REV 0 Page 41
~ 3.3 Rhodium In-core Instrument Model 1
The power distribution statistics presented in this report are primarily based on comparisons of measured in-core detector signals to predicted in-core detector '
signals. Therefore, an analytical model is needed to convert the neutron fluxes calculated with SIMULATE to predicted in-core detector . signals. This conversion from flux to instrument signals is performed by the RHOBURN L program.
3.3.1 RHOBURN 1
The RHOBURN computer program has two main functions. They are to:
i
- 1. Construct fixed rhodium in-core detector signals, and
- 2. Generate data for the CECOR monitoring code used at the ANO-2 and WSES-3 plants. ,
I 4
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0 ENEAD-01-NP REV O Page 42
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k 3.3.2 Instrument Data For the Core Monitoring Codes RHOBURN also calculates the " conversion factor" needed by the plant
^
monitoring software to infer power distributions from signal distributions. .The following equation is used to make this transformation:
I t
i ENEAD-01-NP REV 0 Page.45 i
.i -1 i- 1 i ,
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Table 3.3-1. Detector Depletion Laws ENEAD-01-NP REV O Page 47
_ _ _ . _ .. _ __ _ _ . _ . . _ - . . _ . . _ . . 'i~ _ . . . _ . _ - . - _ . . . _ . . . _ . . - _ - , . _ . . _ . _ . . . . . . _ __, _
l
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l Figure 3.3-1. RHOBURN Program Data Flow q l
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4.0 MODEL VERIFICATION AND RELIABILITY 4.1 Overview The observed differences between a measured and calculated physics parameter form the basis for determining the model " reliability factor" and bias.
The true observed population standard deviation (uncertainty) of (measured -
calculated) physics parameters (o observed) is due to two primary components:
- 1. model uncertainty, amodel
- 2. measurement uncertainty, omeasurement Assuming these tu be independent, the uncertainties are related by:
2 cm = o , + c __ (4.1-1)
Thus, the model uncertainty is obtained as follows:
2 a, = o2 _y 2 (4.1-2)
The unbiased sample variances will be used to construct an estimate for the true variance and standard deviation:
2 o ,ESL =S L -S (4.1-3) ,
where S 2 = model sample variance !
In many cases, the measurement and observed variances are almost equal, indicating that the measurement is the primary source of the error. In these -
cases, for conservatism, the model uncertainty is taken to be that of the observed uncertainty.
The " reliability factor" (RF) is used to describe the allowances to be used in safety related calculations to assure conservatism. The reliability factor includes the uncertainty in the estimation of the true standard deviation from a sample ENEAD-01-NP REV 0 Page 49
. -. l l
1 population. The reliability factor is always larger than the uncertainty factor, and is defined as:
RF = k95%/95%
- Smodel (4.1-4) where S is the sample model uncertainty (standard deviation) baseo on n ,
samples, and k is the one sided tolerance limit factor [ Reference 10] based on calculating S from n samples. This factor accounts for the fact that the sample uncertainty is used to approximate the true standard deviation, o, of the population. k approaches 1.645 for a 95%/95% limit as n approaches infinity.
i The term " bias" (mean) is used to describe the average difference between an observed or measured parameter and the calculated value, and is to be used in !
safety related calculations. I Some of the reliability factors and biases are based on relative differences, defined as (Measured-Calculated)/ Calculated. In this case, a conservative estimate of a parameter X is related to the CASMO/ SIMULATE calculated parameter through Equation 4.1-5.
XSAFETY = Xcalc * (1 + BiasX RFX) (4.1-5) !
Xcalc CASMO/ SIMULATE calculation of parameter X XSAFETY Conservative estimate of parameterXfor use in performing safety evaluations ,
RFx Reliability factor appropriate to parameter X !
Bias x Bias factor appropriate to parameter X !
I' Whether the reliability factor is subtracted or added before multiplying the calculated value depends on the individual parameter being evaluated. For I
) example, over predicting power peaks would be considered to be conservative, j so for power peak calculations the reliability factor would be added to the ;
multiplier. I ENEAD-01-NP REV O Page 50 l
'l I
For those parameters where the reliability factors are calculated based on ;
absolute differences, (Measured-Calculated), such as the temperature ,
coefficient, the reliability factors and biases are additive corrections to .,
CASMO/ SIMULATE calculations. Equation 4.1-6 gives the form of these additive reliability factors.
XSAFETY = Xcalc + (BiasX RFX) (4.1-6) 1 The CASMO/ SIMULATE model for Entergy reactors has been benchmarked ;
i against twenty-one cycles of reactor operations. Measurements made during cycles 7 - 11 of ANO-1, cycles 1 - 10 of ANO-2 and cycles 1 - 6 of WSES-3 are used to quantify the reliability factors to be used in safety related calculations.
The resultant reliability factors and biases for the physics parameters are summarized in Table 4.1-1.
11 is important to note that the safety factors defined in Equation 4.1-5 and i Equation 4.1-6 are computed from comparisons of calculated and measured .
dcta such that one can be 95% confident that 95% of the true values of the parameters being calculated are less than XSAFETY. For example, from -
Table 4.1-1 one may say that there is a 95%/95% confidence / probability that the true HZP critical boron will be less than calculated boron + 45.2 ppm.
i 6
i t
ENEAD-01-NP REV O Page 51
i Table 4.1-1. Reliability Factors for Entergy PWRs ,
PARAMETER RELIABILITY FACTOR BIAS EQUATION Estimated Cntical States Hot Zero Power (PPMB) 37.3 +7.9 Equation 4ci-6 Fg ANO-1 .0500 .00020 Equation 4.1-5 _
ANO-2/WSES-3 .0403 .00484 Equation 4.1-5 Fr: ANO-1 .0399 0.0 Equation 4.1-5 ANO-2/WSES-3 .0323 0.0 Equation 4.1-5
%,: ANC,-1 .0481 0.0 Equation 4.1-5 ANO-2/WSES-3 .0356 0.0 Equation 4.1-5 Rod Worth by Boron Dilution (%p) .117 -0.005 Equation 4.1-6 l by Rod Swap (%p) .155 -0.011 Equation 4.1-6 Inverse Boron Worth (PPMB/%p) 8.58 -0.81 Equation 4.1-6 Temperature Coefficient (p/*F) .084E-4 .077E-4 Equation 4.1-6 Doppler Coefficient 0.10 00 Equation 4.1-5 Isotopics U-235 0020 0.011 Equation 4.1-5 Pu-239 0.015 -0.019 Delayed Neutron Parameters 0.03 00 Equation 4.1-5 i
l I
1 ENEAD-01-NP REV 0 - Page 52 ,
l Y________-__-____-_-__----____-_-_-__-_-______________---
i 4.2 Estimated Critical States The accuracy by which CASMO/ SIMULATE predicts critical states at both hot zero power and power range conditions is established in the following two sub-sections. ,
B 4.2.1 Hot Zero Power Critical Boron Measurements of the critical boron concentration at hot zero power conditions are performed at the initial startup of each cycle to verify conformance with the design assumptions. Estimates of the bias, uncertainty, and reliability factors to i be applied to the CASMO/ SIMULATE predictions of this parameter are reported-in this section.
The observed differences between the measured critical boron and the predicted critical boron are reported in Table 4.2-1 for twenty cycles (four ANO-1, ten .
ANO-2, and six WSES-3 cycles). As can l>e seen, the WSES-3 Cycle 6 data point differs significantly from the bulk of the data. This data point was calculated with three independent methodologies (SIMULATE, Reference 5; NODE-P, Reference 11; and ROCS, Reference 12] and found to show consistently large deviations from the measurement (
). Thus, there is a strong indication that an anomalous measurement or condition existed during the test. As the goal is to evaluate the- ,
predictive ability of CASMO/ SIMULATE, a statistical outlier test [ Thompson's Tau, Reference 13] was used to justify deletion of this data point from the data ,
set (see Table 4.2-2).
The observed differences in critical boron for the remaining nineteen measurements are shown.in Figure 4.2-1 and Figure 4.2-2. The sample mean and standard deviations are found to be +7.89 ppm and 15.39 ppm, respectively.
Figure 4.2-1 demonstrates that the safety limit of the observed population can be
. conservatively estimated by equating it to the tolerance limit from a normal -
distribution characterized by the mean and standard deviation of the observed i differences. All of the data points are seen to lie below the normal 95% ;
1 ENEAD-01-NP REV 0 Page 53
confidence /95% probability tolerance limit. The observed population is normal L
j as the . differences pass the requirements of the W normality check l [ Reference 14]. Therefore, a reliability factor (RF) of 37.29 ppm was determined using the normal one-sided k-factors for nineteen samples [ Reference 10].
L The accuracy of the boron concentration measurements are limited by the titration accuracy, which was established in Reference 1 to be i 1% of the boron concentration. As the measured boron range is from 800 to 1800 ppm, the measured uncertainty is about 15 ppm. Thus, the observed and measured uncertainties are almost identical, leaving an undetermined component for the model uncertainty as calculated from Equation 4.1-3. Therefore, for conservatism, the model standard deviation and mean (bias) will be taken to be -
equal to the observed standard deviation, Sobs, and the mean, m, and the corresponding RF will then be calculated.
Figure 4.2-2 demonstrates that the observed differences are independent of the value of the boron. Hence, the above .nean and RF can be used over the full range of expected boron concentrations.
In summary, the hot zero power critical boron predictions from CASMO/ SIMULATE will be biased by +7.89 ppm and a reliability factor of 37.29 ppm will be applied:
Boron Concsafety = Boron Concealc + 7.89 ppm + 37.29 ppm
= Boron Concealc + 45.18 ppm ENEAD-01-NP REV 0 Page 54
L Figure 4.2-1.HZP Critical Boron Histogram (Observed) ;
HZP Critical Beren vs Normal Histogram
+
,, HzP cateelsare Date 3.5 95 % %
-- mm m g;,
gg , 100% of p
g ,. . ,e
/_
N "==d
'u. / \ ;x.
1
/ .
\
05:/
/
g ,
-26 -21 16 11 4 1 4 9 14 19 24 29 34 33 44 49 WP) Offisteesse. {pped Figure 4.2-2.HZP Critical Boron Differences (Observed) vs. CBC u.
som.a.
- a. unem . nu -
g E. .
t . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . ..
f.
g u. = =
s =
5 e. .
s
- g , .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . u . . . . . . . . ..
3 WD FIB 83 1100 1JUD tino 17D0 1sgG 9tRDE PPI4 l
l ENEAD-01.NP REV 0 Page 55
i.
. Table 4.2-1. Observed HZP Critical Boron Differences PLANT CYCLE M-P
- ANO-1 8 -7 9 -7 10 0 11 -17 ANO-2 1 11 2 23
- 3 22 4 2 5 5 6 3 7 30 8 41 9 19 10 16 WSES3 1 19 2 -6 3 -2 4 11 5 -13 6 68
- units are delta ppm Table 4.2-2. Thornpson's Outlier Test for WSES3 Cycle 6 HZP CBC Data PARAMETER l VALUE For all data sigma = S 20.0 mean = m 11.1 W3C6 data = x 68 lm-xl 56.9 t 1.934 crmcallimit = St 38.7 conclusion outlier ENEAD-01-NP REV 0 Page 56
t 4.2.2 Target Eigenvalue at Power Conditions i The reactivity calculations from SIMULATE for the three PWRs are compared to the measured data in this section. The SIMULATE modols were depleted at the 6 measured critical conditions as defined by core, cycle, burnup, core power, l
xenon, rod position, moderator temperature, and soluble boron concentration.
Data points were chosen which were above 60% power. In addition, each cycle was represented by approximately the same number of time points so as not to bias specific cycles. The time points were chosen to represent about every i 1 GWd/MtU of operation.
The SIMULATE reactivities (called "Eigenvalues") from these depletions are '
shown in Figure 4.2-3. The actual data points are given in Table 4.2-3. The mean eigenvalue and standard deviation are 0.9991 and 0.0017Ak, respectively. ;
All 279 data points fall within 0.00548 Ak. ,
4 1
h i
f 1
i ENEAD-01-NP REV O Page 57 ,
1:16nJo p g-t siWnivig g! auAelna 6 )04SOJAOp( As 34alo gnJund dMH SIWillV13 3lD3NAYl03
!'009 - -
t 4
t'00t - +
+
+
+
'1 1 t E 1'00Z - -+ - * *7 ++, +
3 + + + +
+
+ +
. + ++ ,
+ ..y++. t + +
+4+ l + +$$ + ( + ++
m + + + ,
4+ + +
e t- ++++v++ ,tv++, + +,+ -+t4 ++
+ .
y + + ,
+3 %
_, ,+
g
- %4+ * *++ h.+ ++ + +
- * ,4 + *+++
+ *
+ + ,, t d+, g+ +
++ , +}, + +
, ,+
+++ * +
g O'668 - p+
+~ o- : +:4+ + [,
++ +.++ +-
-++
+ .
+
+
++ + ;+ + ? + +++ +
+p
+
+ +
e+ + + +4 + +
+ +, +* +
0 669 - -
+
, ++ ,
+ + +
+ +
- O'6St l 0 Z t 9 8 !O tZ 1# 19 18 3A313 90HNAd' SMP!Nlif 3N3fhC-OL-Nd 83A 0 de08gg
Table 4.2-3. SIMULATE Eigenvalues (Observed)
PLANT l CYCLE GWD/T LAMBDA PLANT CYCLE GWD/T LAMBDA ANO-1 6 0.205 1.00519 6.277 0.99832 1.500 .99944 7.473 0.99995 2.174 1.00404 8.397 0.99981 3.131 1.00044 9.393 1.00017 3.900 0.99877 10.350 0.99934 4.693 0.99958 10.960 0.99970 5 445 0.99905 12.235 1.00116 6.971 0.99807 13.710 0.99819 8.268 1.00016 ANO-1 9 0.629 1.00354 9.526 0.99914 1.872 1.00183 10.440 0.99930 2.727 1.00182 11.170 0.99963 3.123 0.99980 11.710 0.99923 3.738 1.00024 12.070 0.99962 5.535 0.99933 12.530 0.99951 5.705 0.99022 ANO-1 7 0.900 1.00210 6.352 1.00008 1.597 1.00053 6.875 1.00029
.2.474 1.00054 7.830 0.99980 3.151 0.99998 8.594 0.99951 4.500 0.99804 9.292 099996 5.400 0.99797 11.390 0.99901 6.252 1.00075 ANO-1 10 0.831 1.00083 7.126 0.99978 2.076 1.00235 7.938 0.99951 2.739 1.00081 9.300 0.99881 4.698 0.99903 9.823 0.99962 5.199 0.99377 10.720 0.99893 7.690 0.99870 11.266 0.99962 8.926 0.99850 12.154 0.99950 9.424 0.99629 13.120 1.00038 10.090 0.99755 ANO-1 8 0.159 1.00356 12.020 0.99810 2.002 0.99835 ANO-1 11 0.251 1.00165 3.157 0.99809 0 934 1.0019 3.758 0.99960 1.428 1.00064 4.995 0.99777 2.075 1.00001 ENEAD-01-NP REV 0 Page 59
Table 4.2-3. SIMULATE Eigenvalues (Continued)
PLANT CYCLE G W D/T LAMBDA PLANT CYCLE G W D/T LAMBDA 2.946 0.99970 9.289 1.00051 4.033 0.99846 -10.457 0.99965 5.029 0.99711 11.738 0.99985 6.012 0.99794 12.84 1.00122 6.881 0 99690 13.888 1.00093 9.068 0.99685 WSES3 3 0.661 1.00251 9.923 0.99763 1.445 1.00123 11.025 0.99873 2.595 1.00091 11.934 0.99919 3.16 3.99996 13.256 0.99868 4.351 0.99934 13.914 0.99871 4.927 0.99782 14.568 0.99855 6.078 0.99995 WSES3 1 1.007 0.99738 7.211 0.99966 1.86 1.00007 8.382 0.99991 2.961 0.99829 9.505 1.00053 3.766 0.99835 10.658 0.99965 4.874 0.99828 11.853 0.99891 I 5.942 0.99757 12.89 0.99963 7.047 1.00059 13.977 1.00013 8.045 0.9994 14.973 1.00084 8.596 0.99959 15.792 1.00142 9.916 0.99907 WSES3 4 0.504 1.0037 11.039 1.00036 0.806 1.00285
~
12.143 1.00077 1.797 1,00179 13.034 1.00147 3.234 1.00045 13.9 1.00161 4.453 1.00024 14.418 1.00068 5.288 0.99887 WSES3 2 0.98 1.0007 6.426 0.9995 1.623 1.00185 7.337 0.99852 2.571 0.99948 8.699 0.99847 3.424 1.00013 9.331 0.9979 4.863 0.99725 10.48 1.00069 6.036 0.99801 11.393 0.99865 7.119 0.99974 12.161 0.9998 8.408 0.99857 13.487 0.99929 I
i j
1 ENEAD-01-NP REV O Page 60
! l L
l ..
h Tble 4.2-3. SIMULATE Eigenvalues (Continued) i PLANT CYCLE G W D/T LAMBDA PLANT CYCLE G W D/T LAMBDA 14.386 0.99928 3.207 0.99934 15.999 0.99899 4.901 0.99828 ,
WSES3 5 0.844 1.00225 6.745 0.99672 !
1.457 0.99904 7.685 0.99601 2.315 0.99935 9.61 0.99591 3.792 0.99753 10.661 0.99774 4.935 0.99737 11.102 0.9982 .!
5.426 0.9972 11.397 0.99714 6.157 0 99597 ANO-2 2 0.728 0.99959 7.181 0.9982 1.468 0.99958 8.515 0.99747 1.855 0.9993 ;
9.388 0.99744 2.905 0.99858 10.621 0.99749 3.549 0.99894 [
I 11.626 0.99691 4.339 0.99867 13.367 0.99585 5.446 0.99805 14.481 0.99715 6.546 0.99752 15.76 0.99616 7.627 0.99715 '
16.274 0.99632 8.202 0.9982 17.359 0.99561 9.673 0.99879 l WSES3 6 0.336 1.00061 10.471 0.99631 O.741. 1.00026 ANO-2 3 1.062 0.99637 ;
1.098 1.00022 1.259 0.99724 1.587 1.00005 2.336 0.99865 [
2.169 0.99949 3.77 0.99636 .
3.095 0.99804 4.37 0.99688 t r
4.083 0.99655 5.62 099683 5.294 0.99539 6.52 0.99783 [
6.248 0.99538 8.45 0.99811 6.623 0.99559 ANO-2 4 1.607 0.99926 7.272 0.99608 3.792 0.99867 8.229 0.99574 4.425 0.9989 ,
9.217 0.99619 5.617 0.99811 ,
10.301 0.9964 6.019 0.99949 ANO-2 1 2.768 0.99903 7.405 1.00076 2.925 0.99795 7.915 0.99984
{
i i
ENEAD-01-NP REV 0 Page 61 !
1
i l
-I i
Table 4.2-3. SIMULATE Eigenvalues (Continued)
PLANT CYCLE GWD/T LAMBDA PLANT CYCLE GWD/T LAMBDA 9.26 1.00065 9.47 0.99764 l
9.76 1.00046 13.654 0.99736 }
l 11.324 1.00071 15.083 0.99775 13.169 1.00133 ANO-2 9 0.539 1.00113 1 ANO-2 5 1.615 1.00151 1.34 1.00004 i 2.616 1.00139 2.192 0.99921 ;
3.568 1.00038 2.991 0.99815 4.848 1.0005 3.771 0.99814 5.487 1.00105 4.848 0.99679 I 6.952 1.00108 5.943 0.9971 ,
7.916 1.0012 6.87 0.99884 ,
8.837 1.00072 7.831 0.99781 ,
9.479 1.00095 8.768 0.99775 10.896 1.00161 9.806 0.99685 11.427 1.00203 10.597 0.99626 ANO-2 6 1.731 1.00093 11.704 0.99695 4.28 0.99968 12.684 0.99801 6.468 0.99824 13.685 0.99807 7.563 0.99812 14.543 0.99796 8.973 0.99994 15.627 0.99711 f 9.71 1.00083 16.57 0.99742 ,
10.936 0.99972 ANO-2 10 0.779 1.00242 12.024 1.00059 1.209 1.00065 13.821 0.99954 2.287 1.00006
.l 15.264 1.00073 3.388 0.99891 I
ANO-2 7 2.109 0.99954 4.191 0.99885 0.99859 i 4.713 0.99909 5.277 6.344 0.99759 6.13 0.99765 8.26 0.99944 7.191 0.99810 9.34 0.99934 8.355 0.99934 11.375 0.99877 9.243 0.99914 l
l 13.417 0.99782 10.202 0.99847 10.758 0.99817 i ANO-2 8 1.001 1.00039 I
3.909 0.9971 11.177 0.99869 i f- 6.732 0.9973 i i I
i
'f i
ENEAD-01-NP REV 0 Page 62
=
]
' 4.3 Inverse Boron Worth i
Measurements of the inverse boron worth (IBW) at hot zero power condition are performed at the initial startup of each cycle to verify conformance with the design assumptions. Estimates of the bias, uncertainty, and reliability factors to '
be applied to the CASMO/ SIMULATE predictions of this parameter are reported I I
in this section.
The obsented differences between the measured and predicted IBWs are given in Table 4.3-1 for eighteen cycles (four ANO-1, eight ANO-2, and six WSES-3 cycles). As can be seen, the ANO-2 Cycle 3 data point differs significantly from the bulk of the data. This data point was calculated with two independent methodologies [ SIMULATE, Reference 5 and ROCS, Reference 12) and found to ,
show consistently large deviations from the measurement ( #
). Thus, there is a strong indication that an ;
anomalous measurement or condition existed during the test. As the goal is to evaluate the predictive ability of CASMO/ SIMULATE, a statistical outlier test '
[ Thompson's Tau, Reference 13) was used to justify deletion of this data point from the data set (see Table 4.3-2). '
l A histogram of the remaining seventeen measurements is shown in Figure 4.3-1.
The data is seen to be reasonably symmetric with a sample mean and standard deviation of -0.81 ppm /%Ap and 3.60 ppm /%Ap respectively. This figure t
demonstrates that the safety limit of the observed population can be conservatively estimated by equating it to the tolerance limit from a normal distribution characterized by the mean and standard deviation of the observed ,
differences. All the data points are seen to lie below the normal 95%
confidence /95% probability tolerance limit. The observed population is normal as the differences pass the requirements of the W normality check
[ Reference 14] Therefore,- a reliability factor (RF) of 8.95 ppm /%Ap was- '
determined using the normal one-sided k-factors for seventeen ' samples ,
[ Reference 10).
i ENEAD-01-NP REV O Page 63 ;
c ,
The IBW is measured by comparing the boron concentration and rod position for two critical conditions at hot zero power. The measured IBW is simply the difference in measured boron divided by the difference' in measured' rod worth for the two states. ' Therefore, the measurement uncertainty is due to errors in the measured baron and rod worth. In the above statistics, in order to account .
for the errors caused by rod worth measurements, the IBW was calculated as the difference in calculated boron concentration divided by the difference in the !
measured rod worth. The uncertainty of the measured boron concentration was established in Reference 1 to be 1% of the boron concentration. Use of ,
Equation 4.1-3 results in an estimate of the calculated standard deviation of 3A5 ppm /%Ap. The corresponding RF is 8.58 ppm /%Ap. ,
Figure 4.3-2 demonstrates that the observed differences are not a strong ,
function of the value of the boron worth. Hence, the above mean and RF can be used over the full range of expected boron worth.
In summary, the inverse boron worth predictions from CASMO/ SIMULATE will be biased by -0.81 ppm /%Ap, and a reliability factor of 8.58 ppm /%Ap will be-applied:
IBWsafety= IBWealc-0.81 ppm /% Ap + 8.58 ppm /% Ap
= IBWealc + 7.77 ppm /% Ap ENEAD-01-NP REV 0 Page 64
I I
l Figure 4.3-1. Inverse Boron Worth (Observed) Histogram i
5- + l 5-
- II* 0*I* +
Nonnel
-- homalmstrbuton 95%f95% timt j.us w w.n.w
~
U Bounds 100%
/ /N
.i u a a m.inw n
+
ss- /
I 2- . ,
i
\ - <
i.
0
__ #./j.
N ~_
14 12 10 8 4 4 2 0 2 4 6 8 10 12 14 (MP)Difismeses (ppen!%deha rks) j i
Figure 4.3-2. Inverse Boron Worth Differences (Observed) vs. IBW M . .81 N .17 .
SIGMA . 3.60 m KSIGMA . 8.95 g 10 sa S
E 5- a ;
e .ji. . . . . . . . . ~ . . . . . . . . .. ;
- m Eg
- a ye 0- -
E a m ;
g 3
.. . . .. . . . . . . . . y , . . . . . ..
5 l 3:
" 10 : i 50 75 100 125 150 IBW(PPMi% RHO) i ENEAD-01-NP REV 0 Page 65
1 f
1 Table 4.3-1. Observed IBW Differences 1
PLANT CYCLE M-P' i ANO-1 8 -5.27 f 9 1.55 l 10 1.95 't-11 -4.32 ;
ANO-2 2.26 1
2 -2.40 .
3 11.00 i 4 -5.900 i 5 1.30 [
6 2.23 7 -4.92 -
8 PM f 9 NA !
^t 10 1.52 ;
WSES-3 1 1.85 i 2 3.35 3 -4.97 4 -4.40 - !
5 -2.39 :!
6- 4.76 ;
i
- ppm /%Ap - l
.. t Table 4.3-2. Thompson's Outlier Test for ANO-2 Cycle 3 HZP IBW Data
.i PARAMETER l VALUE For all data l
sigma = S 4.06 mean = m -0.09 A2C3 data = x +11.0 .
lm-xl 11.09 5 t 1.931 .
critical hmit = St 7.88 .f v
conclusion outher E
i i
ENEAD-01-NP REV 0 Page 66 T E'" -"
=>M-- .-
4.4 Rod Worth Measurements of selected control rod banks are made at the initial startup of each cycle to verify conformance with the design criteria for the specific cycle.
Estimates of the bias, uncertainty, and reliability factors to be applied to the CASMO/ SIMULATE predictions of this parameter are reported in this section.
l Rod worths are measured with two different techniques:
- 1. Boron dilution
- 2. Rod swap in the boron dilution technique, control rod insertion is traded for soluble boron.
i The reactor is maintained near critical while the control rod is inserted by dilution i of the boron. The reactivity is measured during this process through use of a reactimeter.
The rod swap technique also uses the boron dilution technique to measure the integral rod worth of a reference bank. The worth of each succeeding bank is then measured by trading reference bank withdrawal for the measured bank insertion. The worth of the measured bank is inferred from the resultant position of the reference bank and the measured integral rod worth curve for the reference bank.
As the two techniques are expected to have different measurement uncertainties associated with the process, statistics have been generated for each technique separately. These are reported in the following two sub-sections. Due to the additional step required for the rod swap process, the overall uncertainties will ,
be seen to be slightly larger for the rod swap than for dilution.
Equation 4.1-3 can be used to eliminate the measurement uncertainty from the observed uncertainty. However, the measurement uncertainty is primarily due to the inaccuracies of the reactimeter. As a reliable estimate of this component is i-not available, the true model uncertainty is taken to be equal to the observed ENEAD-01-NP REV 0 Page 67
uncertainty. This will build a small amount of conservatism into the resultant reliability factors for the rod worth.
4.4.1 Rod Worth by Dilution The observed differences between the measured (by dilution) and predicted control rod worths are given in Table 4.4-1 for sixty rod banks (twelve ANO-1, thirty-five ANO-2, and thirteen WSES-3 banks). A histogram of these differences for the sixty measurements is shown in Figure 4.4-1. The data has a sample mean and standard deviation of -0.005 %p and 0.058 %p, respectively.
This figure demonstrates that the safety limit of the observed population can be conservatively estimated by equating it to the tolerance limit from a normal distribution characterized by the mean and standard deviation of the observed differences. Essentially 95% of the data points are seen to lie above the normal 95% confidence /95% probability tolerance limit. The observed population is normal as the differences pass the requirements of the D' normality check
[ Reference 14]. Therefore, a reliability factor (RF) of 0.117 %p was determined using the normal one-sided k-factors for sixty samples [ Reference 10].
Figure 4.4-2 demonstrates that the observed differences are not a strong function of the value of the rod worth. Hence, the above mean and RF can be used over the full range of expected control rod worth.
As discussed in the introduction to this section, no attempt is made to account for the measurement uncertainty. The observed statistics will be used for the model uncertainty.
In summary, the control rod worth (dilution) predictions from CASMO/ SIMULATE will be biased by -0.005 %p, and a reliability factor of 0.117 %p will be applied:
I RW(dilution) safety = RW(dilution) calc -0.005 %p -0.117 %p
= RW(dilution) calc -0.122 %p 1
ENEAD-01-NP REV 0 Page 68
i-Figure 4.4-1. Observed Rod Worth (Dilution) Histogram 14 -
+ HZP Central Red Mbre Deta
+
brmal95%I95% Lest 12 - (.122% Iml Bounds
~'-- bd Dist6een 952% et Mansured Den
~ ~ SF 10 -
[*~ ,/ "
I s. [ .
- - / . . .
2- /-
/ +
/, + + .N .
8 . . , , ,
N ~. ,,
l
-0.15 0 13 0 11 -0 09 4 07 0 05 -0 03 -0 01 0.01 0 03 0 05 0 07 0 09 0 11 0.13 0 15 unum m a.u Figure 4.4-2. Observed Rod Worth (Dilution) Differences vs Rod Worth
- i l , 0.15 "
= M - .005 N - 60 l $ g,, , ,
SIGMA .0580 8- a %' s KSIGMA .1173 h E 0.05 - = m
- g 2* " "' s " *E" ES 0- e e s',
5E a g , g "a" s s a Q 4.05 - e a
{ 4.1 - -
E . ,
-0.15 0 0.5 ~ 1 1.5 2 2.5 3 MEASURED WDRTH(% RHO) l i
ENEAD-01-NP REV 0 Page 69
l i
Table 4.4-1. Observed Rod Worth (Dilution) Differences PLANT CYCLE - M-P PLANT CYCLE - M-P BANK BANK 1 ANO-2 1-6 0.02 6-A 0.141 :
1-5 0.083 7-B -0.134 14 -0.032 8-B -0.044 l 1-3 0.096 9-B -0.132 1-2 -0.026 10 - B -0.04 1-1 0.075 WSES3 1-6 -0.038 -
2-6 -0.025 1-5 -0.014 2-5 0.005 1-4 -0.035 2-4 0.002 1-3 0.122 ,
2-3 0.017 1-2 0.056 2-2 -0.031 1-1 -0.017 2-1 -0.038 1-P 0.018 3-6 0.012 1-B -0.107 3-5 0 2-B 0.001 >
3-4 -0.01 3-B -0.017 3-3 0.012 4-B -0.021 g 3-2 -0.023 5-B -0.016 3-1 -0.046 6-B -0.016 4-6 -0.041 ANO-1 8-5 0.025 4-5 -0.011 9-5 0.066 4-4 -0.032 10-5 0.034 4-3 -0.022 11 - 5 -0.133 ;
4-2 -0.053 8-6 0.028 4-1 -0.033 9-6. 0.035 t
5-6 -0.041 10-6 0.078 5-5 0.048 11 - 6 0.033 5-4 -0.009 8-7 0.063 5-3 -0.051 7 0.086 5-2 -0.057 10-7 0.038 5-1 -0.09 11 - 7 0.054 i-r
'I ENEAD-01-NP REV 0 Page 70 1
h
4.4.2 Rod Worth by Swap The observed differences between the measured (by swap) and predicted control rod worths are given in Table 4.4-2 for forty rod banks (twenty ANO-2, ,
and twenty WSES-3 banks). A histogram of these differences' for the forty measurements is shown in Figure 4.4-3. The data is seen to have a sample mean and standard deviation of -0.011 %p and 0.073 %p, respectively. This figure demonstrates that the safety limit of the observed population can be conservatively estimated by equating it to the tolerance limit from a normal distribution characterized by the mean and standard deviation of the observed differences. All of the data points are seen to lie above the normal 95%
confidence /95% probability tolerance limit. The observed population is normal as the differences pass the requirements of the W normality check
[ Reference 14). Therefore, a reliability factor (RF) of 0.155 %p was determined using the normal one-sided k-factors for forty samples [ Reference 10].
t Figure 4.4-4 demonstrates that the observed differences are not a. strong function of the value of the rod worth. Hence, the above mean and RF can be used over the full range of expected control rod worth. ,
As discussed in the introduction to this section, no attempt is made to account for the measurement uncertainty. The observed statistics will be used for the model uncertainty.
In summary, the control rod worth (swap) predictions from CASMO/ SIMULATE will be biased by -0.011 %p, and a reliability factor of 0.155 %p will be applied:
RW(dilution) safety = RW(dilution) calc -0.011 %p -0.155 %p
= RW(dilution)cate-0.166 %p
)
1 l
1 I
ENEAD-01-NP REV O Page 71 l l
p[ .
Figure 4.4-3. Observed Rod Worth (Swap) Histogram 12 -
+ HZP Central Red Wert Osts -
'~ - NornalDetrhunon .
bemelS$%l95% Linut - - gp .
8- f.18E% riel Some +
100% et Messmed Data, n ..
E /,mK .
/
/ . .
/~
.N 0
f , , , ,
.x 42 -0.17 -0 14 -011 -0 08 -0 05 -0 02 0 01 0 04 0 07 0.1 0 13 0 16 0 19 0 22 0.25
<memme mw i Figure 4.4-4. Observed Rod Worth (Swap) Differences vs. Rod Worth
. 0.3 es >
E 0.2 <
'h 6 p M - .011 N - 40 t
y E 0.1 g *.
ES 0- % "" % - SIGMA .073 KSIGMA .155 1
$E ,[ #.se [,g :
I iE S 4.1 < = .!
mg e a
- b C.2 <
8
)
-0.3 -
'l 0 0.5 1 1.5 2 2.5 -3 ;
MEASURED WORTH (% RHO) !
i
.{
l i
$E b
ENEAD-01-NP REV 0 Page 72 i
.- ~ - , , ,
1 i
l i
Table 4.4-2. Observed Rod Worth (Swap) Differences PLANT CYCLE - M-P PLANT CYCLE - M-P BANK BANK WSES-3 2-A -0.007 ANO-2 6 - 3+4 0.036 2 - 1+2 -0.026 6 - 5+6 0.077 2 - 4+5 -0.01 .6-B -0.019 2 - 3+6 0.058 6 - 1+2 -0.02 3-A 0.056 6 6+5 -0.061 !
3 - 1+2 -0.058 7-A -0.073 3 - 4+5 -0.008 7 - 3+2 -0.082 3 - 3+6 0.05 7-1+4 -0.126 4-A 0.067 6-4+2 0.018 4 - 1+2 0.019 8-3 -0.031 4 - 4+5 0.055 8 5 -0.051 4 - 3+6 0.098 8-A -0.077 5-A -0.056 9-4+2 -0.097 5 - 1+2 -0.091 9-3 -0.111 5-4+5 -0 038 9-1 -0.127 6 5 - 3+6 -0.052 9 - 5+6 -0.117 !
6-A 0.211 10-5+6 -0.018 6 - 1+2 0.068 10-2+4 0.005 6 - 4+5 0.116 10-3 -0.019 6 - 3+6 0.015 10-1 -0.029 t
ENEAD-01-NP REV 0 Page 73
n A
4.5 Isothermal Temperature Coefficients Measurements of the isothermal temperature coefficient (ITC) at the hot zero power, all rods out condition are performed at the initial startup of each cycle to ,
verify conformance with the design Fssumptions. Estimates of the bias, uncertainty, and-reliability factors to be applied to the CASMO/ SIMULATE predictions of this parameter are reported in this section.
The observed differences between the measured and predicted ITCs are given in Table 4.5-1 for twenty cycles (four ANO-1, ten ANO-2, and six WSES-3 cycles). A histogram of these differences for the twenty measurements is shown >
in Figure 4.5-1. The data is seen to be reasonably symmetric with a sample mean and standard deviation of -0.077x104 Ap/ F and 0.035x104 ApfF, ;
respectively. This figure demonstrates that the safety limit of the observed population can be conservatively estimated by equating it to the tolerance limit ;
from a normal distribution characterized by the mean and standard deviation cf the observed differences. All the data points are seen to lie below the normal 95% confidence /95% probability tolerance limit. The observed population is normal as the differences pass the requirements of the W normality check .
[ Reference 14]. Therefore, a reliability factor (RF) of 0.084x104 ApfF was determined using the normal one-sided k-factors for twenty samples
[ Reference 10].
Figure 4.5-2 demonstrates that the observed differences are not a strong function of the value of the soluble baron concentration. Hence, the above 4 mean and RF can be used over the full range of expected boron conditions.
The accuracy of the ITC measu;ement is limited by that of the reactimeter used '
to measure reactivity changes. As the procedures require several measurements of the ITC at each state, an estimate of the measurement uncertainty can be obtained though comparison of these values. As shown in Table 4.5-2, the uncertainty (one sigma) in the measurement is shown to be ENEAD-01-NP REV 0 Page 74
0.039x104 ApfF. Thus, the observed and measured uncertainties are almost identical, leaving an undetermined component for the model uncertainty as f calculated from Equation 4.1-3. Therefore, for conservatism, the model standard l deviation and mean will be taken to be equal to the observed standard deviation I and the corresponding RF will be calculated. i In summary, the hot zero power isothermal temperature coefficient predictions {
from CASMO/ SIMULATE will be biased by -0.077x104 ApfF and a reliability .f factor of 0.084x104 ApfF will be applied: l ITCsafety= ITCcale -0.077x104 ApfF + 0.084x104 ApfF
= ITCcate + 0.007x104 Ap/ F t
f i
J f
i I
ENEAD-01-NP REV 0 - Page 75 5
s.
.i Figure 4.5-1.HZP ARO ITC (Observed) Histogram ,
asses ;
L.m ;
- - u,m .
- t. Ath m4
=n ;
bounds 10D%
5*
8.e *
-, t I
3 . . . t t
,. /'%
/./ \. r
- i. .
/
.N !
0
/
\x-4.19 4.1$ C.14 4.13 4,12 4.11 4.1 4AD 4A0 4A7 4Al 425 4A4 423 4A2 4A1 e ILD1 0.02 RA3
.)
~
j c % iu n a i
i Figure 4.5-2.HZP ARO ITC Differences (Observed) vs. Boron Conc. t i
M . .077X104 N.20 ,
SIGMA . .035X104 i g 0.03 '
KSIGMA . 084X104
. i s:2 g 0.01 < -
c2 .!
E d -0.01 <
4e e i 8 g -0.03 -
- x >.............
. is =x 4.05<
<b
. . . . Oo . . . .o ,
E E 447< e 1 ,
E I 0.09 - e's " !
EE
- g -0.11 <> . . . . . . . . . . . . . . . . . . . . . . . .
b -0.13 0 500 1000 1500 2000 f BORON, PPM l t
i I
P ENEAD-01-NP REV 0 Page 76 j
Table 4.5-1. Observed HZP ARO ITC Differences -l PLANT CYCLE M-P * !
ANO-1 8 -0.075.
9 -0.09 10 -0.087 11 -0.128 ANO-2 1 -0.098 {
2 -0.034 3 -0.071 4 -0.058 5 -0.023 6 -0.028 i 7 -0.044 8 -0.067 9 -0.05 10 -0.081 ,
WSES-3 1 -0.125 ;
2 -0.09 ,
3 -0.127 ,
4 -0.072 ;
5 -0.046 6 -0.144
- units are 10d Ap/ F .
t t
i i
1 l
)
ENEAD-01-NP REV 0 Page 77 1
Table 4.5-2. Observed ITC Repeatability PLANT CYCLE MEASURED
, UNCERTAINTY 104 Ap/*F ANO-1 8 .106 ,
9 .029 t 10 .050 11 .030 ANO-2 2 .020 3 .023
[
5 .014 6 .013 7 .024 WSES-3 1 .067 '
2 .006 [
3 .065 4 .051 OVERALL -
.039 i
r i
i i
ENEAD-01-NP REV O Page 78 i
' 4.6 Isotopics Isotopic compositions calculated by CASMO have been compared with spent !
fuel data from Yankee Rowe, Zion Unit 1 and Quad Cities Unit 1 [ Reference 7]. .
Some of these calculations were repeated by Entergy personnel to verify Entergy isotopic modeling techniques and accuracy.
The Zion isotopic data was chosen for this benchmark because of its relatively modern PWR fuel design, high power density and high fuel burnup. Zion-1 is a 3,250 MWm Westinghouse PWR reactor. Bumup ranges for the fuel examined are from 23,471 mwd /MtU to 51,754 mwd /MtU and represent insertion in the core from one to four cycles. ;
The Zion-1 high bumup irradiation program included two batch 'C' assemblies with removable fuel rods. Irradiation began in Commonwealth Edison's Zion-1 :
reactor in June of 1973 and proceeded for four cycles [ Reference 16]. Four intemal fuel rods were permanently removed from assemblies C63 and C64 after each of the first four cycles of operation. The empty rod locations were filled ;
with depleted uranium rods for additional depletion. The rods that were removed were highly characterized during fabrication.
Five fuel bumup sections from five fuel rods were analyzed for bumup by ;
standard chemical separation and mass / alpha spectrometry techniques. An -
entire cross section of a fuel pin was dissolved for analysis of each sample. !
Burnup was inferred from uranium isotopics [Pu, U]. Isotopic measurements !
were made for Zion fuel rods numbered 614, 616, 642, 699 and 624 (see Figure 4.6-1). Isotopics were corrected for decay from the time of shutdown to i the time of examination.
i 1
The isotopic calculations presented within this package follow the standard
)
Entergy methodology for CASMO calculations. No attempt has been made to 1 i
remove measurement uncertainty from the observed uncertainty. Therefore the ENEAD-01-NP REV 0 Page 79
)
reported reliability factors include both calculational and measurement uncertainty. This provides additional conservatism in the reliability factors.
The INTERPIN/CASMO programs were run to model the depletion of a 'C' batch Zion fuel assembly shown in Figure 4.6-2. Total U and Pu number densities are calculated as well as U234/U, U235/U, U23s/U, U238/U, Pu239/U238, Pu238/Pu, Pu239/Pu, Pu240/Pu, Pu241/Pu, Pu242/Pu, Am241/Pu239, Am243/Pu239, Cm242/Pu239, and Cm244/Pu239 atom ratios. These number densities and the pin burnups are output for the three CASMO compositions, 22, 23 and 28 corresponding to the Zion pins 616,624,642,699 and 614 (see Table 4.6-1).
Finally the isotopic and burnup information for the CASMO pin locations was )
l interpolated on the CASMO pin burnups to calculate the isotopics at the exact measured pin bumups. Entergy RMS errors are presented along with RMS errors calculated by Yankee Atomic (Reference 7]. Relative differences, (M-C)/C, based on Entergy and Yankee CASMO calculations were also
{ calculated. l 1
Figures 4.6-3 through 4.6-6 are comparisons between calculated isotopic ratios from CASMO and the measured values of isotopic ratios for Zion pins numbered 616, 642 and 614. Table 4.6-2 gives the comparison of sample standard deviation and means of errors for both Entergy and Yankee Atomic based on the relative errors, (M-C)/C. To calculate a conservative isotopic :
Safety Isotopic = Calculated isotopic * (1 + BIAS RF) (4.6-1) where:
Calculated Isotopic is the calculated isotopic from CASMO/ SIMULATE BIAS is the mean of the quantity (M-C)/C from Table 4.6-2 RF is the reliability factor from Table 4.6-2 To calculate a bounding limit on isotopics, first determine the best estimate of the isotopics based on a CASMO/ SIMULATE calculation. For example one may ENEAD-01-NP REV O Page 80
f calculate 100 grams of U235 The reliability factor for U235 /U is 0.01964 from .
Table 4.6-2. Combining the reliability factor with the mean of 0.01115 from Table 4.6-2 according to Equation 4.6-1 gives an upper and lower limit for-the isotopic ratio multiplier of 0.99151 to 1.03079. Applying these limits, the true I U235 weight is expected to be between 99.151 and 103.079 grams. Using the means and reliability factors in Table 4.6-2 all measured data was bounded by .
calculated isotopics using Equation 4.6-1.
l f
i f
ENEAD-01-NP REV 0 Page 81
Figure 4.6-1 Zion Assemblies C63 and C64 Measured Pin Layout 616 sa 614 W 624
. j$i*
l I
( o 699 x ,,
- >a.~
g u: +
, syf' l
l Elf.Thimble Tube $3 3.3% Enriched Fuel 1
l i
. l I
i l
l l
ENEAD-01-NP REV 0 Page 82
- _ _ _ _ _ _ - - _ _ _ _ _ _ _ _ _ . _ _ - __ - ~
i Figure 4.6-2. CASMO 1/8 Zion Assembly Model s
y v
30 31 l
I i
27 28 29 624 1
^ ~
24 25 26 v> s
^ '
gg.' -
.w l
cc 20 21 22 23 614,616, 699 642
~'
16 17 # "l -
18 19 u
[. .. ~ "$ pin 4.get x ; -- ^ ]
ggs 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 l
V ds THIMBLE TUBE TASMO 3.3 % ENRICHED FUEL .
. PIN #
' asy co ;
45 ,
- ' i v ZION PIN #
ENEAD-01-NP REV 0 Page 83 I
1
___j
Figure 4.6-3. Zion isotopics for Pins #616,642 and 614, Part 1 Isotopies fer ZION Pine # 616,642 sad 614 CasMD U-234/U Inxxt + 01 .
...- ------ CAsMO U 23510 1.Dn00E + 00 22C _ _ _ _ _ _ _ . _ _ _ _ _ _ _
CASMD U 236/U
.__.f =- . E~ - :
, p< e. CASMO PU239It!238 1D000EC1 -=*e CASMO PU23BlPU "g =r== _ __
s Mass. U234M
~ ~ ~ ,
1D000EC2 j r- m m___
Mass.U235M e g ,y23sg
~ ~ ~ '
8 5 5 5 5 i
I. I
- n 1
1 w
Pia bersa,in Mwdsg I
m i 1
~
l Figure 4.6-4. Zion isotopics for Pins #616,642 and 614, Part 2 leetopies ier ZION Pine # 816,642 and 614 1 AIKE+ 02 p .J. .._b___.._._ _
l ._
[ . ~ 3 ~ .- CASMO U 238W 1REDE*01 --s"~ ------ CASMO PU23LPU s / CASMO PU240lPU 1D000E + 00 = -
CASMO PU2411PU i
. . wumu I 1RDOE41 ,
, ,,g,g f a pass,pg240py Inrxac2 g g g g g g g g a Mass.PU2411PU I. I I
- I. I I
. I. i
- 1 Pit burag inIAwd!Kg I i
i I
ENEAD-01-NP REV 0 Page 84
Figure 4.6-5. Zion isotopics for Pins #616,642, and 614, Part 3 lentopics for ZlDN Pine # E15,642 end 814
'D000l* 02 g-g. z g = , = == = =w.-. - = -=-- = =. = : ==--gu +.g_== att+2 mz
, _ _ _ _ _ _ CASM0 PU2427U IM
- 0' m=ms;ti:e=z=st 2~a1L=M==w=.. = ie --- -======1 4- _ ------ CABMG AM2417U230 IN'E -"
ss-a 5=y-- .; ygm._
CABM0 AM243FU239 3 , p- ,
1 2 0E41 7 g g_jy Tyy,_yy,_ _. ;;n. .,_ ,mm.ym ==e . . a=,g CASMO CM342/PU239 1D000E42 3:gI----,---.=-.==.--_:=:==-=.====-m=-==--
NE #
e p.,,, Ag241pg23g
'MO ..=-==:-.:.=- - -
-==;-==-==.===2:s
="# N a Mass. AM243!PU239 1A000E04 g g g g g g g 8 MastIM2421NZ39 8 . . . . .
1 1
- 1. I. I i
Pin burnup la ManilNs Figure 4.6-6. Zion isotopics for Pins #616,642,699 and 624 ZION Cm2441Pu239 Ratios 7 7 - - - - - A way from thimble .
i 2 '
6 m:2 x Pin #824 y 7
5 C:
- * - *
- Diagonal to thimble [ ;
I & I C Next to thimble #
- I 3----- >
O E2 Pins #616,642 yf 2-C2 '
A 4
EE 1 ~~
Pin #699
,f l
, 1 1 0 -
- - 2 S R e
2 R, 3. .8
- a. '-
ENEAD-01-NP REV O Page 85
Table 4.6-1. Zion isotopic Comparisons
% U234/U % U235/U % U236/U % U238/U ROD MWDMTU PIN # CASMO MEAS DIFF CASMO l MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF 616 23 471 22 0 018 0 018 0.000 1379 1.386 -0.007 0 363 0 370 -0007 98.239 98 226 0 013 642 37.295 22 0 015 0 016 -0 001 0.706 0.721 -0 015 0463 0.464 -0 001 98.816 98.799 0 017 614 51.754 22 0.011 0 014 -0003 0.301 0.308 -0007 0.501 '507 -0006 99 187 99.171 0 016 699 42 915 23 0 013 0.014 -0 001 0535 0 536 -0 001 0.484 06 -0006 98 968 98 960 0 008 624 49 879 28 0 011 0.013 -0002 0 368 0.370 -0002 0 500 0.503 -0003 99.121 99.114 0 007 EOIRMS 0002 0.008 0 005 0 013 YANKEE O002 0 054 0 004 0 053 DELTA 0 000 -0.046 0 001 -0 040
% PU239/U238 % PU238/PU % PU239/PU % PU240/PU ROD MWD /MTU PIN # CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS OfFF CASMO MEAS DIFF 016 23 471 22 0 481 0.492 -O011 0.790 0 840 -0.050 64 122 63.450 0 672 21.337 21.348 -0011 642 37.295 22 0 512 0508 0 004 1.di6 1982 -0126 52.479 51.849 0 630 25 415 25.655 -0240 614 51.754 22 0 506 0.468 0.017 3 227 3 539 0312 44 909 43 854 1.055 27.138 27.333 -O195 699 42.915 23 0.522 0 507 0 014 2.394 2 600 -0.206 49 394 48.316 1.078 26.172 26 622 -0 450 624 49 879 28 0 526 0 515 0 012 3 146 3.491 0.345 46 266 44.986 1.280 26.616 27.430 -0814 EOl RMS 0012 0 235 0 976 0 438 YANKEE O007 0 212 0.724 0 457 DELTA i 0 005 0.023 0 252 -0 019 l
% PU241/PU % PU242/PU % AM241/PU239 % AM243/PU239 ROD MWD /MTU PIN # CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF 616 23 471 22 11.187 11.563 -0.376 2 564 2 800 -0 236 0.337 0.475 -0.138 0496 0 333 0 163 642 37.295 22 14 095 13 894 0 201 6 155 6 620 -0465 0686 0.780 -0094 7437 1.900 0 537 614 51.754 22 14 439 13 961 0.478 to 297 11.313 -1.026 no data no data 699 42 915 23 14 422 14 190 0 232 7.617 8 272 -O 655 0.799 0 959 -0.160 3 798 2 390 1.408 624 49 879 28 14 597 13 944 0653 9 374 10 149 -0.775 0 916 1.510 -0594 5 912 4 410 1.502 EOl RMS 0422 0.686 0319 1.067 YANKEE- 0.511 0 430 0.319 1 230 DELTA -0 089 0.256 0 000 -0163 ENEAD-01-NP REV 0 Page 86
_ , _ . _ . . - . . , - - - - . e - -. - , , , _ _ . , _ _ _ , _ , . _ . _ _ . _ , . _ , , _ _ , _ _ _ _ , _ . _ _ _ _ _ _ _
~-
+
4' Zion isotopic Ccmpcrisona (continusd)
% CM242/PU239 % CM244/PU239 ROD MWDMTU PIN # CASMO MEAS DIFF CASMO MEAS DIFF 613 23 471 22 0 110 0 098 0 013 0 082 0 093 -0 011 642 37.295 22 0 361 0 332 0 029 0715 0.759 -0 044 614 51.754 22 no data no data 699 42 915 23 0.481 0.432 0 049 1.369 1.450 -0 081 624 49 879 28 0626 0.622 0004 2 646 2 620 0 026 eof RMS 0.029 0 04S YANKEE O 039 . 0134 DELTA -0 010 l 4 086 ENEAD-01-NP REV O Page 87 ,
.______._______..___.______mm_- _ma_
_ - ~..#v, v. w . ...4- u > s ..y,- -.,,.g .%.. v--. .--,-m e , . . _ - , , . , . ,,.,..q-.wmyw,.___,. - ,_,yy,,-. _, , -+,,.. , , ,. , ,
~
']
3 i
I
)
Table 4.6-2. Isotopic Statistics EOl YANKEE ,
ISOTOPIC RATIO S.D. MEAN k RF upper lower S.D, MEAN U234/U 0.10874 0.11253 1.96000 0.21313 1.32566 0.89940 0.11423 0.099 U235/U 001002 0.01115 1 96000 0.01964 1.03079 0.99151 0.08020 0.074 U236/U 0.00653 0.00987 1.96000 0.01279 1.02266 0.99708 0.01085 -0.001 !
U238/U 0.00005 -0.00012 1.96000 0.00009 0.99997 0.99979 0.00033 0.000 [
PU239/U238 0.02238 -0.01378 1.96000 0.04387 1.03009 0.94234 0.01146 0.011 I PU238/PU 0.01958 0.08457 1.96000 0.03837 1.12294 1.04620 0.06393 0.064 i PU239/PU 0.00750 -0.01910 1.96000 0.01470 0.99560 0.96620 0.01616 0.016 ,
PU240/PU 0.01150 0.01298 1.96000 0.02253 1.03551 0.99045 0.01882 0.019 :
PU241/PU 0.02992 -0.01491 1.96000 0.05664 1.04373 0.92646 0.01579 -0.032 PU242/PU 0.00922 0.08718 1.96000 0.01807 1.10525 1.06912 0.04369 0.027 AM241/PU239 0.23125 0.34873 1.96000 0.45324 1.80197 0.89549 0.25025 0.313 AM243/PU239 0.06858 -0.29339 1.96000 0.13441 0.84102 0.57220 0.09200 -0.362 CM242/PU239 0.04811 -0.07549 1.96000 0.09431 1.01881 0.83020 0.10503 -0.015 CM244/PU239 0.05993 0.06203 1.96000 0.11746 1.17950 1 0.94457 0.06827 -0.115 4 e
-t
'l L
-l
~ ;
i
, t t
i 1
i ENEAD-01-NP REV O Page 88 l i
i
~4.7 Doppler Coefficient t
CASMO has previously been benchmarked against the Hellstrand measured i resonance integrals and Doppler coefficients [ References 17 through 19]. A recent survey of computer codes used by the utility industry [ Reference 20] has shown CASMO to be within 3% of the Hellstrand results. Follow-up calculations have benchmarked CASMO against MCNP-3A Monte Carlo calculations
[ Reference 21]. Entergy has used the CASMO computer program to confirm some of the calculations in Reference 21. )
kinrinity and Doppler coefficient results are summarized in Table 4.7-1.
C-alculated results are given for MCNP-3A and CASMO. Comparisons of measured (Hellstrand) to calculated (CASMO) results are presented in Table 4.7-2. The standard CASMO 40 group library was used for all l calculations.
The standard deviations of the (Calculated - Measured)/ Calculated differences from these two populations were pooled with the resulting average Doppler ;
coefficient difference (i.e., bias) being -0.0174 with an uncertainty of 0.0332. ,
Using a one sided 95/95 confidence / probability factor [ Reference 10] of 2.614 ,
(for 14 data points) results in a Doppler reliability factor of 0.0868. l Converting from (Calculated -
Measured)/ Calculated to (Measured - ;
Calculated)/ Calculated results in a sign change on the bias. In summary, the !
Doppler coefficient calculations from CASMO/ SIMULATE will be biased by
+0.0174 and a multipicative reliability factor of .0868 will be applied: ;
Doppler coefficientsafety = Doppler coefficientcalc * (1.00+ .0174 .0868) i I
l ENEAD-01-NP REV 0 Page 89
These calculations confirmed the use of a 10% multiplicative Doppler coefficient reliability factor [previously approved in Reference 1] which will be applied to Entergy PWRs for additional conservatism:
Doppler coefficientsafety = Doppler coefficientcale * (1.00 - 0.1) l i
ENEAD-01-NP REV O Page 90 l
r
.. . I s ,
. Table 4.7-1. Calculated k-inf and Doppler Coefficients it kinfinity Akinfinit Enrichment Temperature (pcm) y ' Doppler Coefficient (pem/K) ,
-% Kelvin - MNCP-3A CASMO-3 MNCP-3A CASMO-3 A(%)
0.7 600 0.66381.0006 380 -5.40.8 -5. 5 +1.6 ;
900 0.6567 .0008 360 '
1.6 600 0.9581t.0006 390 -3.60.3 -3.4 - . -5. 5 ' ,
900 0 9484 .0006 430
~~
2.4 600 1.0961 1.0007 350 -2.7!0.3 -21 +2.9 - l 900 1.0864 .0007 320 !
3.1 600 1.17471.0007 260 -2.620.2- -2.5 -4.3. !
900 1.1641 .0006 300 3.9 600 1.23791.0006 240 -2.420.2 -2.4 + 0.3 000 1.2271 .0006 230 l 3.1 600 1.17421.0007 240 -2.27 0.2 -2.31 + 1. 8 !
900 1.1649 .0005 220 O.71+1%Pu 600 0.9451 .0007 480 -3.6610.3 -3.51 -4.3 900 0.9354 t.0007 510 Table extracted from Reference 21 based on C-M/C i
k o -k o a ric _
ko x k x 300 i
Table 4.7-2. Calc. vs Meas. Resonance Integrals and Doppler Coef.
Measured Resonance Calculated Resonance Difference fuel radius Integral (barns) Integral (barns) (%) .l (cm) 300 K 1000 K 300 K 1000 K 300 K 1000 K Doppler UO2 0.40 23 66 26.29 23 65 26.19 0.0 -0. 4 -3.4 O.52 21.44 23 65 21.31 23.50 -0.6 -0.6 - - -0.3 - 3 0.80 18.37 20.09 18.39 19.99 + 0.1 -0.5 -7.1 1.04 16.80 18.30 16.75 18.19 -0.3 -0.6 -3.7 1.60 14.63 18 86 14.69 15.90 +0.4 + 0. 3 -2.0 i U 0.50 16.61 17.97 15.85 17.19- -4.6 -4.4 +3.3 metal 1.00 12.99 13 94 12.78 13.68 -1.6 -1.9 -3.7 !
Table extracted from Reference 19. i
<+
.I
.. f ENEAD-01-NP REV 0 Page 91
4 4.8 Delayed Neutron Parameters The importance of the reliability factor for the calculated values of the delayed neutron parameters is primarily associated with the core effective delayed neutron fraction, perr. The uncertainty in the calculation of pert si composed of >
several components, the most important of which are listed below;
- a. Experimental values of delayed neutron fractions, p, and delayed neutron decay constants, A, by nuclide;
- b. Calculation of spatial nuclide inventory. These uncertainties are addressed in Section 4.6;
- c. Calculation of the core average p as a flux weighted average over the spatial nuclide inventory; and,
- d. Calculation of pert from the core average, where perr = I x , where I is .
the importance factor.
The experimental determinations of ps and Is are assumed accurate to within ,
1.0% [ Reference 1). The most important nuclides with respect to core pert are [
U238, U235 and Pu239 Section 4.6 demonstrates that the uncertainty in the '
calculation of these concentrations is less than 1.0%.
The uncertainty in the calculation of core average p depends on the relative flux weighting of the individual assemblies in the core. For demonstration purposes ,
consider a three region core, each region with a different average burnup and p.
This is typical of PWR cycles in that about a third of the core has seen two previous cycles of operation, one third has seen one cycle of operation and one third of the core is fresh fuel. Typical regional ps are given below-Region 1 (third cycle fuel) p = 0.005 Region 2 (second cycle fuel)p = 0.006 Region 3 (fresh fuel) p = 0.007 The effect of errors in the calculated flux distribution can be evaluated in terms of the effect on the core average . As a base case, flux weighting factors (FWF) are 1.1 for region 1,1.2 for region 2 and 0.7 for region 3. In this case, ,
the core average p equals 0.00587. Using a rnaximum error in the regional flux weighting of 7% [ Reference 1), the worst error in the calculation of the core ,
1 ENEAD-01-NP REV 0 Page 92 ,
average p is obtained by increasing the weight of region 3 and decreasing the weight of region 2 fuel. It should be noted that the average relative weighting factor is unity. The revised core average p is calculated as follows:
1.00
- p(1)
- FWF(1)= 0.0055 0.93
- p(2)
- FWF(2)= 0.0067 1.07
- p(3)
- FWF(3)= 0.0052 core average p =0.00581 -
As demonstrated by this example, the maximum error in p attributable to a flux weighting error is 1%.
The last uncertainty component concerns the reduction of core average p to obtain pert. The proper definitions of effective kinetics data requires that the :
adjoint flux distribution be used as a weighting function. When edits of kinetics parameters are requested in SIMULATE, a two-group adjoint flux calculation is performed. The reduction of core average p to pert is computed to be about 3 to 4% [ Reference 1); thus an error of 10% in this computation would lead to an error in perg of less than 0.4% (0.04 x 0.10).
If all four of the above uncertainty estimates are combined by summing the variances; the resultant uncertainty is 1.8% (41.o' +1.o' +1.o* +0.4* ). In the previous Topical report [ Reference 1) these components were combined linearly, '
which is more conservative than the current approach. For additional i conservatism (in this calculation) the currently approved 3% reliability factor from Reference 1 will be applied to calculations of delayed neutron parameters.
I 1
l i
ENEAD-01-NP REV O Page 93
1 1
A similar argument is applied to the determination of the effective neutron lifetime (l*) uncertainty. The uncertainty components which constitute the calculation of /* are as follows:
- a. Experimental values of microscopic cross sections;
- b. Calculation of the spatial nuclide inventory; and,
- c. Calculation of the core average effective neutron lifetime, l*, as a flux weighted average over the spatial nuclide inventory which includes the effects of leakage.
Uncertainty components (a) and (b) are assumed to be the same as described for the calculation of err, that is 1% uncertainty in the experimental determination of nuclear cross sections, and 1.0% uncertainty in the ,
determination of the spatial nuclide inventory. The core average neutron lifetime depends on flux weighting of local absorption lifetimes, la If a conservative estimate of the error in the regional power sharing (7%, Reference 1) is used in determining the impact on the core average neutron lifetime (l*), the error in the lifetime is on the order of 1% [ Reference 1). Combining all of these uncertainties (41.o* +1.o* + 1.o' ) results in a total uncertainty of 1.7%. For conservatism, the 3%
reliability factor from Reference 1 will be applied to the neutron lifetime calculation when 1* is used for safety related calculations.
The conservatism of the above arguments was checked by comparing Entergy predictions of perf against best estimate NRC licensed vendor calculations provided for startup tests. Calculations were performed to justify the continued use of the approved 3% delayed neutron fraction reliability factor from Reference 1. pery values as calculated by CASMO/ SIMULATE were compared to pert calculated by two reactor vendors for three reactors over twenty-one reactor cycles. The results of (Calculated - Measured)/ Calculated are j summarized in Table 4.8-1. In Table 4.8-1 the independent vendor calculations are considered as measured.
The reliability factor of 0.03 from Reference 1 bounds all data shown in Table 4.8-1. Therefore, the currently approved 3% multiplicative delayed ENEAD-01-NP REV 0 Page 94
f l'
i h
neutron fraction and neutron lifetime reliability factors will continue to be applied' I to Entergy PWRs. :
)
To summarize:
Delayed neutron fraction psafety = Ecalc * (1.00 03) !
Neutron lifetime l* safety = l* calc * (1.00 .03) i
' i, i
1 5
i j b l
i
- )
ENEAD-01-NP REV 0 - Page 95
1 Table 4.8-1. Delayed Neutron Fraction Comparisons AND-1 Vendor E01 rol diff abs diff 57@0wd 6 0.00633 0.006269 -0.00967 0.00006 8@37.5wd 7 0.00626 0.006292 0.005086 0.00003 8 0.006109 0.006253 0.022998 0.00014 179 9 0.006160 0.006181 0.003462 0.00002 100wd 10 0.006120 0.006130 0.001667 0.00001 AND-2 Vandor E01 rol diff abs diff ARO 1 0.00715 0.007144 -0.00078 0.00001 2 0.006113 0.006114 0.000213 0.00000 3 0.006035 0.005937 0.01654 0.00010 4 0.006129 0.006092 -0.00606 4 00004 5 0.006078 0.006084 0.001019 0.00001 6 0.006195 0.006244 0.0078 0.00005 7 0.006134 0.006164 0.004883 0.00003 -
8 0.006107 0.006122 0.002418 0.00001 9 0.006142 0.00619 0.00777 0.00005 10 0.006273 0.006306 0.005202 0.00003 Bank B in B- 0.006184 0.006276 0.014643 0.00009 9 0.006224 0.006367 0.022412 0.00014 10 0.006301 0.006409 0.01679 0.00011 WSES 3 Vendor E01 rei diff abs diff ARD 1 0.007238 0.007142 401338 -0.00010 2 0.006223 0.006341 0.018594 0.00012 3 0.006111 0.006189 0.012651 0.00008 4 0.006087 0.006171 0.013595 0.00008 5 0.006076 0.006166 0.014581 0.00009 6 0.006144 0.006225 0.013043 0.00008 Bank 8 in 2 0.006214 0.006382 0.026339 0.00017 3 0.006125 0.006248 0.019733 0.00012
'4 0.006095 0.00622 0.020114 -0.00013 5 0.006083 0.006216 0.021396 0.00013 6 0.006109 0.006222 0.018144 0.00011 NOTE: Relative Difference = (Calculated - Measured)/ Calculated ENEAD-01-NP REV 0 Page 96
4.9 Power Distributions The physics model reliability factors for calculating power distributions are based on two components: The first component is the global or " nodal" power distribution uncertainty and is based on the uncertainty associated with the prediction of assembly powers. The second component is the " local" power uncertainty and is based on the uncertainty associated with the prediction of the ratio of individual fuel pin powers to the assembly average pin power. These two components are then combined together to give the overall core peaking uncertainty and reliability factors.
Reliability factors were calculated for the following three calculated power distribution parameters:
(1) F, - the maximum local peak pin power to average power ratio (2) F, - the maximum axially integrated peak pin power to core average power ratio (3) F,,. - the maximum planar peak pin power to planar average power ratio 4.9.1 Nodal Peaking Uncertainty .
The physics model reliability factors to be applied to calculated nodal power distributions are based, in part, on comparisons of measured and predicted in-core detector signals for normal operating core conditions. The measured background-corrected signals from the in-core detectors are collected by the on-site process computer- while the predicted signals are calculated with the ,
RHOBURN 'model. The absolute differences between the measured and
_ predicted signals are then statistically analyzed from the data.
ENEAD-01-NP REV 0 Page 97 i
q 1
The simulated detector signals are calculated in a manner which is consistent with the calculation of local power peaking factors used in safety evaluations. !
That is, the nodal power distributions are calculated (generally in quarter radial core fraction) using 2X2 nodes per fuel assembly, with 24 to 30 axial levels. The lattice and nodal parameters are combined together as shown in Figure 3.3-1 to calculate the instrument signal for each detector segment.
Consistency between the above calculations of instrument signals and the calculation of power peaking factors is assured by: '
a) Using a common 3-D nodal simulator code, SIMULATE; and, b) Using a common cross section generation code, CASMO Two hundred and seventy-six (276) core statepoints were chosen for .the 1
purpose of comparing measured and predicted in-core reaction rates. These statepoints span cycles 7 through 11 of ANO-1, cycles 1 through 10 of ANO-2 and cycles 1 through 6 of WSES-3. These statepoints span reactor power levels from approximately 73% to 100% of rated power. The CASMO/ SIMULATE model is expected to perform adequately at all power levels and indeed ,
extended low power operation in cycles 7, 8 and 9 of ANO-1 showed no increase in model uncertainty. The specific core conditions for the statepoints are given in Appendix A. '
j Examples of the comparisons of measured and predicted detector signals are.
provided in Appendices B, C and D for ANO-1, ANO-2 and WSES-3, respectively. A representative cycle was chosen for each reactor and information is presented for beginning, middle and end of cycle statepoints. The representative cycle was selected by choosing a cycle with a model standard !
deviation close to the composite of all cycles for a specific reactor. I i
Radial and axial comparisons are given for each statepoint. Radial comparisons -
are provided which present the differences between measured and predicted integral signals for all functioning instrument locations. Axial comparisons are :
then given for two specific instrumented core locations. The measurements are i shown at five axial detector levels (for ANO-2 and WSES-3) or seven axial ENEAD-01-NP REV O Page 98 i i
detector levels (for ANO-1). The two core' locations were chosen as typical of regions of high power density and those showing the influence of inserted control rods, if any.
-l, 1
i t
k e
'h l
5 i
c t
l i
I ENEAD-01-NP REV O Page 99 I
4.9.1.1 3-D Peaking Factor, Fq Fq is the ratio of peak pin power to core average pin power, defined in a nodal model as:
F, = max [P,) (4.9-1) e where Pgis the pin by pin power density within the fuel assembly located at the -
(i, j) radial location and the #h axial location. The powers are normalized such that the volume averaged value of pg is unity.
The nodal component of the total peaking factor-calculational uncertainty is determined from a comparison of measured and calculated detector signals for all functioning detector locations throughout the core. The measured and calculated signals were each normalized to a value of unity on a core-wide-basis. As the peak power (i.e., the product 'of Fq and nodal power) is not expected to be limiting in the core regions monitored by the top or bottom detectors, the top and bottom detector levels were eliminated from the comparison of differences between measured and calculated . signals for calculation of the nodal Fq uncertainty. (The ANO-2 and WSES-3 core monitoring programs exclude the upper and lower 15% of the core planes from their search for the peak power location.) Therefore, all subsequent statistical analysis on the nodal Fq has been performed on a ccmbined level basis. This procedure creates a small bias in the calculated and measured differences.
The following statistics were obtained over the remaining axial detector levels (three for ANO-2 and WSES-3 and five for ANO-1) for each statepoint and combined together on a core-wide basis:
ENEAD-01-NP REV 0 Page 100
Observed Differences:
AX(i,() = RR,(i,()- RR,(i,() (4.9-2)
Bias of Observed Differences:
X= AX(i,t) (4.9-3) i = radial detector location index
( = axial detector level index RRc= calculated detector signal ,
RRm = measured detector signal ,
N = total number of detector locations Sample Standard Deviation of Observed Differences, Sobserved: ,
Sm = (AX(i,t)-X)' (4.9-4)
The distribution of the nodal Fq observed differences between measured and calculated instrument signals were tested for normality (see Figure 4.9-5). The f D' test (Reference 14) was used for testing of observed differences for normality-because of the large number of samples. The results demonstrated that the distributions agreed well with theoretical normal distributions. Some of the observed difference distributions did not pass the D' test for normality at the 5% .;
significance level, but histograms of the data were bounded by the-normal distribution in the areas of interest. Plots of the observed differences encompassing all cycles of each Entergy PWR reactor along with the theoretical normal distribution with the same S observed and mean are presented in Figures 4.9-1 through 4.9-3.
The objective is to determine the population parameter, amodel, which represents the uncertainty of the model's calculation of nodal power distribution using the above statistics. The general problem is that the statistics previously defined f
ENEAD-01-NP REV 0 Page 101
contain several other effects which are of the same order of magnitude as the model uncertainty. The following is a list of examples of the more probable !
effects contained in the statistics of the observed differences between measured l and calculated in-core detector signals. The observed differences may contain:
{
- 1. Model Errors ;
a) Errors in the calculation of the core nodal power distribution. ,
b) Errors in the conversion of nodal power distribution to predicted in-core detector signals.
- 2. Measurement Errors 5 a) In-core detectors cannot be cross calibrated. The only calibration is done during manufacture.
b) Detector depletion corrections. .
c) Leakage corrections.
i d) Detector failures.
t
- 3. Simulation Errors a) Control rod position and/or core power level used as model input to '
simulate the statepoint differs from the actual statepoint condition.
b) The control rod and/or core power level history prior to the map used as model input to simulate the statepoint differs from the actual history..
c) The statepoint is simulated assuming an equilibrium xenon distribution.
However, the reactor will be experiencing a minor xenon transient, which effects the power distribution.
In an attempt to minimize simulation errors, a careful investigation was made of plant operating records to define the actual hourly power and rod history for 48 ;
hours around each statepoint. This investigation identified a few simulation and !
measurement problems which could not be adequately handled. A general problem was that almost none of the statepoints represented equilibrium steady - .
state conditions. The operating conditions for all plants were'almost always [
characterized by on-going axial xenon perturbations on the order of a few i percent. "
A typical example is shown in Figure 4.9-4 for a WSES-3 Cycle 6 case. These perturbations in some cases appeared to be correlated with changes in control i rod position or power level. ANO-2 and WSES-3 tend to have more problems l ENEAD-01-NP REV O - Page 102
. -t
, , , _ i
with axial xenon oscillations than ANO-1 because of the longer active fuel region. The most practical solution was to simulate all statepoints as equilibrium conditions and select statepoints that were taken near the equilibrium axial shape. The remaining simulation errors were taken as an additional penalty in the estimate of S model-The only aspect of the measurement error for which some credit has been taken l is for the lack of inter-detector calibration. These errors manifest themselves as asymmetries among radially symmetric in-core detectors. The magnitude of this uncertainty can be estimated for each flux map according to Equation 4.9-5:
S,, _ = x (RR,,,(k,g,t)- RR,(g,t))* (4,9-5)'
t is the axial detector location ]
k is the radial detector location g is the symmetric tilt group j RR,(k,g,t) is the measured signal for location k within group g
[RR(k,g,t)
RR,,,(g,t) =
- is the average reaction rate at location (k,
() in group g N is the total number of locations considered The standard deviations of the measurement errors in nodal Fq are presented for representative cycles in Appendix E for ANO-1, ANO-2 and WSES-3. The effect of the inter-calibration measurement error, S measurement, has been subtracted from the standard deviation of observed differences, Sobs, as-described below. This has been done on a map by map basis. The net result for each flux map, Smodel, has been assigned as a conservative estimate of the model standard deviation of a small sample of model errors.
S, = ]SL -S 2 (4.9-6)
ENEAD-01-NP REV 0 Page 103
The Fq Smodei results are presented for representative cycles in Appendix F.
Since the observed difference distribution for all cycles of each reactor was essentially normal, the relationship in Equation 4.9-10 was used to calculate the model standard deviation, Smodel, for each reactor.
The model standard deviation, which was in absolute units, was converted to relative units by dividing by a nominal peaking factor. The peaking factor used was the minimum of the calculated Fq peaking factor for all cycles of each reactor. The results are given in Table 4.9-1.
ENEAD-01-NP REV 0 Page 104
i, Figure 4.9-1. ANO-1 Fq Normal Distribution AI Fq vs Normal Histagram levels 2 through 6 gg . tas n iertass tem s w. ,
susetm eone 1100 - +f /%.
^s 1000 - */ + +
gan . +
/
{ 700 - [ .
'+ - AI Fq Dats 8 g, [
g ,4 s - - no w usi
~a- '
e0 /+ + -- 9s%ss% m u,,a a- /*
+
+
++
r a-4*, ;- g*t 100 -
0 J d * -* -* ~ # N" *^A'**^****
15 10 5 0 5 10 15 s-,s-Figure 4.9-2. ANO-2 Fq Normal Distribution A2 Fq vs Normal Histogram 1400 - ,
1300 -
1200 - ++ 4.16 hermal
+
1100 95%f35% Lrnit 6 Emmda 96% of 1000 -
Mesmaed Deta r
~
+ A2 Fq Dats y, 800 -
B +
horinal Est4mn ,
[ yao 800 .- +
- g. ,
95%fD$% RF Unst 400 - + +
300 - . %*
- 23) -
[
'4 [
N g.
,.M 10 4 4 7 4 4 4 4 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 Neessed Proestedinst Ene .i t
ENEAD-01-NP REV 0 Page 105 -
Figure 4.9-3. WSES-3 Fq Normal Distribution W3 Fq rs Normal Histogram Detector Levels 2.3, and 4 tsoo ,
+ W3 Fg data 4.31% herme! 95%95% Last
- Eaunds 95.1% of Measured 1400 -
hermalDutrbuten + + Disth 1200 - ,O I- 95% 195% RF Lett \
, 1000 -
s sao - j
./ .
I +
/ *\4 i soo .
/
\
, / \
.-: . b O
- -***~
12 10 4 4 4 2 0 2 4 8 8 10 12 sme n= ssri l
1 l
ENEAD-01-NP REV 0 Page 106 i
i
I 1
Figure 4.9-4. WSES-3 Cycle 6 ASI Context of Snapshot W7746DF I
031 l
1
- ~* a 0J05 7 '
p2m a i yM qi It'=
l t 0 ,' _,
l \
g O ,/
N h l _ . ..
. s .
I s /
Tme of Snapshot \, / ,
'm.p 2 4A15 D 5 10 15 23 25 30 35 40 45 50 Thee,IAmreb 18 sad 17 of 1993, hears t
l l
ASI =
""" ~ """* ,
POWER %_ + POWER,s , ;
Table 4.9-1. Overall Nodal Fq Uncertainties I Absolute Differences l Relative Differences Minimum Reactor S. S. Sw,, Mean pq S,, Mean ANO-1 0 03359 0.00611 0 03303 0.00054 1.391 0.02373 0.00039 ANO-2 0 02166 0.00666 0.02061 0.00544 1.093 0 01886 0.00498 WSES-3 0.02299 0.01081 0.02029 0.00469 1.213 0.01673 0.00386 i
j i
I I
.l j
1 l
ENEAD-01-NP REV O Page 107 l
Figure 4.9-5. Error Component Reliability Factor Calc. Flowchart l
I 1
l l
f Page 108 -1 ENEAD-01-NP REV 0
4.9.1.2 Integrated Radial Peaking Factor, Fr Fr is the ratio of axially integrated peak pin power to core average pin power, defined in a nodal model as:
F, = max [Py] (4.9-7) where 14 is the pin by pin axially integrated power density within the fuel assembly located at the (i, j) radial location. The powers are normalized such that the volume averaged value of P, is unity.
The nodal component of the integrated radial peaking factor calculational uncertainty is determined from a comparison of the axially summed measured i and calculated detector signals for all operating detector strings in the core (all detectors of a string must be functional). The normalization of the measured and calculated detector signals to unity causes the mean difference between measured and calculated channel integrated signals to be zero for any given flux map. Therefore, the standard deviation of the observed differences between measured and predicted channel integrated detector signals has been computed as follows:
1 Sm= x (AX, -X)2 (4.9-8)
AXi = IRRm (i)-IRR,(i) '
IRRmis the axially summed measured detector signals IRRc is the axially summed calculated detector signals ;
i is the radial detector location index N is the total number of operable strings (all segments in a string must be operating)
By definition, the bias between measured and calculated (X) is identically zero.
The distribution of Fr observed differences between measured and calculated instrument signals were tested for normality (see Figure 4.9-5). The D' test i
ENEAD-01-NP REV 0 Page 109
l I
[ Reference 14] was used for testing of observed differences for normality.
because of the large number of samples. The results demonstrate that the distributions agreed well with theoretical normal distributions. Some of the observed difference distributions did not pass the D' test for normality at the 5%
significance level, but histograms of the data were bounded by the normal distribution in the areas of interest. Plots of the observed differences for all cycles of each of the Entergy PWR reactors along with the theoretical normal distribution with the same Sobserved and mean are presented in Figures 4.9-6 through 4.9-8.
The standard deviation of detector inter-calibration errors for channel integrated detector signals has been computed in a manner similar to that for individual detector values discussed above. The Fr measurement uncertainty, Smeasurement, for each statepoint is inferred as follows:
' (49-9)
S_ _ =jN,-1 x(((RR,(k,g)-k(g)f
,i where:
gis the symmetric detector group index kis the radial detector location index within group g RR,(k,g) is the measured channel integrated reaction rate for location k within group g RR,(g) N x [RR,(k,g) is the average integral signal in group g Ngg is the number of channels considered The standard deviations of the integral measurement errors for each flux map of a representative cycle are presented in Appendix E for ANO-1, ANO-2, WSES-3.
The effect of the inter-calibration measurement error, Smeasurement, has been subtracted from the standard deviation of observed differences, Sobserved, as ;
described below. This has been done on a map by map basis. The net result for each flux map, Smodet, has been assigned as a conservative estimate of the model standard deviation of a small sample of model errors. ;
ENEAD-01-NP REV 0 Page 110
.>3
- c. n S ,=]S L -S 2
_ (4.9-10)
The net result for each flux map, Fr Smodel, has been assigned as a conservative estimate of the standard deviation of a small sample of model errors.
The Fr Smodel results for representative cycles are presented in Appendix F for ANO-1, ANO-2 and WSES-3. Since the observed difference distribution for all cycles of each reactor were essentially normal, the relationship in Equation 4.9-10 was used to calculate the model standard deviation, Smodel, for each reactor.
The model standard deviation, which was in absolute units, was converted to relative units by dividing by a nominal peaking factor. The peaking factor used was the minimum of the calculated Fr peaking factor for all cycles. The results are given in Table 4.9-2.
Figure 4.9-6. ANO-1 Fr Normal Distribution AI Fr ee lternal Histogram
=- .. "=.".1T
.x
~~
.. ../ \.
- Al Fr Dats r f x _ , _ _
I..
.. ./ \s.
/
.. / x
, . - - a. +/ ^ + s.
-10 4 8 4 -2 0 2 4 6 0 10 Emr has ENEAD-01-NP REV 0 Page 111 t
Figure 4.9-7. ANO-2 Fr Normal Distribution -
A2 Fr vs Normal Histegram 700 - <
. * ' 226 lunnel E~
95%f5% Laret Eaunds 94.7% of 500 - Wansured Data j
- A2 Fe Data (G-B 1 honnel Dist4uten
~
+ 95%!96% RF Urmt
[ .
f .
,, . ./ ['<v .
to 4 4 7 4 4 4 4 -2 l 0 1 2 3 4 5 6 7 8 9 to Maesvred . Predicted Error lhes Figure 4.9-8. WSES-3 Fr Normal Distribution W3 fr vs Normal Histogram
~
+
W3 Fr Data
~
"*""D"'*"'""
. s 2.tes manniiesstess inmi
- a. ,5g.35g ,, ,, .
N a.und,esa.t n t Drstributen
, soo -
/
I a- /
f ./ ~
n.
.. 'N .
+ s 100 -
. is 0 +- :
+-
4 4 2 0 2 4 6 em ,num w e i
I ENEAD-01-NP REV 0 Page 112
l Table 4.9-2. Overall Nodal Fr Uncertainties Absolute Differences l l Relative ,
Minimum '
Reactor Sm S.
m S nu.i Fr S mw ANO-1 0.02197 0.00175 0.02190 1.324 0.01654 ANO-2 0 01397 0.00398 0 01339 1.044 0.01283 i WSES-3 0.01295 0.00303 0.01259 1.132 0.01112 ,
t i
b 7
l f
I l
l l
l 1
ENEAD-01-NP REV 0 Page 113 l
1 I
4 4.9.1.3 Planar Peaking Factor, Fxy Fxy is the ratio of planar peak pin power to planar average pin power in plane k, defined in a nodal model as: I i '
F[ = max [P,3] (4.9-11) i where P,, is the pin by pin power density within the fuel assembly located at the
~
(i, j) radial location and the kth axial location. The powers are normalized such !
that the average value of P,, is unity for each plane k.
The nodal component of the planar peaking factor calculational uncertainty is -
determined from a comparison of measured and calculated detector signals for >
all operating detectors at each detector level. The measured and calculated signals were normalized on a planar basis rather than on a core-wide basis as was done for Fq. This procedure causes the mean difference (X) to be identically zero. !
c The standard deviation of the observed differences between measured and predicted detector signals at plane k has been computed as follows:
- S'm= x (AX(i,k)-X)
(4.9-12)
AXt i,k) = RRm(i,k) - RRc(i,k)
RRmis the measured detector signal RR, is the calculated detector signal l
i is the radial detector location inde, ,
k is the axial detector level in string i Ng is the total number of operable strings at level k The distribution of observed differences between measured and calculated instrument signals were tested for normality (see Figure 4.9-5). The ' D' test
- [ Reference 14) was used for testing of observed differences for normality ,
ENEAD-01-NP REV 0 Page 114 !
because of the large number of samples. The results demonstrated that the distributions agreed well with theoretical normal distributions. Some of the observed difference distributioris did not pass the D' test for normality at the 5%
significance level, but histograms of the data were bounded by the normal distribution in the areas of interest. Plots of the observed differences for all cycles of each of the Entergy PWR reactors along with the theoretical normal distribution with the same Sobserved and mean are presented in Figure 4.9-9 through Figure 4.9-11.
o The standard deviations of the measurement errors (defined in a similar fashion to Equation 4.9-5 but at each detector level) are presented for representative cycles in Appendix E. The effect of the inter-calibration measurement error, Smeasurement(L), has been subtracted from the standard deviation of observed j differences, Sobserved(L), as shown in Equation 4.9-10. This has been done on a map by map basis. The net result for each flux map, Smodel(L), has been assigned as a conservative estimate of the model standard deviation of a small ,
sample of model errors.
-l The Fxy Smodet(L) results are presented for representative cycles in Appendix F.
Since the observed difference distribution for all cycles of each reactor are ,
essentially normal, the relationship in Equation 4.9-10 was used to calculate the model standard deviation, Smodel, for each reactor.
1 The model standard deviation, which was in absolute units, was converted to relative units by dividing by a nominal peaking factor. The peaking factor used was the minimum of the calculated Fq peaking factor for all cycles. The results are given in Table 4.9-3.
('
ENEAD-01-NP REV O Page 115 L ______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Figure 4.9-9. ANO-1 Fxy Normal Distribution A1 Fry vs Normal Histogram 4.grt h.esasiof195% ben 9 ase no- .ui a 1800 -
1800 - / N
+/ \
/ % *
- AI E'Y O
1200 - g
/
- s in . -- ho,w o nem.
F / g am - / .\ -- 95%s5w una f a- ,{.
a- +f e .\.x
,,-----s',*
tw -
l h. .d+a+ ~---
15 10 -5 0 5 10 15 Error Bass r
i Figure 4.9-10. ANO-2 Fxy Normal Distribution 1
^
A2 Fry vs Normal Histegram **'""*
hermal Dist4unon 2700 - + "
05%S5% RF Unst gy _ . y.s
~
. 95%95% unst 2100 - Eaunds 94A% of
+ Mansured Data 1800 -
k 1500 -
8 +
[ 12 2 - .
{
==- . .
\
600 - +\
3m - ,g . + b
^+
o 't--
11 -10 4 4 7 4 4 4 4 -2 -1 0 1 2 3 4 5 6 7 'S 9 ,
konsored Predicted Error Bine i
P ENEAD-01-NP REV O Page 116
- n. .. . .. .. . .
Figure 4.9-11. WSES-3 Fxy Normal Distribution W3 Fry vs Normal Histogram 2500 -
+ W3 Fsy Date
~- - .
+
'q 232% Nommt 95%f95% Umst 2500 - 95%fB5% RF Laut T Bounds 94.7% et hommi
/ *\ o, .
,I
/ \, *
. ism -
,ow .
./ *
/
soo -
, / y 0
4 4 4 2 0 2 4 6 8 mm,n wn Table 4.9-3. Overall Nodal Fxy Uncertainties Absolute Differences l l Relative Minimum Reactor Sm S-. S moda Fxy Sm ANO-1 0.02908 0 00475 0.02869 1.272 0.02256 ANO-2 0 01770 0.00609 0.01662 1.042 0.01595 WSES-3 0.01751 0.00712 0.01599 1.131 0.01414 ENEAD-01-NP REV 0 Page 117
4.9.2 Local Peaking Uncertainty To. quantify the uncertainty in the calculation of local peaking, CASMO and SIMULATE were used to model ten critical experiments [ References 22, 23, 24]. These experiments were based on advanced PWR fuel designs that used gadolinium (Gd) and erbium (Er) as burnable poisons (BP) within the UO 2 fuel-matrix. The Gd-based core measurements were performed by Babcock and Wilcox (B&W); the Er-based core meast.rements were performed by ABB Combustion Engineering (ABB/CE). There are two Gd lattice / core dasigns, one similar to a B&W fuel design (15X15 fuel pin array with 17 small water holes per assembly) and one similar to an ABB/CE fuel design (16X16 fuel pin array with 5 large water holes per assembly). The Er lattice / core design is similar to an ABB/CE fuel design (16X16 fuel pin array with.5 large water holes per assembly). A total of 10 cores were analyzed. For the Gd cores, this consisted of varying the U235 enrichment and the number of fuel pins containing the BP.
l For the Er core, the number of Er-bearing pins was varied. A summary of the t
} relevant information for each core is presented in Tables 4.9-4 through 4.9-6.
Core configurations are provided in Figures 4.9-12 through 4.9-21.
i Absolute differences between the measured and CASMO/ SIMUL _ ATE pin' powers of the central assemblies for each core design were calculated, and categorized into four groups: 1) all cores, 2) B&W cores without Gd, 3) B&W cores with Gd, and 4) ABB/CE cores. Variances and standard deviations of these model differences are summarized in Tables 4.9-7 through 4.9-10. The standard deviation of the measurement error, Smeasurement, was either used as reported in the experiments or estimated from symmetry considerations.
The standard deviation of the absolute observed differences, Sobserved. is shown in Table 4.9-12. The standard deviation of the observed differences and the standard deviation of the measurement error Smeasurement, were used to estimate the standard deviation of the modeling error, Smodel, using Equation 4.9-10. The Smodei values computed in this manner are in agreement with the values
.. reported in Tables 4.9-7 through 4.9-10, which were derived from the root of the averaged variances.
ENEAD-01-NP REV O Page 118 q l
The local peaking standard deviations discussed thus far have been based on absolute differences referenced to an average power of unity. To obtain the .
l standard deviation in terms of relative power a conversion factor is needed. The relative standard deviations were obtained by dividing the absolute values by the calculated minimum- value of the local peaking factor (LPF) for its specific category. Table 4.9-11 presents the calculated minimum LPFs for each core. ;
(The core types in Table 4.9-11 identified as "CE" are B&W designs that are similar to the ABB/CE design, as described above).
The standard deviation of each core-type category group (items 1 through 4 l above) was divided by its appropriate calculated minimum LPF to determine the ,
relative standard deviation. These values are reported in True 4.9-12.
Although an 'All' value for relative standard deviation and mean are gated in >
Table 4.9-12, testing of the data with Bartlett's test (References 15 and 25) indicated that the data from the different core-type categories were not poolable.
For conservatism, the largest standard deviation for local peaking error was ;
used to determine the combined tolerance limit for the nodal and local peaking.
uncertainties. This value from CE-type cores, is expected to bound local peaking uncertainty for cores containing no gadolinium, gadolinium, erbium, >
stainless steel and other advanced fuel pin designs.
k b
i g.
ENEAD-01-NP REV O Page 119
. .4 Figure 4.9-12. B&W Core Design 1 w ..
]
"l i
L O 2.4e wt % u-23s Ericned Fuel ,
Vacant water filled position Center line
-i ENEAD-01-NP REV O Page 120
l l
1 l
Figure 4.9-13. B&W Core Design 5 E
l I E E E '
E E E l
i E >
c ,
.O 2.46 wt % U-235 Eriched Fuel Vacant water filled position Center line N 4 wt% Gd203/1.94 wt% U-235 Enriched Fuel I
ENEAD-01-NP REV 0 Page 121
i6 ,
e . Figure 4.9-1'4.' B&W Core Design 12 innerZone
': /
/
/
/I'
- -F
/
X k
A 7, ,
k J 9's N m
'N
'N
\ uterZone O
I 2.46 wt % U-235 Eriched Fuel, Outer Zone 4.02 wt % U-235 Eriched Fuel, inner Zone Vacant water filled position Centerline ENEAD-01-NP REV O Page 122
Figure 4.9-15. B&W Core Design 14 Inner Zone E - .
/ '
. Y E E .'
E /
s E
E E m
]
w s k N m N
\ uterZone O
t O 2.46 wt % U-235 Eriched Fuel, Outer Zone O 4.02 wt % U-235 Eriched Fuel, inner Zone Vacant water filled position Center line E 4 wt% Gd203/1.94 wt% U-235 Enriched Fue!
i i
ENEAD-01-NP REV O Page 123
[: Figure 4.9-16. . B&W Core Design 18 InnerZone
/
/
/
/,
/
/
, V')
\
\
\
\
Outer Zone O 2.4s wt
- u-23s Eriched Fuel, Outer Zone O 4.02 wt % U-235 Eriched Fuel, innerZone -
Vacant water filled position Center line ENEAD-01-NP REV O Page 124
Figure 4.9-17. B&W Core Design 20 inner Zone j
/ l f .l
/
E E /
/
/ k
.i E E , (
E E E E
\
\
\
\
Outer Zone O 2.46 wt % U-235 Eriched Fuel, Outer Zone O 4.02 wt % U-235 Eriched Fuel, inner Zone E 4 wt% Gd203/1.94 wt% U-235 Eriched Fuel Vacant water filled position Center line 1
ENEAD-01-NP REV 0 Page 125
-l l
Figure 4.9-18. CE Core Design 1 I I
t
(
l i
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i 9
s-b P
?
ENEAD-01-NP REV 0 Page 126
Figure 4.919. CE Core Design 2 .
P t
i e
]
1 i
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l j
i l
J l
l l
l ENEAD-01-NP REV O Page 127
Figure 4.9-20. CE Core Design 3 h
.i 4
.i 5
i c
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P ENEAD-01-NP REV O - Page 128 [
.)
1 i
Figure 4.9-21. CE Core Design 4 .
t i
'r b
t t
t L
t i
i I
i j
i ENEAD-01-NP REV O Page 129 4
1
g E
t e Table 4.9-4. Gadolinia Core Information ;
Fuel information Fuel Type 1 Fuel Type 2 Fuel Type 3 Fuel Ennehment (w/o) 2.46 4 02 1.944 GdeO, Enrichment (w/o) None None 4.0 Fuel Density (gm/cc) 10.24 9.46 10.11 ;
Fuel Pellet Radius (cm) 0.514858 0.563880 0.514985 Clad Matenal 6061 Aluminum SS304 6063 Aluminum j Clad Outer Radius (cm) 0.602996 0.60325 0.603250 i Clad Thickness (cm) 0.08128 0.03937 0.08128 Clad Inner Radius (cm) 0.521716 0.563880 0.521970 1 Fuel Pan Pitch (cm) 1.63576 1.63576 1.63576 -I Detector information Small Tube inner Radius (cm) 0.11811 Small Tube Outer Radius (cm) 0.15875 Small Tube Matenal inconel Large Tube inner Radius (cm) 0.32258 Large Tube Outer Radius (cm) 0.40132 Large Tube Material inconel Vessel information Vessel Material Aluminum Vessel Inner Radius (cm) 76.2 Vessel Wall Thickness Icm) 1.27 i
ENEAD-01-NP REV 0 Page 130
Table 4.9-5. Erbium Core information Fuel Information Fuel Ennchment Ergo, Ennchment Fuel Density (gm/cc)
Fuel Pellet Radius (cm)
Clad Material Clad Outer Radius (cm)
Clad Thickness (cm)
Clad inner Radius (cm)
Fuel Pin Pitch (cm)
NOTE: This table contains information considered PROPRIETARY by ABB/CE.
Table 4.9-6. Summary of Core Designs Analyzed w/o Gd in U-235 enriched pin w/o Er in Core U-235 enrichment U-235 enriched pin Type B&W Core Design 1 2 46 - - B&W B&W Core i Design 5 2.46 4.00/1.94 - B&W ,
B&W Core 2.46 inner zone Design 12 4.02 outer zone - - B&W d B&W Core 2.46 inner zone '
Design 14 4.02 outer zone 4.00/1.94 - B&W B&W Core 2.46 inner zone .
Design 18 4.02 outer zone - - "C E" B&W Core 2.46 inner zone Design 20 4.02 outer zone 4.00/1.94 - "C E" a CE Core Design 1 CE Core Designs 2 i through 4 NOTE: This table contains information considered PROPRIETARY by ABB/CE. j l
t i
I I
l ENEAD-01-NP REV O Page 131 !
Table 4.9-7. LPF Statistical Model Error Summary: All Cores All cores vanance d f.
BWO5 0.000169 31 BW14 0.000081 31 BW20 0.000144 31 BWO1 0 000009 31 BW12 0 000036 31 BW18 0.000064 31 CE01 0.000225 31 CE02 0.000361 31 CE03 0.000196 31 CE04 0.000196 31 avg var 0.000148 310 std dev 0.01217 Table 4.9-8. LPF Statistical Model Error Summary: B&W No-Gd Cores Non-Gd Variance d f.
BWD1 0.000009 31 BW12 0.000036 31 BW18 0 000064 31 avg var 3 63E-05 93 std dev 0.006028 Table 4.9-9. LPF Statistical Model Error Summary: B&W Gd Cores
~
Gd Vanance d.t BWD5 0 000169 31 BW14 0.000081 31 f BW20 0.000144 31 avg var 0.000131 93 std dev 0.01146 ENEAD-01-NP REV 0 Page 132
I D
CE01 0.000225 31 CE02 0.000361 31 CE03 - 0.000196 31 CE04 0.000196 31 avg var 0.000245 124 std dev 0.015636 I
Table 4.9-11. Pin Power Distribution Results Core Burnable Calculated Core Type poison peak pin BWO1 B&W none 1.109 BWOS B&W Gd 1.172 BW12 B&W none 1.144 BW14 B&W Gd 1.185 BW18 "C E" none 1.214 BW20 C E" Cd 1.289 CE01 CE CE02 CE CE03 CE CE04 CE Table 4.9-12. Overall Local Peaking Uncertainty Absolute Differences Relative 1 Degrees of Core type Se S-.. S mnd.: Mean S mod.i freedom All 0.01424 0.0074 0.01217 0.0 0.01097 310 B&W Non-Gd 0.00816 0.0055 0.00603 0.0 0.00541 93 B&W Gd 0 01273 0.0055 0.01146 0.0 0.00978 93 CE 0.01831 0.0095 0.01564 0.0 0.01261 124 NOTE: n is the total number of data points in the difference population; the degrees of freedom are the totals presented in Tables 4.9-7 through 4.9-10. The minimum LPFs (obtained from Table 4.9-11) used to Convert the absolute values to relative values are as folloWs: 1.109,1.109,1.172-and 1.240.
l l
ENEAD-01-NP REV O Page 133
4.9.3 Combined Nodal and Local Peaking Tolerance Limit -
Since both the nodal and local peaking factor relative difference distributions appeared to be normal and independent, the combined uncertainty can be obtained by combining variances. The equation for the combined sample standard deviation (uncertainty) is:
Su=]SL+S 2 (4.9-13)
A one sided tolerance limit is constructed from the uncertainty components such that the total peaking factor uncertainties can be estimated on a 95%/95% . _
confidence / probability level. The uncertainty components' degrees of freedom will be used to construct the overall tolerance limit. It has been shown in Reference 26 that the effective degrees of freedom when two population variances are combined is:
f u = S,. , "'S,a
. (4.9-14) f.a fw The overall number of degrees of freedom, ftotal is determined from Equation 4.9-14 and the kg3%fg5% is determined from Reference 10. The one sided tolerance limit for differences between measured and calculated power distribution peaking factors is then determined from the total standard deviation and the k95%/95% as shown in Table 4.9-13.
Table 4.9-13. Power Reliability Factors Based on Signals Unit Paremeter s o,, Sw,, S,.,,,, f by RF Mean ANO-1 Fq 002375 0.01261 0.02689 2349 1.703 0.0458 0.00039 Fr 0.01654 0.01261 0.02080 818 1.737 0.0362 0.0 Fxy 0 02256 0.01261 0.02584 2076 1.703 0.0440 0.0 ANO-2 Fq 0.01886 0.01261 0.02269 1233 1.727 0.0392 0.00498 Fr 0.01283 0.01261 0.01799 494 1.766 0.0318 0.0 Fry 0 01595 0.01261 0.02033 824 1.737 0 0353 00 WsEs- Fq 0.01673 0.01261 0.02095 919 1.732 0.0363 0.00386 3 Fr 0.01112 0.01261 0.01682 385 1.780 0.0300 0.0 Fxy 0.01414 0.01261 0.01895 626 1.750 0.0332 00 I
ENEAD-01-NP REV 0 Page 134 1
n The detector " power" is related to the detector signal through a conversion factor, previously . defined as W which varies from detector. to detector.
Therefore, the nodal population statistics based on power are expected to be somewhat different from that based on signals. The overall statistics based on using powers for both nodal and local uncertainty components were evaluated and are reported in Table 4.9-14 for the three units. Small differences in RF and biases are noted.
I Table 4.9-14. Power Reliability Factors Based on Powers Urut Parameter So m, S im, S,,,,, f ky , RF Mean ANO-1 Fq 0.02671 0.01261 0.02954 3260 1.692 0.0500 0.00020 Fr 0.01936 0.01261 0.02311 1138 1.727 0.0399 0.0 Fxy 0.02529 0.01261 0.02826 2886 1.703 0.0481 0.0 ANO-2 Fq 0.01966 0.01261 00.2336 1373 1.727 0.0403 0.00484 Fr 0.01333 0.01261 0.01835 532 1.760 0.0323 0.0 Fxy 0 01703 0.01261 0.02119 968 1.729 0.0366 0.0 WsEs- Fq 0.01959 0.01261 0.02330 1374 1.727 0.0402 0.00391 3 Fr 0.01149 0.01261 0.01706 407 1.778 0.0303 0.0 Fxy 0 01550 0 01261 0.01998 772 1.741 0.0348 0.0 1
t i
i o
ENEAD-01-NP REV 0 Page 135
4.9.4 Reliability Factors Up to this point, statistics and reliability factors for each of the Entergy PWRs have been kept separate. Similarities between in-core detector systems, reactor vendor, operation and power distribution measurement techniques make it reasonable that ANO-2 and WSES-3 reactors should be grouped together. The standard deviations and means of ANO-2 and WSES-3 are very similar, so it was decided to use the more limiting reliability factor (RF) and mean from ANO-2 l for both ANO-2 and WSES-3 and to use the ANO-1 reliability factor and mean for ANO-1 only.
l l
The reliability factors (based on power differences) to be used are presented in Table 4.9-15.
Table 4.9-15. Power Distribution Reliability Factors Reliabihty Reactor Parameter Factor Mean Fq 0.0500 0.00020 ANO-1 Fr 0.0399 0.0 Fry 0.0481 0.0 Fq 0.0403 0 00484 ANO-2/WSES-3 Fr 0.0323 0.0 Fxy 0.0366 0. 0 ENEAD-01-NP REV 0 Page 136
_ _ _ _.________ ~ -.- -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ' - - - - - - - - - ~ - - - - - - ' - - -
5.0 REFERENCES
- 1. MSS-NA1-P, Qualification of Reactor Physics Methods for Application to Pressurized Water Reactors of the Middle South Utilities System. 08-04-80; Approved for Use in Licensing Actions per. Letter, R. A. Clark and J. F. Stolz (USNRC) to W. Cavanaugh (AP&L), 08-11-82.
- 2. STUDSVIKISOA-91/01, INTERPIN-CS. Studsvik CMS Fuel Performance Code. Studsvik of America, Inc.,1991.
- 3. STUDSVIKINFA-89/3, CASMO-3. A Fuel Assembly Burnup Proaram User's Manual. Studsvik of America, Inc.,1989.
- 4. STUDSVIK/NFA-89/12, MICBURN-3 Microscopic Burnup in Burnable Absorber Rods User's Manual. Studsvik of America, Inc.,1989.
l 5. STUDSVIK/SOA-92/1, SIMULATE-3. Advanced Three-Dimensional Two-Group Reactor Analysis Code. Studsvik of America, Inc.,1992.
- 6. STUDSVIK/SOA-89/5, TABLES-3. Library Preparation Code For SIMULATE-3. Studsvik of America, Inc.,1989.
- 7. YAEC-1363, CASMO-3G Validation. Yankee Atomic,1988.
I 8. YAEC-1659, SIMULATE-3 Validation and Verification. Yankee Atomic,1988. ,
- 9. DPC-NE-1004, Nuclear Desian Methodoloav Usina CASMO-3/ SIMULATE-3.
i Duke Power Company,1990.
- 10. Tables for Normal Tolerance Limits. Samplina Plans and Screenina. - Robert E. Odeh, Marcel Dekker, Inc.,1980.
11.CCM-3, ARMP: Advanced Reevele Methodo!oav Proaram. Electric Power Research Institute,1977.
12.CENPD-266-A, The ROCS and DIT Computer Codes for Nuclear Desian.
Combustion EngineeVing,1983.
- 13. AEDC-TR-73-5, Uncerainty in Gas Turbine Measurements. Arnold Engineering Development Center, Arnold Air Force Base,1973.
- 14. ANSI N15.15-1974, American National Standard Assessment of the ,
Assumption of Normality (Emplovino Individual Observed Values).10/3/73.
- 15. Probability and Statistics for Enaineers and Scientists. Ronald E. Walpole l
and Raymond H. Meyers, Macmillan Publishers,1972, p. 358.
16.WCAP-10473, Final Report EP80-16. Hot Cell Examination of ZION Fuel Cveles 1 throuah 4. Westinghouse, M. G. Balfour et. al.,4/85.
Page 137 ENEAD-01-NP REV 0
- 17. Measurements of Resonance /nlegrals, Reactor Physics in the Resonance and Thermal Reaions. Volume 2, E. Hellstrand,1966.
18.STUDSVIK/SOA-91/5, Benchmarkina of CASMO Resonance Intearals for U-238 Aaainst Hellstrand's Measurements. Studsvik of America, Inc., M.
Edenius and H. Haggblom,1991.
19.STUDSVIK/SOA-93/4, Benchmarkina of CASMO Resoncnce Intearals for U-238 Aaainst Hellstrand's Measurements. Comparisons between CASMO-3.
Versions 4.4 and 4.7. Studsvik of America, Inc., M. Edenius,1993.
20.EPRI-NP-6147, Evaluation of Discrepancies in Assembly Cross-Section Generator Codes. Volume 4: Doppler Evaluation, Electric Power Research Institute, 07-93.
21.STUDSVIK/SOA-93/06, CASMO Doppler Coefficients versus MONP-3A Monte Carlo Calculations. Studsvik of America, Inc., M. Edenius,1993.
22.BAW-1810, Urania Gadolinia: Nuclear Model Development and Critical Experiment Benchmark. Babcock and Wilcox,1984. '
23.CENPD-382-P, Methodoloav for Core Desians Containina Erbium Burnable Absorbers. Combustion Engineering,1990.
24.CENPD-382-P Supplement 1-P, Methodoloav for Core Desians Containina Erbium Bumable Absorbers. Combustion Engineering,1992.
25.BMDP Statistical Software. J. Dixon, University of California Press,1983.
26.Biometrika. B. L. Welch, Volume 34, Page 28-35,1947.
ENEAD-01-NP REV 0 Page 138 t
APPENDIX A: BENCHMARKING STATEPOINTS Table A.0-1. ANO-1 Cycle 7 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
1 03/21/85 29 60 962 99.79 32 100 88 l 2 04/19/85 50.93 949 99.88 31 100 88 3 05/17/85 78.92 897 100.1 31 100 90 4 06/10/85 100.5 858 99.63 31 100 90 5 07/08/85 126.9 780 99.63 31 100 91 6 07/29/85 148.0 759 99.61 31 100 92 !
7 09/12/85 178.7 676 96.78 31 100 91 8 10/17/85 199 4 613 97.05 31 100 93 9 11/21/85 227.3 553 94.55 31 100 92 10 12/20/85 253.2 491 91.31 30 100 91 11 02/12/86 283.7 410 89.55 32 100 94 12 03/18/86 313.3 333 84.16 32 100 93 13 04/23/86 341.8 264 81.96 32 100 94 14 06/09/86 379.3 163 77.64 32 100 94 15 07/11/86 404.2 96 75.96 32 100 95 16 07/31/Be 418.5 83 75 61 100 100 95 ,
Table A.0-2. ANO-1 Cycle 8 Statepoints CEA Position (% withdrawn) i Map Exposure Boron Powe
1 01/09/87 5.08 1026 99.18 33 100 91 -
2 03/26/87 63.92 1026 65.72 31 100 88 3 04/17/87 78.30 1001 68.08 31 100 89 4 05/22/87 100.8 956 65.73 31 100 90 )
5 06/17/87 120.0 856 80.20 32 100 90 6 07/24/87 149.5 786 80.27 32 100 90 7 08/24/87 170 4 739 70 03 31 100 90 i 8 10/06/87 200 4 658 70.88 32 100 92 ,
9 12/23/87 238 6 523 80.20 32 100 92 l 10 01/06/88 249.8 483 80.00 32 100 91 l 11 01/29/88 268.1 437 12 03/11/88 299.9 80.29 32 100 93 ~ I 337 79.87 32 100 93 {
13 04/18/88 330.6 253 80.39 32 100 93 .!
14 05/12/88 349.9 189 8086 31 100 93 I 15 06/08/B8 371.5 131 8515 30 100 94 !
16 07/01/88 390 9 88 85 00 100 100 93 ENEAD-01-NP REV 0 Page 139
Table A.0-3. ANO-1 Cycle 9 Statepoints CEA Position (% withdrawn)
Map Exposure l
Boron Power
- Date (EFPD) (opm) (%) PLR Group 6 Group 7 1 01/03/89 12 08 1008 99.83 27 99 91 2 01/13/89 20 08 988 99 81 27 99 90 3 06/14/89 59 79 981 79 84 25 100 91 [
4 07/17/89 87.10 916 79 88 25 100 90 [
5 08/04/89 99 74 909 73.97 26 100 90 6 08/30/89 119 4 856 73 96 27 100 91 7 11/21/89 176.8 713 73 71 27 100 91 8 01/26/90 202.9 636 79.98 26 100 92 l' 9 07/16/90 219 6 585 79.72 26 100 91 1P -
0/93 250.1 501 80.01 27 100 91 .
1 *. 90 296.8 362 80.05 28 100 92 12 l - /S0 363.9 171 80.07 26 100 91 Tam._ . 0-4. ANO-1 Cycle 10 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 6 Group 7 1 01/25/91 5 48 1019 99.22 29 99 91 2 03/26/91 66 34 878 99 91 29 100 89 $
3 05/06/91 87.50 850 99.92 29 100 91 4 *
(
07/05/91 '1 710 99 46 25 100 91 5 07/22/91 ,.1 667 99.93 24 100 89 6 10/10/91 245.7 443 99.79 31 100 91 7 11/20/91 285.2 329 99.94 30 100 91 ,
8 12/06/91 301.1 309 100.0 31 100 93 9 12/27/91 322.3 231 100.2 30 100 92 10 01/24/92 349 6 158 99.30 99 100 92 P
.l 0
i J
ENEAD-01-NP REV O Page 140 wf
4 Table A.0-5. ANO-1 Cycle 11 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 6 Group 7 1 05/19d32 8 01 1271 99 84 29 100 91 2 06/05/92 24.71 1195 99 95 28 100 91 3 07/02/92 51.61 1184 99.91 28 100 91 4 07/24/92 73.25 1147 99.84 29 100 91
- 5 08/21/92 101.0 1084 99.91 30 100 91 6 09/18/92 128.9 1015 99.94 29 100 91 7 10/20/92 160.7 942 99.96 29 100 90 8 11/06/92 178 0 881 100.1 30 100- 91 9 1*f20/92 192.1 842 99.95 30 100 91 10 01/04/93 237.0 727 100.0 29 100 91 .
11 01/18/93 250.9 680 99.30 29 100 92 -
12 02/11/93 275.0 614 99.95 29 100 91 13 03/11/93 300.1 538 99.93 29 100 90 14 04/16/93 335.3 407 9986 29 100 90- i 15 05/14/93 361.3 313 99.99 28 100 90 ;
16 06/17/93 394.2 214 99 91 29 100 91 1 17 07/16/93 423.6 151 99.93 'i OO 100 91 18 08/06/93 444 6 86 99.96 100 100 90 t
Table A.0-6. ANO-2 Cycle 1 Statepoints CEA Posrtion (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 01/29/80 72.19 609 99.29 100.0 100.0 99.2 2 03/27/80 76.28 610 100.0 100.0 100.0 100.0 -
3 04/07/80 83.62 585 99 86 98.7 98.7 98 8 4 05/16/80 127.8 516 100.1 99.0 99.0 90.2 5 08/15/80 175.9 441 100.2 98.7 98.7 98.4 6 10/10/80 200.4 400 99.89 98.7 98.7 - 98.7 7 12/31/80 250.6 314 89.66 98.7 98.7 99.0 8 01/27/81 278.0 218 99.48 98.7 98.7 98.2 9 02/13/81 289.5 185 90.87 98.7 98.7 96.0 !
10 02/23/81 297.2 175 99.74 98.8 98.7 98.2 i I
l ENEAD-01-NP REV 0 Page 141 ;
l
Table A.0-7. ANO-2 Cycle 2 Statepoints CEA Posrtion (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 08/03/81 19 0 785 100.0 100.0 100.0 99.8 2 08/31/81 38.3 730 99.15 100.0 100.0 100.0 3 09/11/81 48.4 702 100.0 100.0 100 0 100.0 4 09/24/81 60.9 708 77.70 100.0 100.0 94.5 5 10/28/81 75.8 626 100.0 100.0 100.0 100.0 6 11/18/81 92 6 571 99.58 99.5 99.5 99.5 7 12/10/81 113.2 510 99.81 99.5 99.5 99.5 8 01/30/82 142.1 425 100.1 99.5 99.5 99.5 9 02/24/82 170.8 340 99.63 99.5 99.5 95.5 10 03/30/82 199.0 255 1001 98.9 98.9 98.9 -
11 04/15/82 214.0 200 99 94 99.1 98.9 98 4
~
12 05/14/82 225.0 206 84.55 98.9 98.9 97.3 13 06/29/82 252 4 79 99.49 98.6 98.1 95.8 14 07/18/82 273.2 40 99.30 98.1 98.1 96 6
} 15 08/17/82 290.5 22 76.12 98.1 98.1 98.1 l
Table A.0-8. ANO-2 Cycle 3 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 01/06/83 28 21 794 100.0 100.0 100.0 100.0 2 02/07/83 33 44 757 99.34 100.0 100.0 100.0 3 03/16/83 62.03 657 99.66 100.0 100.0 100.0 4 04/10/83 96.16 552 100.1 99.5 99.5 99.5 ENEAD-01-NP REV 0 Page 142
a
. -j i
l l
Table A.0-9. ANO-2 Cycle 4 Statepoints i CEA Position (% withdrawn) l Map Exposure Boron Power
2 05/29/84 101.8 847 99.97 99 5 99.5 99 5 3 06/15/84 118.8 785 99.29 99.5 99.5 99.5 4 07/19/84 150.8 678 99.75 99.5 99.5 99.5 ;
5 08/10/84 161.6 626 99.66 99.5 99.5 99.5 0 09/24/84 198 8 484 99.72 99.0 99 0 99.0 7 10/08/84 212.5 446 100.1 99.0 99.0 99.0 8 11/21/84 248 6 318 99.69 99.0 99.0 99.0 9 12/05/84 262.0 275 99.97 99 0 99.0 99.0 10 01/16/85 304 0 140 99.55 99.5 99.5 - 99.5 11 03/13/85 353 6 7 89.86 99 5 99 5 99.5 Table A.0-10. ANO-2 Cycle 5 Statepoints CEA Posttion (% w:thdrawn)
Map Exposure Boron Power __
1 07/30/85 43.00 895 99 87 99.3 100.0 99.7 2 08/30/85 69.64 816 99.48 100.0 100.0 100 0 3 10/14/85 94.98 748 99.62 99.5 99.5 99.5 4 11/25/85 129.1 638 99.95 99.5 99.5 99.5 5 12/23/85 146.1 582 99.47 99.5 99.5 97.5 6 01/31/86 185.1 462 99.79 99.0 99.0 99.0 7 02/28/86 210.8 383 99.99 99.0 99.0 99.0 8 03/25/86 235 3 314 100.1 99.0 99 0 99.0 i 9 04/11/86 252.4 261 100.1 99.0 99.0 99.0 10 05/22/86 290.1 145 99.60 98.5 98.5 98.5 11 06/05/86 304.2 99 100.2 98 5 98.5 98.5 i
ENEAD-01-NP REV 0 _Page 143
b Table A.0-11. ANO-2 Cycle 6 Statepoints CEA Position (% witharawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 i 1 11/15/86 45.28 1054 99.89 100.0 100.0 100.0 2 01/21/Br 112.0 899 99 55 99.5 99.5 99.5 3 03/20/87 169.2 762 100.0 99.5 99.5 95.5 4 04/18/87 197.9 688 99.60 99.0 99.0 99.0 5 06/30/87 234.7 569 99 47 99.0 99.0 99.0 6 07/30/87 254 0 506 99 91 99.0 99.0 99 0 7 08/31/87 286.1 433 09.60 98.6 98.6 98.6 -
8 09/30/87- 314 6 345 99 72 98.5 98.5 96.0
- 9 10/22/87 336.4 295 99.82 98.5 98.5 98.5 10 11/21/87 361.6 224 100.1 98.8 98.5 98.5 11 12/29/87 399 3 107 99.08 98.5 98.5 98.5 12 01/29/88 430.3 23 99.66 98.5 98.5 98.5 Table A.0-12. ANO-2 Cycle 7 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power :"
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 07/20/88 54.27 976 99.38 100 0 100.0 100.0 2 10/19/88 121.3 815 100.1 99.5 99.5 99.5 ;
3 11/30/88 163.2 724 99.62 99.5 99.5 95.5 -
4 01/31/89 212.5 570 99.83 99 0 99.0 99.0 5 02/28/89 240.3 493 99.79 99.0 99.0 99 0 6 05/12/89 292.7 351 99.46 99.0 99.0 99.0 [
7 07/17/89 345.2 203 99 98- 98.5 98 5 98.5 Table A.0-13. ANO-2 Cycle 8 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
2 12/11/90 234 7 155 99 83 98.5 98.5 98.5 3 - 01/17/91 254.0 50 99.98 G8.5 98.5 98.5 >
ENEAD-01-NP REV 0 Page 144
Table A.0-14. ANO-2 Cycle 9 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 05/07/91 13.88 1050 99.90 100.0 100.0 100 0 2 05/28/91 34 51 1007 100.0 100.0 100.0 100.0 3 06/19/91 56.45 965 100 1 100.0 100.0 100.0 4 07/10/91 77.03 927 99.65 100.0 100.0 100.0 5 07/31/91 97.11 875 99.70 99.5 99 5 99.5 6 08/28/91 124.8 818 99.68 99.5 99.5 99.5 7 09/25/91 153.1 739 99 97 99.5 99.5 99.5 8 10/23/91 176.9 656 99.67 99.5 99.5 99.5 9 11/22/91 201.7 602 100.2 99.5 99.5 99.5 10 12/17/91 225.8 540 99.89 99.0 99.0 99.0 11 01/12/92 252.5 480 99.96 99 0 99.0 99.0 12 02/02/92 272.9 432 100.3 99.0 99.0 99.0 13 03/02/92 301.4 350 99.85 99.0 99.0 99.0 14 05/22/92 326.7 271 99.85 99.0 99.0 99.0 15 06/18/92 352.4 201 99 68 98.5 98 5 98.5 16 07/10/92 374.5 141 100.0 98.5 98.5 98.5 17 08/07/92 402.4 72 99 89 98 5 98.5 98.5 Table A.0-15. ANO-2 Cycle 10 Statepoints CEA Position (% withdrawn)
Map Exposure Boron
- Date (EFPD) (ppm) l Power
(%) PLR Group 5 Group 6 1 11/12/92 20.09 1113 '99.97 100.0 100.0 100 0 2 12/01/92 37.69 1098 99 81 100.0 100 0 99.9 3 12/07/92 49.11 1089 99.68 100.0 100.0 100.0 4 12/17/92 53 99 1072 99.68 100.0 100.0 100.0 5 12/31/92 68.65 1051 99.54 100.0 100.0 100.0 6 01/19/93 87.38 -1009 -100.1 100.0 100.0 100.0 7 01/25/93 92.61 983 99.62 100.0 100.0 100.0 8 03/12/93 138.73 888 99.54 99.5 99.5 99.5 9 04/16/93 173.36 809 99.95 99.5 99.5 99.5-10 06/18/93 219.47 676 99.99 99.5 99.5 99.5 11 06/25/93 22G.65 661 99.80 99.4 99.4 - 99.4 12 06/30/93 232.18 648 100.1 99.0 99 0 99.0 13 08/01/93 263.13 580 99.91 - 99.0 99.0 99.0 14 08/08/93 270.46 563 99.94 99.0 99.0 99.0 15 08/26/93 288 26 514 99 88 99.0 99.0 99.0 ENEAD-01-NP REV 0 Page 145
Table A.0-16. WSES-3 Cycle 1 Statepoints CEA Posrtion (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 10/24/85 49.02 475 99 84 100 100 100 2 12/30/85 99 24 465 99.70 99 99 99 3 02/27/86 156.59 420 99.10 99 99' 99 l 4 04/07/86 171.43 390 99.60 98 98 98 l 5 06/16/86 236.30 300 99 77 98 98 98 l 6 07/22/86 261.30 261 100.04 100 100 100 7 08/07/86 276.97 225 99.92 100 100 100 8 09/22/86 320 00 131 99 44 98 98 98 9 10/31/86 354.80 47 99.38 94 98 98 Table A.0-17. WSES-3 Cycle 2 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR- Group 5 Group 6 1 02/11/87 1.42 1235 68.48 100 100 100 2 02/18/87 7.18 1195 84.61 100 100 100 3 02/24/87 12 34 1137 99.94 100 100 100 4 03/31/87 42 83 980 99.73 100 100 100 5 05/20/87 90.35 866 99.52 99 99 99 6 07/31/87 159.26 684 99 85 99 99 99 7 08/10/87 167.45 640 99.80 99 99 99 8 08/31/87 187.83 582 99 93 98 98 98 9 09/17/87 201.83 554 99.59 98 98 98 ,
10 10/26/87 221 86 494 99.56 99 99 99 ,
11 11/19/87 245.10 407 99 50 98 98 98 12 12/22/87 275 91 323 99.93 98 98 98 13 01/31/88 309.70 222 99.68 99 99 99 >
14 02/29/88 338 79 124 100.C2 99 99 99 15 03/31/88 366.44 47 99.80 98 98 98 ,
c P
ENEAD-01-NP REV O Page 146 '
Table A.0-18. WSES-3 Cycle 3 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 06/27/88 17.45 1010 99 97 99 99 99 2 07/15/88 38.13 976 99.35 100 100 100 3 08/17/88 68.46 907 99.37 98 98 98 4 09/01/88 83.38 880 99.89 98 98 98 5 09/16/88 97.38 874 90.00 98 98 98 -
6 10/07/88 114 80 829 90 60 100 100 100 7 12/01/88 140.77 737 99 37 98 98 98 8 12/22/88 160.36 685 99.87 99 99 99 9 03/31/89 253 33 454 99.73 99 99 99 10 06/02/89 315.95 318 99.21 99 99 99 11 06/30/89 343.54 240 99.65 99 99 99 12 09/01/89 399.05 84 99.60 100 100 100 13 09/15/89 414.01 43 99.48 100 100 100 14 09/22/89 420.95 22 99.50 100 100 100 Table A.0-19. WSES-3 Cycle 4 Statepoints CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 12/06/89 13 25 996 99.56 99 99 99 2 12/14/89 21.20 985 99.70 99 99 99 3 04/10/90 117.05 797 99.71 100 100 100 4 05/02/90 139 00 758 99.98 100 100 100 5 06/01/90 168 93 677 99.81 100 100 100 6 06/25/90 192.87 629 99 81 99 99 99 7 07/31/90 228.67 541 99.75 100 100 100 t 8 10/23/90 299 49 361 99 85 100 100 100 ,
9 11/12/90 319.67 297 100.04 100 100 100 10 12/17/90 354.53 213 99.74 95 100 100 11 01/10/91 378.18 151 99.86 100 100 100 12 02/22/91 420.57 40 99.85 100 100 100 13 03/12/91 438 39 43 96.36 93 100 100 i
l l
l i
I ENEAD-01-NP REV 0 Page 147 !
1 l
Table A.0-20. WSES-3 Cycle 5 Statepoints
'CEA Position (% withdrawn)
Map Exposure Boron Power
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 06/07/91 8.45 1030 - 99 84 100 100 100 2 06"21/91 22.19 995 99.74 100 100 100-3 07/09/91 38.31 999 99 75 100 100 100 4 08/02/91 60 49 945 99.90 100 100 100 5 09/10/91 99.06 873 99.77 100 100 100 6 10/09/91 128.91 000 99.83 100 100 100 7 11/11/91 160.86 736 99.94- 100 100 100 8 02/07/92 245.25 507 99.86 100 100 100 9 03/18/92 277.47 425 99.84 99 99 99 10 04/16/92 303.71 365 99 69 100 100 100-11 06/02/92 -349.21 258 99.82 99 99 99 07/30/92 405.87
~
12 103 99.80 100 100 100 13 08/05/92 411.72 87 99.89 100 100 100
)
ENEAD-01-NP REV 0 Page 148 L .
i -_ . -
l
Table A.0-21. WSES-3 Cycle 6 Statepoints CEA Position (% withdrawn) ;
Map Exposure Boron Power ;
- Date (EFPD) (ppm) (%) PLR Group 5 Group 6 1 11/20/92 8.77 1089 99.53 100 100 100 2 12/02/92 19.35 1063 99.52 100 100 100 3 12/10/92 28.68 1043 1000< 100 100 100 4 12/16/92 34.45 1033 99.59 100 100 100 5 12/23/92 41.46 1021 100 15 100 100 100 ,
6 01/04/93 50.05 1007 99.72 100 100 100 4
_ 7 01/07/93 56.66 997 100.15 100 100 100 8 01/15/93 64.34 986 99 44 100 100 100 )
9 01/20/93 69.28 979 100.04 100 100 100 .j 10 01/29/93 80 84 963 99.56 100 100 100 !
11 02/04/93 84.24 958 99.95 100 100 100 4 12 02/12/93 92.16 946 99.86 100 100 100 !
13 02/16/93 96.09 940 99.39 100 100 100 14 02/26/93 106 67 922 99.56 100 100 100 15 03/17/93 122 94 893 99.78 100 100 100 16 03/24/93 129.94 878 99.76 100 100 100 17 04/02/93 138.31 861 99.88 100 100 100 18 04/14/93 149.84 834 99.C6 100 100 100 19 04/16/93 152.00 829 99.66 100 10u 100 20 04/26/93 163.25 802 99.89 100 100 100 21 05/04/93 171.33 782 100.25 100 100 100 22 05/06/93 173.03 777 99.78 100 100 100 23 05/18/93 184.98 746 99.76 99.5 99.5 99.5 24 05/24/93 191.10 430 99.85 99.5 99.5 99.5 ,
25 06/02/93 199.93 708 100.28 99.5 99.5 99.5 -)
26 06/11/93 209.22 685 100.26 99.5 99.5 99.5 27 06/18/93 214.10 674 99.51 99.0 99.0 99.0 28 06/21/93 217.09 657 99.95 99.0 99.0 99.0 29 06/25/93 220.00 660 99.80 99.0 99.0 99.0 30 07/01/93 225.92 648 100.34 99.0 99.0 99.0 31 07/14/93 240.79 607 99.69 99.0 99.0 99.0 32 07/20/93 246.83 595 100.03 99.0 99.0 99.0 33 07/28/93 254.34 582 98.87 100 100 100 34 08/05/93 262.21 560 99.71 100 100 96.8 35 08/12/93 269.10 540 99.76 100 100 100 f
ENEAD-01-NP REV 0 Page 149
APPENDIX B: ANO-1 REPRESENTATIVE CYCLE COMPARISONS Figure B.0-1 thrc;gh Figure B.0-3 provide radial map comparisons of measured and predicted detector reaction rates. Figure B.0-4 through Figure B.0-9 provide axial comparisons of selected detector strings showing measured and predicted detector reaction rates.
1 1
l l
l ENEAD-01-NP REV O Page 150
Figure B.0-1. ANO-1 Cycle 9 Radial Map, BOC 001-00 002-00 003-00 004-00 005-00 Figure 7.0-14 Statistics foe Integral Peactica Rates ANO-1 CYCLE 09 FLUlt MAP 81 .378 CWD/M7U 006-00 001-00 008-00 009-31 010-30 011-00 012-00 013-00 014-00 1.132 .599
.022 .021 015-00 016-00 017-00 018-32 019-M 020-00 021-29 022-28 023-00 024-00 025-52 1.465 1.211 1.474 .386
.004 .031 005 .003 026-00 027-00 028-00 029-33 030-00 031-00 032-00 033-00 034-27 035-00 016-00 037-00 038-51
.956 783 .314
.008 .011 .002 039-00 040-00 041-34 042-00 043-00 044-07 045-00 046-05 047-00 048-26 049-00 050-00 051-00
.973 1.113 1.114 .000
.027 .002 .000 .000 {
052-00 053-00 054-35 055-00 056-00 057-00 058-06 039-04 060-00 061-00 062-00 063-24 064-23 065-00 066-00 'li 1.495 - 1.027 1.166 1.136 1.449 l
.025 .009 .020 .028 s 022 067-00 058-36 069-00 070-00 071-09 072-08 073-00 074-00 075-03 076-00 077-25 078-00 079-22 080-00 081-00 1.181 1.117 1.021 .000 1.308 1.155
.063 - .007 .010 .000 052 .026 082-37 083-00 084-00 085-00 086-10 087-00 088 00 089-01 090-02 091-00 092-00 093-00 094-21 095-00 096-00
.341 704 .000 1.109 .807 005 .029 .000 .050 .009 h 097-00 098-00 099-00 100-00 101-11 102-00 103-00 104-00 105-00 106-00 107-19 108-20 109-00 110-00 111-00 f 1.098 1.072 1.195 l .011 .038 .C10 112-00 113-38 114-39 115-00 116-00 117-12 118-00 119-00 120-00 121-00 122-18 123-00 124-50 125-00 126-00 l .531 1.483 1.223 .793 1.469
.007
.013 .014 021 .001 127-00 128-40 129-00 130-00 131-00 132-13 133-00 134-16 135-17 136-00 137-00 138-00 139-49
) - 1.017 1.129 1.111 .981 .621
.014 .015 . 004 .002 .008 140-00 141-00 142-41 143-00 144-00 145-00 146-14 147-15 148-00 149-00 150-00 151-00 152-00 PICTURE FOP.*AT
.000- 1.0$0 .991 ASSEMBLY 8 - INSTRUMENT STRING 8
.000 .012 .011 MEASURED REACTION RATE EP 153-00 154-00 155-42 156-43 157-00 158-00 159-00 160-47 161-00 162-48 163-00 1.001 .000 1.482 .987 - PEAK 5 MEASURED CALCULATED f +.003 .000 .013 .045 Fr 1.49 1.47 l
164-00 165-00 166-44 167-00 168-00 169-00 170-00 171-00 172-00 NORMAL 015TRIBUTION . YE5
.526 ' STANDARD DEVIATION e .02177
.008 s1AS - .00000 173-00 174-45 175-00 176-00 177-46 423 .278
. 13 .008 1
i ENEAD-01-NP REV O Page 151
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Figure B.0-4. ANO-1 Cycle 9 String 18, BOC AND 1 Cycle 9 Flux Map 1 l
l Measured and Calculated Reaction Rates at 12.08 EFPD Core Location L11 1
1.50 -
l 1.25 -
{ 1.00 -
. 0.75 - ,
030- + Calculated i 0.25 -
- Measured 0.00 0 10 20 30 40 50 60 70 80 90 100 Percent of Core Height
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Figure B.0-6. ANO-1 Cycle 9 String 18, MOC AND-1 Cycle 9 Flux Map 7 Measured and Calculated Reaction Rates at 176.8 EFPD Core Location L11 1.50 - .]
1.25 -
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1 Figure B.0-8. ANO-1 Cycle 9 String 18, EOC AND 1 Cycle 9 Flux Map 12 Measured and Calculated Reaction Rates at 363.9 EFPD Core Location L11 1.50 -
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APPENDIX C: ANO-2 REPRESENTATIVE CYCLE COMPARISONS Figure C.0-1 through Figure C.0-3 provide radial map comparisons of measured and predicted detector reaction rates. Figure C.0-4 through Figure C.0-9 Provide axial comparisons of select detector strings showing measured and predicted detector reaction rates.
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APPENDIX D: WSES-3 REPRESENTATIVE CYCLE COMPARISONS Figure D.0-1 through Figure D.0-3 provide radial map comparisons of measured and predicted detector reaction rates. Figure D.0-4 through Figure D.0-9 provide axial comparisons of select detector strings showing measured and predicted detector reation rates.
1 l
ENEAD-01-NP REV 0 Page 164
~I
Figure D.0-1. WSES-3 Cycle 3 Radial Map, BOC 001-00 002-00 003-00 004-00 FIGJRE A.X.R Statistics for Inteoral Peaction Rates 4tSES-3 CYC1E 03 F1UK MAP # 2 1.445 O O/WTU 005-01006-00 007-02 008-00 009-03 010+00 011-04 012-00 013-05
.369 .000 1.090 1.030 .376
.007 .000 .025 .028 .014 014-00 015-00 016-00 017-00 018-00 019-00 020-00 021-00 022-00 023-00 024-00 c25-06 026-00 027-07 028-00 029-05 030-00 031-09 032-00 033-10 034-00 035-11036-00 037-12
.378 1.134 1.261 1.279 1.269 1.158 .378
.008 -020
. .009 .003 .001 .024 .008 038-00 039-00 040-00 041-00 042-00 043-00 044-00 045-00 046-00 047-00 048-00 049-00 050-00 051-00 052-00 053-00 054-13 055-00 056-14 057-00 058-15 059-00 060-16 061-00 062-17 063-00 064-18 065-00 066-19 067-00 1.194 1.169 1.087 1.183 1.098 1.204 1.191
.011 .012 .031 .020 .019 .022 .009 068-00 069-00 070-00 071-00 072-00 073-00 074-00 075-00 076-00 077-00 078-00 079-00 080-00 081-00 082-00 083-20 084-21 f .390 .387 i .015 .012 I
085-00 086-22 087-00 088-23 089 4 090-24 091-00 092-25 093-00 094-26 095-00 096-27 097-00 098-28 099-00 100-00 1.272 1.194 1.134 1.086 1.165 1.232 1.263 101-00 ,
.019 .031 .049 .038 .018 .007 .010 102-00 103-00 104-00 105-00 106-00 107-00 108-00 109-00 110-00 111-00 112-00 113-00 114-00 115-0 ) 116-00 117-00 118-00 119-00 120-29 121-00 122-30 123-00 124-31 125 00 126-32 127-00 128-33 129-00 130-34 131-00 132-35 133-00 134-36 1.268 1.197 .000 1.083 1.145 1.245 .000 135-37
.000 .015 .028 .000 .041 037 .020 .000 .382
.000 .007 136-00 137-00 138-00 139-00 140-00 141-00 142-00 143-00 144-00 145-00 146-00 147-00 148-00 149-00 150-00 l
151-00 152-38 153-00 154-19 155-00 156-40 157-00 158-41 159-00 160-42 161-00 162-43 163-00 164-44 165-00 1.197 1.197 1.086 1.190 1.096 1.176 1.181
.014 .016 .032 .012 .022 .005 .002 166-00 167-00 168-00 169-00 170-00 171-00 172-00 173-00 174-00 175-00 176-00 177-00 178-00 179-00 180-00 181-45 182-00 183-46 134-00 195-47 186-00 187-49 188-00 189 49 190-00 191-50 192-00 193-51 PICTURE FORMAT
.377 1.130 1.275 1.290 1.281 1.129 .379 A35EMBLY # - INSTRt.atENT STRinc a
.007 .016. .006 .008 .0 12 .016 .009 MEASURED REACTION RATE M-P 194-00 195-00 196-00 197-00 198-00 199-00 200 'O 201-00 202-00 203-00 204-00 PEAL 5 MEASUREO CALCULATED Fr 1.27 1.28 I
1 205-52 206-00 207-53 208-00 209-54 210-00 2 P-55 212-00 213-56
.370 .000 .000 .04 .378 40RMAL 015TR18 TIT 10M . 43
.008 .000 .000 .061 .016 STANDAftD DEVIATION = .02005 8tA3 . .c0000 214-00 215-00 216-00 217-00 ENEAD-01-NP REV O Page 165
i Figure D.0-2. WSES-3 Cycle 3 Radial Map, MOC 001-00 002-00 003-00 004-00 FIGURE A.K.X Statistics fW Integral Reaction Rates .l W5ES-3 CYCLE 03 R.UX MAP 8 4 3.160 odd /MTU l 005-01 006-00 007-02 008-00 009-03 010-00 011-04 012-00 013-05 l
.381 .000 1.101 1.025 .390 i
.002 .000 .014 .018 .011 l
014-00 015-00 016-00 017-00 018-00 019-00 020-00 021-00 022-00 023-00 024-00 l
025-06 026-00 027-07 028-00 029-08 030-00 031-09 032-00 033-10 034-00 035-11 036-00 037-12 ,
.392 1.140 1.249 1.269 1.258 1.146 .391 i i
.005 .011 .010 - . 003 .002 .017 004 038-00 039-00 040-00 041-00 042 00 043-00 044-00 045-00 046-00 047-00 048-00 049-00 050-00 051-00 052-00 053-00 054-13 055-00 056-14 057-00 058-15 059-00 060-16 061-00 062-17 063-00 064-18 065-00 066-19 067-00 1.189 1.176 1.105 1.210 1.113 1.206 1.185
.003 .011 .022 .010 .013 .019 .001 068-00 069-00 070-00 071-00 072-00 073-00 074-00 075-00 076-00 C77-00 078-00 079-00 080-00 081-00 082-00 083-20 084-21 l 405 .401 l .012 .007 085-00 086-22 087-00 088-23 089-00 090-24 091-00 092-25 093-00 094-26 095-00 096-27 097-00 098-28 099-00 100-00 1.265 1.207 1.151 .000 1.179 1.237 1.254 101-00
.017 .023 .037 .000 .009 .007 .006 102-00 103-00 104-00 105-00 106-00 107-00 108-00 109-00 110-00 111-00 112-00 113-00 114-00 115-00 116-00 117-00 ,118-00 119-00 120-29 121-00 122-30 123-00 124-31 125-00 126-32 127-00 128-33 129-00 130-34 131-00 132-35 133-00 134-36 1.261 .000 .000 1.093 1.158 1.252 .000 135-37
.000 .013 .000 .000 .031 .030 .022 .000 .394 000 .001 136-00 137-00 138-00 139-00 140-00 141-00 142-00 143-00 144-00 145-00 146-00 147-00 148-00 149-00 150-00 151-00 152-38 153-00 154-39 155-00 1',5-40 157-00 158-41 159-00 160-42 161-00 162-43 163-00 364-44 165-00 1.193 1.204 _1.103 1.218 1.110 1 179 1.172
.007 .016 .024 .003 .016 .008 .014 166-00 167-00 168-00 169-00 !?0-00 171-00 172-00 173-00 174-00 175-00 176-00 177-00 178-00 179-00 180-00 L'
181-45 182-00 183-46 184-00 185-47 186-00 187-48 188-00 189-49 190-00 191-50 192-00 193-51 PICTURE FORMAT
.391 1.139 1.263 1.280 1.267 1.134 .392 ASSEMBLY 8 - INSTRUMENT STRING 8
.004 .01E .004 .008 .008 .005 .005 MEASURED REACTION RATE M-P f 194-00 195-c0 196-00 197-00 198-00 199-00 200-00 201-00 202-00 203-00 204-00 PEAK 5 MEASURED CALCULATED f Fr 1.28 1.2/
205-52 206-00 207-53 208-00 209-54 210-00 21!-55 212-00 213-56
.383 .000 .000 .000 .590 NORPEL DISTRIBLFTION - No
.004 .000 000 '.000 .011 STANDARD DEVIATICM = .01419 81A5 - .00000 214-00 215-00 216-00 217-00 ENEAD-01-NP REV 0 Page 166 w__-_- .__ I
4 Figure U.0-3. WSES-3 Cycle 3 Radial Map, EOC 001-00 002-00 003-00 004-00 FIGURE A.I.X 5tatitttCS & Integral IBeattice Rates W5ES-3 CYCLE 03 FLU 4 sqAP #14 15,954 (3dQ/9f7Q 00,-01 006-00 007-02 009-00 009-03 010-00 012-04 012-00 013-05 460 .000 1.185 1.018 472
.017 .030 .014 . 009 .006 014-00 015-09 015-00 017-00 018-00 019-00 020-00 021-00 022-00 023-00 024-00 025-06 029-00 027-07 029-00 029-08 030-00 031-09 032-00 033-10 034-00 035-11 035-00 037-12 4 T9 1.139 1.165 1.198 1.167 1.141 475
.016 .002 004 .0C2 .002 .004 .020 038-00 039-00 040-00 041-00 042-00 043-00 044-00 045-00 046-00 047-00 048-00 049-00 050-00 051-00 052-00 053-00 054-13 055-00 056-14 057-00 058-15 059-00 060-16 061-00 062-17 063-00 064-18 065-00 066-19 067-00 1.164 1.181 1.173 1.273 1.169 1.180 1.150
.000 .015 .024 .014 .020 .014 .014 068-00 069-00 070-00 071-00 072-00 073-00 074-00 075-00 076-00 077-00 078-00 079-00 080-00 081-00 082-00 083-20 084-21 485 492
.011 .018 085-00 086-22 087-00 088-23 089-00 090-24 091-00 092-25 093-00 094-26 095-00 096-27 097-00 098-28 099-00 100-00 1.199 1.229 1.169 000 1.201 1.229 1.180 101-00
.010 .0 12 .008 .000 .023 .013 .009 102-00 103-00 104-00 105-00 106-00 107-00 108-00 109-00 110-00 111-00 112-00 113-00 114-00 115-00 116-00 118-00 117-00 119-00 120-29 121-00 122-30 123-00 124-31 125-00 126-12 127-00 128-33 129-00 130-34 131-00 132-35 133-00 134-36 1.194 .000 .000 1.087 1.160 1.262 .000 135-37 000 .004 .000 .000 .016 .0 18 .046 .000 479
.000 .024 136-00 137-00 138-00 139-00 140-00 141-00 142-40 143-00 144-00 145-00 146-00 147-00 143-00 149-00 150-00 151-00 152-38 153-00 154-39 155-00 156-40 157-00 158-41 159-00 160-42 161-00 152-43 163-00 164-44 165-00 1.167 1.187 1.146 1.273 1.149 1.178 1.1' 1
.003 .021 .003 .014 .000 .012 .G1 166-00 167-00 168-00 169-00 170-00 171-00 172-00 173-00 174-00 175-00 176-00 177-00 178-00 179-00 180-00 181-45 182-00 183-46 184-00 185-47 186-00 187-48 188-00 189-49 190-00 191-50 192-00 193-51 PICTURE FORPuf 1.171 .000 1.186 1.129 477 ASSEnggly a - li5trassENT 5t*IwG e 479 1.142 peEASURED REACTION 9 ATE
.016 .005 .002 000 .017 .008 .018 m-P 194-00 195-00 196-00 197-00 198-00 199-00 200-00 201-00 202-00 203-00 204-00 PEAK $ p*EASURED CALCULATED Fr 1.27 1.26 205-52 206-00 207-53 208-00 209-54 210-00 211-55 212-00 213-56 i 465 .000 .000 .704 466 NORPut 015TR18UT10N = YES
.0 12 .000 .000 .010 .011 STANDARD DEVIAT10N = .01511 BIA5 = .00000 214-00 215-00 216-00 217-00 ENEAD-01-NP REV 0 Page 167
. ~_ _ -.- - . . ._. -. . . . . _ - - - . - , - .-. - . . - - - - - . . . ~. ..- - ,. .- .-
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ENEAD-01-NP REV O Page 169 t
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APPENDIX E: REPRESENTATIVE MEASUREMENT UNCERTAINTIES Table E.0-1. ANO-1 Cycle 9 Inferred Measurement Uncertainties :
Bumup Power Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 tNTGRL PEAK case Snapshot (EFPD) (%) (Fry) (Fwv) (Fry) (Frv) (Fxy) (Fxy) (Fry) (Ft) (Fqi 1 A890103 12.08 99.8 0.54 0.95 1.01 0.88 1.06 0.84 1.04 0.65 0.89 2 A890113 20.08 99.9 0.47 0.88 0 96 0.88 1.10 0.78 1.03 0.60 0.87 .;
3 A890614 59.79 79 8 0.37 0.62 0.63 0 65 0.87 0.66 0.65 0.45 0.63 4 AB90717 87.10 79.9 0.33 0.56 0.56 0.60 0.84 0.62 0.76 0 41 0.61 :
5 A890804 99.74 74 0 021 0.48 0 44 0.55 0.70 0 60 0.83 0.35 0.55 6 A890830 119 4 73.9 022 0.50 0.50 0.56 0.66 0.52 0.69 0.38 0.52 7 A891121 176.8 73.7 025 0.45 0.51 . 0.53 0.56 0.49 .0.73 0.35 0.50 8 A900126 202.9 80.0 0.34 0.55 C.70 0.76 0.58 0.63 0 80 0.51 0.62 9 A900216 219.6 79.7 0.32 0 60 0.80 0.81 0.90 0.79 0.81 0.48 0.72 10 A900330 250.1 80.0 0 45 0.51 0.53 0.54- 0.85 0.60 0 86 0.42 0.62 11 A900529 296.8 80.1 0 51 0.63 0.59 0.70 0.80 0.60 0.64 0.46 0.62 12 A900822 363 9 80.1 0.55 0.69 0.70 0.68 0.65 0.46 0.60 0.46 l 0.56 Table E.0-2. ANO-2 Cycle 2 Inferred Measurement Uncertainties Bumup Power Leve11 Level 2 Level 3 Level 4 Level 5 INTGRL PEAK case Snapshot (EFPD) (%) (Fxy) (Fry) (Fry) (Fry) (Fry) (Fr) (Fq) 1 A3502LL 19.0 100.0 0.65 1,10 0.88 0.89 0.85 0.73 0.88 2 A3530NR 38.3 95.2 0.60 1.00 0.76 0.78 0.81 0.64 0.79 3 A3541D1 48.4 100.0 0.63 1.03 0.76 0.79 0.81 0.64 0.81 4 A3554LQ 60,9 77.7 0 45 0.68 0.55 0.60 0.67 0.47 0.59 5 A35S8KQ 75.6 100.0 0.62 1.01 0.70 0.76 0.81 0.63 0.78 6 A3609LT 92.6 99.6 0.61 0.97 0.66 0.73 0.78 0.60 0.76 7 A3631ME 1132 99.8 0 62 0.92 0.63 0.69 0.72 0.57 0.72 0 A3317HY 142.1 100.1 0.60 0.91 0.58 0.64 0.74 0.55 0.70 9 A3707NL 170.8 99 6 0 60 0.80 0.57 0 63 0.69 0.51 0.66 10 A3741DF 1990 1002 0.59 0.77 0.52 0.59 0.64 0 49 0.62 11 A3757CD 214.0 99.4 0.57 0.75 0.50 0.57 0.61 0.47 0.60 12 A3786KX 225.0 84.6 0.53 0.59 0.46 0.51 0.55 0.43 0.52 13 A3832ER 252 4 99.5 0.68 0.78 0.57 0.64 0.68 0.55 0.66 14 A3851G1 273 2 99 3 0.68 0.76 0.56 0.59 0.63 0.53 0.64 15 A3881NV 290.5 .76.1 0 48 0.50 0.35 0.44 0.52 0.28 0.46 i
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1 Table E.0-3. WSES-3 Cycle 3 Inferred Measurement Uncertainties ;
Bumup Power Level 1 Level 2 Level 3 Level 4 Level 5 j INTGRL PEAK case Snapshot (EFPD) (%) (Fry) (Fry) (Fry) (Fry) (Frv) l (Fr) (Fq) ,
1 W6019LJ 17 45 100 00 1.81 0.92 1.07 1.10 0.72 0.59 1.18 I 2 WR6040B 38.13 99.30 1,76 0.86 1.01 1.07 0.72 0.55 1.14 3 W6073CU 68 46 99.40 1.53 0.B3 0.95 1.03 0.68 0.51 1.04 4 W6088CX 83.38 99.90 1.55 0.82 0.85 1.03 0 68 0.48 1.03 !
5 W6103CU 97.38 90.00 0.57 0.73 0.71 0.95 0 63 0 44 0.72 6 W6124JE 114.80 90 60 0.56' O.72 0.71 0.94 0.62 0.43 0.71 7 W6179CW 140.77 99.40 0.62 0.80 0.80 0.98 0.67 0.45 0.77 8 W6200JC 160.3S 99 90 0.62 0.79 0.78 0.97 0.67 0 44 0.77 9 W6299DQ 253.33 99.70 0 68 0.78 0.76 0.94 0.65 0 45 0.76 10 W6362F G 315 95 99.20 0.74 0.78 0.75 0.90 0.69 0.47 0.77 11 W6390NF 343.54 99,70 0.73 0.76 0.74 0.92 0.69 0.47 0.76 12 W6453BE 399 05 99.60 1.88 2.34 2 05 2.18 1.56 0.46 2.00 13 W6467CD 414.01 99.50 1.85 2.32 2.05 220 1.56 0 46 1.99 14 W6474DZ 420 95 99.50 1.89 2.32 2.05 2.18 1.54 0.45 2.00 t
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APPENDIX F: REPRESENTATIVE MODEL UNCERTAINTIES i
Table F.0-1. ANO-1 Cycle 9 Model Uncertainties Bumup Power Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 INTGRL PEAK ;
case Snapshot (EFPD) (%) (Fxy) (Fry) (Fry) (Fxy) (Fry) (Fry) (Fry) (Fq)
(Fr) 1 A890103 12.08 99.8 2.11 2.80 2.60 223 2 48 2.78 4.48 2.08 2.90 2 AB90113 20.08 99.9 1.94 2.62 2.41 2.15 2 42 2.74 4.26 1.95 2.90 3 AB90614 59.79 79.8 1.76 225 2.03 2.12 2.41 2.49 3.98 1.72 2.67 4 A890717 87.10 79.9 1.56 2.16 2.00 2.38 2.56 2.75 4.53 1.81 2.91 5 A890804 99.74 74.0 1.44 2.22 1.88 221 2.61 2.54 5.07 1.94 2.58 6 A890830 119 4 73.9 1.51 2.35 1.95 224 2.65 2.82 4.60 1.88 322 7 A891121 176.8 73.7 1.58 2.40 2.34 2.69 3.05 3.14 5.31 2.34 3.39 8 A900126 202.9 80.0 2.02 2.94 3.09 3.59 4 01 4.06 5.62 3.13 4.08 7 9 A900216 219.6 79.7 1.96 2.99 3.06 3 48 3.93 3.94 5.65 3.11 3.88 10 A900330 250.1 80.0 2.08 2.92 2.87 3.19 3.66 3 64 5.29 2.79 3.74 11 A900529 296.8 80.1 2.10 2.73 2.74 3.13 3.39 3.50 4.52 2.56 3.89 12 A900822 363 9 80.1 2.00 2.78 2.63 3.04 3.42 325 4.16 2.61 3.19 Table F.0-2. ANO-2 Cycle 2 Model Uncertainties Bumup Power Level 1 Level 2 Level 3 Level 4 Level 5 (NTGRL PEAK .,
car,e Snapshot (EFPD) (%) (Fxy) (Fry) (Fry) (Fry) (Fry) (Fr) (Fq) ,
1 A3502LL 19.0 100.0 2.12 1.78 128 1.33 1.78 1.35 3.06 2 A3530NR 38.3 952 1.87 1.74 1.26 128 1.74 126 2.67 ,
3 A3541D1 48 4 100.0 1 78 1.64 1.18 127 1.60 1.19 3.03 4 A3554LQ 60 9 77.7 1.79 1.63 1.23 1.33 1.66 120 2.09 5 A35BSKQ 75.8 100.0 1.64 1,56 1.10 1.18 1.51 - 1.10 2.90 6 A3609LT 92.6 99.6 1.42 1.45 1.06 1.18 1.42 0 99 3.11 7 A3631ME 113.2 99.8 1.36 1.41 1.05 1.17 1.30 0.96 1.90 8 A3317HY 142.1 100.1 1.49 1.46 1.03 1 21 1.38 1.04 2.18 9 A3707NL 1708 99 6 1.31 128 0 99 124 123 0.93 2.41 10 A3741DF 199.0 1002 126 124 0.96 1.14 1.22 0.89 2.61 11 A3757CD 214.0 99 4 126 122 0.97 1.11 1.17 0.07 2.74 12 A3786KX 225 0 84 6 1.57 1.36 1.07 121 1.15 0.99 1.73 t 13 A3832ER 252.4 99.5 1.31 129 1.02 1.20 1.18 0.97 2.36 ,
14 A3551G1 273.2 99.3 1.45 1.32 1.03 1.13 1.17 1.03 227 15 A3881NV 290.5 76.1 1.64 1.40 0.97 123 1.18 0.92 1.57 .
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l Table F.0-3. WSES-3 Cycle 3 Model Uncertainties ;
i Bumup Power Level l Level 2 Level 3 Level 4 Level 5 INTGRL PEAK ]
case Snapshot (Frv) (Fry) (Fry) (Fry) (Fry) (Fr) (Fq) )
(E FPD) (%) '
1 W6019Li 17 45 100 (1.74) 2.22 2 68 2.82 2.2 1.96 429 2 WR6040B 38.13 99.3 (1.75) 2.19 2 74 2.73 226 1.93 31 3 W6073CU 68.46 99 4 0.65 1.93 2.37 2.32 1.77 1.5 5 29 ;
4 W6068CX 83.38 99.9 0.25 1.06 2 05 1.99 1.76 1.33 3 91 5 W6103CU 97.38 90 1.47 1.77 1.98 2.04 1.71 128 3.6 6 W6124JE 114 80 90 6 1 41 1.71 1.83 1.99 1.75 125 2.47 7 W6179CW 140.77 99 4 1.3 1.7 1.77 1.79 1.58 1.06 4.98 6 W6200JC 160.36 99.9 1.32 1.67 1.72 1.77 1.59 1.07 2.47 9 W6299DQ 253.33 99.7 1.42 1.69 1.5 1.54 1.55 1.02 2.79 10 W6362F G 315 95 99 2 1.6 1.82 1.55 1.67 1.67 1.2 2.19 11 W6390NF 343.54 99.7 1.61 1.87 1.61 1,7 1.68 124 3.13 ;
12 W6453BE 399 05 99 6 0.38 (2.07) (1.72) (1.97) 1 21 1.36 1.B4 13 W6467CD 414 01 99.5 0.61 (2.09) (1.77) (1.98) 121 1.39 2.43 14 W6474DZ 420 95 99.5 0 59 (2 08) (1.81) (2.07) 1.30 1.44 1.74 NOTE: Numbers enclosed in parentheses are actually observed uncertainties.
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