ML20149D698
| ML20149D698 | |
| Person / Time | |
|---|---|
| Site: | Peach Bottom  |
| Issue date: | 01/13/1988 |
| From: | Hesse S, Willie Lee, Rubino L PECO ENERGY CO., (FORMERLY PHILADELPHIA ELECTRIC |
| To: | |
| Shared Package | |
| ML20149D647 | List: |
| References | |
| PECO-FMS-0005, PECO-FMS-5, NUDOCS 8802090594 | |
| Download: ML20149D698 (436) | |
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{{#Wiki_filter:______ -_ - h$9 l 1 1 m r METHODS POR PERPORMING BWR STEADY-STATE REACTOR PHYSICS ANALYSES l l ( PREPARED BY: , I f ~S.R. Hesse, Encflheer-Supervisory Date Methods Development Group Puel Technology Branch -
) Puel Management Section REVIEWED BY: / ~3 W.G. Vee, SenI M ERgineer 'Da te
[ Puel Technol6gy Branch edent Section PuelManag/ APPROVED BY: d b ' I3 !b & ! L. P. Rubino 'Date i Superintendent l Puel Management Section l l l l OPERATING LICENSE DPR-44 AND DPR-56 l l i PHILADELPHIA ELECTRIC COMPANY NUCLEAR OPERATIONS NUCLEAR SUPPORT DIVISION 2301 MARKET STREET PHILADELPHIA, PA 19101 8002090594 DR 000201 ADOCK 05000277 PDR
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DISCLAIMER OF RESPONSIBILITY i This document was prepared by the Philadelphia Electric Company and is believed to be true and accurate to the best of its knowledge and information. , f This document and the information contained herein are authorized for use only by Philadelphia Electric Company and appropriate sub-divisions within the U.S. Nuclear Regulatory Commission for review purposes. With regard to any unauthorized use whatsoever, Philadelphia Electric Company and its officers, directors, agents, employees, and contractors assume no liability nor make any warranty or representation with regard to the contents of this document or its accuracy 1 or completeness. I 9 l l l
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( ACKNOWLEDGEMENT This report represents the combined efforts of a i number of Philadelphia Electric and contractor personnel. Particular acknowledgement is extended to Mr. Vincent DeMasi of NUCOMP, Inc., for co-authoring this report, and for providing technical direction in its planning and preparation. Additional acknowledgements are extended to Mr. James Tusar, Mr. J. Fred Buckley, Ms. Lesley Andres, Mr. William Gassmann, Mr. Joseph Waldman, and Mr. Gregory Storey of the PECo Fuel Management Section for their contributions in the preparation of the necessary technical data presented in the various sections. Final thanks go to Ms. Lynda McGuire for providing the stenographic services required in the typing and layout of the manuscript. l l l l l i i 1 l I l - f
ABSTRACT t This report describes the reactor physics methods employed by Philadelphia Electric Company in the steady-state analysis of BWR reload cores. It further provides a basis for confidence in these methods via benchmarks to available measured data and higher order calculations, as well as through reference to previous qualification efforts, l 1 l 1 l l j
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TABLE OF CONTENTS PAGE i DISCLAIMER . . . . . . . ............................................ 1 ACKNOWLEDGEMENT . . . . . . . ............................................ 11 ABSTRACT . . . . . . . ............................................ iii TABLE OF CONTENTS . . . . . . . ............................................ iv LIST OF TABLES .. 4 . . . ............................................ vii LIST OF FIGURES . . . . . . . ............................................ x
1.0 INTRODUCTION
. . . . . . . ............................................ 1-1
2.0 DESCRIPTION
OF PECO CALCULATIONAL METHODS AND COMPUTER CODE SEQUENCE ................................. 2-1 2.1 PROGRAM FUNCTIONAL DESCRIPTIONS ......................... 2-7 3.0 PECo EXPERIENCE Wl'IH THE USE OF PHYSICS METHODS IN SUPPORT OF REACTOR OPERATIONS ................................. 3-1 3.1 PREDICTION OF HOT REACTOR CRITICALS ........................ 3-2 3.2 PREDICTION OF COLD STARTUP REACTOR CRITICALS ...... ...... 3-18 3.3 VERIFICATION OF MARGIN TO THERMAL OPERATING LIM" ... 3-34 4.0 QUALIFICATION OF PECO PHYSICS METH00S FOR USE IN CORE DESIGN AND LICENSING .................................... 4-1 4.1 FUEL ASSEMBLY POWER DISTRIBUTION COMPARIS0NS ............... 4-1 4.1.1 MEASURED DATA ...................................... 4-2 4.1.2 DATA PROCESSING .................................... 4-2 4.1.3 STATISTICAL ANALYSES ............................... 4-5 4.2 FUEL PIN FISSION RATE DISTRIBUTION COMPARISONS ............. 4-112 4.2.1 QUALIFICATION OF CASH 0-1 FUEL R00 FISSION RATE PREDICTIONS .......................... 4-117 4.2.2 COMPARISONS BETWEEN PDQ-7-E AND CASM0-1 FUEL PIN FISSION RATE PREDICTIONS .................. 4-159 4.2.3 QUALIFICATION OF MULTI-ASSEMBLY GE0 METRY METHODS ........................................... 4-188
- 4.2.4 OVERALL LOCAL PEAKING FACTOR STATISTICAL j EVALUATION ......................................... 4-203
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h TABLE OF CONTENTS PAGE 6 4.3 BENCHMARKING OF REACTIVITY PARAMETERS ...................... 4-204 4.3.1 BENCHMARKING OF DOPPLER REACTIVITY CALCULATIONS ....................................... 4-205 4.3.1.1 LATTICE PHYSICS BENCHMARKS ................. 4-205 4.3.1.2 NORGE-B CROSS SECTION FIT ANALYSIS ...... 4-209 4.3.1.3 OVERALL D0PPLER REACTIVITY STATISTICS ...... 4-213 4.3.2 BENCHMARKING 0F V0ID REACTIVITY CALCULATIONS ....................................... 4-214 4.3.2.1 LATTICE PHYSICS BENCHMARKS ................. 4-214 4.3.2.2 NORGE-B CROSS SECTION FIT ANALYSIS ......... 4-220 4.3.2.3 OVERALL VOID REACTIVITY STATISTICS ......... 4-226 4.3.3 BENCHMARKING OF CONTROL R00 REACTIVITIES ......... 4-227
- 4. 3.3.1 LATTICE PHYSICS BENCHMARKS . . . . . . . . . . . . . . . . . 4-227 i
4.3.3.2 NORGE-B CROSS SECTION FIT ANALYSIS ...... 4-230 4.3.3.3 OVERALL CONTROL R00 WORTH STATISTICS ...... 4-233 4.4 EENCHMARKING OF IS0 TOPICS CALCULATIONS ................ 4-234 4.4.1 CASM0-1 IS0 TOPICS BENCHMARK
SUMMARY
................ 4-234 4.4.2 CASMO-1 IS0 TOPICS SENSITIVITY STUDY ................ 4-237 1
4.5 QUALIFICATION OF DELAYED NEUTRON KINETICS PARAMETERS ...... 4-242 5.0 MODEL APPLICATIONS IN CORE DESIGN AND LICENSING ................. 5-1 l 5.1 PREDICTION OF MAXIMUM AVERAGE PLANAR LINEAR j HEAT GENERATION RATE (MAPLHGR) ............................ 5-1 5.1.1 MAPLHGR UNCERTAINTY ............................ 5-2 5.2 PREDICTION OF PEAK PIN LINEAR HEAT GENERATION RATE (PPLHGR) ................................ 5-3 5.2.1 PPLHGR UNCERTAINTY ................................ 5-3 5.3 PREDICTION OF MINIMUM CRITICAL POWER RATIO (MCPR) .......... 5-5 l 5.3.1 MCPR UNCERTAINTY ................................ 5-5 l 4
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l TABLE OF CONTENTS I l PAGE i i l 5.4 PREDICTION OF D0PPLER REACTIVITY AS A FUNCTION OF . l l FUEL TEMPERATURE ........................................... 5-11 5.5 PREDICTION OF VOID REACTIVITY AS A FUNCTION OF l MODERATOR DENSITY .......................................... 5-16 5.6 PREDICTION OF CONTROL R00 SCRAM REACTIVITY AS A FUNCTION OF R00 INSERTION DISTANCE ......................... 5-21 5.7 PREDICTION OF DELAYED NEUTRON KINETICS PARAMETERS .......... 5-25 5.8 PREDICTION OF PROMPT NEUTRON VELOCITIES .................... 5-29 5.9 PREDICTION OF COLD SHUTDOWN MARGIN (CSDM) .................. 5-31 5.10 TRANSIENT AND SPECIAL EVENT ANALYSES USING SIMULATE-E ........................................... 5-37
6.0 REFERENCES
..................................................... 6-1 1
i APPENDICES l APPENDIX A: R00 WITHDRAWAL ERROR (RWE) .................... A-1 APPENDIX B: MISL0CATED BUNDLE LOADING ERROR (MBLE) .................... B-1 APPENDIX C: LOSS OF FEEDWATER HEATING (LFWH) .................... C-1 APPENDIX D: STANDBY LIQUID CONTROL SYSTEM (SLCS) .................... D-1 l I 1 l I a i l
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1 LIST OF TABLES
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TABli NO. , TITLE PAGE 3.1.1 SIMU ATE-E Hot Critical Core K-effective Predictions, j Peach Bottom 2, Cycle 5 3-4 3.1.2 SIMULATE Hot Critical Core K-effective Predictions, Peach Bottom 2 Cycle 6 3-5 3.1.3 SIMULATE-1 Hot Critical Core X-effective Predictions, Peach Bottom 3, Cycle 4 3-6 3.1.4 SIMULATE-1 llot Critical Core K-effective Predictions, Peach Bottom 3, Cycle 5 3-7 3.1.b SIMULATE Hot Critical Core K-effective Predictions, Peach Bottom 3, Cycle 6 3-8 3.2.1 SIMULATE-E Cold Critical Core K-effective Predictions, Peach Bottom 2, Cycle 5 3-20 3.2.2 SIMULATE Cold Critical Core K-effective Predictions, Peach Botton 2, Cycle 6 3-21 3.2.3 SIMULATE-1 Cold Critical Core K-effective Predictions, 1 Peach Bottom 3, Cycle 4 3-22 l 3.2.4 SIMULATE-1 Cold Critical Core K-effective Predictions, Peach Bottom 3 Cycle 5 3-23 3.2.5 SIMULATE Cold Critical Core K-effective Predictions. I Peach Bottom 3, Cycle 6 3-24 ; I 4.1.1 Peach Bottom Unit 2 Cycle 5 00-1 Statepoint Reactor Conditions 4-8 l 1 l 4.1.P Peach Bottom Unit 2 Cycle 6 00-1 Statepoint Reactor i Conditions 4-9 l l 4.1.3 Peach Botton Unit 3 Cycle 4 00-1 Statepoint Reactor ; Conditions 4-10 ' 4.1.4 Peach Bottom Unit 3 Cycle 5 00-1 Statepoint Reactor Conditions 4-11 4.1.5 Peach Botton Unit 3 Cycle 6 OD-1 Statepoint Reactor l Conditions 4-12 1 4.1.6 Peach Botton Unit 2 Cycle 5 00-1 Statepoint SIMULATE-E Predicted vs. 00-1 Measurement TIP Difference Statistics 4-13 4.1.7 Peach Botton Unit 2 Cycle 6 00-1 Statepoint SIMULATE-E , Predicted vs. 00-1 Measurement TIP Difference Statistics 4-14 ' J
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1 LIST OF TABLES i TABLL j NO. TITLE PAGE 4.1.8 Peach Bottom Unit 3 Cycle 4 00-1 Statepoint SIMULATE-1 Predicted vs. 00-1 Measurement TIP Difference Statistics 4-15 4.1.9 Peach Botton Unit 3 Cycle 5 00-1 Statepoint SIMULATE-E Predicted vs. 00-1 Measurement TIP Difference Statistics 4-16 4.1.10 Peach Botton Unit 3 Cycle 6 00-1 Statepoint SIMULATE-E Predicted vs. 00-1 Measurement TIP Difference Statistics 4-17 4.2.1.1 KRITZ BWR Lattice Experiments 4-120 4.2.1.2 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distributions 4-121 4.2.2.1 Comparison of PDQ-7-E/ HARMONY and CASM0-1 Fuel Pin Fission Rate Distributions 4-162 4.2.3.1 Comparison of PDQ-7-E and PINUP Fuel Pin Fission Rates 4-193 4.3.1.1 Doppler Coefficient Comparisons, CASM0-1 Predictions vs. Empirical Correlations Derived from Swedish D2 0 Reactor Measurements 4-208 4.3.1.2 CASM0-1 Doppler Coefficient Sensitivities 4-212 4.3.2.1 KENO-IV Criticals Benchmark 4-217 4.3.2.2 CASM0-1 vs. KENO-IV Void Coefficient Comparison 4-218 4.3.2.3 Uncontrolled K-infinity Differences Between CASM0-1 and NORGE-B Curve Fits 4-224 4.3.2.4 CASMO-1 Rodded Mode Void Coefficient Study 4-225 j 4.3.3.1 CASM0-1 vs. KENO-IV Control Rod Worth Comparison 4-229 4.3.3.2 CASM0-1 Control Rod Worth Study 4-232 4.4.1 CASM0-1 Isotopics Qualification using Saxton Core II Data 4-238 4.5.1 ENDF/B-V Delayed Neutronics Data 4-244 5.3.1 Relative Change In Minimu: Critical Power Ratio As A Function of Relative Change in Assembly Integral Power (Peach Bottom 3 Cycle 7 - Statepoint #1) 5-8
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! N0. TITLE PAGE 5.3.P Relative Change In Minimum Critical Power Ratio As A Function of Relative Change in Assembly Integral Power (Peach Botton 3 Cycle 7 - Statepoint #2) 5-9 5.9.1 Calculated Cold Shutdown Margin As A Function of Cycle Exposure, Peach Bottom 3 Cycle 7 5-35 A-1 Rod Withdrawal Error Qualification Study Results Peach Botton 2 Cycle 6 A-13 A-2 Rod Withdrawal Error Qualification Study Results Peach Botton 2 Cycle 7 A-14 A-3 Rod Withdrawal Error Qualif! cation Study Results Peach Bottom 3 Cycle G A-15 A-4 Rod Withdrawal Error Qualification Study Results Peach Bottom 3 Cycle 7 A-16 B-1 Peach Bottom 3 Cycle 7 MBLE Results.
Haling Depletion Methods B-8 B-2 Peach Bottom 3 Cycle 7 MBLE Sensitivity Study Results Rodded Depletion Method B-9 B-3 Peach Bottom 3 Cycle 7 MBLE Results Database B-13 C-1 Peach Bottom 2 Cycle 7 LFWH Qualification Study Results C-8 I ] C-2 Peach Bottom 3 Cycle 7 LFWH Qualification Study Results C-8 C-3 Peach Bottom 2 Cycle 7 LFWH Sensitivity Study Results C-12 C-4 Peach Bottom 3 Cycle 7 LFWH Sensitivity Study Results C-12 D-1 Peach Bottom 3 Cycle 7 SLCS Shutdown Margin Results D-8 D-2 PECO SLCS Moderator Temperature Sensitivity Results 0-11 0-3 SLCS Haling Depletion Sensitivity Results (Peach Bottom 3 Cycle 7) D-12 ; D-4 Bases for PECO SLCS Shutdown Margin Criterion 0-16 1
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1 LIST OF FIGURES j s FIGURE NO. TITLE PAGE 2.1 PECo Steady-State Physics Computer Code Sequence .......... 2-14 1 3.1.1 SIMULATE-E Hot Critical K-effective As A Function Of Cycle Exposure, Peach Bottom 2, Cycle 5 ................... 3-9
} 3.1.2 SIMULATE-E Hot Critical K-effective As A Function Of Cycle Exposure, Peach Bottos 2. Cycle 6 ................... 3-10 3.1.3 SIMULATE-1 Hot Critical K-effective As A Function Of Cycle Exposure, Peach Bottom 3. Cycle 4 ................... 3-11 l 3.1.4 SIMULATE-1 Hot Critical K-effective As A Function Of Cycle Exposure, Peach Bottom 3 Cycle 5 ................... 3-12 I l
3.1.5 SIMULATE-E Hot Critical K-effective As A function Of ' Cycle Exposure, Peach Bottom 3. Cycle 6 ................... 3-13 3.1.6 Hot Critical K-Effective <s. Total Reactor Exposure Peach Botton Unit 2 SIMULATE-E .......................... 3-14 3.1.7 Hot Critical K-Effective vs. Total Reactor Exposure Peach Bottom Unit 3, SIMULATE-E and SIMULATE-1 ............ 3-15 3.1.8 Hot Critical K-Effective vs. Cycle Exposure Peach Bottom Unit 2. Cycle 6 SIMULATE-E and SIMULATE-1 ... 3-16 3.1.9 Hot Critical K-Effective vs. Cycle Exposure, Peach Botton Unit 3. Cycle 6, SIMULATE-E and SIMULATE-1... 3-17 ; 3.2.1 SIMULATE-E Period Corrected Cold Critic 1 K-Effective As A Function of Cycle Exposure Peaca sotton 2. Cycle 5 .. 3-25 3.2.P SIMULATE-E Period Corrected Cold Critical K-Effective As A Function of Cycle Exposure, Peach Bottom 2, Cycle 6 .. 3-26 3.2.3 SIMULATE-1 Period Corrected Cold Critical K-Effective As A Function of Cycle Exposure, Peach Bottom 3 Cycle 4 .. 3-27 3.2.4 SIMULATE-1 Period Corrected Cold Critical K-Effective As A Function of Cycle Exposure, Peach Bottom 3, Cycle 5 .. 3-28 I 3.2.5 SIMULATE-E Period Corrected Cold Critical K-Effective i ) As A Function of Cycle Exposure, Peach Bottom 3, Cycle 6 .. 3-29 3.2.6 Period Corrected Cold Critical K-Effective vs. l l Cycle Exposure, Peach Botton Unit 2, SIMULATE-E .......... 3-30 3.2.7 Period Corrected Cold Critical K-Effective vs. l l Cycle Exposure, Peach Botton Unit 3 I SIMULATE-E and SIMULATE-1 ................................ 3-31 ! i 1
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I LIST OF FIGURES i FIGURE NO. TITLE PAGE 3.2.8 Period Corrected Cold Critical K-Effective vs. Cycle Exposure, Peach Botton 2, Cycle 6 SIMULATE-E and SIMULATE-1 ................................ 3-32 3.2.9 Period Corrected Cold Critical K-Effective vs. Cycle Exposure, Peach Botton 3. Cycle 6, SIMULATE-E and SIMULATE-1 ................................ 3-33 4.1.1 Peach Botton Symmetric LPRM Tube Locations ............... 4-18 4.1.2 Axial Nodes Used in Statistical Comparisons of Predicted and Measured TIP Readings ....................... 4-19 4.1.3 Peach Bottom 2 Cycle 5 00-1 Statepoint 9-5-80 Core Average Axial TIP Trace ............................. 4-20 4.1.4 Peach Botton 2, Cycle 5 00-1 Statepoint 12-3-80 Core Average Axial TIP Trace ............................. 4-21 4 .1. !, Peach Bottom 2. Cycle 5 00-1 Statepoint 2-25-81 l Core Average Axial 11P Trace ............................. 4-22 4.1.6 Peach Bottom 2 Cycle 5 00-1 Statepoint 7-9-81 Core Average Axial TIP Trace ............................. 4-23 4.1.7 Peach Bottom 2, Cycle 5 00-1 Statepoint 9-2-81 i Core Average Axial TIP Trace ............................. 4-24 4.1.8 Peach Botton 2. Cycle 5 00-1 Statepoint 10-1-81 Core Average Axial TIP Trace ............................. 4-25 4.1.9 Peach Botton 2, Cycle 5 00-1 Statepoint 12-22-81 Core Average Axial TIP Trace ............................. 4-26 4.1.10 Peach Botton 2 Cycle 6 00-1 Statepoint 7-14-82 Core Average Axial TIP Trace ............................. 4-27 4.1.11 Peach Botton 2, Cycle 6 00-1 Statepoint 11-9-82 Core Average Axial TIP Trace ............................. 4-28 4.1.12 Peach Botton 2, Cycle 6 00-1 Statepoint 12-28-82 I
- Core Average Axial TIP Trace ............................. 4-29 i
4.1.13 Peach Bottom 2, Cycle 6 00-1 Statepoint 5-13-83 Core Average Axial TIP Trace ............................. 4-30 ! 4.1.14 Peach Botton 2. Cycle 6 00-1 Statepoint 6-23-83 j Core Average Axial TIP Trace ............................. 4-31 l -xi- ! I
l LIST OF FIGURES i FIGURE NO. TITLE PAGE 4.1.15 Peach Botton 2, Cycle 6 00-1 Statepoint 12-13-83 Core Average Axial TIP Trace ............................. 4-32 4.1.16 Peach Botton 2. Cycic 6 00-1 Statepoint 1-9-84 Core Average Axial TIP Trace ............................. 4-33 4.1.17 Peach Bottom 2. Cycle 6 00-1 Statepoint 3-2-84 Core Average Axial TIP Trace ............................. 4-34 4.1.18 Peach Botton 2. Cycle 6 00-1 Statepoint 3-20-84 Core Average Axial TIP Trace ............................. 4-35 4.1.19 Peach Bottom 3, Cycle 4 00-1 Statepoint 12-21-79 Core Average Axial TIP Trace ............................. 4-36 4.1.20 Peach Bottom 3, Cycle 4 00-1 Statepoint 1-23-80 Core Average Axial TIP Trace ............................. 4-37 4.1.P1 Peach Bottom 3 Cycle 4 00-1 Statepoint 2-27-80 Core Average Axial TIP Trace ............................. 4-38 4.1.?2 Peach Bottom 3. Cycle 4 00-1 Statepoint 4-16-80 Core Average Axial TIP Trace ............................. 4-39 4.1.23 Peach Bottom 3. Cycle 4 00-1 Statepoint 6-25-80 j Core Average Axial TIP Trace ............................. 4-40 4.1.P4 Peach Bottom 3. Cycle 4 00-1 Statepoint 8-14-80 i Core Average Axial TIP Trace ............................. 4-41 l 4.1.P5 Peach Bottom 3. Cycle 4 00-1 Statepoint 12-16-80 Core Average Axial TIP Trace ............................. 4-42 4.1.26 Peach Bottom 3, Cycle 4 00-1 Statepoint 2-6-81 Core Average Axial TIP Trace ............................. 4-43 4.1.?7 Peach Bottom 3. Cycle 5 00-1 Statepoint 12-2-81 Core Average Axial TIP Trace ............................. 4-44 1 4.1.28 Peach Bottom 3. Cycle 5 00-1 Statepoint 1-22-82 Core Average Axial TIP Trace ............................. 4-45 4.1.29 Peach Bottom 3. Cycle 5 00-1 Statepoint 2-25-82 l Core Average Axial TIP Trace ............................. 4-46 l 4.1.30 Peach Bottom 3. Cycle 5 00-1 Statepo ut 4-15-82 Core Average Axial TIP Trace ............................. 4-47 l 4.1.31 Peach Bottom 3. Cycle 5 00-1 Statepoint 5-17-82 I Core Average Axial TIP Trace ............................. 4-48 j
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LIST OF FIGURES FIGURE NO._ TITLE PAGE l 4.1.32 Peach Bottom 3 Cycle 5 00-1 Statepoint 6-30-82 Core Average Axial TIP Trace ............................. 4-49 4.1.33 Peach Bottom 3. Cycle 5 00-1 Statepoint 8-3-82 Core Average Axial TIP Trace ............................. 4-50 4.1.34 Peach Botton 3. Cycle 5 00-1 Statepoint 9-16-82 Core Average Axial TIP Trace ............................. 4-51 4.1.35 Peach Botton 3. Cycle 5 00-1 Statepoint 10-26-82 Core Average Axial TIP Trace ............................. 4-52 4.1.36 Peach Bottom 3 Cycle 5 00-1 Statepoint 12-9-82 Core Average Axial TIP Trace ............................. 4-53 4.1.37 Peach Bottom 3. Cycle 6 00-1 Statepoint 10-26-83 Core Average Axial TIP Trace ............................. 4-54 4.1.38 Peach Bottom 3 Cycle 6 00-1 Statepoint 11-9-83 < Core Average Axial TIP Trace ............................. 4-55 4.1.39 Peach Bottom 3 Cycle 6 00-1 Statepoint 1-4-84 Core Average Axial TIP Trace ............................. 4-56 4.1.40 Peach Bottom 3, Cycle 6 00-1 Statepoint 2-2-84 Core Average Axial TIP Trace ............................. 4-57 4.1.41 Peach Botton 3 Cycle 6 00-1 Statepoint 2-18-84 Core Average Axial TIP Trace ............................. 4-58 4,1.42 Peach Botton 3 Cycle 6 00-1 Statepoint 3-23-84 Core Average Axial TIP Trace ............................. 4-59 4.1.43 Peach Bottom 3. Cycle 6 00-1 Statepoint 4-26-84 Core Average Axial TIP Trace ............................. 4-60 l 4.1.44 Peach Bottom 3 Cycle 6 00-1 Statepoint 7-5-84 Core Average Axial TIP Trace ............................. 4-61 4.1.45 Peach Bottom 3. Cycle 6 00-1 Statepoint 8-14-84 Core Average Axial TIP Trace ............................. 4-62 4.1.46 Peach Bottom 3, Cycle 6 00-1 Statepcint 9-21-84 Core Average Axial TIP Trace ............................. 4-63 i 4.1.47 Peach Bottom 3, Cycle 6 00-1 Statepoint 12-28-84 l Core Average Axial TIP Trace ............................. 4-64 i 4 j -xtil-
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LIST OF FIGURES FIGURE NO. TITLE PAGE 4 4.1.48 Peach Bottom 3 Cycle 6 00-1 Statepoint 3-5-85 Core Average Axial TIP Trace ............................. 4-65 4.1.49 Peach Bottom 3 Cycle 6 00-1 Statepoint 5-23-85 Core Average Axial TIP Trace ............................. 4-66 4.1.b0 Peach Botton 2, Cycle 5 00-1 Statepoint 9-5-80 .......... 4-67 4.1.61 Peach Botton 2. Cycle 5 00-1 Statepoint 12-3-80 .......... 4-70 4.1.52 Peach Botton 2. Cycle 5 00-1 Statepoint 9-2-81 .......... 4-73 4.1.53 Peach Botton 2. Cycle 6 00-1 Statepoint 7-14-82 .......... 4-76 4.1.54 Peach Botton 2, Cycle 6 00-1 Statepoint 12-28-82 .......... 4-79 4.1.b5 Peach Botton 2, Cycle 6 00-1 Statepoint 3-2-84 .......... 4-82 4.1.56 Peach Bottom 3 Cycle 4 00-1 Statepoint 12-21-79 .......... 4-85 4.1.57 Peach Bottom 3, Cycle 4 00-1 Statepoint 4-16-80 .......... 4-88 4.1.b8 Peach Bottom 3 Cycle 4 00-1 Statepoint 12-16-80 .......... 4-91 4.1.b9 Peach Bottom 3. Cycle 5 00-1 Statepoint 12-P-81 .......... 4-94 4.1.60 Peach Bottom 3. Cycle 5 00-1 Statecoint 6-30-82 .......... 4-97 4.1.61 Peach Bottom 3. Cycle 5 00-1 Statepoint 10-26-82 .......... 4-100 l 4.1.62 Peach Bottom 3. Cycle 6 00-1 Statepoint 10-26-83 .......... 4-103 4.1.63 Peach Bottom 3 Cycle 6 00-1 Statepoint 2-18-84 .......... 4-106 4.1.64 Peach Bottom 3. Cycle 6 00-1 Statepoint 9-21-84 .......... 4-109 4.2.1 Control Rod Configurations Employed in SIMULATE-E ! Local Peaking Factor Methodology ......................... 4-116 1 4.2.1.1 Deviation in Percent Between Calculated And ] Measured Fission Rates in an 8x8 002 Assembly With 3 Gd Poisoned Rods Case BWR 1 ....................... 4-122 4.2.1.2 Deviation in Percent Between Calculated And Measured Fission Rates in an 8x8 U02 Assembly Without Gadolinium, Case BWR 2 ............................ 4-123 1 4.2.1.3 Deviation in Percent Between Calculated And Measured Fission Rates in an 8x8 U02 Assembly With 5 Gd Posioned Rods, Case BWR 3 ....................... 4-124 ! -xiv-
l i LIST OF FIGURES FIGURE NO. TITLE PAGE 4.2.1.4 Deviation in Percent Between Calculated And Measured Fission Rates in an 8x8 002 Assembly of the Pu Island Type. Case BWR 4 ............................. 4-125 4.2.1.5 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 1: Peach Botton 8x8 Fuel Lattice With Gadolinium, Unrodded. 0% In-Channel Volds ............................. 4-126 4.2.1.6 Caparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 2: Peach Botton 8x8 fuel lattice With Gadolinium, Unrodded, 40% In-Channel Voids ............................ 4-127 4.2.1.7 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 3: Peach Bottom 8x8 fuel Lattice With Gadolinium. Unrodded, 70% In-Channel Voids ............................ 4-128 4.2.1.8 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 4: Peach Bottom 8x8 Fuel Lattice With Gadolinium, Rodded. 0% In-Channel Voids ............................... 4-129 4.2.1.9 Comparison of KENO-IV and CASM0-1 Fuel Pin
'; Fission Rate Distribution Case No. 5:
Peach Bottom 8x8 fuel Lattice With Gadolinium, Rodded, 40% In-Channel Voids .............................. 4-130 4.2.1.10 Comparison of KENO-IV and CASM0-1 fuel Pin Fission Rate Distribution, Case No. 6: Peach Bottom 8x8 fuel Lattice With Gadolinium, Rodded 70% In-Channel Voids .............................. 4-131 4.2.1.11 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 7: Peach Bottom 8x8 fuel lattice With Gadolinium, Unrodded. 0% In-Channel Voids ............................. 4-132
- 4.2.1.12 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 8
Peach Botton 8x8 fuel Lattice With Gadolinium, Unrodded, 40% In-Channel Volds ............................ 4-133 ! 4.2.1.13 Comparison of KENO-IV (nd CASM0-1 Fuel Pin Fission Rate Distribution Case No. 9: ' Peach Bottom 8x8 fuel lattice With Gadolinium, Unrodded, 70% In-Channel Volds ............................ 4-134
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I LIST OF FIGURES 4 FIGURE
, N0. TITLE PAGE 4.2.1.14 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 10:
Peach Botton 8x8 fuel Lattice With Gadolinium, Rodded. 0% In-Channel Volds ............................... 4-135 4.2.1.15 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 11: Peach Bottom 8x8 fuel Lattice With Gadolinium, Rodded, 40% In-Channel Voids .............................. 4-136 4.2.1.16 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 12: Peach Botton 8x8 Fuel Lattice With Gadolinium, Rodded, 70% In-Channel Voids .............................. 4-137 4.2.1.17 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution, Case No. 13: Peach Bottom 8x8 Fuel Lattice With Gadolinium, Unrodded. 0% In-Channel Voids ............................. 4-138 L 4.2.1.18 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 14: Peach Bottom 8x8 Fuel lattice With Gadolinium. Unrodded 40% In-Channel Volds ............................ 4-139 4.2.1.19 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 15: Peach Bottom 8x8 fuel Lattice With Gadolinium, Rodded, 70% in-Channel Voids .............................. 4-140 4.2.1.20 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Fate Distribution Case No. 16: Peach Botton 8x8 Fuel Lattice With Gadolinium, ; Rodded. 0% In-Channel Volds ............................... 4-141 4.2.1.21 Comparison of KENO-IV and CASM0-1 Fuel Pin , Fission Ratt Distribution, Case No. 17: 1 Peach Botton 8x8 fuel Lattice With Gadolinium, l Rodded, 401 In-Channel Voids .............................. 4-142 4.2.1.22 Comparison of KENO. M and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 18: . Peach Botton 8x8 fuel Lattice With Gadolinium, Rodded, 70% in-Channel Voids .............................. 4-143 4.2.1.23 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 19: Peach Bottom 8x8 Fuel Lattice With Gadolinium, i Unrodded. 0% In-Channel Voids ............................. 4-144
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LIST OF FIGURES ! FIGURE ! NO . _ TITLE PAGE 3 l 4.2.1.24 Comparison of KENO-1V and CASM0-1 Fuel Pin i Fission Rate Dirtribution Case No. 20: l Peach Bottom 8xb' Fuel Lattice With Gadolinium, ! Unrodded, 401 In-Channel Voids ............................ 4-145 l 4.2.1.25 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 21: , Peach Botton 8x8-Fuel Lattice With Gadolinium,
- Unrodded, 705 In-Channel Voids ............................ 4-146 ,
4.2.1.26 Comparison of KENO-IV and CASM0-1 Fuel Pin ' Fission Rate Distribution, Case No. 22: :' Peach Botton 8x8 fuel Lattice With Gadolinium, Rodded Of In-Channel Voids ............................... 4-147 . i 4 4.2.1.27 Comparison of KENO-IV and CASM0-1 Fuel Pin f fission Rate Distribution, Case No. 23: i Peach Botton 8x8 Fuel Lattice With Gadolinium, Rodded 405 In-Channel Voids .............................. 4-148 , 4.2.1.28 Comparison of KENO-IV and CASM0-1 Fuel Pin ! Fission Rate Distribution, Case No. 24: Peach Botton 8x8 fuel Lattice With Gadolinium, l Rodded, 701 In-Channel Voids .............................. 4-149 4.2.1.29 Comparison of KENO-IV and CASM0-1 Fuel Pin i fission Rate Distribution, Case No. 25: j Verimont Yankee 8x8 fuel Lattice With Gadolinium, i Unrodded, Of In-Channel Voids ............................. 4-150 l 4.2.1.30 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 26: Vermont fankee 8x8 fuel Lattice With Gadolinium, Unrodded, 405 In-Channel Voids ............................ 4-151 4.2.1.31 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate bistribution, Case No. 27: Vermont Yankee 8x8 fuel Lattice With Gadolinium, Unrodded, 701 In-Channel Voids ............................ 4-152 4.2.1.32 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 28: Vermont Yankee 8xd fuel Lattice With Gadolinium, Rodded. Of In-Channel Voids ............................... 4-153 i 4.2.1.33 Comparison of KENO-IV and CASM0-1 Fuel Pin l Fission Rate Distribution, Case No. 29: j Vermont Yankee 8x8 f uel Lattice With Gadolinium, Rodded, 40f in-Channel Voids .............................. 4-154 l I ! -xvil-
h LIST OF FIGURES FIGURE 3 NO. TI1LE PAGE 4.2.1.34 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 30: Vermont Yankee 8x8 fuel Lattice With Gadolinium, Rodded, 70% In-Channel Volds .............................. 4-155
- 4.2.1.35 Comparison of KENO-IV and CASM0-1 Fuel Pin j Fission Rate Distribution Case No. 31:
Vermont Yankee 8x8 fuel Lattice With Gadolinium, Unrodded. 0% In-Channel Voids ............................. 4-156 4.2.1.36 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution, Case No. 32: l Vermont Yankee 8x8 fuel Lattice With Gadolinium, i Unrodded, 40% In-Channel Voids ............................ 4-157 i ! I 4.2.1.37 Comparison of KENO-IV and CASM0-1 Fuel Pin ' Fission Rate Distribution, Case No. 33: Vermont Yankee 8x8 fuel Lattice With Gadolinium, Unrodded, 70% In-Channel Voids ............................ 4-158
. 4.2.2.1 PDQ-7-E 8x8 Single Assembly Model Geometry Description ............................................... 4-163 4.2.2.2 Comparison of CASMO-1 and PDQ-7-E fuel Pin Fission Rate Distribution Case No. 1: Peach Bottom 8x8 . Fuel Lattice with Gadolinium, Unrodded. 0%
In-Char.nel Voids, Exposure = 0 GWO/MTU ...... 4-164 1 l 4.2.2.3 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 2: Peach Botton 8x8 ] fuel Lattice with Gadolinium, Unrodded. 0% . 1 In-Channel Voids. Exposure = 11 GWO/MTU ...... 4-165 i 4.2.2.4 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 3: Peach Botton 8x8 fuel Lattice with Gadolinium Unrodded. 0% l j In-Channel Voids. Exposure = 21 GWD/MTU ...... 4-166 l 4.2.2.5 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission j Rate Distribution, Case No. 4: Peach Bottom 8x8 Fuel Lattice with Gadolinium, Unrodded. 0% j In-Channel Veids. Exposure = 32 GWD/MTU ...... 4-167 4.2.2.6 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 5: Peach Botton 8x8 l Fuel Lattice with Gadolinium, Unrodded, 40% l In-Channel Voids, Exposure = 0 GWD/MTU ...... 4-168 J i
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J LIST OF FIGURES , FIGURE NO. TITLE PAGE 4.2.2.7 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution Case No. 6: Peach Botton 8x8 fuel Lattice with Gadolinium, Unrodded, 40% In-Channel Voids Exposure = 11 GWD/MTU ...... 4-169 f 4.2.2.8 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fissicn Rate Distribution, Case No. 7: Peach Botton 8x8 fuel Lattice with Gadolinium, Unrodded, 40% in-Channel Volds Exposure = 21 GWD/MTU ...... 4-170 4.2.2.9 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 8: Peach Bottom 8x8 fuel Lattice with Gadolinium, Unrodded, 40% . In-Channel Voids. Exposure = 32 GWD/MTU ...... 4-171 4.2.2.10 Comparison of CASMO-1 and PDQ-7-E fuel Pin Fission Rate Distribution Case No. 9: Peach Bottom 8x8 fuel lattice with Gadolinium Unrodded, 70% in-Channel Voids. Exposure = 0 GWD/MTU ...... 4-172 4.2.P.11 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case No. 10: Peach Bottom 8x8 fuel Lattice with Gadolinium, Unrodded, 70% In-Channel Voids. Exposure = 11 GWO/MTU ...... 4-173 4.2.P.12 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution. Cese No. 11: Peach Bottom 8x8 fuel Lattice with Gadolinium, Unrodded, 70% i In-Channel Voids, Exposure = 21 GWD/MTU ...... 4-174 4.2.2.13 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 12: Peach Bottom 8x8 Fuel Lattice with Gadolinium, Unrodded, 70% In-Channel Voids, Exposure = 32 GWD/MTU ...... a-175 4.2.2.14 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 13: Peach Bottom 8x8 fuel Lattice with Gadolinium, Rodded. 0% In-Channel Voids. Exposure = 0 GWD/MTU ....... 4-176 4.2.P.15 Comparison of CA!H0-1 and PDQ-7-E fuel Pin Fission l Rate Distribution, Case No. 14: Peach Bottom 8x8 fuel lattice with Gadolinium, Rodded. 0% In-Channel Voids, Exposure = 10 GWD/MTU ...... 4-177 ) 4.2.P.16 Comparison of CASM0-1 and PDQ-7 E fuel Pin Fission Rate Distribution, Case No. 15: Peach Botton 8x8 Fuel Lattice with Gadolinium, Rodded. 0% In-Channel Voids. Exposure = 21 GWD/MTU ...... 4-178
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LIST OF FIGURES FIGURE NO. TITLE PAGE 4.2.P.17 Comparison of CASM0-1 and PDQ-7-E fuel Pin Fission Rate Distribution, Case No. 16: Peach Bottom 8x8 fuel Lattice with Gadolinium, Rodded. 0% In-Channel Voids. Exposure = 32 GWD/MTU ...... 4-179 4.2.2.18 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case No. 17: Peach Bottom 8x8 Fuel Lattice with Gadolinium, Rodded, 40% In-Channel Voids, Exposure = 0 GWD/MTU ...... 4-180 4.2.2.19 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case No. 18: Peach Bottom 8x8 Fuel Lattice with Gadolinium, Rodded, 40% In-Channel Volds, Exposure = 10 GWD/MTU ...... 4-181 4.2.2.20 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case No. 19: Peach Botton 8x8 Fuel Lattice with Gadolinium, Rodded, 40% In-Channel Volds Exposure = 21 GWD/MTU ...... 4-182 4.2.2.21 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission l Rate Distribution, Case No. 20: Pach Bottom 8x8 Fuel Lattice with Gadolinium, Rodded, 40% in-Channel Voids. Exposure = 32 GWD/MTU ...... 4-183 4.2.P.22 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case No. 21: Peach Bottom 8x8 fuel Lattice with Gadolinium, Rodded, 70% In-Channel Voids Exposure = 0 GWD/MTU ...... 4-184 4.2.2.23 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case rio. 22: Peach Botton 8x8 Fuel Lattice with hiolintur., Rodded, 70% in-Channel Volds, Lxposure = 10 GWD/MTU ...... 4-185 4.2.P.24 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution, Case Mo. 23: Peach Bottom 8x8 Fuel Lattice with Gadolinium, Rodded, 70% < In-Channel Voids. Exposure = 21 GWD/MTU ...... 4-186 l l 4.2.P.25 Comparison of CASM0-1 and PDQ-7-E Fuel Pin Fission Rate Distribution Case No. 24: Peach Bottom 8x8 l 1 Fuel Lattice with Gadolinium, Rodded, 70% In-Channel Voids. Exposure = 32 GWD/MTU ...... 4-187 4.2.3.1 PDQ-7-E Multi-Assembly Model Geometry Description .......... 4 197 j 4.2.3.2 PDQ-7-E Multi-Assembly 3eowtry Configurations ............. 4 198
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LIST OF FIGURES i FIGURE NO. TITLE PAGE 4.2.3.3 PDQ-7-E Multi-Assembly Geometry Relative Pin Power Distribution, Fuel Configuration #4, 800, 0% Void, Rod Configuration #9 ...................................... 4-199 4.2.3.4 P0Q-7-E Multiple Assembly Geometry Relative Pin Power Distribution, Fuel Configuration #9, BOC, 40% Void. Rod Configuration ill ..................................... 4-200 4.2.3.5 PDQ-7-E Multiple Assembly Geometry Relative Pin Power Distribution, Fuel Configuration #9, BOC, 70% Void, Rod Configuration #12 ..................................... 4-201 4.2.3.6 PINUP Code Geometry Description ........................... 4-202 4.3.P.1 PECo KENO-IV 8x8 Single Assembly Model Geometry Description ............................................... 4-219 4.4.1 Yankee Rowe Core 1. Pu-239/Pu-240 Isotopic Ratio, CASM0-1 vs. Experiment .................................... 4-239 4.4.P Yankee Rowe Core 1. Pu-240/Pu-241 Isotopic Ratio. CASM0-1 vs. Experiment .................................... 4-240 i 4.4.3 Yankee Rowe Core 1. Pu-241/Pu-242 1sotopic Ratio, 1 CASM0-1 vs. Experiment .................................... 4-241 5.3.1 Relative Change in Critical Power Ratio As A Function of Relative Change in Bundle Power ............... 5-10 5.4.1 3-0 Doppler Reactivity As A Function of Core Average fuel Temperature Peach Bottom 3. Cycle 7 ................. 5-14 5.4.? 3-D Doppler Coefficient As A Function of Core Average Fuel Temperature, Peach Bottom 3, Cycle 7 ................. 5-15 , 5.5.1 3-D Model Void Reactivity As A Function of Core Average Moderator Density, Peach Bottom 3. Cycle 7 ................ 5-19 , 5.5.? 3-D Model Void Worth As A function of Core Average l Percent in-Channel Void, Peach Botton 3, Cycle 7 .......... 5-70 5.6.1 Scram Reactivity As A function of Control Rod Insertion, Peach Botton 3. Cycle 7 ........................ 5-24 5.7.1 CASM0-1 Effective Delayed Neutron Fractions As ) A Function of Exposure, Unrodded State, Nominal j Peach Botton 8x8 Raioad fuel Lattice ...................... 5-27 3 i l l
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i LIST Of FIGURES . i FIGURE , N0. TITLE PAGE l I S.7.2 CASM0-1 Effective Delayed Neutron fractions As i A function of Exposure, Rodded State, Nominal
- Peach Botton 8x8 Reload fuel Lattice ...................... 5-28 5.9.1 Predicted Cold Shetdown Margin As A function Of Cycle Exposure, Peach Bottom 3. Cycle 7 ................... 5-36 A-1 Limiting RWE Rod Pattern, Peach Bottom 2 Cycle 6 ......... A-17 '
A-2 Limiting RWE Rod Pattern, Peach Bottom 2, Cycle 7 ......... A-18 A-3 Limiting RWE Rod Pattern, Peach Bottom 3, Cycle 6 ......... A-19 l A-4 Limiting RWE Rod Pattern, Peach Bottom 3 Cycle 7 ......... A-20 4 A-5 Peach Botton 2 Cycle 6 RWE Analysis . 2 Delta CPR vs. Error Rod Position ........................ A-21 ! 1 A-6 Peach Botton 2. Cycle 7 RWE Analysis i Delta CPR vs. Error Red Position ........................ A-22 l A-7 Peach Bottom 3. Cycle 6 RWE Analysis , Delta CPR vs. Error Rod Position ........................ A-23
, A-8 Peach Bottom 3 Cycle 7 RWE Analysis Delta CPR vs. Error Rod Position ........................ A-24 A-9 Peach Botton 2, Cycle 6 RWE Analysis i a Rod Block Reading vs. Error Rod Position ................ A-25
- A-10 Peach Botton 2. Cycle 7 RWE Analysis ,
l Rod Block Reading vs. Error Rod Position .....,.......... A-26 i i A-ll Peach Bottom 3. Cycle ti RWE Analysis Rod Block Reading vs. Error Rod Position ................ A-27 1 l A-12 Peach Botton 3 Cycle 7 RWE Analysis l Rod Block Reading vs. Error Rod Position ................ A-28 j A-13 Peach Bottom 3 Cycle 7 RWE Analysis Relative Delta CPR vs. Cycle Exposure .................. A-29 B-1 Hislocated Bundle Loading Error Results Peach Bottom 3 Cycle 7 ................ B-14 l
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1.0 INTRODUCTION
The Philadelphia Electric Company (PECo) BWR Steady-State Reactor Physics Methods Report describes and qualifies these methods which PEco employs in the steady-state core physics analyses of the Peach Bottom and Limerick Boiling Water Reactors (BWRs). Methods are comprised of an integrated sequence of detailed reactor analysis computer programs, including the modeling application of those programs to the various calculations associated with the design, licensing, and operations support of BWR reload core configurations. Primary computer codes used by PECo in the steady-state analysis of the BWR core are based on the Electric Power Research Institute (EPRI) Advanced Recycle Methodology Program (fRMP). These programs have been the subject of significant benchmarking efforts on the part of EPRI, their contractors, and numerous member utilities. Similar, and in some cases, identical versions of these primary codes have been previously reviewed by the NRC for other utilities. Reactor < analysis techniques embodied in these programs are consistent with current industry standards, and have a ; l well-established basis for application to reload core , I design, licensing, and operations support calculations, i i l l-1
l PECo steady-state reactor physics methods have been qualified by comparison of in-house calculational ; results to both measured data and higher order calculations. In all cases these qualification studies l generated results typical of those observed elsewhere in the industry. Methods were further qualified via reference to benchmark ctudies perforued by code developers and utilities with similar, approved licensing methods. Philadelphia Electric Company will continue to monitor the accuracy of the reactor physics methods described herein with respect to the steady-state analysis of BWR reload cores. I i i l l 1-2 l
2.0 DESCRIPTION
OF PECO CALCULATIONAL METHODS AND COMPUTER CODE SEQUENCE l l The steady-state physics computer code sequence , which Philadelphia Electric Company currently employs in the analysis of reload core designs is depicted in Figure 2.1. Primary codes were originally supplied by The Electric Power Research Institute (EPRI) as part of EPRI's Advanced Recycle Methodology Program (ARMP) package. Boiling Water Reactor analysis techniques embodied in these codes are consistent with current industry standards and have a well-established basis for application to PECo reload licensing calculations. A brief history of each of the primary analysis programs is presented here, including references to previous qualification efforts. , The CASMO-1-PECoO) program (hereafter referred to as CASMO-1), performs the single assembly lattice physics cai .. tion as required to generate neutronics data for both the 3-dimensional simulator program, SIMULATE-E-PECo 02), i and the PDQ-7-E/ HARMONY 03)U) fine mesh diffusion theory ) l program. Philadelphia Electric Company's version of 4 CASMO-1 is based on the original STUDSVIK ENERGITEKNIK AB program as described in References 5 and 6. Coding modifications in the PECO version include ENDF/B-V 4 updates to delayed neutron data as recommended by both the code developer and EPRI. All other changes to the FORTRAN source are related to input / output enhancements, 2-1
l l the installation of the program onto the IBM operating system, and the expansion of various arrays to allow for the modeling of more complex fuel designs. PECo modifications do not alter the fundamental calculational methods of the original CASMO-1 as developed by STUDSVIK and reviewed by NRC under Docket No. 50-271 for Yankee Atomic Electric Company (7). The MICBURN(8) program is used to provide CASMO-1 with 25 energy group gadolinium cross sections for Gd 023 loaded fuel pins. The version of MICBURN used by PECo remains unchanged from the original program developed by STUDSVIK for EPRI under research project 118-1. This version has also been reviewed by NRC for Yankee Atomic under Docket No. 50-271. The SIMULATE-E-PECo program (hereafter referred to as SIMULATE-E) performs a three-dimensional simulation of the LWR core in a state of nuclear and thermal-hydraulic equilibrium. It is an enhanced version of the original EPRI SIMULATE-E(9) code, which in turn was derived from the Yankee Atomic Electric Company program as described in ; report YAEC-123800) and reviewed by NRC under Docket No. 50-271. The only significant enhancement incorporated into the code by EPRI was the FIBWR(H) thermal-hydraulics l l calculation. FIBWR, as described in Yankee Atomic Report YAEC-123402), has also been reviewed by NRC under Docket No. 50-271, and was recently approved for PECo applicationsO3). , i l 2-2
l Philadelphia Electric's SIMULATE-E is an enhanced j version of the EPRI program. As in the case of CASMO-1, PECo modifications are primarily related to input /cutput enhancements, accommodations for installation ont6 the PECo IBM operating system, and the expansion of coding dimensionality to allow for larger problem sizes. Two somewhat more substantial modifications were also implemented by PECo:
- 1) The incorporation of a series of subroutines which calculate margin to both (1) fuel related Technical Specification operating limits (MCPR, LHGR, MAPLUGR), and (2) vendor recommendations regarding fuel heat up rates (GE PCIOMRs). These routines are based on General Electric process computer algorithms such as the GEXL correlation (M).
They execute external to the SIMULATE-E nuclear-hydraulic iterations, and are considered to be post processors. Qualification of thermal limit routines will be discussed in detail in Section 5.
- 2) The incorporation of a cross section dependency on !
moderator temperature to allow for improved accuracy in the prediction of zero power reactor criticality. Qualification of the cold model, including the moderator temperature enhancement, is discussed in Section 3.2. i 2-3
The fundamental nuclear-hydraulic calculations performed by PECo's SIMULATE-E are consistent with methods previously approved by NRC for Yankee Atomic under Docket No. 50-271. It should be noted that the analyses of two Peach Bottom cycles referenced in this report were performed with the SIMULATE-1-PECoOS) program (hereafter referred to as SIMULATE-1). The only significant differences between SIMULATE-1 and SIMULATE-E are:
- 1) SIMULATE-1 BWR thermal-hydraulic calculations are based on the EPRI THERM-BO6) algorithms.
THERM-B methods have been submitted to NRC for review as part of Northern States Power Company 1 Reactor Physics Methods report NSPNAD-8609 for the ' Monticello Plant under Docket No. 50-263.
- 2) SIMULATE-1 does not include the optimized partial cross section look-up interpolation scheme found in the approved Yankee version of the program. This option reduces code execution times, but has no significant impact on results. The original i
SIMULATE-1 interpolation scheme remains as an ; option in the PECo SIMULATE-E version to demonstrate consistency between the table look-up methods. 2-4
SIMULATE-E and SIMULATE-1 were executed in parallel in the hot and cold analyses of two Peach Bottom cycles 1 as discussed in Section 3. Results verify the interconsistency between the program versions. It should be noted that the only SIMULATE-1 generated I values reported in this document relate to the : prediction of hot and cold K-effective and thermal power distribution. All PECo generated safety parameters (MCPR,LHGR,MAPLHGR) and reactivity coefficients referenced in this report were derived using SIMULATE-E. l PDQ-7-E/RARMONY is an EPRI released version of the PDQ-7/ HARMONY fine mesh diffusion theory program which 1 is currently in widespread use throughout the industry. ' It is an enhanced version of an earlier Argonne National Laboratories' releaseUI) of the code, and has not been , altered by PECo. The above computer codes have been previously qualified and benchmarked via studies performed or sponsored by the NRC, code vendors, EPRI, National Laboratories, and other utilities. Documentation for much of this work is in the public literature, and has been reviewed previously by the NRC when referenced within licensing reports submitted for other BWRs. At I the risk of redundancy, some of these code benchmarking comparisons have again been explicitly referenced in l this report. The criterion used to select ' generic' data for inclusion in this report was based en the 2-5 l _y
objective of qualifying Philadelphia Electric's application of these codes specifically towards the design and licensing of the Peach Bottom and Limerick BWR units. Where relevant to the demonstration of the calculational accuracy of the codes in this application, some generic code benchmarking data has been cited in this report. With the exception of these, all other data herein displayed have been generated by Philadelphia Electric Company, and wherever possible, benchmarking comparisons were made specific to the intended code application. For the most part, generic code qualification data have not been explicitly displayed in this report, but are indirectly referenced f rom previous submittals made to the NRC(1)(10)(12) , l l 2-6
l J 2.1 Program Functional Descriptions l l A brief functional description of each of the current PECo programs, including linkage codes and post processors, follows: MICBURN is a one-dimensional cylindrical geometry I pin cell code which PEco uses in the development of 25 energy group microscopic gadolinium cross sections for Gd 023 loaded fuel pins. The program generates a table of effective 25 group gadolinium pin cross sections as a function of an equivalent total Gd-155 and Gd-157 number density. This 25-group gadolinium library is written to an external file for use by the CASMO-1 single assembly lattice physics code. CASMO-1 is a two-dimensional, single assembly, transport theory lattice physics code. It utilizes an ENDF/B-III based 25 energy group cross section library for all non-burnable absorber isotopes. Gadolinum pin cross sections are derived from the same library via the MICBURN pin cell depletion program. For PECo applications, CASMO-1 is used to develop two group assembly averaged cross sections and instrument response factors as neutronics input for the three-dimensional reactor analysis code, SIMULATE-E. Cross sections are generated as a function of the following primary BWR nodal parameters: 2-7
l t o Exposure History (E) , o Exposure Averaged Relative Moderator Density (VB) l ! o ' Control Rod Presence (CT) l l o Instantaneous Relative Moderator Density (U) l o Fuel Temperature (TP) o Moderator Temperature (TM) o Xenon Concentration (CXE) o Boron Concentration (CB) CASMO-1 is also employed in the generation of fine mesh four group cross section data for input to the PDQ-7-E diffusion theory program. NORGE-B-PECo(18) (hereafter referred to as NORGE-B) 1 is an enhanced version of the original EPRI NORGE-B(I9) code, and provides an automated data link between CASMO-1 i and SIMULATE-E. The code accesses formatted data files as generated by CASMO-1 and prepares SIMULATE-E partial cross sections in the form of two-dimensional l interpolating tables and/or coefficients for lower order ! l polynomial fits. The original EPRI NORGE-B accommodated l l cross section dependencies on exposure, control rod I presence, instantaneous relative moderator density, exposure averaged relative moderator density (void i history), fuel temperature, and xenon number density. Additional cross section dependencies on boron concentration and moderator temperature have been incorporated into the NORGE-3 cold model by PECo. 2-8
Polynomial fits for isotopic fission product yields and neutrons per fission are also generated by the program. SIMULATE-E is the three-dimensional reactor physics program used by PECo in the steady-state simulation of BWR cores. The code models the reactor core as a matrix of neutronically coupled nodes, each of which is representative of a six-inch axial segment of one BWR fuel assembly. Typically, 19,100 (= 764 x 25) of these nodes are employed in the modeling of a 150 inch active fuel height, 764 assembly BWR core. At each node, SIMULATF-E accesses CASMO-1 generated two group cross section data (It ri Ear Eri VEfs KEf) as processed by the NORGE-B program. As previously Gh noted, each of these cross sections are expressed, where appropriate, as functions of the following nodal j parameters: o Exposure History (E) o Exposure-Averaged Relative Moderator Density (VH) o Control Rod Presence (CT) i o Instantaneous Relative Moderator Density (U) o Fuel Temperature (TF) o Moderator Temperature (TM) j l o Xenon Concentration (CXE) o Boron Concentration (CB) , 1 l l 2-9
The thermal neutron flux distribution is evaluated by solving the Modified Coarse Mesh Diffusion Theory (i.e., PRESTO) equations for the thermal group. The fast neutron flux distribution is then inferred from the thermal fluxes based on the' steady-state balance of the ; l slowing down and thermal capture reaction rates. The FIBWR computer program has been incorporated into SIMULATE-E to model BWR thermal-hydraulic two phase flow phenomena. In-channel flows and core bypass flow are calculated based on a detailed pressure drop analysis. FIBWR is called at the beginning of each void iteration. After completion of the FIBWR flow balancing calculation, nodal qualities are determined from the most recent evaluation of the thermal power distribution. At each node the in-channel relative moderator density is finally calculated using the Zolatar-Lellouche void quality profile fit model (i.e., EPRI Void Correlation). As previously noted, the PECo SIMULATE-E program now includes a process computer emulation option. Converged power and flow distributions are used to l predict margins to Technical Specification operating limits, including Minimum Critical Power Ratio (MCPR), Linear Heat Generatior. Rate (LHGR), and Maximum Average i i Planar Linear Heat Generation Rate (MAPLHGR). These core performance parameters are calculated by SIMULATE-E in a manner nearly identical to that of the Peach Bottom l l 1 2-10 l
plant process computer software. In particular, MCPR is evaluated using the GEXL correlation in conjunction with R-factor data supplied by GE. For purposes of performing reload safety evaluations, SIMULATE-E is employed in: (1) the generation of core average Doppler, void, and scram reactivities for the RETRAN-02(N) point kinetics model. (2) the generation of three-dimensional power and cross section data to be input to the SIMTRAN-E(21)(22)/RETRAN-02 one-dimensional kinetics model. This will be discussed in detail in PECo's Reload Safety l Evaluation (RSE) Methods Report, to be submitted to NRC at a later date. (3) the analysis of the Rod Withdrawal Error (RWE) event, Mislocated Bundle Loading Error (MBLE) event, Loss of Feedwater Heating (LFWH) Transient, and Standby Liquid Control System (SLCS) Shutdown Capability. The RSE applications of SIMULATE-E are further described in Section 5 and the appendices of this report. COPHIN(23) is an EPRI developed program which links the CASMO-1 single assembly transport theory code to the PDQ-7-E/ HARMONY multi-assembly diffusion theory program. I I 2-11
COPHIN automates the PDQ-7-E model development process. The program accesses CASMO-1 formatted output files and generates virtually complete PDQ-7-E/RARMONY multi-assembly input decks, including few group microscopic cross section data, geometry input, mesh specifications, etc. PDQ-7-E/ HARMONY is a diffusion theory based multi-assembly, two-dimensional lattice physics program. PECo uses the code to evaluate the local fission rate distribution within a group of adjacent fuel assemblies. Local peaking factors are then calculated accounting for the effects of flux gradients produced by control rods and/or dissimilar neighboring fuel assemblies. These I 1 local peaking factors are ultimately used by the nodal code SIMULATE-E in the calculation of peak pin linear heat generation rate. I PINUP is a PECo-developed production code used in the approximate evaluation of 2x2 assembly geometry fuel pin fission rate distributions and associated local l peaking factors. PINUP reads single assembly geometry fuel rod fission rate data from either CASMO-1 or . PDQ-7-E, and assembly power data from either SIMULATE-E . I or PDQ-7-E. Fuel rod fission rates in multi-assembly geometries are then calculated by the program based on flux reconstruction techniques. PECo has qualified the PINUP program by comparisons to fine-mesh multi-assembly l geometry PDQ-7-E solutions. 2-12
RWEASY is a SIMULATE-E post processor which was developed by PECo in order to simplify the data reduction process associated with the control rod withdrawal error analysis. The program uses SIMULATE-E calculated Local Power Range Monitor (LPRM) readings to predict Rod Block Monitor (RBM) responses as a function of error rod notch position and failed LPRM strings. RWEASY also generates a thermal li.mit summary edit which lists MCPR, delta-MCPR and MLHGR as a function of fuel type and error rod position. Application of RWEASY to PECo methods is discussed in detail in Appendix A. SIGMA-PECo and TOPS perform statistical comparisons between SIMULATE-E predictions of Traversing Incore Probe (TIP) readings and measured flux trace data. The comparisons are used to infer uncertainties in SIMULATE-E predictions of nodal and assembly integral powers. ; 2-13
FIGURE 2.1 PECO STEADY-STATE PHYSICS COMPUTER CODE SEQUENCE (8-1-87) PRlW ARY AN ALYSIS CODE l_____ l AUXlLI ARY CODE LINK AGE CODE MICBURN (GAD X-SECTIONS) l l CASMO 1-PECO _ COPHIN _ i -PECO (SINGLE ASSEMBLY I LATitCE PHYSICS) \ y H PD O E/H A R M O N Y NORGE-8 , I i (M ULTIPLE ASSEM B LY -PECO l LATTICE PHYSICS)
" U e-----------
i PINUP , SI M U L ATE-E -PE C O I l _
~ (WITH flBWR) .
l (LOCAL PEAKING i
',____ FACT 0R5). _ _ , , , , ,e (3-D SIMUL ATOR) 1 i
r-~~-----~~~ i r----------- , i RWEASY i SIG M A-PECO/ , I TOPS "i ' s (ROD WITHDRAWAL l
!" i l l ER R O R) I (STATISTICS)
-____________i _____________
I 2-14 .
3.0 PECO EXPERIENCE WITH THE USE OF PHYSICS METHODS IN SUPPORT OF REACTOR OPERATIONS Philarlelphia Electric Company has used the steady-state physics methods described in Section 2 in support of the Peach Bottom and Limerick nuclear units - since mid-1981. Specific applications have included the development of control rod patterns and power maneuver l strategies, independent verification of vendor reload core designs, and the evaluation of alternate operating techniques. Of particular interest for purposes of qualifying PECo steady-state physics methods is the data derived from those routine core tracking calculations which were performed to monitor reactor core performance. These analyses included the prediction of criticality at various hot and cold reactor operating conditions, as I well as the evaluation of both margin to fuel thermal operating limits and Traversing In-Core Probe (TIP) neutron flux traces. Criticality and thermal limits l benchmarking will be discussed in this section; results from TIP analyses will be presented in Section 4.1. i 3-1
e 3.1 Prediction of Hot Reactor Criticals SIMULATE predicted critical eigenvalues were calculated for 140 hot equilibrium statepoints from five recent Peach Bottom reload cycles. Reactor critical l conditions selected encompass all cycle exposures, with ( power levels ranging from 80% to 100% of rated, and core flows ranging from 80% to 109% of rated. Statepoint information and predicted K-effectives are reported in Tables 3.1.1 through 3.1.5 for Peach Bottom 2 Cycles 5 and 6, and Peach Bottom 3 Cycles 4, 5, and 6, respectively. Results for the individual cycles are displayed graphically in Figures 3.1.1 through 3.1.5. Plots of SIMULATE predicted hot eigenvalues as a function of integrated reactor exposure for Units 2 and 3 are shown in Figures 3.1.6 and 3.1.7, as well. i i Statistical analysis of the SIMULATE predictions demonstrates an overall mean hot critical eigenvalue of 0.9946 with a standard deviation of 0.0033AK. When i results are referenced to the mean eigenvalue of their respective cycles this overall standard deviation drops i to 0.0021AK. Included in these reactivity statistics l are those uncertainties associated with the measured core operating conditions as recorded for the criticals. Uncertainties in measured core flow, reactor pressure, feedwater flow, and feedwater temperature as defined in Reference 14 ultimately propagate into the SIMULATE input stream. Based on a series of sensitivity calculations, 3-2
s PECo has demonstrated that these measurement 5 uncertainties potentially constitute 0.09% AK of the , l overall hot K-effective standard deviation of 0.33% AK. i
)
l It should be noted that Peach Bottom 3 Cycles 4 and 5 criticality calculations were originally performed with the SIMULATE-1 program, while the remaining three cycles were analyzed with SIMULATE-E. Differences between the two models wete demonstrated to be small by reanalyzing the Peach Bottom 2 Cycle 6 and Peach Bottom 3 Cycle 6 hot criticals with the SIMULATE-1 code. K-effectives as generated by the two SIMULATE models exhibited RMS differences of less than 0.13% AK. SIMULATE-E and SIMULATE-1 eigenvalue solutions for the Peach Bottom 2 Cycle 6 and 3 Cycle 6 hot criticals are plotted in Pigures 3.1.8 and 3.1.9, respectively. {
)
3-3
TABLE 3.1.1 [ SIMULATE-E HOT CRITICAL CORE K-EFFECTIVE PREDICTIONS 5 PEACH BOTTOM 2 CYCLE 5 I CYCLE THERMAL CORE ROD DATE EXPOSURE POWER FLOW DENSITY (GWD/ST) (MWTH) (MLBM/HR) (% INSERTED) K-EFF 09/05/80 0.365 3132.0 102.4 5.8 0.9934 09/30/80 0.852 3264.0 101.7 5.1 0.9931 10/26/80 1.407 3292.0 100.5 5.1 0.9929 - 12/03/80 2.126 3269.0 102.3 5.7 0.9916 01/01/31 2.614 3141.0 100.9 7.5 0.9901 01/28/81 3.120 3281.0 100.7 6.3 0.9928 02/25/81 3.736 3210.0 94.3 5.6 0.9930 03/30/81 4.352 3284.0 100.5 7.8 0.9933 04/21/81 4.822 3270.0 101.1 7.8 0.9943 07/09/81 5.064 3135.0 100.2 8.4 0.9940 08/12/81 5.709 3187.0 101.5 7.9 0.9955 09/02/81 5.967 3265.0 99.9 4.8 0.9954 10/01/81 6.546 3107.0 101.7 5.1 0.9956 10/26/81 6.965 3212.0 93.7 3.2 0.9940 1.1/20/81 7.510 3156.0 105.8 3.2 0.9952 12/11/81 7.911 3040.0 107.3 3.2 0.9953 12/22/81 8.111 2963.0 107.3 1.1 0.9955 01/29/82 8.792 2715.0 109.5 1.1 0.9952 02/19/82 9.103 2650.0 109.0 1.1 0.9944 s 8 I CYCLE MEAN HOT CRITICAL d-EFFECTIVE = 0.9939
)
STANDARD DEVIATION ABOUT THE MEAN = 0.0015 I I 3-4 , i
TABLE 3.1.2 SIMULATE HOT CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 2 CYCLE 6 CYCLE THERMAL CORE ROD DATE EXPOSURE POWER FLOW DENSITY K-EFF (GWD/ST) (MWTH) (MLBM/HR) (% INSERTED) SIM-E SIM-1 07/14/82 0.195 3226.0 101.7 6.2 0.9937 0.9929 07/23/82 0.381 3282.0 97.0 5.0 0.9963 0.9942 08/06/82 0.681 3283.0 97.5 5.1 0.9960 0.9941 08/26/82 0.933 3278.0 100.6 4.9 0.9957 0.9938 09/16/82 1.326 3277.0 102.2 7.2 0.9953 0.9932 10/07/82 1.774 3282.0 99.0 7.2 0.9950 0.9931 10/22/82 2.095 3280.0 98.6 7.4 0.9950 0.9931 11/09/82 2.363 3287.0 101.4 6.4 0.9942 0.9933 11/26/82 2.726 3279.0 99.4 6.4 0.9946 0.9926 12/09/82 2.997 3287.0 100.8 7.8 0.9942 0.9923 12/28/82 3.235 3290.0 101.2 8.1 0.9941 0.9933 , 01/25/83 3.823 3297.0 99.5 8.1 0.9947 0.9928 1 03/01/83 4.532 3283.0 101.5 9.7 0.9953 0.9933 04/21/83 5.385 3260.0 102.5 9.5 0.9960 0.9953 05/13/83 5.710 3024.0 102.4 12.6 0.9953 0.9946 l 05/19/83 5.827 3278.0 99.0 7.9 0.9956 0.9939 06/06/83 6.013 3288.0 101.2 8.6 0.9963 0.9946 06/23/83 6.366 3268.0 97.9 6.7 0.9985 0.9983 06/30/83 6.515 3281.0 100.8 6.7 0.9986 0.9970 12/13/83 6.776 3272.0 101.3 4.9 1.0000 0.9998 01/03/84 7.176 3289.0 97.4 4.1 1.0000 0.9993 01/09/84 7.283 3280.0 102.4 4.1 1.0006 1.0008 01/26/84 7.632 3092.0 102.3 4.1 1.0014 1.0002 02/17/84 7.990 3243.0 107.9 3.1 1.0009 0.9995 03/02/84 8.114 3286.0 107.0 1.4 0.9991 0.9995 03/20/84 8.482 3148.0 108.6 0.9 0.9993 0.9994 03/29/84 8.663 3069.0 108.8 0.6 0.9993 0.9978 04/11/84 8.918 2961.0 108.9 0.6 0.9993 0.9978 04/23/84 9.147 2908.0 109.4 0.6 0.9992 0.9977 CYCLE MEAN HOT CRITICAL K-EFFECTIVE = 0.9970 0.9958 STANDARD DEVIATION ABOUT THE MEAN = 0.0024 0.0029 3-5
k / TABLE 3.1.3 i s
- SIMDLATE-1 HOT CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 3 CYCLE 4 i
CYCLE THERMAL CORE ROD i DATE EXPOSURE POWER FLOW DENSIT" (GWD/ST) (MWTH) (MLBM/HR) ( % INSERTED) K-EFF 11/20/79 0.170 3264.0 87.9 8.3 0.9896 ~ 12/03/79 0.386 2487.0 56.5 8.0 0.9911 12/21/79 0.607 3277.0 93.3 7.6 0.9888 12/24/79 0.671 3288.0 94.5 7.6 0.9884 01/11/80 1.058 3290.0 93.9 7.6 0.9887 01/21/80 1.124 3274.0 93.4 7.5 0.9879 01/23/80 1.167 3289.0 95.0 7.5 0.9886 , 02/20/80 1.583 3282.0 99.4 7.7 0.9874 02/27/80 1.734 3288.0 102.1 7.7 0.9897 03/19/80 1.925 3273.0 99.6 8.6 0.9876 04/16/80 2.520 3277.0 100.3 8.4 0.9898 04/25/80 2.713 3279.0 100.5 8.4 0.9891 05/16/80 2.928 3290.0 93.4 8.2 0.9888 06/06/80 3.092 3279.0 101.9 8.7 0.9888 06/25/80 3.498 3276.0 96.0 8.2 0.9904 ; 08/14/80 4.528 3287.0 103.0 13.2 0.9909 10/06/80 5.511 3284.0 100.5 9.9 0.9906 11/04/80 5.804 3280.0 101.9 9.7 0.9902 12/16/80 6.780 3284.0 101.4 7.2 0.9933 12/23/80 6.803 3216.0 102.5 7.7 0.9903 02/06/81 7.771 3219.0 102.5 4.7 0.9946 03/07/81 8.334 3178.0 102.5 2.1 0.9939 i
) )
CYCLE MEAN HOT CRITICAL K-EFFECTIVE = 0.9899 STANDARD DEVIATION ABOUT THE MEAN = 0.0019 , l i l 1 h l l 1 3-6
TABLE 3.1.4 h , SIMULATE-1 HOT CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 3 CYCLE 5 ) CYCLE THERMAL POWER CORE FLOW ROD DENSITY ) DATE EXPOSURE (GWD/ST) (MWTH) (MLBM/HR) (% INSERTED) K-EFF 12/02/81 0.743 3283.0 100.0 6.9 0.9925 12/18/81 1.060 3215.0 94.5 6.9 0.9912 12/29/81 1.289 3285.0 96.6 5.1 0.9907 01/22/82 1.802 3286.0 100.1 5.4 0.9908 02/05/82 2.083 3280.0 101.8 6.3 0.9900 02/19/82 2.302 3281.0 100.4 6.3 0.9899 02/25/82 2.430 3277.0 100.0 6.3 0.9914 03/05/82 2.601 3290.0 99.6 6.3 0.9904 03/19/82 2.894 3289.0 100.5 6.6 0.9908 04/15/82 3.232 3283.0 98.8 7.2 0.9915 04/19/82 3.317 3287.0 98.5 7.2 0.9901 05/05/82 3.659 3297.0 98.7 7.2 0.9910 05/17/82 3.915 3287.0 98.4 7.2 0.9925 06/04/82 4.215 3275.0 100.7 9.1 0.9913 06/30/82 4.763 3262.0 102.1 9.0 0.9935 ; 07/13/82 5.037 3225.0 102.0 9.0 0.9925 07/23/82 5.246 3205.0 102.0 9.0 0.9929
) 08/03/82 5.465 3255.0 102.0 6.1 0.9943 j 08/10/82 5.613 3291.0 100.7 5.9 0.9930 .
08/26/82 5.951 3262.0 102.1 5.9 0.9936 l 09/16/82 6.409 3149.0 102.2 5.9 0.9953 i 10/07/82 6.819 3196.0 102.2 3.9 0.9959 l 10/26/82 7.207 3204.0 102.2 1.9 0.9981 l 11/12/82 7.546 3062.0 102.5 1.9 0.9969 11/22/82 7.752 3187.0 105.1 1.4 0.9965 1 1 12/09/82 8.098 3085.0 107.6 1.4 0.9986 12/30/82 8.498 2916.0 108.5 1.4 0.9968
) 01/17/83 8.827 2742.0 109.7 1.4 0.996G 1 02/13/83 9.259 2539.0 110.1 1.4 0.9962 CYCLE MEAN HOT CRITICAL K-EFFECTIVE = 0.9933 STANDARD DEVIATION ABOUT THE MEAN = 0.0027 l
l l i 3-7 I
TABLE 3.1.5 SIMULATE HOT CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 3 CYCLE 6 CYCLE THERMAL CORE ROD DATE EXPOSURE POWER FLOW DENSITY K-EFF (GWD/ST) (MWTH) (MLBM/ER) (% INSERTED) SIM-E SIM-1 10/26/83 0.162 2942.0 102.5 9.1 0.9951 0.9945 11/01/83 0.273 3169.0 101.8 6.9 0.9959 0.9943 11/09/83 0.438 3229.0 102.2 6.6 0.9973 0.9967 l 12/01/83 0.791 3290.0 98.9 5.2 0.9972 0.9960 12/16/83 1.109 3186.0 91.1 5.2 0.9967 0.9964 01/04/84 1.464 3289.0 100.9 5.8 0.9960 0.9957 01/14/84 1.676 3265.0 98.6 5.8 0.9960 0.9950 02/02/84 1.795 3265.0 101.0 7.0 0.9953 0.9951 02/09/84 1.943 3282.0 96.2 7.0 0.9943 0.9935 02/18/84 2.081 3290.0 100.0 7.0 0.9953 0.9950 02/28/84 2.295 3276.0 99.4 7.0 0.9966 0.9954 03/23/84 2.796 3272.0 102.5 9.0 0.9955 0.9952 03/30/84 2.946 3286.0 99.9 9.1 0.9955 0.9943 04/09/84 3.160 3292.0 99.3 9.1 0.9958 0.9946 04/16/84 3.310 3285.0 98.5 9.1 0.9958 0.9948 04/26/84 3.520 3208.0 97.0 9.9 0.9952 0.9952 04/30/84 3.605 3285.0 99.8 9.9 0.9953 0.9942 05/21/84 4.053 3282.0 98.1 9.9 0.9956 0.9947 05/31/84 4.251 3032.0 82.6 10.0 0.9949 0.9955 07/05/84 4.544 3266.0 96.0 10.3 0.9954 0.9954 07/09/84 4.627 3286.0 98.0 10.0 0.9959 0.9950 08/08/84 5.175 3288.0 100.2 10.0 0.9968 0.9957 08/14/84 5.303 3288.0 101.0 10.0 0.9970 0.9971 08/20/84 5.430 3292.0 101.1 10.0 0.9968 0.9958 09/06/84 5.712 3287.0 101.1 9.6 0.9964 0.9954 09/13/84 5.862 3290.0 101.8 9.6 0.9963 0.9952 09/21/84 6.031 3229.0 102.0 9.6 0.9970 0.9971 09/27/84 6.157 3220.0 102.3 9.6 0.9970 0.9958 10/]S/84 6.512 3155.0 96.4 7.4 0.9968 0.9965 10/25/84 6.714 3153.0 99.2 7.4 0.9971 0.9963 11/26/84 7.073 2595.0 65.0 7.4 0.9937 0.9958 12/10/84 7.319 2802.0 83.4 7.4 0.9958 0.9967 12/28/84 7.606 2794.0 78.0 4.3 0.9966 0.9973 01/22/85 8.059 2912.0 93.6 4.1 0.9975 0.9977 01/31/85 8.217 2944.0 97.8 3.8 0.9983 0.9980 03/05/85 8.291 2955.0 99.4 3.9 0.9975 0.9980 04/08/85 8.937 2950.0 108.9 0.4 0.9993 0.9981 05/06/85 9.461 2867.0 109.4 0.0 0.9992 0.9977 05/23/85 9.767 2715.0 109.0 0.0 0.9992 0.9998 05/30/85 9.883 2666.0 110.0 0.0 1.0031 0.9981 07/12/85 10.55 2334.0 112.0 0.0 1.0012 0.9994 CYCLE MEAN HOT CRITICAL K-EFFECTIVE = 0.9967 0.9960 STANDARD DEVIATION ABOUT THE MEAN = 0.0018 0.0015 3-8
FIGURE 3.1.1 SIMULATE-E HOT CRmCAL K-EFFECTIVE AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 2 CYCLE 5 1.005 . . . . u3 . . . . . . .
;> 1.000- - - - - - . - - - - - - - - - - - - - - - - . - - - - - - - . - - - - - - - . - - - - - . - - - - - . - - - - - - - - - - - - . - - - - - - - - - -
F- . . . . . . O . . uy . . Lu . . . . . . . . w . W 0.995- - - - - - - . - - - - - - . - - - - - - - . - - - - - - ~ ~ - - - - - " - -
- ~-
w 1 . . . . . w s x . : , g .
<f -
(y . . . . 0 . 9 a. n . . . . . . . . F-CC - () p_ . C) - - - - -
;c 0.985- ---- ----- --- .--------. - --- .--c- - - - . - - - - - - - . - - - - - - - - - - - - - . - - - - - - - - = - - - - . - - - - -
t \ l 0.980 i i $ l i i i i i i 0 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD ST) 1
- r. . < -x_ r --- '
FIGURE 3.1.2 SIMULATE-E HOT CRITICAL K-EFFECTIVE AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 2 CYCLE 6 1.005 . y . . . . . . . 1.000- -- ----.- ------------ . - - ----------.------- ---- - I--- . . . . . . . . O . . . w 1.a : : : . . : : : g . . . W 0.995- - - - - - -- - -- -- -
, I . . . . .
, y .
( . y o a . 4 . o 0.990- - - - - - - . H 1 . g . g . . g . . . . o 0.985-3 . 4 . . . . . . 0.980 i i i i i e i i i i 0 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD ST) 1 ' e _ - . _ - - _ - . - _ - . - . . _ _ _ _ - _ . _ _ _ _ - - - -___ _ - - _u- ____ - - _ - - - _ - - - _ _ _ - _ . - . - _ _ _ - - . . - -
- - - - - . . - - - - - ~ w FIGURE 3.1.3 SIMULATE-1 HOT CRITICAL K-EFFECTIVE AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 4 1.005 .
LJ - - - -
;> 1.000- -----.---.--- . ---.--------.----------.--- .
F- . . . . . O . . . . LJ -
- a. . . . . .
g . . . 0.995- - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - .- - - .-- ------------- ---- - h1 . . g . . . sa . . . . . . y o.. . y . .
~ g . .
4 . . o
- 0.990-
- - - - - - rs : -
- - - - - '- - : - - - - - - - - - - - - - :---- U.-----:------.-------
F-g; . O . V - F- - - C)
;c 0.985- - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - -
0.980 $ i 6 i i i i i i i 0 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD ST) ' - - - - _ - - - _ m____-. . _ _ _ . . _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _
- - - - - , c- w FIGURE 3.1.4 SIMULATE-1 HOT CRITICAL K-EFFECTIVE AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 5 1.005 . . . . .
LJ - - - - - - - -
;> 1.000- - - - - - . - - - - -------.-------------.-----------.---
1-- . . . . . . . . O . . . . . . w
- m. .
- u. . . . . . . .
g . . . . w w o,995 ................................... ................ ...................................... u y . . i
. \
s . . . _J .
. r7 . . .
<x .
o
- 0.990-
.. s s
--. -- --- .~-
-- .--- - - .~- -----
cc . . () p_ . c) . . . . . . . . 3c 0.985- -----. ------ .------ -.-- - ---------- .--- ----- ------------- --- --- ----- - -------- 0.980- i i i i i i i , i i 0 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD ST)
- _-a
l i a i FIGURE 3.1.5 SIMULATE-E HOT CRITICAL K-EFFECTIVE AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 6 1.005 . 4 y . . . . . . . . . . y 1.000- -------.-----------.---------------.-----.---------------------,,-J--------
- v0:
F- . . . . . . . . o . LJ . . . . u_ . ou - - w w o.995- ...;. ... .... .....
- I : : : :
6a M . . . . J -
<t . .
ty . -
- 0.990- -------------:--------- .----------:---
F-g . O . F- : : O 0.985-I : : 0.980 , , i i i e i i i i O 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD/ST)
FIGURE 3.1.6 HOT CRITICAL K-EFFECTIVE VS. TOTAL RF ACTOR EXPOSURE PEACH BOTTOM UNIT 2 SIMULATE-E 1.005 . . . . . . . g . . . . . . . . y 1.000- - - - - - - . - - - - - - - - - -
~--- -
F-- . . . . . O . y . L . . . . . . u_ - - - - W O.995- ------ :------ - :----- - w g s . .
- a. ] . . .
s
- x .-
.a o 0.990-
.t 1--- . . . . . . . . x . . . . . . o : I- : : o 0.985-
.---------- ----- .-------- ~.~-- --- ---- ----
y .
=
- CYCLE. 5
= = CYC. LE 6 =
0.980- , i , , , , i e i j 30 32 34 36 38 40 42 44 46 48 50 TOTAL REACTOR EXPOSURE (GWD/ST) 4 _ _ _ _ _ _ . _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ..m
FIGURE 3.1.7 HOT CRITICAL K-EFFECTIVE VS. TOTAL REACTOR EXPOSURE PEACH BOTTOM UNIT 3 SIMULATE-E & SIMULATE-1 1.005 . . . . . . y . . . . . . . . .
;> 1.000- -----.--- -.-----.----- .-- - . . . .
----.----- ~. ----.----- .------
F- . . . . . . O . w 7 y . v .- u_ T. A g . . . . . k-W 0.995- -- --.--- -~------- - l---
-------.o ------ h I
sa i y
- o. sj .
O. .
~
g . e, N
,. - . n ry -
Q . s ., ,, . . . G..--- s-0.990- --
- - 6 n - - - - -- ~
. ." ---~. ~-- .--
--- .- - - ~. ------ -- ---- --- ---
~.
Of - - g . F- - C) - - - - - - - I 0.985- ----- ------ - -- ----- ~---- Ci. CLEi 4 .
.=
-= -----iCYCl E 5!- - - =-
- ---= C Y C L.E 6 ~ .
=.
.i . ,
0.980 , , ; i i i i i i i i , i ; i 1 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 TOTAL REACTOR EXPOSURE (GWD/ST)
- ~ .- - _. _.
FIGURE 3.1.8 HOT CRITICAL K-EFFECTIVE VS. CYCLE EXPOSURE PEACH BOTTOM 2 CYCLE 6 SIMULATE-E & SIMULATE-1 1.005 . . w : LJ -
.d&-'---:--------------
> 1.000- -- - - - - -
? en3 :
- m F i . .
F- . 7 () . .
. 2 A n. em.3 .
fg~ w . . .
'I La_ : . . . .
w g '
- W 0.995- ,- -- - :-- - '----h-
,b'---------.--.------
w , -s
. w . . .
, l . e': . . . . h,4.G . E -{ 3.88s S /j] v - Y M : : 5 EI. J . . u . .
<g . .
tj f--- 0.990- ---- or . . . . c) . . . p_ . . . (y 0.985- - ---
-b----- ----- :.--- --- ;-- -- :.---- - .------ :.-----
2 - :- - - 3 . l . j i i ; O PB2C6 (SIM-E) i i i i : i - E PB2C6 (SIM--1),_ 0.980 , , , i i , , , , i O 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD/ST)
FIGURE 3.1.9 HOT CRITICAL K-EFFECTIVE VS. CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 6 SIMULATE-E & SIMULATE-1 1.005 . . . . . . . . y . . . . . . . . . . y 1.000- ----.-----.------.--------*------.-------.------.-----------------,--ry.---.G----
. i .,
H . y. O . . _ S. . w u_
. R- ..
u_ S* *
;, S - -
W w 0.995- J :-@--- &:S m l
? = ~ e.p
- g - -(.,;,
u, , 3 y . .
*s .
w a .
<f -
ty . . . . . . . 0.990- --------:---------------:----------------------------:------------:------- F D: . . . . . . . .- . O . F- : : : . . : C) - - - - - - - - 7 0.985- -------.-------------------------------.--------------------
- i O PB3C6 (SIM-E)
- i i .
i i
. . G PB_ _3C_6 S!M_ _ _1)_
0.980 i i i i e i i i i 3 0 1 2 3 4 5 6 7 8 9 10 11 CYCLE EXPOSURE (GWD/ST)
3.2 Prediction of Cold Startup Reactor Criticals As in the case of the hot model, predictions of 31 recent Peach Bottom startup criticals were used to qualify PECo's cold physics methods. These xenon-free insequence criticals, as summarized in Tables 3.2.1 through 3.2.5, represent a wide range of exposure and moderator temperature conditions for Peach Bottom 2 Cycles 5 and 6 and Peach Bottom 3 Cycles 4, 5, and 6, respectively. It should be noted that predicted cold K-effectives reflect dependencies on exposure history, void history, control blades, and moderator temperature. PECo's SIMULATE cold model accounts for these effects i via an explicit cross section representation, where cross sections were developed with appropriate CASMO-1 branch calculations. Eigenvalues were corrected downward by hand (typically by less than 0.0006AK) to account for slightly positive reactor periods as recorded during the startups. Corrected K-effectives for the five cycles analyzed are plotted in Figures 3.2.1 through 3.2.5. Multi-cycle K-effective trend plots for Units 2 and 3 are displayed in Figures 3.2.6 i and 3.2.7. j 1 Pooling of period corrected eigenvalue predictions 4 yields a mean SIMULATE cold critical K-effective of l 0.9916 with a standard deviation of 0.00356K. As in the case of the hot model, this standard deviation drops (to 0.0013 AK) when individual predictions are l l i 3-18 l
l f referenced to the average K-effective of their respective cycles. These uncertainties are small, and serve to verify SIMULATE'S overall consistency in calculating cold reactor criticality. l l Comparisons between cold critical K-effective predictions as generated by SIMULATE-E and SIMULATE-1 l for Peach Bottom 2 Cycle 6 and Peach Bottom 3 Cycle 6 once again served to demonstrate the high degree of consistency between the two program versions. The RMS difference between eigenvclue solutions for the 18 statepoints was less than 0.03%AK. Comparisons of the results from both code versions are displayed graphically in Figures 3.2.8 and 3.2.9. Philadelphia Electric will continue to monitor both ' hot and cold critical eigenvalue biases and uncertainties to assure the applicability of PECo steady-state methods to design and licensing i calculations. I I 1 3-19
l l TABLE 3.2.1 SI.MULATE-E COLD CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 2 CYCLE 5 l CYCLE MODERATOR REACTOR PERIOD DATE EXPOSURE TEMPERATURE PERIOD UNCORRECTED CORRECTED (GWD/ST) (DEG. F) (SEC) K-EFF K-EFF 06/09/81 4.860 158 90 0.9895 0.9889 06/20/81 4.861 195 100 0.9893 0.9888 CYCLE MEAN COLD CRITICAL K-EFFECTIVE = 0.9889 STANDARD DEVIATION ABOUT THE MEAN = 0.0001 i 3-20 i
l l ! TABLE 3.2.2 l SIMULATE COLD CRITICAL CORE K-EFFECTIVE PREDICTIONS 1 PEACH BOTTOM 2 CYCLE 6 ; 1 CYCLE MODERATOR REACTOR UNCORRECTED PERIOD CORRECTED DATE EXPOSURE TEMPERATURE PERIOD K-EFF K-EFF (CWD/ST) (DEG. F) (SEC) SIM-E SIM-1 SIM-E SIM-1 06/25/82 0.000 150 185 0.9950 0.9947 0.9947 0.9944 08/12/82 0.681 205 150 0.~9 9 5 6 0.9959 0.9952 0.9955 10/26/82 2.096 205 100 0.9930 0.9928 0.9924 0.9923 12/13/82 2.997 210 80 0.9933 0.9931 0.9926 0.9925 12/16/82 2.997 215 100 0.9926 0.9920 0.9921 0.9915 05/08/83 5.629 213 100 0.9940 0.9938 0.9935 0.9933 ! 05/28/83 5.843 200 125 0.9929 0.9928 0.9925 0.9923 12/01/83 6.589 159 200 0.9943 0.9943 0.9940 0.9940 i CYCLE MEAN COLD CRITICAL K-EFFECTIVE = 0.9934 0.9929 STANDARD DEVIATION ABOUT THE MEAN = 0.0012 0.0010 l l l 3-21 l
l t l TABLE 3.2.3 SIMULATE-1 COLD CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 3 CYCLE 4 CYCLE MODERATOR REACTOR PERIOD DATE EXPOSURE TEMPERATURE PERIOD UNCORRECTED CORRECTED (GWD/ST) (DEG. F) (SEC) K-EFF K-EFF 11/05/79 0.000 165 60 0.9884 0.9875 01/14/80 1.056 210 100 0.9895 0.9888 02/04/80 1.287 190 200 0.9876 0.9873 02/06/80 1.287 161 100 0.9878 0.9871 f 05/13/80 2.879 155 40 0.9862 0.9851 06/03/80 3.028 212 100 0.9856 0.9850 10/29/80 5.787 202 100 0.9862 0.9857 12/22/80 6.797 220 80 0.9881 0.9875 CYCLE MEAN COLD CRITICAL K-EFFECTIVE = 0.9868 STANDARD DEVIATION ABOUT THE MEAN = 0.0013 I 3-22 i
TABLE 3.2.4 1 ; c SIMULATE-1 COLD CRITICAL CORE K-EFFECTIVE PREDICTIONS PEACH BOTTOM 3 CYCLE 5 CYCLE MODERATOR REACTOR PERIOD DATE EXPOSURE TEMPERATURE PERIOD UNCORRECTED CORRECTED j (GWD/ST) (DEG. F) (SEC) K-EFF K-EFF c.t 10/02/81 0.000 160 100 0.9940 0.9935 02/08/82 2.084 200 100 0.9933 0.9928 04/08/82 3.117 170 200 0.9903 0.9900 CYCLE MEAN COLD CRITICAL K-EFFECTIVE = 0.9921 l i STANDARD DEVIATION ABOUT THE MEAN - = 0.0019 I I l i I i i
, l 3-23 t
1 l l i l l l TABLE 3.2.5 SIMULATE COLD CRITICAL CORE K-EFFECTIVE PREDICTIONS l I PEACH BOTTOM 3 CYCLE 6 l CYCLE MODERATOR REACTOR UNCORRECTED PERIOD CORRECTED DATE EXPOSURE TEMPERATURE PERIOD K-EFF K-EFF l (GWD/ST) (DEG. F) (SEC) SIM-E SIM-1 SIM-E SIM-1 09/03/83 0.000 140 163 0.9976 0.9973 0.9972 0.9969 09/23/83 0.000 142 100 0.9966 0.9963 0.9960 0.9958 10/02/83 0.000 166 100 0.9965 0.9962 0.9959 0.9957 10/12/83 0.000 178 100 0.9968 0.9964 0.9962 0.9959 01/24/84 1.676 214 100 0.9956 0.9954 0.9951 0.9949 06/20/84 4.271 192 100 0.9943 0.9941 0.9937 0.9936 11/12/84 6.874 208 100 0.9931 0.9929 0.9925 0.9924
)
02/25/85 8.231 170 100 0.9934 0.9934 0.9929 0.9929 02/26/85 8.231 180 100 0.9938 0.9938 0.9933 0.9933 02/28/85 8.231 160 100 0.9949 0.9950 0.9944 0.9944 i CYCLE MEAN COLD CRITICAL K-EPPECTIVE = 0.9947 0.9946 STANDARD DEVIATION ABOUT THE MEAN = 0.0016 0.0015 I i 3-24 1 l
t FIGURE 3.2.1 SIMULATE-E PERIOD CORRECTED COLD CRITICAL K-EFF AS A FUNCTION OF CYCLE EXPOSURE ' PEACH BOTTOM 2 CYCLE 5 L_ 1.005 . . . . . . . . . L_ . . . . . . . . W . l . . M . J . . . . . . . . .
< 1.000- - - - - - - - ~ . - - - - - - - - - - - . - - .- - - - - - - - - . - - - - - - - . - - - - - - - .. - - - - - - - - .. - - - - - - . -. - - - - - - . - .- - - - - - - -
O . . . . p m . . . . . . . O . O 0.995- - - J . . . . . . . . . w g on O . Q . . . . . . W . . . . . p D.990- - - - - - . - - - - - - . - - - - - - - . - - - - - - - - . - - - - - - - - . - - - - - - - . - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - A. O . . . . W . E . E, L O 0.985- - - - Q . o m . w . . . . . . .i O_ O.980 i i i i i i i i 4 5 7 8 0 1 2 3 4 6 9 10 CYCLE EXPOSURE (GWD ST) l 1 l
FIGURE 3.2.2 SNULATE-E PERIOD CORRECTED COLD CRITICAL K-EFF AS A FLNCTION OF CYCLE EXPOSURE PEACH BOTTOM 2 CYCLE 6 L- 1.005
- u. . . . . . . . . .
W . l . . M . J . . . . . . . . . 4 1.000- -- ----. - --.~ --- -- . - -----.-------- .------ - .-- -- --.--- -----~- ------ -------- . O p._ . . m . O . . w O 0.995I - i J . O . . . . . . .
- u. . . .
O . u Q . . Wp._ 0.990- - - - .--- --- -.---- ------------.- -- --- .-- O . . . . . . . . . W . . . . . . . . T . . T . O . . . . . . . . . O 0.985- - -- - -. --------~- ----- .-- -----.--- --------------.--------.-- -----.-------- .---- --- Q . \ O x . W . O_ 0.980 , . . . . . . i , 0 1 2 3 4 5 6 7 8 9 10 l CYCLE EXPOSURE (GWD ST)
FIGURE 3.2.3 SIMULATE-1 PERIOD CORRECTED COLD CRmCAL K-EFF AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 4 L 1.005 . . . . . . . . . u_- . . . . . . . . . w . l . . . . . . . . . M . J . . . . . . . . .
< 1.000- - - - - -
o , p x . O . O 0.995- - - - - . - - - - - - - - - - - - - - - - - - - - - - - . - - - g g .
. O .
u y o . Q W 0.990- - - - - - - . p . o . . w . x . . , x . O . . . . . - . . .
. . .s <. . . .
o 0.985- --------------:---- u Q . . . O x . w . O 0.980 . . . . . . . . . 0 1 2 3 4 5 6 7 8 9 10 CYCLE EXPOSURE (GWD ST)
FIGURE 3.2.4 SIMULATE-1 PERIOD CORRECTED COLD CRITICAL K-EFF AS A FUNCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 5 L- 1.005 . . . . . u_ g . I . . . . . . . . . Y .
._J . . . . . . . . .
< 1.000- - - - - . - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - -. - - - * - . - - - - - - ~ ~ . - - - - - - - - - - - - - - - - - - - - - - - - -
O p m . O . . . . . . . . . O 0.995- - - - - - - - . - - - . - - - - - - - - - - - - - - . - - - - - - . - - - * - - - . - - - - - - - . * - - w g , , y V . _ O . O . . W 0.990-p . . . . O W . E . T . O . o 0.985- - - - - - - - - . - - - - - - - - - - - - - - - - ..- - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - -.- - - - - - - - Q . . . . . . . o m . w . O_ O.980 4 4 , 4 6 . . . . 0 1 2 3 4 5 6 7 8 9 10 CYCLE EXPOSURE (GWD ST)
FIGURE 3.2.5 SIMULATE-E PERIOD CORRECTED COLD CRITICAL K-EFF AS A FLHCTION OF CYCLE EXPOSURE PEACH BOTTOM 3 CYCLE 6 L. 1.005 . . . . . . . . .
- u. . . . . . . . . .
w . l . . . . . . . . . x . 4 1.000- - - - - - - - . - - - - - - - . -. - - - - - - - - -. - - - - - - - . -. - - - - - - . - .- - - - - - - - -.. - - - - - - - - .. - - - - - - - . .- - - - - - - - -.- - - - - - - - O p x ( .y . O . t . w 099%- O .------.------.-------.---------*--.-------O
. u g .
- O -
. ~. .
~
~
" O, .
O .
. . . . . . y. . .
O . . . . . . . . . W D.990-p . . . . . . . O . . . . . . . . . w . x . x . O . . . . . . . . . O 0.985- --- ----.- O . o x . w .
- a. 0.980 i i i 6 . 6 i , 6 0 1 2 3 4 5 6 7 8 9 10 CYCLE EXPOSURE (GWD ST)
~ - __
FIGURE 3.2.6 PERIOD CORRECTED COLD CRITICAL K-EFF VS. CYCLE EXPOSURE PEACH BOTTOM UNIT 2 SNULATE-E 1.005 . . . . . . . . . L . . . . . . . . . u_ . . . . . . . . w . l . . y . J 1.000- --------.- ------.------- --- -----.------- . - - - - - - - - . - - - - - - - - - . - - - - - - - - . ~ - - - - - - -. - - - - - - - - g W_ g . o . C3 0.995- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -~-- - -- ------- -
1 . . w . . . . O . . . . . . . . i g O . o . . . . . . . . . O : : : : : : : : . g . . . . . . . H 0990- - - - - - . - - - * - - - ~ - - - - - - - - - - - - - - - . - ~ ~ ~ ~ - - ' *.------- ----- O : : A: : : : : . y . . . . . . . . . o- . . x . O . . U . . . . . . . . 0.985- -----------------.------------------------- .----------- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - o =
- CYCLE. 5 =
=. CYC. LE 6 .=
O x . 1 w n_ . . . . . . . . . 0.980 , 3 , , , i 3 , , 30 32 34 36 38 40 42 44 46 48 50 TOTAL REACTOR EXPOSURE (GWD ST)
_ _ ,_ m .. x FIGURE 3.2.7 PERIOD CORRECTED COLD CRmCAL K-EFF VS. CYCLE EXPOSURE PEACH BOTTOM UNIT 3 SNULATE-E & SNULATE-1 1.005 . . . . . . . . . . . . . L. . . . . . . . . . . . . u_ . LJ . l . bd . l
. . . . . . . . . . . . . . 1
-I g,090 .............. ...-.........
....... ~. .... . ............
. ...... . ............................ 1
_cy . . . . . . . . . . F- . . . . . . . . . . . . O x . (y . C3 0.995- - ---.----- --~ ~--------- - - - - ~ ~ - - - ' ~ - - ' ' - -
---- - - - ~ - - - - - - - - - - - - - -
J . . . . . . . . . . .. . w . O . . . . . . . . . . . . O w . v . . . . . . . . . . . Q . . y ,
.- a.990- ~ ~ ~ . ~ ~ . - ~ ~ ~ ~ ~ - - - - ~ ~.~-~J-'~.'-~.~~-~- - ~ ~ .-- ~ .-- -- . -- ~ .~ ~ ~ ~. ~ ~
cy . . . . . u3 . oc . K , . . . . . . . . . . . . O . . . . . . . . . . . U . . . . . . . 0.985- - - : - '.. - ~ .- ~ ~ : - ~ : ~ ~ : ~ ~ - - - - ~ .~ - ~ ~ - ---- :--- -~---~.~--~ :--- :-~-- O O . CY. CLE: 4
.=
=.
.: CYCL. E 5.:
=- =
C. YCL.E 6
=.
1 g . y . . 1 . . . . . . . . . . . . 0.980 3 4 , , i i 4 3 i , , , , , 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 TOTAL REACTOR EXPOSURE (GWD ST)
.. - - - - - . - , - . .. . , ,-- , , - - , c-FIGURE 3.2.8 PERIOD CORRECTED COLD CRITICAL K-EFF VS. CYCLE EXPOSURE PEACH BOTTOM 2 CYCLE 6 SNULATE-E & SNULATE-1 L. 1.005 . . . . . . . . .
LL . . . . . . . . g . l . . . M _J . . . . . . . . .
<t 1.000- - - - - - - - . - - - - - - - - - - -
. ---.------.--------.--------.------~.~------.-------
O . . . . . . . p- . . . . . x . O . . . . w ..........-...........................-...........................~..................
, O o.995[ .
, g .
u O . . . . O . . w-- W Q W 0.990- -- -
.- - - .--- --- -.---------~.-- ---- - --
-. --------~--
p . . . . . O . . . . . . . . . W . 2 . K . . . . . . . O . . . . . . . . O 0.985- --- --------- -- -~ --- - ---------- -------- 5---- o . . . . . m i i i ! i w . . . . .
. a PB_2C6 SIM_ _ _1).
O_ 0.980 , , i i i , , i i 0 1 2 3 4 5 6 7 8 9 10 CYCLE EXPOSURE (GWD ST)
- - - - -. - .. -- -~
FIGURE 3.2.9 PERIOD CORRECTED COLD CRITICAL K-EFF VS. CYCLE EXPOSURE , PEACH BOTTOM 3 CYCLE 6 SNULATE-E & SNULATE-1 L. 1.005 Lu . : : : : : : : : g . l . . M _1 . . . . . . . . . 4 1.000- ---- -- . ------ .- ------- ----
. .---- - - .- -- - .- --- -. ---- -- .~-- -- .
O . . . . . . . .
- p._- . . . . . .
g ( .n a O . .
~~_ . . . . . . . .
s,o O 0.995- -- - -.=. ' ~ _-.------- -- ---.-----
. -- ----- -- .- --- --. - --- - .~-
.G --- - .-- -- --
g . . g O O O
- w %.
_ a. - O : . : : : : : : W 0.990-
--- - --.--------~~.~--- ---. -------.------ -~. -------- -- -- -.---- ----~------- --------'
. .~
- p. . .
O : . . W . l Z . . . . . . O 0.985- -------------------------:-----------------------:------
-- ^^^^ - ----- -
O o PB3C6 (,SIM-E) O : _O . . .- .- . .- m i i i i i i a PB3C6 bSIM_1 _ 2 w . . . . . . ______ __ CL 0.980 i i i i i i i i i 0 1 2 3 4 5 6 7 8 9 10 CYCLE EXPOSURE (GWD ST)
i I L 3.3 Verification of Margin to Thermal Operating Limits Philadelphia Electric Company. reactor engineers regularly develop control rod patterns and power i / maneuver strategies as required to support the operation l of PECo nuclear units using the SIMULATE based methods , f described in Section 2. The accurate prediction of margin to fuel related Technical Specification operating ( limits is essential to this process, where specific parameters of interest are Critical Power Ratio (CPR), Linear Heat Generation Rate (LHGR), and Average Planar LHGR (APLHGR). This section describes the method by which PECo evaluates thermal limits in the operations support mode. I As stated above, PEco reactor engineers use the SIMULATE program to develop target control rod patterns which optimize power shape, exposure distribution, and margins to thermal operating limits. Once a pattern is ! I actually established and the core is allowed to equilibriate, site reactor engineers initiate the OD-1 and P-1 process computer programs. The primary objectives of OD-1 are to: 1) update the base TIP flux distributions, and 2) update the LPRM calibration constant distribution. Given an updated TIP distribution, the P-1 program perftv'. the power / flow calculation and edits various core performance parameters, including margin to LHGR, CPR, and APLHGR j l operating limits. A SIMULATE calculation is then 3-34 1
L ! r 1 performed based on the exact conditions edited by the , 9 process computer. SIMULATE calculated TIP responses for the case are then statistically compared with the measured flux traces to define the current hot model , bias. Thic bias is ultimately fed back into subsequent SIMULATE predictions to best estimate the process computer thermal margin response. The operating experience embodied in these bias distributions provides an excellent basis for the application of the PECo steady-state model to design and licensing calculations. Qualification of SIMULATE thermal nargin j calculations will be treated in detail in Section S. s
)
1 i 3-35
I I 4.0 QUALIFICATION OP PECo PHYSICS METHODS POR USE IN CORE ; DESIGN AND LICENSING The eigenvalue statistica reported in Section 3 L demonstrate the ability of PEco's steady-state physics methods to reliably predict overall core wide reactivity. These results additionally lend significant credibility [ to PECc methods regarding the determination of individua' reactivity effects and localized phenomena, both of which must be evaluated in the core reload design and licensing process. Section 4 quantifies modeling biases and uncertainties associated with the calculation of assembly j i j integral, nodal, and local pin power distributions, as l well as for discrete Doppler, void, and control rod I reactivities. Brief discussions of uncertainties inherent in the prediction of fuel isotopic compositions I and delayed neutron kinetics parameters are also included. i : 4.1 Fuel Assembly Power Distribution Comparisons t
) The ability to reliably predict assembly integral and nodal power distributions is essential to the BWR reload design process. In this section, measured incore flux traces are statistically compared to SIMULATE predicted reaction rates in order to qualify the PECo power distribution methodology.
t 4-1
l 4.1.1 Measured Data Traversing Incore Probe (TIP) neutron flux traces are periodically generated for the Peach Bottom units as part of the plant process computer (OD-1 Program) Local Power Range Monitor calibration and base TIP distribution update processes. Five independent probes f axially traverse the core at 43 LPRM radial locations (see Figure 4.1.1), generating raw instrument readings which are in turn machine normalized and full power adjusted by OD-1. These values are ultimately collapsed to 48 axial elevations and edited by the process computer for each LPRM string location. Forty-seven (47) steady-state OD-1 statepoints from five recent Peach Bottom cycles were selected for the ! purpose of qualifying the SIMULATE power distribution calculation. Data encompasses all cycle exposures, with , reactor operating conditions ranging from 85% to 100% of rated. OD-1 statepoint summary information is reported
! in Tables 4.1.1 through 4.1.5 for Peach Bottom 2 Cycles 5 and 6 and Peach Bottom 3 Cycles 4, 5, and 6, respectively.
+ 4.1.2 Data Processing
- In order to qualify the OD-1 flux readings, it was l necessary to establish certain data acceptance criteria.
Erroneous or unreliable TIP measurements were omitted l from the statistical database in accordance with the I following guidelines: 4-2
- 1) TIP data corresponding to. the top and bottom 18 inches of the 150 inch active fuel region were t l rejected. Flux gradients at the core boundaries are s
large, tending to make measurements at these f L locations sensitive to small axial misalignments of ' i the sensors, and therefore unreliable. Further, ( t these regions do not represent the core's peak power axial location. and are consequently not relevant to [ j the evaluation of margin to thermal operating limits (e.g., LUGR and MAPLBGR). i Elimination of TIP readings corresponding to the too i and bottom 18 inches of the active core reduces the ' number of axial locations evaluated in the , I statistical analyses from 48 to 38, as shown in j Figure 4.1.2. ) 2) Integrated neutron flux readings for each TIP trace b were compared with values from diagonally symmetric l ; i locations where symmetric TIP string locations are l defined in Figure 4.1.1. If the absolute difference in integrated flux for symmetrically located TIPS I was demonstrated to be greater than 9%, both TIP traces were considered to be unreliable, and were consequently eliminated from the statistical database. This 9% difference criterion is based on j I inherent to the the measurement uncertainties l neutron TIP detector system as described in l Reference 14. ; i 4-3
[ SIMULATE 24 node calculated detector responses were expanded to 48 axial levels by the SIGMA-PECo program' to achieve compatibility with the measured data. Calculated [ 5 readings corresponding to rejected measured data were necessarily omitted from the statistical analyses. . Measured versus predicted core average TIP trace distributions for the 47 OD-l's analyzed are plotted in Figures 4.1.3 through 4.1.49. Additionally, individual
)
string comparison plots for one representative j beginning-of-cycle (BOC), middle-of-cycle (MOC), and end-of-cycle (EOC) statepoint from each cycle have been l included in Figures 4.1.50 to 4.1.64. Blank panels indicate statistically rejected measured TIP data.
)
l I l 4 i 4-4
4.1.3 Statistical _ Analyses OD-1 measured TIP data is routinely compared to calculated incore flux traces by PECo reactor engineers in order to monitor the SIMULATE model's predictive capabilities. Differences between measured and predicted readings are subsequently analyzed statistically to quantify modeling biases and uncertainties. These biases are then applied to later SIMULATE calculations to allow the reactor engineer to most accurately predict margin to thermal operating limits. In order to maintain consistency with this practice, the same approach was applied to the qualification of the SIMULATE power l distribution methodology. Average SIMULATE modeling I biases as determined for the Beginning of Cycle, Middle A of Cycle, and End of Cycle exposure ranges were applied to the raw SIMULATE calculated powar distributions. The , resulting bias adjusted OD-1 flux distributions were then statistically compared to measured TIP readings. Tables 4.1.6 through 4.1.10 aummarize the statistical analyses performed for the 47 individual 0D-1 statepoints described in Tables 4.1.1 to 4.1.5. Results have been broken out into pointwise nodal and integral statistics. 4-5
Pointwise Difference Statistics refer to the comparison of predicted and measured neutron flux readings at each TIP location. Thus. the nodal RMS l difference is the root of the mean of the squarer. of the ( reaction rate differences at all TIP coordinate locations (1,K):
~ ~
1/2 . N KMAX K K NODAL RMS (%) = 100.0* [I=1 K=1 [ (Txi - TC l)2 , ((N*KMAX) - 1)
)
K l j Where Tg1 = Measured TIP reading for string i at axial IcVel K, normalized to the i 3 statepoint core average. i K TiC = Calculated TIP reading for string i at 1 axial level K, normalized to the ! i i statepoint core average. i KMAX = Number of axial nodes per TIP string used in the statistical comparison. N = Number of TIP strings used in the statistical comparison ! (43 if no strings are rejected). i 4-6 i
The Integral RMS difference is a similar statistic, reflecting differences in axially integrated predicted and measured reaction rates at all TIP coordinate locations (i):
- ~
1/2 N (YMi - ECi) INTEGRAL RMS (%) = 100.0* [1 i= i (N-1) l Where Tgi = Axial average of all relative measured values for TIP string i 1 KMAX K J (T_Mi = KMAX [ K=1 Ti M ) TiC = Axial average of all relative calculated values for TIP string i L 1 KMAX g (T_Ci = KMAX K=1 [ Ti C ) Overall difference statistics are thus based on the five cycles of Peach Bottom to-1 data. Overall nodal and integral pointwise RMS differences were demonstrated in this manner to be 6.9% and 4.1%, respectively. These results are consistent with values reported elsewhere in the industry and serve to qualify Philadelphia Electric Company's power distribution calculation methods. 4-7
l TABLE 4.1.1 PEACH BOTTOM UNIT 2 CYCLE 5 00-I STATEPOINT REACTOR CONDITIONS CORE CORE CONTROL STEAM CYCLE THERMAL CORE INLET R00 DOME CORE l EXPOSURE
- POWER FLOW SUBC00 LING DENSITY PRESSURE EXIT SIM-E DATE (GWD/ST) (MWTH) (MLB/HR) (BTU /LBM) (NOTCHES) (PSIA) QUALITY K-EFF 09-05-80 0.365 3132.0 102.40 23.36 518 1019.0 0.1259 0.993435 12-03-80 2.126 3269.0 102.30 23.55 506 1002.0 0.1322 0.991561
,7 m 02-25-81 3.736 3210.0 94.28 25.76 498 1009.0 0.1401 0.992836 07-09-81 5.064 3135.0 100.20 23.69 744 1004.0 0.1285 0.994049 09-02-81 5.967 3265.0 99.94 24.53 430 1008.0 0.1346 0.995410 ! 10-01-81 6.546 3107.0 101.67 23.00 1002.0 454 0.1256 0.995609 12-22-81 8.111 2963.0 107.33 24.70 96 1012.0 0.1078 0.995507 O BOC CORE AVERAGE EXPOSURE = 8.919 GWD
- M
- - v w TABLE 4.1.2 PEACH BOTTOM UNIT 2 CYCLE 6 0D-1 STATEPOINI REACTOR CONDITIONS CORE CORE CONTROL STEAM CYCLE THERMAL CORE INLET R00 DOME CORE EXPOSURE
- POWER FLOW SUBC00 LING DENSITY PRESSURE EXIT SIM-E DATE (GWD/ST) (MWTH) (MLB/HR) (BTU /LBM) (NOTCHES) (PSIA) QUALITY K-EFF 07-14-82 0.195 3226.0 101.70 23.86 550.0 1009.0 0.1307 0.993736 11-09-82 2.363 3287.0 101.37 24.40 570.0 1005.0 0.1334 0.994158 12-28-82 3.235 3290.0 101.18 24.20 718.0 996.0 0.1339 0.994124 05-13-83 5.710 3024.0 102.38 22.57 1118.0 998.0 0.1208 0.995336 06-23-83 6.366 3268.0 97.91 25.44 592.0 1016.0 0.1373 0.998538 12-13-83 6.776 3272.0 101.29 24.27 432.0 1003.0 0.1329 0.999969 :
01-09-84 7.283 3280.0 102.42 24.02 360.0 1001.0 0.1318 1.000620 i 03-02-84 8.114 3286.0 107.00 27.00 128.0 998.0 0.1201 0.999133 03-20-84 8.482 3137.0 108.57 25.25 76.0 997.0 0.1132 0.999259
- BOC CORE AVERAGE EXPOSURE = 9.868 GWD ST
_ __ _ _______._______._-________._____________._______.____._____m__
- - , _ -v- u w TABLE 4.1.3 PEACH BOTTOM UNIT 3 CYCLE 4 00-1 STATEPOINT REACTOR CONDITIONS CORE CORE CONTROL STEAM CYCLE THERMAL CORE INLET R0D DOME CORE EXPOSURE
- POWER FLOW SUBC00 LING DENSITY PRESSURE EXIT SIM-1 DATE (GWD/ST) (ETH) (MLB/HR) (BTU /LBM) (NOTCHES) (PSIA) QUALITY K-EFF 12-21-79 0.607 3277.0 93.30 26.58 672.0 1000.0 0.1441 0.988819
, 01-23-80 1.167 3289.0 95.00 26.10 668.0 997.0 0.1421 0.988573 l s 1 ~ c, 02-27-80 1.734 3288.0 102.10 24.02 680.0 995.0 0.1325 p ';39,674 1 04-16-80 2.520 3277.0 100.31 24.48 750.0 996.0 0.1342 0.989839 06-25-80 3.498 3276.0 95.96 25.76 732.0 1001.0 0.1402 0.990444 08-14-80 4.528 3287.0 103.00 24.29 1168.0 1000.0 0.1307 0.990938 12-16-80 6.780 3284.0 101.40 24.58 640.0 1005.0 0.1330 0.993322 02-06-81 7.771 3219.0 102.50 23.92 418.0 1006.0 0.1288 0.994550
- 80C CORE AVERAGE EXPOSURE = 8.359 GWD ST
- - - w v w TABLE 4.1.4 PEACH BOTTOM UNIT 3 CYCLE 5 00-1 STATEPOINT REACTOR CONDITIONS CORE CORE CONTROL STEAM CYCLE THERMAL CORE INLET R0D DOME CORE .
EXPOSURE
- POWER FLOW SUBC00 LING DENSITY PRESSURE EXIT SIM-E DATE (GWD/ST) (MITH) (MLB/HR) (BTU /LBM) (NOTCHES) (PSIA) QUALITY K-EFF 12-02-81 0.743 3283.0 100,80 24.73 616.0 1009.0 0.1338 0.992500 01-22-82 1.802 3286.0 99.98 24.94 480.0 1011.0 0.1352 0.99194 02-25-82 2.430 3277.0 100.00 24.77 558.0 1008.0 0.1348 0.991369 04-15-82 3.232 3283.0 98.78 25.41 638.0 1004.0 0.1361 0.991466 05-17-82 3.915 3287.0 98.36 25.64 638.0 1003.0 0.1367 0.992495 06-30-82 4.763 3262.0 102.12 24.20 798.0 1002.0 0.1311 0.993500 08-03-82 5.465 3255.0 102.04 24.26 544.0 1003.0 0.1308 0.994342 09-16-82 6.409 3149.0 102.23 23.50 520.0 1000.0 0.1261 0.995305 10-26-82 7.207 3204.0 102.23 23.88 172.0 998.0 0.1283 0.998060-12-09-82 8.098 3085.0 107.59 25.42 120.0 1007.0 0.1121 0.998637
- BOC CORE AVERAGE EXPOSURE = 10.590 GWD/ST
- - - -- w w TABLE 4.1.5 PEACH BOTTOM UNIT 3 CYCLE 6 00-1 STATEPOINT REACTOR CONDITIONS l
l CORE CORE CONTROL STEAM
- CYCLE THERMAL CORE INLET R00 DOME CORE l EXPOSURE
- POWER FLOW SUBC00 LING DENSITY PRESSURE EXIT SIM-E DATE (GWD/ST) (MWTH) (MLB/HR) (BTU /LBM) (NOTCHES) (PSIA) QUALITY K-EFF 10-26-83 0.162 2942.0 102.50 22.00 804.0 993.0 0.1171 0.995141 11-09-83 0.438 3229.0 102.15 23.78 584.0 995.0 0.17a7 0.997309 01-04-84 1.464 3289.0 100.92 24.39 512.0 994.0 0.1339 0.995988 02-02-84 1.795 3265.0 101.00 24.22 624.0 999.0 0.1330 0.995343 02-18-84 2.081 3290.0 100.00 25.30 626.0 993.0 0.1341 0.995268 03-23-84 2.796 3272.0 102.45 23.91 800.0 997.0 0.1313 0.995512 04-26-84 3.520 3208.0 97.00 24.83 882.0 996.0 0.1358 0.995243 l 07-05-84 4.544 3266.0 96.00 25.50 890.0 994.0 0.1397 0.995435 08-14-84 5.303 3288.0 101.00 24.40 890.0 996.0 0.1338 0.99702' 09-21-84 6.031 3229.0 102.00 23.66 852.0 995.0 0.1301 0.956970 12-28-84 7.606 2794.0 78.00 28.82 384.0 998.0 0.1442 0.996516 03-05-85 8.291 2955.0 99.41 22.90 344.0 997.0 0.1212 0.997477 05-23-85 9.767 2715.0 109.00 22.45 0.0 996.0 0.0965 0.999226
- BOC CORE AVERAGE EXPOSURE = 10.001 GWD/ST
TABLE 4.1.6 PEACH BOTTOM UNIT 2 CYCLE 5 OD-1 STATEPOINT SIMULATE-E PREDICTED VS OD-1 MEASUREMENT TIP DIFFERENCE STATISTICS CYCLE CYCLE
- l OD-1 EXPOSURE EXPOSURE POINTWISE DIFFERENCES (%)
DATE GWD/ST RANGE NODAL RMS INTEGRAL RMS 09-05-80 0.365 BOC 6.86 4.97 12-03-80 2.126 MOC 6.52 5.34 02-25-81 3.736 MOC 7.02 5.14 07-09-81 5.064 MOC 6.79 5.53 09-02-81 5.967 EOC 7.98 5.01 10-01-81 6.546 EOC 6.37 4.90 12-22-81 8.111 EOC 5.27 3.82
- CYCLE EXPOSURE RANGES ARE DEFINED AS FOLLOWS:
BOC: 0<E< 2.0 GWD/ST MOC: 2.0 < E < 5.5 GWD/ST EOC: 5.5 < E < 9.1 GWD/ST l. t l l l l 4-13
TABLE 4.1.7 l PEACH BOTTOM UNIT 2 CYCLE'6 OD-1 STATEPOINT SIMULATE-E PREDICTED VS OD-1 MEASUREMENT l TIP DIFFERENCE STATISTICS CYCLE CYCLE
- OD-1 EXPOSURE EXPOSURE POINTWISE DIFFERENCES (%)
DATE GWD/ST RANGE NODAL RMS INTEGRAL RMS 07-14-82 0.195 BOC 6.61 3.61 11-09-82 2.363 MOC 5.05 3.32 12-28-82 3.235 MOC 5.44 3.76 05-13-83 5.710 EOC 8.24 3.90 06-23-83 6.366 EOC 8.05 4.23 12-13-83 6.776 'EOC 8.38 4.10 l 01-09-84 7.283 EOC 8.05 4.38 02-84 8.114 EOC 6.48 3.97 1 03-20-84 8.482 EOC 6.23 3.95 i i
- CYCLE EXPOSURE RANGES ARE DEFINED AS FOLLOWS: j BOC: 0<E<_ 2.0 GWD/ST MOC: 2.0 < E < 5.5 GWD/ST EOC: 5.5 < E < 9.2 GWD/ST 4-14
I TABLE 4.1.8 PEACH BOTTOM UNIT 3 CYCLE 4 OD-1 STATEPOINT SIMULATE-1 PREDICTED VS OD-1 MEASUREMENT TIP DIFFERENCE STATISTICS CYCLE CYCLE
- OD-1 EXPOSURE EXPOSURE POINTWISE DIFFERENCES (%)
DATE GWD/ST RANGE NODAL RMS INTEGRAL RMS 12-21-79 0.607 BOC 4.56 3.15 01-23-80 1.167 BOC 4.97 3.21 02-27-80 1.734 BOC 5.75 3.26 { 04-16-80 2.520 MOC 5.60 4.07 1 06-25-80 3.498 MOC 0.01 4.35 08-14-80 4.528 MOC 5.66 3.87 12-16-80 6.780 EOC 5.52 3.65 02-06-81 7.771 EOC 6.18 4.32
- CYCLE EXPOSURE RANGES ARE DE?INED AS FOLLOWS:
( BOC: 0<E< 2.0 GWD/ST MOC: 2.0 < E <_ 5.5 GWD/ST EOC: 5.5 < E <_ 8.3 GWD/ST l 4-15
h TABLE 4.1.9 l PEACH BOTTOM UNIT 3 CYCLE 5 OD-1 STATEPOINT SIMULATE-E PREDICTED VS OD-1 MEASUREMENT TIP DIFFERENCE STATISTICS 4 CYCLE CYCLE
- OD-1 EXPOSURE EXPOSURE POINTWISE DIFFEREN6ES (%)
DATE GWD/ST RANGE NODAL RMS INTEGRAL RMS 12-02-81 0.743 BOC 5.34 3.82 01-22-82 1.802 BOC 5.02 3.77 02-25-82 2.430 MOC 8.12 4.40 04-15-82 3.232 MOC 6.77 4.00 05-17-82 3.915 MOC 7.34 4.15 06-30-82 4.763 MOC 5.57 3.72 08-03-82 5.465 MOC 7.65 4.42 09-16-82 6.409 EOC 6.12 4.08 l 10-26-82 7.207 EOC 6.66 3.45 l 1 12-09-82 8.098 EOC 6.74 3.67 l
- CYCLE EXPOSURE RANGES ARE DEFINED AS FOLLOWS:
BOC: 0<E< 2.0 GWD/ST MOC: 2.0 < E < 5.5 GWD/ST EOC: 5.5 < E < 9.3 GWD/ST 4-16
L [ 1 TABLE 4.1.10 l PEACH BOTTOM UNIT 3 CYCLE 6 OD-1 STATEPOINT SIMULATE-E PREDICTED VS OD-1 MEASUREMENT TIP DIFFERENCE STATISTICS CYCLE CYCLE
- OD-1 EXPOSURE EXPOSURE POINTWISE DIFFERENCES (%)
DATE GWD/ST RANGE NODAL RMS INTEGRAL RMS 10-26-83 0.162 BOC 7.82 4.18 f 11-09-83 0.438 BOC 8.23 4.32 01-04-84 1.464 BOC 10.06 4.45 02-02-84 1.795 BOC 10.79 4.66 02-18-84 2.081 MOC 5.95 4.43 03-23-84 2.796 MOC 7.53 4.39 04-26-84 3.520 MOC 9.23 4.24 07-05-84 4.544 MOC 8.93 4.05 08-14-84 5.303 MOC 7.55 4.20 09-21-84 6.031 EOC 8.91 4.25 12-28-84 7.606 EOC 5.06 3.66 { 03-05-85 8.291 EOC 5.17 3.78 05-23-85 9.767 EOC 7.01 3.90 l
- CYCLE EXPOSURE RANGES ARE DEFINED AS FOLLOWS:
BOC: 0<E5 2.0 GWD/ST MOC: 2.0 < E 5 5.5 GWD/ST EOC: 5.5 < E 5 10.6 GWD/ST 4-17
) ) ) Figure 4.1.1 i Peach Bottom Symmetric LPRM Tube Locations a CD GDOD une of l: o g b' g 'B B B F k 'DP, Boo sv-"v
'~
6 hD 0D o% o F QDh$3oo F o b b o o b 'o b ko'd b Df 0b'o hn0[ 5'
'0 00 bbo o
- BBBfEBB08805B8% BB ,8 BB b
~bbbDdbb b d YD -b 00 ' }b D
o 000 bb h o , 0 o ~, og, , 3 b b b o b o,d loo o bDo 00
! bbb ,-bo o n ,
+0 C ,b b o
~bbbDo 00 D bDo , k b b,o o
'::b880 ge Be,jBaE0b8gSB8gb8Gb o Obh o o bb bC0bbD bho i2 00F30000 QDon0DnnGD nnoo
/ 0 0 0 00 -
sesesesesesese 1 3 6 7 9 1113161719 2123262729313336373 41 43 46 47 49 61 63 66 67 69 4-18
l l , Figure 4.1.2 Axial Nodes Used in Statistical Comparisons of Predicted and Measured TIP Readings l I o o a TOP OF CORE l 50 Unmonitored 49 _
, , (no TIP data available) 48 47 Top 18" of active fuel deleted from -
46 statistics. 45 ,,
^
44 f 43
)
[ . 38 intermediate nodes (114 inches) used in statistical comparisons. 9 8 7 ,,
^
6 5 4 Bottom 18" of active fuel deleted from 3 statistics. 2 BOTTOM OF CORE ) 4-19
- _ ~ - _ _ - _
FIGURE 4.1.3 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-5-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.353 O MEASURED AVERAGE = 1.000 m 16-MEASURED: o 1.4 - MAXIMUM = 1.350 _;- - -s '- AVERAGE = 1.000
,- s
,_.,s
- O 1'2 - e 4 0 ,
e s,~, o 0 s x 1. 0 - , AN 0.8- ,' i 's 30.6- ,' 's h 0.4 - ,' s O \ Z 0.2 - - Bottom To p 0.0- i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF l 9.284 3132.0 102.40 0.99344 i
-- _J
FIGURE 4.1.4 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 12-3-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.465 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: c , o 1.4 - MAXIMUM = 1.431
? 3:
AVERAGE = 1.300
" 1.2- 's, 8 ,
o e s-_ ' x 1. 0 - i
~
1 AN s 0.8 -
/
e
- 's '
j 0.6 - i s s , h 0.4- 's ' O Z 0.2 - Bottom To p 0.0- i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height ' inches) CAVEX CTP WT K-EFF 11.054 3269.0 102.30 0.99156
FIGURE 4.1.5 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 2-25-81 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.598 O MEASURED AVERAGE = 1.000 m 1. 6 -
, s '
MEASURED: MAX 1 MUM = 1.632 O 1.4 - ,'
; , s AVERAGE = 1.000 . o 1.2 - '
L 0 i w e ~ m 1. 0 - / s
- i
-"s_ ______
A 0.8 - ,' 's s'
.e , ',
O 0.6 - ,' 's 1 h 0.4 - s, O Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 120 132 144 Core Height (inches)
'CAVEX CTP WT K-EFF 12.673 3210.0 94.28 0.99284
FIGURE 4.1.6 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 7-9-81 CORE AVERAGE AXIAL TIP TRACE 2.0 l PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.400 E MEASURED AVERAGE = 1.000 ac 1. 6 - MEASURED: c MAXIMUM: 1.403 O l'# ~ '
, AVERAGE = 1.000 g 1.2- , ,
7 , O $ 1.0- , e
~~
s 30.8- ' e
's s 0.6 - / 's h 0.4 - / 's O
Z 0.2 - Bottom To p 0.0- i i i i i i i i i i i l 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 14.010 3135.O 100.20 O.99405
1 FIGURE 4.1.7 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-2-81 CORE AVERAGE AX1AL TIP TRACE
- PREDICTED PREDICTED:
o 1. 8 - MAXIMUM = 1.391 MEASURED o AVERAGE = 1.000 x 1. 6 - MEASURED: 1.4 - MAXIMUM = 1.486 O --
' s AVERAGE = 1.000 e
s
? @ 1.2 - s e ,' '
~,- - ,
rx 1. 0 - i O i
's '
e 0.8 - i
.t! ' 's '
3 0.6 - / \ E 0.4 - u O \ ' Z 0.2 - Bottom Top 0.0- i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 14.960 3265.0 99.94 0.99541
1 1 FIGURE 4.1.8 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 10-1-61 CORE AVERAGE AX1AL TIP TRACE 2.0 PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.307 15 MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: 1.4 - MAXIMUM = 1.324 o __, AVERAGE = 1.000
- O ' ' '-
12-
$ 1.0- ,' 's_--
A 0.8-
.e ~,
3 0. 6 - , e s b 0.4 - e s O N Z 0.2 - Bottom Top 0.0 i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 15.501 3107.0 101.67 0.99561
l l FIGURE 4.1.9 ) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 12-22-81 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: j e 1. 8 - --------- MAXIMUM = 1.336 o MEASURED AVERAGE = 1.000 Of 1. 6 - MEASURED: O 1.4 - MAXlMUM= 1.306 _;- ,~s AVERAGE = 1.000
, 8 1.2- -
s
'~
k 1. 0 - 4 e 0.8 - , ' N 1 s s g 0.6 - ,' ' h 0.4 - N O Z 0.2 - N Bottom Top 0.0 i i i i i i i i i i i
! 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches)
CAVEX CTP WF K-EFF 17.096 2963.0 107.33 0.99551
FIGURE 4.1.10 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 7-14-82 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED I PREDICTED: e 1. 8 - MAXIMUM = 1.369 o MEASURED AVERAGE = 1.000 m 16-MEASURED: o 1.4 - '- MAXIMUM = 1.317
's AVERAGE = 1.000 1.2 - ,
'~ ~ ,__
x 1. 0 -
's y 's '
e 0.8 - ~, N i N
] O.6- ,' '
s
,E o .4 _
s b ' s Z 0.2 - ' Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WF K-EFF 10.060 3226.0 101.70 0.99374
FIGURE 4.1.11 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEP0lNT 11-9-82 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.596 o MEASURED AVERAGE = 1.000 m 1. 6 -
,s ' MEASURED:
o 1.4 - ' s MAXIMUM = 1.511 AVERAGE = 1.000
; @ 1.2 - ,' '
$ 1.0-
~
~'K _
o 0. 8 - '
.6 i 3 0. 6 - ,'
h 0.4 - O Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 144 Core Height (inches) CAVEX CTP WT K-EFF 12.230 3287.0 101.37 0.99416
FIGURE 4.1.12 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 12-28-82 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
~
a) 1. 8 - MAXIMUM = 1.406 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - ' MAXIMUM = 1.399 s AVERAGE = 1.000
% j,o _ ,'
Y e N a) 0.8 - i 0.6 - i h 0.4- s O
- Z 0.2 -
Bottom To p 0.0 , , , , i , , , , , i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 13.103 3290.0 101.18 0.99412
FIGURE 4.1.13 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 5-13-83 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
~
o 1. 8 - MAXIMUM = 1.402 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - -, MAXIMUM = 1.311 s ' '~- s AVERAGE = 1.000 1.2-1 8 - s- ~s [ 1. 0 - f s
~~
9 , e 0.8 - ,- N / 50.6- ' e s h 0.4 - ,' s O ' i ~ Z 0.2 - To p i 0.0 , Bottomi i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 15.581 3024.0 102.38 0.99534
FIGURE 4.1.14 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 6-23-83 CORE AVERAGE AX1AL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.275 O MEASURED AVERAGE = 1.000 m 16- MEASURED: , o 1.4 - MAXIMUM = 1.356 _;- AVERAGE = 1.000 o 12- 7,_ - O '
- 1. 0 -
, 'N
~
O e a) 0. 8 - i 's N N / 50.6- / h 0.4 - f
\
O N Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches)
'CAVEX CTP WT K-EFF 16.238 3268.0 97.91 0.99854
FIGURE 4.1.15 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 12-13-83 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.289 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.353 _;- ,__ AVERAGE = 1.000 . @ 1. 2 - p',' -
' - ___N_-, '
b $ j , c _. A 0. 8 - i
.6 l 3 0. 6 - j h 0.4 - i
\
O N Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF " 16.649 3272.O 101 29 0.99997
l FIGURE 4.1.10 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 1-9-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.276 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: 1.4 - MAXIMUM = 1.243 o AVERAGE = 1.000 , 1.2 - ,- , y , _\ x 1. 0 - - A 0.8- ' N
.e /','
3 0.6 - , h 0.4 - ,' \ s O s Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 120 132 14 4 Core Height (inches) - CAVEX CTP V/F K-EFF 17.156 3280.0 102.42 1.00062
__ _ ___ ,- ,m 1 , FIGURE 4.1.17 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 3-2-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: I - e 1. 8 - MAXIMUM = 1.312 O MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.343 - AVERAGE = 1.000 0 ' O 1'2 - - s s-
? , -
s Y c@ 1, o _ , N' ' ' ' ' ' ' s s,,_
~0 l e 0. 8 - i -
N ! 50.6- / s h 0.4 - ' s O s l Z 0.2 - l Bottom To p 0.0 i i i i i i i i i i i O 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 17.989 3286.0 107.00 0.99913
FIGURE 4.1.18 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 3-20-84 CORE AVERAGE AXIAL TIP TRACE 2.0 l PREDICTED PREDICTED: l a) 1. 8 - MAXIMUM = 1.276 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: O 1.4 - MAXlMUM= 1.279 a: AVERAGE = 1.000 8 1.2- _, T ' % ,.____ d, q) -s v, g 1, o _ - s_ ~ AN 0.8 - i
~
50.6-r /
/ 's
\
E 0.4 - s i O 's ! z 0.2 - l 1 Bottom Top O.0 , i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 144 ' Core Height (inches)
~
CAVEX CTP WT K-EFF 18.357 3137.0 108.57 0.99926
FIGURE 4.1.19 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12-21-79 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.377 o MEASURED AVERAGE = 1.000 x 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.402 s - AVERAGE = 1.000 0 1.2 - -
, a s ~~~ ,
s e / 's M cr 1. 0 - ,' - O '
's s_
e 0.8 - ,'
.U i l g 0.6 - ,/
h 0.4 - s O s Z 0.2 - Bottom To p O.0 - i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) l CAVEX CTP WT K-EFF l 8.966 3277.0 93.30 0.98882 l
m FIGURE 4.1.20 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 1-23-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.425 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - -s MAXIMUM = 1.467 s-AVERAGE = 1.000 g 1.2- , 1 Q # 's ' 0 x 1. 0 - ,' s. A 0.8 - ,' 's '
.e ,
5 0. 6 - ,' s h 0.4-o s Z 0.2 - Top i 0.0 , Bottomi i i i i i i , , , , O 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 9.529 3289.0 95.00 0.98857
_ -- _ _ _ m - m- m w - FIGURE 4.1.21 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 2-27-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
--~~-----
- 1. 8 - MAXIMUM = 1.424 2 MEASURED AVERAGE = 1.000 o
CE 1. 6 - MEASURED: MAXIMUM = 1.482 o 1.4 - x ' ' AVERAGE = 1.000
- y _
, s g o -
$ 1.0- ,' __
~
A 0.8- ' N -
.e g 0. 6 -
s h 0.4 - ' s , O ' Z 0.2 - Bottom To p 0.0 i i i , i i 3 i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) , CAVEX CTP WT K-EFF 10.098 3288.0 102.10 0.98967
- - ~- w w FIGURE 4.1.22 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 4-16-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
~
e 1. 8 - MAXIMUM = 1.490 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - ' - s MAXIMUM = 1.445 z
,- N,_, ' AVERAGE = 1.000
? O 1.2 - e
~
cr 1. 0 - ' 9 1 _ ..%- - m 0. 8 - '
.d i g 0. 6 - /
h 0.4-1 O Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 10.892 3277.0 100.31 0.98984
~ - .- . _ - - _ ~ -w-w-FIGURE 4.1.23 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 6-25-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
1.8 - MAXIMUM = 1.582 S 1.6 - e MEASURED: c ' s MAXIMUM = 1.546 o 1.4 - ,- 's '
; e ~ AVERAGE = 1.000
; 8 1.2- ,' 's s
y ' ' a 's 1,o _ ,' IN 0.8- ,' i 50.6-O.4 - Z 0.2 - Bottom To p 0.0 , , , , , , , i , , i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 11.872 3276.0 95.96 0.99044
FIGURE 4.1.24 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEP0lNT 8-14-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.372 o MEASURED AVERAGE = 1.000 m .6-MEASURED: o 1.4 -
- N-MAXIMUM = 1.412 AVERAGE = 1.000 , 8 1.2- ,
e, s b $ 1.0-i e
-~~,
l q) 0.8 - - s N ' 50.6- 'N l h 0.4- x O Z 0.2 - Bottom To p - 0.0 , i i i i i i i , , 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 4 Core Height (inches) CAVEX CTP WT K-EFF 12.907 3287.0 103.00 0.99094
~- _ _ - _
FIGURE 4.1.25 ( PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12-16-80 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: i e 1. 8 - MAXIMUM = 1.259
'o MEASURED AVERAGE = 1.000 m 1. 6 -
MEASURED: o 1.4 - MAXlMUM= 1.285
. ;: AVERAGE = 1.000 1 1. 2 - ,~~
@ _/
~,, -- -
tr 1. 0 - A 0.8 - '
.d 3 0.6 - N h
O 0.4 - \N I Z 0.2 - j Bottom Top 0.0 - i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) I CAVEX CTP WT K-EFF 15.172 3284.0 101.40 0.99332
FIGURE 4.1.26 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 2-6-81 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.174 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXlMUM= 1.187
- - AVERAGE = 1.000 12- . ,- --
0, m 1. 0 - -- A 0.8- ' ' s
.t!
3 0. 6 - s E o.4_ \ 8 , Z 0.2 - l Bottom To p i 1 0.0 i i . . . i i i i i i 1 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 l Core Height (inches) CAVEX CTP WT K-EFF 16.147 3219.0 102.50 0.99455
-. . _ - - _ . ~
_ - _ ___-_ - _ _ _ - - -- _ - ~ ~ - , w FIGURE 4.1.27 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 12-2-81 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.281 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.265
;- ,_s ____ AVERAGE = 1.000 y 1.2- -- g
- m a>
- 1. 0 - ,-
' _ _W 's, AN 0.8 - ,' ' -
s r 50.6- ' s h 0.4- Ns O ' Z 0.2 - Bottom To p 0.0- i i i i i i i i i i i 0 12- 24 36 48 60 72 84 96 10 8 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 11.333 3283.0 100.80 0.99250
FIGURE 4.1.28 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 1-22-82 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.438 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.437
- AVERAGE = 1.000 -
. 1. 2 - ~~ s
@ f cp 3,g _ / ' ' N -__
o e 0. 8 -
/ N s
~~
.t2 0 0.6 -
h O 0.4 -
\ s l
Z 0.2 - - Bottom Top O.0 i , i i i i i i i , i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 12.393 3286.0 99.98 0.99194
_ _ _ - _ - _ _ _ _ - _- - _ -- ~ w FIGURE 4.1.29 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 2-25-82 CORE AVERAGE AXIAL TIP TRACE PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.568 4 o MEASURED AVERAGE = 1.000 x 1. 6 - '
,~s MEASURED:
o 1.4 - -
's MAXIMUM = 1.413 l
z e' s-s AVERAGE = 1.000 O ' ' I
- 1. 2 - i
~
s O , s e , s_-~~_ 's Cr 1. 0 - i , _ _ _ _w - 1 ~- 9 , e 0.8 - , 's ~ N r s f 0.6 - l ~ h 0.4 - N O Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF i 13.022 3277.0 100.00 0.99137
FIGURE 4.1.30 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 4-15-82 CORE AVERAGE AXIAL TIP TRACE
?
~~O PREDICTED PREDICTED:
e 1. S - MAXIMUM = 1 559 O MEASURED AVERAGE = 1.000 x 1. 6 - ,' MEASURED: o 1.4 - -
' ' MAXIMUM = 1.446
' s s AVERAGE = 1.000 o 1~2 - ' '
. O ,' '
s,, 5 $ 1.0-
' s , ; _ __ _ w O -
s e 0.8 - ,' s s
.M i g 0. 6 - ,'
h 0.4 - O Z 0.2 - Bottom To p 0.0 - ! i i i i i i i i i i i 1 0 12 24 36 48 60 72 84 96 10 8 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 13.824 3283.0 98.78 0.99147
_ - _ _ _ _ _ _ - - _ - _ _ _ -- -- _, ----w--~ ,- w FIGURE 4.1.31 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 5-17-82 CORE AVERAGE AXIAL TIP TRACE 9 '0
'~ -
PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.594 o MEASURED AVERAGE = 1.000 x 1. 6 - ' i - s MEASURED: E 1.4- ,'
' s MAX 1 MUM = 1.459
. =0 i AVERAGE = 1.000
.i O 1.2 - ,' '
's s
1.0- '
~ -
~3'
A 0.8- ,' 's
.6 ! ~
3 0. 6 - ,' ' h 0.4 - N O Z 0.2 - ) Bottom To p i 0.0 - i i i i i i i , , , i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) l CAVEX CTP WT K-EFF 14.510 3287.0 98.36 0.99250
FIGURE 4.1.32 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 6-30-82 CORE AVERAGE AXIAL TIP TRACE
~
PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.393 O MEASURED AVERAGE = 1.000 x 1. 6 - MEASURED: O 1.4 - ,'- MAXIMUM = 1.319 e AVERAGE = 1.000
- O 1.2 - - -
- O ,
' s, -g
$ 1.0- ,' ' '
'~~~~%___
AN O.8-
/
i s 50.6- 's s h 0.4 - s O Z 0.2 - l Bottom Top 0.0 , i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFFI 15.359 3262.O 102.12 O.99350l
-- ,-------w- - - , -
FIGURE 4.1.33 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 8-3-82 CORE AVERAGE AX1AL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.657 5 ,s MEASURED AVERAGE = 1.000 m 1. 6 - , s MEASURED: o 1.4 - i s MAXIMUM = 1.492 AVERAGE = 1.000 1.2-
. 8 ,'
i
. ~
x 1. 0 - i N -~~_, y e s_,__ s_,____ , e 0.8 - i ~, N / 's
] 0.6 -
's s h 0.4 - N O
Z 0.2 - Bottom To p 0.0 , i i i i i i i i i i , 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WF K--EFF 16.062 3255.0 102.04 0.99434
FIGURE 4.1.34 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 9-16-82 CORE AVERAGE AXIAL TiP TRACE 2.0 PREDICTED PREDICTED:
--------~
a) 1. 8 - MAXIMUM = 1.272 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.268 AVERAGE = 1.000 1.2- , --
'd s
$ 1.0-
/
i
's-AN 0.8 -
~'N s
@ 0.6 - s h
O 0.4- \ s Z 0.2 - Bottom Top 0.0 : i , i i i i 3 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 17.008 3149.0 102.23 0.99531
FIGURE 4.1.35 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 10-26-82 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.260 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.251
; AVERAGE = 1.000 y @ 1.2 -
,- 's'-~~s,, -
o g m 1. 0 - ~~, o 's ' e 0.8 - s
.d ' \
3 0.6 - ,' 's 0.4 - '
\ l O s
' l Z 0.2 -
Bottom To p O.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 17.808 3204.O 102 23 O.99806
FIGURE 4.1.36 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 12-9-82 CORE AVERAGE AX1AL TIP TRACE 2.0 PREDICTED PREDICTED: o 1. 8 - MAXIMUM = 1.271 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: 1.4 - MAXIMUM = 1.195 o AVERAGE = 1.000
- o 1.2 - '
' ' ~ ' ',____'s-5 @
~ ,
tr 1. 0 -
, 's ~,
y e 0.8 - 's
.d 's 3 0.6 -- , N 0.4 - ,/ \ '
O Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 18.701 3085.0 107.59 0.99864
FIGURE 4.1.37 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 10-26-83 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: c) 1. 8 - MAXIMUM = 1.322 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.244
;: -s _ AVERAGE = 1.000
~'
- 1. 2 - ,- -
^ x 1. 0 - ,
, ~
s AN 0.8 - i
,' - Ns ] O.6 - ,' s h C.4- ,' \ s o '
Z 0.2 - Bottom To p 0.0- i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 10.163 2942.0 102.50 0.99514
FIGURE 4.1.38 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 11-9-83 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.356 o MEASURED AVERAGE = 1.000 x 1. 6 - MEASURED: 1.4 - MAX 1 MUM: 1.288 o
~
- 1. 2 - s~
h cE 1.0- e N ~' .s AN 0.8 -
/
,' s, s
f 0.6 - i \' E u 0.4 - ,' ' s O ' Z 0.2 - ' Bottom Top 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WF K-EFF 10.439 3229.0 102.15 0.99730
FIGURE 4.1.39 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 1-4-84 , CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.353 o MEASURED AVERAGE = 1.000 x 1. 6 - MEASURED: E MAXIMUM = 1.482 l 1.4- '-- N, AVERAGE = 1.000
@ 1.2 - ,' , ,,'N _
e
- 1. 0 -
's_ '-
s - ,, ~
. Er - ~
b 30.8- i 0.6 - ,' ' I
\
/
h O 0.4 - f
\ s Z 0.2 -
Bottom To p O.0 i i i i i e i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 11.466 3289.0 100.92 0.99599
FIGURE 4.1.40 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 2-2-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: a) 1. 8 - MAXIMUM = 1.354 o MEASURED AVERAGE = 1.000 i m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.354
~~-
AVERAGE = 1.000 0 1. 2 - -
1 s O s' % s ~~, d w Q)
- 1. 0 - ,'
/
's tr ,
x ~~, D q3 0.8 - i s' s
~ '
- 0. 6 - i h 0.4-i s i O s l Z 0.2 - '
Bottom To p 0.0 , , i i i , , , , , i i l 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 l Core Height (inches) l CAVEX CTP WT K-EFF l 11.797 3265.0 101.00 0.99534 L___----_--_--_______--__-. - -- _ . - - - - - - - -
FIGURE 4.1.41 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 2-18-84 CORE AVERAGE AX1AL TIP TRACE 2.0 PREDICTED PREDICTED: 2 1. 8 - MAXIMUM = 1.336 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAX 1 MUM: 1.379
= ,
~.._' '
AVERAGE = 1.000
- 1. 2 - ','
@ ~
j cE 1.0 - ,' 'y ___ ' y i e 0.8 - s
.6 i 5 0.6 - ,'
h 0.4- ' O Z O.2 - Bottom Top 0.0 i i i i , i i , i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K--EFF 12.084 3290.0 100.00 0.99527
FIGURE 4.1.42 PEACH BOTTOM 3 CYCLE e6 OD-1 STATEPOINT 3-23-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
--- -~~--
o 1. 8 -- MAXIMUM = 1.320 0 MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: 5 i,4_ MAXlMUM= 1.339
;: ~~_ AVERAGE = 1.000 O 1.2 -
s O e s - --- ,i
- m , ,
m
- 1. 0 -
X-s ' O e '- e 0. 8 - - s
.r2 ,' '. s g 0.6 - ,' 's h 0.4- ,'
O Z 0.2 - Bottom Top 0.0- , i i i , i i i i i , 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 12.799 3272.0 102.45 0.99551
FIGURE 4.1.43 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 4-26-84 CORE AVERAGE AXIAL TIP TRACE
- 2.0 PREDICTED PREDICTED:
o 1. 8 - MAXIMUM = 1.272 o MEASURED AVERAGE = 1.000 x 1. 6 - MEASURED:
- c. MAX 1 MUM = 1.376 l
o 1.4 - 3 _ ' AVERAGE = 1.000
- t 1.2 - ,-
; s_ s _ ,
@ 's,-
g o e s m '
- 1. 0 - ,
s s a) 0.8 - e
/
~'s '
.N ,' s
's 0.6 - e a , s E 0.4 - ,'
u o Z 0.2 - Top 0.0 ,Bollomi i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 13.524 3208.0 97.00 0.99524 i
FIGURE 4.1.44 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 7-5-84 CORE AVERAGE AXIAL TIP TRACE 2.0-- PREDICTED PREDICTED:
- l8- ---------
MAXIMUM = 1.294 0 MEASURED AVERAGE = 1.000 cr 1. 6 - c MEASURED: o 1.4 - MAXIMUM 1.451 I ,- -
~
AVERAGE: 1.000
- 1. 2 - ,
s _, tr 1. 0 - , 1 -~~Ts_ ____ m ,' ' s e 0.8 - , s
.N ' 's 5 0.6 - ,' 's, h 0.4 - e'
- O Z 0.2 -
Bottom Top 0.0- i , , , i i , , i i , 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 14.549 3266.0 96.00 0.99544 m . ..
_ _ _ - m m _x -- m l FIGURE 4.1.45 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 8-14-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
~~~~~~~--
I a) 1. 8 -- MAXIMUM: 1.291 l o MEASURED AVERAGE = 1.000
" I'
~
MEASURED: o 1.4 - MAXIMUM = 1.402
= _ _ _ , . _s AVERAGE = 1.000 1.2 - '- ~~ -
t @ - s ,_ r$ 1.0 - ,' 'N.. -- s o 0.8 - s_ a) , N i s
~j 0. 6 - ,' 's 0.4 - i ,
l O Z 0.2 - Bollom Top O.0 l I 3 i i , , i i , , i l 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 l Core Height (inches) CAVEX CTP WT K-EFF 15.309 3288.0 101.00 0.99702
- ~
-- w- ---
FIGURE 4.1.46 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 9-21-84 CORK ,WERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
---~~~---
3 18- MAXIMUM = 1.308 D A M AGE = 1.000 O 1.6-MEASURED: c: o 1.4 - MAX l MUM = 1.372 g - -~s_ ~ s AVERAGE = 1.000
, o 1.2 - ,- s
' ~'
b $ 1.0- ,-
' ' - '~~~ s O ,'
a) 0.8 - i
~
.b! ,' 's '
0 0.6 - i h 0.4- i s O
\ '
Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 i Core Height (inches) l CAVEX CTP WT K-EFF 16.038 3229.0 102.00 0.99697
_ __ _ _m m-x ,- FIGURE 4.1.47 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 12-28-84 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
-----~~~-
3 1. 8 - - MAXIMUM = 1.436 o MEASURED AVERAGE = 1.000 1 1. 6 - MEASURED: c ~ o 1.4 - - s MAX 1 MUM = 1.388
~-
Z ,' N AVERAGE = 1.000
- 1. 2 - e s-b cE 1.0- / -- -
A O.8- N
's
.6 g 0.6 - s h 0.4- s
\
O ' Z 0.2 - l Bottom To p 0.0- i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 12 0 132 14 4 Core Height (inches) CAVEX CTP WF K-EFF 17.615 2794.0 78.00 0.99662
-_ ____-___-_-____~__-_- - - - - -_- - - - -
FIGURE 4.1.48 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 3-5-85 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED: e 1. 8 - MAXIMUM = 1.245 o MEASURED AVERAGE = 1.000 m 16-MEASURED: o 1.4 - MAXIMUM = 1.237
;: AVERAGE = 1.000 12-
{ Cr 1. 0 - ,' '- s A 0.8- ,'
.e 3 0. 6 - s h 0.4 - s O s Z 0.2 - -
Bottom To p O.0 i i i i i i i i i i i ; O 12 24 36 48 60 72 84 96 10 8 12 0 132 14 4 l Core Height (inches) I CAVEX CTP WT K-EFF 18.301 2955.0 99.41 0.99748
d FIGURE 4.1.49 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 5-23-85 CORE AVERAGE AXIAL TIP TRACE 2.0 PREDICTED PREDICTED:
------~~-
e 1. 8 - MAXIMUM = 1.187 o MEASURED AVERAGE = 1.000 m 1. 6 - MEASURED: o 1.4 - MAXIMUM = 1.232 4: AVERAGE = 1.000 1.2 - -s g -- i { m g o '
' - ~~~
m 1. 0 - -
's A 0.8 - i
.6 / s 3 0.6 - i s h 0.4- s O
Z 0.2 - Bottom To p 0.0 i i i i i i i i i i i 0 12 24 36 48 60 72 84 96 108 120 132 14 4 Core Height (inches) CAVEX CTP WT K-EFF 19.738 2715.0 109.00 0.99923
~~ ~ ~
FICURE 4.1.50 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-5-80 849 841 ; 833 : 825
/
i
, .~,
I k i t i R R R I 9 R I 1 1 E t I a t E I t t I t I t f I I I I E E I f 1657 1649 1641
~ -
8 17
~
- - . ss, s
N 1 i f,__ i
)
~ 1625 1633 1617 1609
- ~
-ess ,
ss , ss ,
/ g N e f
's ti i, '
2457 2449 2441 2433
~ ~
, s, ,
s PREDICTED CAVEX CTP WT K-EFF -------- 9.284 3132.0 102.40 0.99344 MEASURED
- - - - - -- -- ~ ~
FIGURE 4.1.50 (CONT.) PEACH BOTTOM 2 CYCLE //5 OD-1 STATEPOINT 9-5-80 2425 2417 2409
~
3257 s_ s iss ,-
's, #
\s /
s _ / [',,,, . , , .. . . . . . ...... 3249 3241 3233 3225
~ ~ ~
s-
/ v*
i m ,1 e r e f I t . . . t . .f . 3217
~
~
3209 ' 4057 4049
's '\ , ~,,,,
s 4041 : 4033 3
% _ 4025 : 4017
'<, ~~.
T
\
w
,1 (1
e i e PREDICTED CAVEX CTP WT K-EFF -------- 9.284 3132.0 102.40 0.99344 MEASURED
-- _ _ _ _ ~ __
FIGURE 4.1.50 (CONT.) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-5-80 4009 4849 4841 4833
~
f/ i ,
/
j l/
. ...I a .
s l/
\
4825 4817 4809 5641 e D s I h! .......... l 5633 5625 ~ 5617 AVG.
- s-s_
i / j CAVEX CTP WT K-EFF SE E9 9.284 3132.0 102.40 0.99344 MEASURED
FIGURE 4.1.51 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 12-3-80
- 849
- 841 833 -
825
\_ i t r s t I a R i e f f I e R R I E I I t I I 1 E E t E 1 A i1 f I t i E E 9 I E t I 1 iiI 817 1657 1649 1641 s
~
s - is ,
\ % - % , s
', i N
1625 1633 1617 1609
' ~
- ' - ' s e
N N, j '
\
5 _ 2457 2449 2441 2433
- ~ ~
- -s
\s -g s s_ _ N , N I \ f PREDICTED CAVEX CTP WT K-EFF --------
11.054 3269.0 102.30 0.99156 l MEASURED
FIGURE 4.1.51 (CONT.) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 12-3-80 2425 ~ 2417 2409 ~ 3257
- ~
~
t a t t t t I t t 9 i i f f A E b I t 1 I t I e e t i t t t t t 3249 : 3241 : 3233 3225
- s
\
m W i it t , i t I i1 . 3217 3209 ~ 4057 4049
, _ s s
s . -_ s
\ \
4041
~
4033 4025 4017 s
- s
,, y -
s_
\ \ \
\ 1
\
r .
\
CAVEX CTP WT K-EFF E0EEE9 11.054 3269.0 102.30 0.99156 MEASURED
_ - - - - ~ FIGURE 4.1.51 (CONT.) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 12-3-80 4009 4849 4841 4833
*s.
- s. -
s 's-s t , e sg s 4825 4817 : 4809 : 5641 ? - s_ s
- \, ~
f f f E A t A I E I f G 1 f R S t i R R R f f 5633 5625 : 5617 : AVG. Y '
%f CAVEX CTP WT K-EFF NEEE9 11.054 3269.0 102.30 0.99156 1 MEASURED
FIGURE 4.1.52 PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-2-81 849 841 ; , 833 ; 825
" " ~
7 .( .[ f
/ r F F 7
g g a 3 9 R E 1 3 f I 3 A i I 1 I k I t t R f a 1 1 R R E I I I I k i I I 1 I f 8 17 ; 1657 _ 1649 : 1641
' i y -g i %,
t 1625 1633
~
1617 1609
- ~-~ . ,
, ' ~, ,
," N ,^ I
% / s g %, \s
\ f s f f ' ' '
t .c 2457
~
2449 2441
~
2433
,, r~ ,
1 -'. { t R PREDICTED CAVEX CTP WT K-EFF -------- 14.960 3265.0 99.94 0.99541 MEASURED o
FIGURE 4.1.52 (CONT.) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-2-81 2425
~
2417 2409k 3257
' ~ -
j,C%. s e -
, s s_ ,
;l ;, .
I I I I a e a e a t I t a f R I E t I E a t i E a 9 9 f E t t t t 3249 3241 3233 3225
' ~
~
/
,1 2
t i f I t I E T I t 3209 4057 4049 3 217
- - ~ ~
ss
/ ,
/ *s - -
[I
't
\ .f /
I f 404-1 : 4033 : 4025 4017
,--er, ,
- i -.,
\w / N lf/
c
;l PREDICTED CAVEX CTP WT K-EFF --------
14.960 3265.0 99.94 0.99541 MEASURED
FIGURE 4.1.52 (CONT.) PEACH BOTTOM 2 CYCLE #5 OD-1 STATEPOINT 9-2-81 4009 4849
~
4841
~
4833 j ll
?
4825 : _ 4-8 17 : 4809 : 5641
-u~ ' '
. s ,, ~,
- l s , , _
y , , .
;, ~
,I i1 1 , , , t I 1 1 , 1 , I 1 1 f E I E 5633 5625 5617 AVG.
- ~
PREDICTED CAVEX CTP WT K-EFF -------- 14.960 3265.0 99.94 0.99541 MEASURED
FIGURE 4.1.53 PEACH BOTTOM 2 CYCLE //6 OD-1 STATEPOINT 7-14-82 849 841 , 833 ' 825 s m............ .... ..... 817 1657 1S49
- ~
1641 s , s_s e
~ ~ ,
~
~
'N j/' W <
1625 1633 1609 1617 s ss s
\ [
\
2457 2449 2441 2433
- '~
_s, e - s-s-
\ \
- ,/
g N ' b
\, L PREDICTED CAVEX CTP WT K-EFF --------
10.060 3226.0 101.70 0.99374 MEASURED
i FIGURE 4.1.53 (CONT.) PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 7-14-82 2425 2417 2409 - 3257
/ "w~es g
% /
r ' I t t 1 1 A A E t I a f [ 1 A E A I E I E I 1 g 3249' 3241 3233 - 3225 s s-
& 5 f y y
~ .. .. . . ...
3217 3209 : 4057 : _ 4049
% ' N / N- /
f \ ( y 4041 4033 4025
~
4017
~
- -, - i I
k ' yf CAVEX CTP WT K-EFF NEE 10.060 3226.0 101.70 0.99374 MEASURED
FIGURE 4.1.53 (CONT.) PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 7-14-82 4-0 0 9 4849 ~ 4841 : 4833
- s-
~ .
\.
. . . .1 R .
4825 4817 4809 5641
~ '
~
~
f ; ,
- = ~ - - -
5633 . 5625 5617 : AVG.
% \
'g ~
f N ~ CAVEX CTP WT K-EFF M(MI(D 10.060 3226.0 101.70 0.99374 MEASURED
FIGURE 4.1.54 PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 12-28-82 849 841 833 -
- 825 7 %s /
\ /
f
\ -I I , _
! 's ;'
E E R I t i E f f f I E I E 9 E I $ 1 1 I f f 1 E I I b I I t I E i t I I I E I E I I 1 1657 1649 1641
~ ~
8 17
- s j' s . _.
- ~x\
- .(~W _,m 1625 1633 1617 1609
., : i
\:
/
2457 2449 2441
~
2433 e g i
/
e s
'N
/
PREDICTED CAVEX CTP WT K-EFF i 1 13.103 3290.0 101.18 0.99412 MEASURED
FIGURE 4.1.54 (CONT.)
- PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 12-28-82
,s 2425 2417 2409 : 3257 1 1 E I f f I I E I f f I f f f I E f I f E R f I I f f f I E E f R 3249 3241 3233 ~ 3225
? l l I f I f k I f I f I f 3217 3209 4057
~
4049
/% ' -
y s ~
/
s_ f \s 4041 4033 4025 4017
~ '
~ '
I s / / , / ,_
-t ~* ~ 1 l
~
'/ if I .
\
r N i PREDICTED CAVEX CTP WT K-EFF -------- 13.103 3290.0 101.18 0.99412 MEASURED
FIGURE 4.1.54 (CONT.) PEACH BOTTOM 2 CYCLE //6 OD-1 STATEPOINT 12-28-82 4009 : 4840f 4841 : 4833 N : E E t t t t I I E I I i t t t I t t I 1 I f 4825 4817 4809 5641
' ~
~
/
/ ' mps, x '
b I f I I 1 E I i 1 1 1 1 1 1 9 t E I E t t t [3 5625 5617 AVG.
~
5633 ; :
'\ ,
CAVEX CTP WT K-EFF MD_@KD 13.103 3290.0 101.18 0.99412 MEASURED
- - % T-'-
FIGURE 4.1.55 PEACH BOTTOM 2 CYCLE //6 OD-1 STATEPOINT 3-2-84 849 841 833 825
~ -
s'. , D A i R R 1 I E E I b f I I t 1 1 1 I f 3 g E R 9 I E 6 1 b t 1 I t 1 I t g I ig 3 1657 1649 8 17 1641 s.- '- 1625 1633 1617 1609
~
, s,, - -
\,
t
. \ -
,,/
2457 2449 2441 2433
~ ~ -
% % b *me
\'.
PREDICTED CAVEX CTP WT K-EFF -------- 17.989 3286.0 107.00 0.99913 MEASURED
FIGURE 4.1.S5 (CONT.) PEACH BOTTOM 2 CYCLE #6 OD-1 STATEPOINT 3-2-84 2425 2417 2409 3257 i s j'
~
.~
? i 1 E I i I t a f 1 I e t t t I t t t t t I t t t t I t I i t I i1 3249 .
3241 : 3233 3225 s~ s-
~ ? -
5 t I I I I f f I I E f 3217
~
3209 - 4057 4049
~
~ '
i . ~ . T
/ s 4041 4033 4025 '
4017
- ,' ~
s~_ i
\ .
J 1 CAVEX CTP WT K-EFF EE E9 u17.989 3286.0 107.00 0.99913 MEASURED u
FIGURE 4.1.55 (CONT.) PEACH BOTTOM 2 CYCLE //6 OD-1 STATEPOINT 3-2-84 4009 4849 4841 4833
~ -
~~
' ~
~ ~
, .l 4825 4817 4809
~
5641
~ ~
7 s .s s ,. 3 ma s S E A f I f E A E E E f I t I 1 1 I E it 5633 ; 5625 : 5617 : AVG. s < CAVEX CTP WT K-EFF NEEES 17.989 3286.0 107.00 0.99913 MEASURED i
FIGURE 4.1.56 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12 79 849 841 833 ' 825
's
~
, 'N n
i r , 4 %: t ( x 1657 1649 1641
' ~
8 17
~
<s_ Ns ,
, s,
# F
.J u .$
N i E g ui , , j i 1625 : 1633 1617 ; 1609
~'
i ' - , 2457 2449 2441
~
2433 e %
\ r
\ .
PREDICTED l CAVEX CTP WT K-EFF -------- 8.966 3277.0 93.30 0.98882 MEASURED
- w -- w - -
FIGURE 4.1.56 (CONT.) PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12 79 2425h 2417 2409 3257
~ -
4-*5 ( / l' I 1 I i t a I a a a t t 9 9 e a e e a t i t a i t e i a I a 1 3249 3241 3233 3225
~ ~ ~
( ,
\ ;
\
n e a t 1 i e I f I f 3217 3209 4057 4049
~ ~ ~
/ ,
/
/ ]
4041 4033 4025 4017
' ' ~
\
i l l CAVEX CTP WT K-EFF M[D@KD 8.966 3277.0 93.30 0.98882 MEASURED 1
FIGURE 4.1.56 (CONT.) PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12 79 4009 4849 4841 : 4833 t . A t t t f A E I f R A 1 1 I I e f I f 4825 4817 : 4809 : 5641
; T - .
. ... ... .. .........t .
5633 5625 5617 AVG.
~
/ N CAVEX CTP WT K-EFF NEEES 8.966 3277.0 93.30 0.98882 MEASURED
____ -_ ___________________-________________ ~ ___ - . -- --. - . . - - ~ FIGURE 4.1.57 PEACH BOTTOM 3 CYCLE //4 OD-1 STATEPOINT 4-16-80 849 : s 841 s 833 : s 825
's 's .
s i a I f f 2 E a i a E I 1 it iE I I E 1 I f I E E t I f 1 I I I E I I I I i 8 17 1657 : 1649 : 1641 s% / i i 1625 1633 1609 1617
~
l
,*' '.__, s - l
' ' /
s - -, - . V , l 2457 . ,, 2449 : 2441 2433 CAVEX CTP WT K-EFF NE ES 10.892 3277.0 100.31 0.98984 MEASURED
FIGURE 4.1.57 (CONT.) PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 4-16-80 2425 2417 ~ r 2409 3257 s- s
~,s
- - r
/ , s f
2 1 1 B E 1 9 I t I E t & A i 1 I iB B 1 9 f 1 1 I E f a 1 t 3249 3241 3233 3225
's_ -
s_ s-3217 3209 4057 4049 s e -
/ N /
/
~
i
~
~' -
! f 4041
~
4033 ~ 4025 4017
- s.
t
] r PREDICTED CAVEX CTP WT K-EFF --------
10.892 3277.0 100.31 0.98984 MEASURED
_ _ _ _ _ _-_ _ - _ . .-.x , _ FIGURE 4.1.57 (CONT.) PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 4-16-80
,e 4009 4849 ; 4841 ,
4833 I
/
)
1 R I .if I E I I i I E a a 1 1 I I 4826 4817 : 4809 . 5641 N S633 5625 5617 AVG.
/~
i CAVEX CTP WT K-EFF MDM _ 10.892 3277.0 100.31 0.98984 MEASURED
FIGURE 4.1.58 PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12 8 0 849 841 833 825
~
!, i
~ < * -
f _ [,&.%' r I a L 1 1 E 1 1 1 I i i E A i 1 E i E 1 i E I E A 1657 1649 1641 8 17 y . 1625 1633 1617 1609
~ -
~
2457 2449
~
2441
~
2433
~
s* - - - PREDICTED CAVEX CTP WT K-EFF -------- 15.172 3284.0 101.40 0.99332 M.EASURED
- - . ._-~ - - -
FIGURE 4.1.58 (CONT.) PEACH BOTTOM 3 CYCLE #4 OD-1 STATEPOINT 12 8 0 2425 2417 2409 3257
,__ N- - s_ <ss
; c s
/ ,
a t I a 1 1 1 I i & J t 1 I a 1 3249 3241 3233 3225
'~ ' ' - s~ ~' s E K L 3217 3209 4057 4049
~'~~~ ~
4041 4033 4025 4017
.V .
CAVEX CTP WT K-EFF M ( M I(D 15.172 3284.0 101.40 0.99332 MEASURED
FIGURE 4.1.58 (CONT.) PEACH BOTTOM 3 CYCLE //4 OD-1 STATEPOINT 12 8 0 4009 4849 4841 4833
'~ '
' - - , ~,
I i i 1 B 1 iR R 3 1 9 d I f i I f 4825 4817 4809 5641 o 7 t t t A B k i E E 1 0 2 I t 1 I ia 1 1 5633 5625 5617 AVG.
~
< v - -
CAVEX CTP WT K-EFF SE ES 15.172 3284.0 101.40 0.99332 MEASURED
FIGURE 4.1.59 PEACH BOTTOM 3 CYCLE //5 OD-1 STATEPOINT 12-2-81 849 841 833 825
' '~
~
if A 3 E I E i f f i a i E E I f d t A 1 A k E R 1 R 1 1 I a a E E E A f f f i 8 17 1657 : 1649 . 1641 s '
, . - s. ,
1 ,. rl r 1625 1633 1617 1609
~ ' ~
- .. ~ i
\
2457 2449 2441 2433
- ~
s s s s. CAVEX CTP WT K-EFF NE ES 11.333 3283.0 100.80 0.99250 MEASURED
FIGURE 4.1.59 (CONT.) PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 12-2-81 2425 2417 2409 3257
/ g
- ' o e
& I t h i i E i R E 1 R 1 1 1 3249 3241 3233 '
3225 l 1 iii 1 3217 3209 4057 4049
. s s s-
, \ f %%
(
\ s s..
4041 4033 4025 4017 s CAVEX CTP WT K-EFF NEDC'IE9-11.333 3283.0 100.80 0.99250 MEASURED
FIGURE 4.1.59 (CONT.) PEACH BOTTOM 3 CYCLE //5 OD-1 STATEPOINT 12-2-81 4009 4849 4841 4833 s
\' \,
1 1 E 1 i f t I f B R 1 1 I a E a f 4825 4817 4809 5641
~ '
~ '
g
~
~ _
ig i b a f k a f I L 5633 5625 5617 AVG.
~ ~
\/ < <
CAVEX CTP WT K-EFF M (D g (Q 11.333 3283.0 100.80 0.99250 MEASURED
FIGURE 4.1.60 PEACH BOTTOM 3 CYCLE //5 OD-1 STATEPOINT 6-30-82 849 841
~
833 825 s s-s,,
/*
~
1657 1649 1641 8 17 1625 1633 1617 : 1609
~
~ ,,
2457
< 2449 : ,
2441 ; 2433 s
/ x CAVEX CTP WT K-EFF E0EEES 15.359 3262.0 102.12 0.99350 MEASURED
s_ h ._ u A Au_ _.L__h . W . L_ . _ +- - - - - . - --'-- ---- - - ' FIGURE 4.1.60 (CONT.) PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 6-30-82 2425
~
2417 2409 3257 i r%,
\
1 1 R 1 I i 1 1 iiI I E G 1 E 1 1 1 A 1 if 1 3249 3241
~
3233 3225 3217 ; 3209 : 4057 , 4049 s- s 4041
~
4033 ; 4025 , 4017 s CAVEX CTP WT K-EFF gg[E[D 15.359 3262.0 102.12 0.99350 MEASURED
FIGURE 4.1.60 (CONT.) PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 6-30-82 4849 4841 4833
~
4009
*~~ - ' -
s_
/ N ,
h . .....
< 4825 4817 4809 5641 I
5633 5625 5617 AVG.
~
f . j CAVEX CTP WT K-EFF M[M[D 15 359 3262.0 102.12 0.99350 MEASURED
FIGURE 4.1.61 PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 10-26-82 849 841
~
833 825 1657 1649 1641
' ~
8 17 s, ,
, b 1625 1633 1617 1609
;' %g 1
2457 2449
~
2441 2433
~
. s .
CAVEX CTP WT K-EFF M(E(D 17.808 3204.0 102.23 0.99806 MEASURED
FIGURE 4.1.61 (CONT.) PEACH BOTTOM 3 CYCLE #5 OD-1 STATEPOINT 10-26-82 2425 2417 2409 3257 NA 3249 3241 3233 ' 3225
, ,i f I. <
.. 1 E 1 I .
3217 3209 4057 4049 w ' '~ s 4041 4033 4025 4017
\
CAVEX CTP WT K-EFF N E E IES 17.808 3204.0 102.23 0.99806 MEASURED
FIGURE 4.1.61 (CONT.) PEACH BOTTOM 3 CYCLE //5 OD-1 STATEPOINT 10-26-82 4009 4849 ; 4841 4833
~
s y '; V 4825 4817 4809 S641
-: /
5633 5625 5617 AVG. CAVEX CTP WT K-EFF M( (D 17.808 3204.0 102.23 0.99806 MEASURED
FIGURE 4.1.62 PEACH BOTTOM 3 CYCLE //6 OD-1 STATEPOINT 10-26-83 849 841 L 833 825 l . 1 E 1 A A A 1 1 f 1 1 b iE a 1 & 1 1 A R H E E a k a A E f 1 1 g A t 1657 1649 1641 8 17 es,
,,-ss-u
\
"g y.
[ ' 1625 1633 1617 1609
- ~
~ i -- ,,
~
i - t 1; .,e y 2457 2449 2441 2433
' ~ ~
~ ~, , ~ '- - , 'r~,,
b s \ CAVEX CTP WT K-EFF EEE 14.318 3293.0 102.50 0.99642 MEASURED m' O _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ . _ _ _ - _ _ _ _ _ _ _ _ _ _ _ - - - - *-= -
l FIGURE 4.1.62 (CONT.) PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 10-26-83 2425
~
2417 2409 3257
- - s s, , s s_,
T "' J e
. '/ ,.
't
\.. '-
s 1 1 e I 1 1 1 1 1 E E E E i 1 2 1 0 a 9 I i E d 1 i 3249 3241 3233 322S
~
"' ~~
, ~- ~ < ,
, ' ~,
\,',
y t
. r ct 1.
,o , ,,,,. ...
3217 3209 4057 4049
- ~
i .
\
// A
\ o t
4041 4033 ~ 4025 - 4017
. s
,l
\ \
f PREDICTED CAVEX CTP WT K-EFF - - - - - - - - 14.318 3293.0 102.50 0.99642 MEASURED
_--.-.-_----___-- - ---_-_ - - - - -_---__ _ ~ ~
--. . _ _ _- _ - - _ . _= .- -- . _ _
FIGURE 4.1.62 (CONT.) PEACH BOTTOM 3 CYCLE //6 OD-1 STATEPOINT 10-26-83 4009 ' 4849 ' 4841
~
4833 l 1 . 1 i .A 1 i I E e 1 e . 1 3 1 4825 4817 4809 5641
' ~ ~
? '
g . , ...... . . . .. .
- 5633 5625 '
5617' AVG. f N,' ,D;
- CAVEX CTP WT K-EFF NEEES 14.318 3293.0 102.50 0.99642 MEASURED
-- --.- - __---_ - - - - . - - - - - - - , e -- s , ,, wn--- . - - -- - - - - - - - -- - --
FIGURE 4.1.63 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 2-18-84 849 841 ; 833 : , 825 r s 1 F A A 1 a 1 I A A R I 1 I I R 1 2 3 A 1657 1649
~
817 1641
~
j 1025 1633 1609 1617
,~.. , ,
~
/
g \ l' 2457 2449 2441~ 2433
~
j ,
\ .
CAVEX CTP WT K--E F F SEEES 12.084 3290.0 100.00 0.99527 MEASURED _ _ _ _ . - - - . _ _ - - _ _ _ - _ . _ - _ _ _ _ _ _ - _ - - _ _ _ _ _ _ _ _ - - _ . - - _ _ - _ - - - - -.-- - -_ _ _ _ <- - . - - - - - -- + ,- - - - - , . - - -- - - ~ _ __
FIGURE 4.1.63 (CONT.) 1 PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 2-18-84 2425 2417 2409 ~ 3257
- ' s-s 1 1 1 1 i A I d b i1 1 A k 1 i f E A B 1 1 3249 3241 3233 3225
- s s_ ,
~s 7 .' - '\
t . . . .. o 3217 3209 ' 4057 4049
,-s #
1 / % ,- I 4041 4033 4025 4017
~ ~ ~
, h \'.jf'
! CAVEX CTP WT K-EFF M(D@I(D_ 12.084 3290.0 100.00 0.99527 MEASURED ?_____ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - _ _ _ - - _ - - _ _ - _ _ _ _ _ _ _ - _ , -- _- -
FIGURE 4.1.63 (CONT.) PEACH BOTTOM 3 CYCLE //6 OD-1 STATEPOINT 2-18-84 4009 4849 4841 4833
~ '
l % i
, s gN ,
s
?
r
/
1 1 9 t I 1 2 a i e a 1 E 1 1 1 i E 4825 4817 4809 5641
- ~ ~
< r 5633 5625 : 5617 : AVG.
t ' t CAVEX CTP WT K-EFF N E E IE9 12.084 3290.0 100.00 0.99527 MEASURED W 1 I FIGURE 4.1.64
~
PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 9-21-84 849 841 833 ' 825
- s -
! s ( '%,,, I '
r r r
~
/
f
/ 1 1657 1649 1641
~
l 8 17
' * ~
r . l 1625 1633 1617 1609 e u s-
,' '-,- e i . ,
1 4r i 2457 2449 2441 2433
- ~ ~
e , - ~ ',
~ , - , s i s - s 1., ,t' ,
- r i
1 r h p ; r t l PREDICTED l CAVEX CTP WT K-EFF -------- 16.038 3229.0 102.00 0.99697 MEASURED l l l - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - . _ . - - - _ - _ - _ _ _ _ _ _ _ _ . - - _ _ _ - _ _ _ . _ _ - _ _ _ _ _ . _ _ _ _ . - . _ _ _ _ . _ _ _ _ _ _ _ . _ . .-
l l l FIGURE 4.1.64 (CONT.) l' PEACH BOTTOM 3 CYCLE #6 OD-1 STATEPOINT 9-21-84 2425 2417 2409 3257 e s , i e t e : , 3249 3241 3233 3225
' ~
~
es - e ~<g / s-,-s'~ A:,e '-
, s 4
L' r t e t r Nt r i
~
3217 3209 : 4057 : 4049 y p' f ~s-- 1 / m fl e ,
/ P 4041 4033 4025 4017
~
W <
' ~~ r ,' ~\'~ ~'
l PREDICTED CAVEX CTP WT K-EFF -------- l16.038 3229.0 102.00 0.99697 MEASURED
~ _
FIGURE 4.1.64 (CONT.) PEACH BOTTOM 3 CYCLE //6 OD-1 STATEPOINT 9-21-84
! 4009 ! 4649 4841 4833
~
[ , 1 l \ 4825 - 4817 4809
~
5641
~', <
~_
~
/
/
\
[, h j ', . 5633 5625 5617 AVG.
- s, e ' N' s s, ,
e .i L' k PREDICTED CAVEX CTP WT K-EFF --------
,16.038 3229.0 102.00 0.99697 MEASURED
4.2 Fuel Pin Fission Rate Distribution Comparisons The PECo SIMULATE-E model is used to evaluate peak fuel rod linear power density (kw/ft) at each node in the reactor core., To accomplish this, the converged SIMULATE-E nodal power is multiplied by the product of a conversion factor and the local pin peaking factor. The local peaking factor (LPF) is defined, at a given node, l to be the ratio of the peak-to-assembly average fuel rod fission rates. LPF values are input parameters to SIMULATE-E, and are accurately represented for each fut1 lattice as a function of three nodal parameters: (1) fuel assembly nodal exposure, Eijke h (2) instantaneous in-channel nodal void fraction, Vi jk, and (3) the 2x2 control rod configuration, M, surrounding the fuel node. 1 In this representation, SIMULATE-E models six different control rod configurations relative to the surrounding 2x2 control rod array. Fuel nodes may either bet (1) directly controlled (in 2 ways, M=6 or M=9); (2) laterally controlled (in 2 ways, M=5 or M=10); , l (3) diagonally controlled (M=ll);
) or (4) uncontrolled (M=12).
4-112
i These six control rod configuration states are portrayed . In Figure 4.2.1. Consideration of these control rod configuration states in the SIMULATE-E local peaking factor methodology allows a more accurate representation of the flux gradients produced within an assembly by the surrounding control rod pattern. PECo computer codes used in the generation of SIMULATE-E l local peaking factor data ares l (1) CASMO-1, the aingle assembly geometry lattice ; physics code. CASMO-1 provides fine-mesh cross section data for each of the regions comprising the BWR fuel assembly geometry. These cross sections are generated at different exposure and void conditions characterizing the fuel depletion h process. (2) COPHIN compiles and processes the CASMO-1 cross section data described above into PDQ-7-E/HMIMONY
> input format.
(3) PDQ-7 -E/ HARMONY , the sult1-assembly geometry lattice physics code. PDO-7-E/ HARMONY performs a fine mesh, four energy group, diffusion theory evaluation of the fuel pin flusion rate I l distributions within each assembly. The effects of flux gradients produced by neutronically dissimilar ! fuel assemblies and/or different control rod i I patterns are explicitly modeled. ; l l 4-113 1
(4) PINUP, a PECo production program used in the approximate evaluation of 2x2 assembly geometry fuel pin fission rate distributions, and associated local peaking factors based on flux reconstruction techniques. PINUP reads the single assembly CASMO-1 fuel rod fission rate distributions, together with nodal assembly power distributions
/
calculated by SIMULATE-E. Superposition of the i inferred flux distributions results in an approximate evaluation of the fuel pin fission rate distribution within the 2x2 assembly geometry. As outlined in this report, PEco methods used for the generation of local peaking factors have been qualified in a step-wice fashion, beginning with the basic single assembly geometry methods, and culminating with the methods used for the more complex i 1 multi-assembly geometries. Briefly stated, these steps l were:
)
(1) In the single assembly geometry case, CASMO-1 fuel l rod fission rate predictions were qualified via comparisons to Swedish measurements and Monte Carlo calculations. Data to support this claim are presented in Section 4.2.1. \ 4-114
(2) PDQ-7-E multi-assembly geometry methods were in turn qualified by comparing PDQ-7-E single assembly predictions with those generated by CASMO-1. These l results are presented in Section 4.2.2. i (3) Finally, 2x2 assembly geometry fuel pin fission ( rate predictions generated with the approximate PINUP code method were benchmarked against those from the PDQ-7-E model. This benchmark completes , the qualification process, and is described in ' Section 4.2.3.
}
I l
)
l l 1 l 1
)
i 4-115 l 1
FIGURE 4.2.1 CONTROL ROD CONFIGUHATIONS EMPLOYED IN SIMULATE-E LOCAL PEAKING FACTOR METHODOLOGY Configuration Valu e Blade (M) Configuration 12 11 I ) 10 / 5 9 (
- l
> 6
- Asterisk notes the assembly location where the local peaking factor is evoluoted. .
4-116
4.2.1 Qualification of CASMO-1 Puel Rod Plssion Rate Predictions The CASMO-1 code has been extensively benchmarked by the code vendor, Studevik Energiteknik-ABYU. Most notably, CASMO-1 predictions of fuel rod fission i rate distributions were qualified by comparison to measurements from the KRITZ high temperature criticals facility. Included in these experiments were measurements recorded for four 8x8 BWR lattices, both with and without gadolinium, which are summarized in Table 4.2.1.1. The KRITZ BWR test measurements and CASMO-1 4 predictions are compared in Figures 4.2.1.1 to 4.2.1.4. These comparisons demonstrate excellent agreement between the CASMO-1 fission rate predictions and the KRITZ test data. When data from all four experiments are combined, the mean and RMS difference statistics between the CASMO-1 predictions and the measurement data are determined to be: 1 ( pc/m = .2% Mean Difference in CASMO-1 Predictions vs. KRITZ Measurements oc/m = 1.6% Standard Deviation in Differences Between CASMO-1 Prediction vs. KRITZ Measurements I i 4-117
CASMO-1 predictions of fuel pin fission rate distributions have also been qualified by comparisons to KENO-IVIN Monte Carlo calculations. The case sequence for these comparisons consisted of fuel pin l fission rate distribution predictions for a total of 33 . cases, representing operating states and fuel lattices typical of Peach Bottom design analysis conditions. . Twenty-four of these cases were generated by PEco, while l the remaining nine cases were quoted from a similar study performed previously at Yankee Atomic Electric CompanyII). The 33 fuel rod fission rate distribution predictions were based on results from i three different 8x8 BWR fuel lattices, containing various gadolinia loadings, both in the rodded and '
! unrodded control state. Three steam void conditions , (0%, 40%, 70%) were modeled for each combination of gadolinium loading and control rod state selected. This case sequence, along with the overall RMS percent difference between KENO-IV and CASMO-1 results, is summarized in Table 4.2.1.2. Puel pin fission rate distribution comparisons are displayed for each of the 33 cases in Figures 4.2.1.5 through 4.2.1.37. The
( overall agreement between CASMO-1 and KENO-IV is excellent, exhibiting an overall RMS fuel rod fission rate difference of approximately 2.4%. l
)
l 4 4-118 I i
In summary, comparisons to both Swedish measurements and Monte Carlo results serve to qualify the PECo CASMO-1 model for the accurate prediction of fuel pin fission rate distributions in single assenibly l infinite lattice geometries. The percent uncertainty in i the CASMO-1 prediction of relative fuel pin fission l rates is, as evidenced by benchmarking to both measurements and KENO-IV calculations, approximately 2%. 1 I l l 4-119
TABLE 4.2.1.l* 1 KRITZ BWR LATTICE EXPSRIMENTS 1 EXPERIMENT 1: (Figure 4.2.1.1) BWR 1 - 8x8 Lattice, U02 Puel Pellets, 470 0F, Three GD O23 Fuel Rods - 2 w/o Gd 023 EXPERIMENT 2: (Figure 4.2.1.2) l ( BWR 2 - 8x8 Lattice, 002 Fuel Pellets, 470 0F, No Gd2 03 Fuel Rods ( l EXPERIMENT 3: (Figure 4.2.1.3) BWR 3 - 8x8 Lattice, U02 Fustl Pellets, 470 0F, Five Gd 023 Fuel Rods - 2 w/o Gd 023 1 EXPERIMENT 4: (Figure 4.2.1.4) BWR 4 - 8x8 Lattice s UO 2 , MO 2 ** Fuel Pellets, 470 F, No Gd 023 Fuel Rods ) l
- *Taken from Reference 24, Studsvik RF-78/6293.
l
**UO2 = Uranium Dioxide Fuel Pellets MO2 = Uranium Dioxide, Plutoniun Dioxide (Mixed Oxide)
Fuel Pellets. l l l 4-120
TABLE 4.2.1.2 COMPARISON OF KENO-IV and CASMO-1 FUEL PIN FISSION RATE DISTRIBUTIONS CASE LATTICE NO., W/0 CONTROL IN-CHANNEL FIGURE RMS(%) NO. NO. GAD RODS RODS VOIDS (%) NUMBER DIFFERENCE 1 1 (PECO)* 7 04 w/o NO 0% 4.2.1.5 2.0% 2 40% 4.2.1.6 1.9% 3 70% 4.2.1.7 1.7% 4 YES 0% 4.2.1.8 2.5% 5 40% 4.2.1.9 2.4% 6 70% 4.2.1.10 3.3% 7 N0 GAD NO 0% 4.2.1.11 1.9% 8 40% 4.2.1.12 1.8%
- 9 70% 4.2.1.13 1.5%
10 YES 0% 4.2.1.14 2.1% 11 40% 4.2.1.15 2.3% 12 70% 4.2.1.16 2.3%
? 13 2 (PECo)* 7 94 w/o NO 0% 4.2.1.17 1.8%
> ~ 14 40% 4.2.1.18 1.5% Sf 15 70% 4.2.1.19 1.9% 16 YES 0% 4.2.1.20 2.3% 17 40% 4.2.1.21 2.7% 18 70% 4.2.1.22 3.4% 19 N0 GAD NO 0% 4.2.1.23 1.7% 20 40% 4.2.1.24 2.0% 21 70% 4.2.1.25 1.6% 22 YES 0% 4.2.1.26 2.1% 23 40% 4.2.1.27 2.5% i 24 70% 4.2.1.28 2.4% 25 3 (YAEC)** 3 9 4 w/o NO 0% 4.2.1.29 2.9% 26 40% 4.2.1.30 2.9% 27 70% 4.2.1.31 2.4% 28 YES 0% 4.2.1.32 4.3% 29 40% 4.2.1.33 2.9% 30 70% 4.2.1.34 4.3% 31 N0 GAD NO 0% 4.2.1.35 2.2% 32 40% 4.2.1.36 2.1% 33 70% 4.2.1.37 1.6%
- CALCULATIONS PERFORMED BY PECO
** RESULTS QUOTED FROM REFERENCE 7, YAEC-1232 OVERALL RMS % DIFFERENCE 2.4%
1 Figure 4.2.1.1* Deviation in per cent between calculated and measured fission rates in an 8 x 8 UO, assembly with 3 Gd poisoned rods C ASE B WR 1 T=245'C (470*F') wId e g ap
-2.9 +2.5 -0.7
-1.9 -0.2 +1.8
)
-0.4 -4.0 +1.4 a "
-1.3 +1.1 l
e 2 :
* -0.6 e c
-0.4 40.6 l
-0.6 -2.7 +1.2 40.5 4
0.0 +1.0 narrow gap Ordinary fuel pin Gd pin (2 w/o Cd 03 ) Th e fig u re sn o w s 6, = 1,0 0 (PCASMO - PEXP)/PCASMO f or all me as ured p osition s-
' Fro m ref ere nce 24. STU DSVIK/RF-78/629 3 4-122
1 l l f Figure 4.2.1.2 # 1 Deviation in per cent between calculated and measured fission rates in on 8 x 8 UO, assembly without Eodolinium. C AS E B W R 2. T-245 C (470* F)
/
wide gap
-3.7 +1.9
-0.3 +1.1 4. 9 0.0 @.1 @. I a +1.2 +1.4 I 5 "
l t 3 t
* +1.0 o i
c
%.9 +1.2
-1.7 %.5 0.0 -1.8
-3.0 %.2 -1.1 narrow gap l Ordinary fuel pin
{ The figure shows 6; = 100 (PCASM O - PEXP)/PCASMO f or oli m easured position s. l l
' Fro m ref erence 24. STUD SVlk/R F-78/629 3 4-123
l Figure 4.2.1.3* l I Deviation in per cent between calculated < and measured fission rates in an 8 x 8 00, assembly with 5 Gd poisoned rods C ASE B WR 3. T=245'C (470*F)
/
wide gap )
-2.3 +2.1 -0.9
\ I
-0.7 -5.1 +1.3 40.4 -0.8 a 40.1 +2.3 -2.3 +3.1 I l 5 "
3 $
- t
-1.0 o
-0.6 40.9 40.3 -1.0 -4.1 +1.2
-0.6 narrow gap Ordinary fuel pin Gd pin (2 w/o Gd,0 ) 3 The figure shows 6, = 100 (P for all measured positions. CASMO - PEXP)/PCASMO
'From ref erence 24 STUDSVIK/RF-78/629 3 4-124
Figure 4.2.1.4* Deviation in per cent between calculated and measured fission rates in on 8 x 8 t assembly of the Pu-island type. - l C ASE 8 WR 4, T=2A5'C (470*F) l wide gap I
-2.0 UO2 rods *#
CASMO
+1.8 I l
--0 . 1 +0.1 I i i i f .
c. o
-0.5 '+0.9 l
+1.6 M0 2 rods i S l &
- I I a
$ l
- 0 +2.9 l0 i 40.6 ' $
o I . __ > I I I I i --0. 3 -1.7 +1.2i l___. , .___I I I
-0.8 -0.1 I+1.1 +1.21 + 1. 2 -0.3 I I
-3.5 -0.1 -0.9 -0.5 -2.6 narrow gap The figure shows di = 100 (P; - Pexp)/Pi and I P; = E P,xp for all nrosured positions.
Exper irrental uncertainty (le)in NC: rods 21.4 %
"W rods 20.7 %
for the overage fission rote in NO rods relative to LO rods ~ 21.6 %
' Fro m ref erence 24, STU DSVIK/R F-78/629 3 4-125
Figure 4.2.1.5 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.1: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded, 0% In-Channel Voids I WIDE #ATER GAP i 1.01 : : : : : ( 1.06 :
.05 . : . :
..... ..!. . ......'.... CASMO-1 Fission Rate * ....
1.03 0.23
- 1.07 0.25 . :
KENO-IV Fission Rate * -
.04 .02 -
, Delta '
1.13 0.89 1.06 ' 1.15 0 90 1.05
- No rm alized to 1.0 0
.02 .01 0.01 . .
..........: ....... . ..................z e .
< 1.23 0.98 1.07 1.18
- 2 0 1.22 1.00 1.05 1.13 : ;$
0.01-
$ .02 0 02 0.05 -
g y ........ .s....... w 1.17 0.26 1.02 0.00 1.15
.M $ 1.17 0.28 1.00 0.00 1.12 m g 0.00 .02 0.02 0.00 0.03 l g 1.26 1.10 0.97 1.06 1.00 0.85 1.26 1.10 0.99 1.05 0.97 0.85 0.00~ 0 03 .02 0.01 0 03 0.00 1.23 1.13 0.26 1.00 0.98 0.25 1.05 1.23 1.13 0.28 0.99 0.97 0.27 1.06 0.00 0.00 .02 0.01 1 .01 .02 .01 l
1.20 1.12 1.05 1.28 1.25 1.11 1.11 1.17 1 21 1.12 1.06 1.23 1.22 1.11 1.10 1.18
- 01
. 0.00 .01 0.05 0.03 0.00 0.01 .01 I l
NARROW WATER GAP i l l I l l 4-126 i
Figure 4.2.1.6 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 2. Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids WlDE W$TER GAP 1.06 i i ! ! 1.11 :
.05 : : :
l .........!.......'. CASMo-1 Fission Rate * .....: 1$ [2 ; [ KENO-IV Fission Rate *
.03 .03 - - -
'.............. Delta "
1.16 0.93 1.08 . 1.16 0.94 1.07 -
*No rm alized to 1.0 0 ,
0 00 .01 0.01 i l
.....................,...........,...........,z a . .>
0 1.25 1.01 1.07 1.15
- m "
1 1.22 1.01 1.05 1.10 I
$ 0 03 0 00 0.02 0.05 i j lg g
g 1.19 0.31 1.02 0.00 1.10
. . :>u 1.19 0 33
- M
$ 1.01 0 00 1.06 : .x 3-0 00 .02 0.01 0 00 0.04 o
,..........o 1.27 1.13 0.98 1.02 0.96 0.84 1.27 1.14 0.97 1.00 0 94 0.84 -
0 00 .01 0 01 0 02 0 02 0 00 . 1.23 1.14 0.31 0.98 0.96 0.30 1.03 i 1.23 1.16 0.33 0.98 0.95 0.31 1.07 . 0 00 .02 - 02 0 00 0 01 - 01
. .04 1.20 1.11 1.03 1.23 1.20 1.07 1.06 1.10 1.22 1.10 1.03 1.21 1.17 1.07 1.05 1.12
- 02
. 0.01 0.00 0.02 0.03 0.00 0.01 .02 NARROW WATER GAP 4-127
Figure 4.2.1.7 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 3: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% in-Channel Voids i . WIDE #ATER GAP
~
i 1.10 i ! I
. l i l 1.13 : :
.03 -
CASMO-1 Fission Rate * ......: 1.13 0.34 - i 1.16 0.37 : : KENO-IV Fission Rate *
.03 .63
.........>.. '"'i Delta 1.19 0.97 1.11 -
1.19 0.98 1.09 . *No rm alized to 1.0 0 : 0.00 .01 0.02 -
. .................................. ..... z Q s *
.> I
< 1.26 1.04 1.08 1.14 . :
O 1.24 1.05 1.06 1.11 : ; ; $
$ 0.02 .01 0.02 0 03 :
. g i g ..........;.........; g 1.20 0.37. 1.03 0.00 1.06 . : . . . . . . . .; h
$ 1.20_ 0 40 1.03 0.00 1. 03__
;o 3-0.00 .03 0.00 0.00 0.03 .
.o
.. v 1.27 1.15 0.99 1.00 0.93 0.83 ! .
1.26 1.14 1.00 0.98 0 91 0.83 I 0.01 0.01 .01 0 02 0 02 0 00 '
, )
1.22 1.15 0.37 0.97 0.93 0.35 1.01 1.21 1.16 0.39 0.96 0.94 0.37 1.03 - l 1 .01 .01 .02 0.01 .01 - 02
- . 02 .
1.18 1.09 1.01 1.19 1.14 1.02 1.00 1.03 1.19 1.09 1.00 1.17 1.13 0 99 0.99 1.03
.01 0.00 0.01 0.02 0.01 0.03 0.01 0.00 NARROW WATER GAP 1
1 4-128
Figure 4.2.1.8 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 4: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded, 0% in-Channel Voids
// //////////////////////////////////////
1
/
I
/ / . .
WTDE WATER GAP
/
0.35 i i i i t
/ / 0.36 . :
i i i
.01 : : / /
CASMO-1 Fission Rate. ......:
/ @j / / @.2 ; i KENO-IV Fission Rate
- i
.01 . . 02 : : / . . /
g,g, ......
/ 0.57 0.67 0.98
, Normalized to 1.00 0 58 0 69 0.98 f/ .01 .02 0.00
/
/ c.
....,.........,.....................z
< 0.68 0.80 1
// 0 0 66 0 81 1.09 1.09 1.34 1.32
'I l
0.02
/ /
q
.01 0.00 0.02 :
g l
/ s:: / 0.68 0.27 1.13 0.00 1.44 .M //
g 0 68 0.00 0.29
.02 1.12 0.01 0.00 0.00 1.36 0.08 x
o
/ : . /, 0.83 1.01 1.09 1.30 1.28 1.12 : i / 0.82 1.02 1.10 1.25 1.24 1.12 / 0.01 .01 .01 0.05 0.04 0.00
[/
/ 0.93 1.09 0.31 1.26 1.28 0.34 1.43 / /
0.96
.03 1.13
- 04 0.34
- 03 1.24 0.02 1.27 0.01 0.36
.02
__1. 4 8
.05 Z
1.08 1.16 1.22 1.61 1.65 1.50 1.53 1.61 1 11 1.16 1.21 1.58 1.61 1.49 1.51 1.59
.03 0.00 0.01 0.03 0.04 0.01 0.02 0.02 NARROW WATER GAP 4-129
Figure 4.2.1.9 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 5. Peach Bottorn 8X8 Fuel Lattice With Gadolinium Rodded,40% In-Channel Voids f/////////////////////////////////////// 1 /
,/ ...
Wide WATER GAP
/ 0.39 :
l
/ / 0.39 - *
- 0.00 -
// .. ...... ..............
CASMO-1 Fission Rate * ......i j/ 0.47 0.25 :
/
p 0 49 0 27 - - KENO-IV Fission Rate
- l
.02 .02 7
y .............. g ,,,, ..... . 0.59 0.66 0.94
/ _0 59 0.67 0 92
- No rm alize d to 1.0 0 :
/p/ 0.00 .01 0.02 . . .
/
. . . . . . . . . .. . . . . . . . . . . .....................z
/, a O
0.69 0.78 0.80 1.04 1.27
~2 // y
_0_68 0.01 - . 02 1.03 0.01 1.21 0 06
,g j/ ~
// 0.71 0.33 1.10 0.00 1.37
' >a j/ . r1
$ 0 73 0 36 1.08 0.00 1.32 m
j/ g .02 .03 0.02 0.00 0 05 ,' ,o
/ / / /
0.85 0.86 1.02
- 1. C+3 1.09 1.08 1.26 1.21 1.24 1.20 1.12 1.11
/ .01 .0i 0.01 0.05 0.04 0.01 : ,' / / / 0.95 1.11 0.38 1.25 1.27 0.41 1.45 / /
0 99
.04 1.13
.02 0.42
.04 1.23 0 02 1.25 0 02 0.45
- 04 1.48 7 03-1.11 1.16 1.21 1.57 1.61 1.48 1.49 1.56 1.16 _1.18 1.23 1 53 1.54 1.46 1.48 1.56
-.05 .02 .02 0.04 0 07 0.02 0.01 0 00 NARROW WATER GAP 4-130
Figure 4.2.1.10 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 6. Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,70% In-Channel Voids
//////////////////////////////////////// / / WIDE WATER GAP / . /
l 0.42 5 ! ! l / 0.43 :
/
.0i :
.........;.............. CASMO-1 Fission Rate * ......:
8j @j i : KENO-IV Fission Rate *
.02 .02 : .
/
'"'l Delta 0.60 0.66 0.90
/ 0,61 0.68 0.91
/
// .01 .02 .01
- No rm alized to 1.0 0 .
.........................................Z '/ e . . / < 0.70 0.78 1.00 1.21 %
O O 72 0 80 1.01 1.16
'/
.02 i $
/
/
q
.02 .01 0.05 -
. , g
......... ........ ........... a
/
/
g 0.74 0.41 1.07 0.00 1.32
.R. / /
g 0 75
.01 0 44
.03 1 06 0.01 0 00_
0.00 1.24 0.08 x ;
/ .
,g
/ ........ ........ . , '
/
/
0.88 0 89 1.04 1.06 1.08 1.08 1.22 1.19 1.20 1 17 1.12 1.11
)
/
/
.01 .02 0.00 0.03 ~6.lTJ~ 0.01 !
/
/ 0.98 1.12 0.47 1.23 1.25 0.50 1.45
/
/
1.02
.04 1.16
.04 0 51
.04 1.23 0.00 1.23 0 53 1.46 .
0 02 .03 - 01 Z 1.13 1.16 1.20 1.53 1.55 1.45 1.45 1.51 1 18 1 16 1 18 1.47 1.50 1.38 1.39 1.48
.05 0.00 0.02 0.06 0.05 0.07 0.06 0.03 l NARROW WATER GAP I
1 I l l 1 4-131 i l 1
l Figure 4.2.1.11 i Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 7: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded, 0% In-Channel Voids WlDE WATER GAP 0.89 i i ! ! ! 0.94 . .
.05 : : : :
..........!.............. CASMO-1 Fission Rate * ......!
Og kg , KENO-IV Fission Rate *
.04 .04 ,-
DeHa ; 1.03 0.92 1.03 1.05 0.93 1.02 . *No rm alized to 1.00
.02 .01 0.01 :
a.
..............................,...........,'z < 1.10 0.99 1.01 1.06 '2 0 1.10 0 99 1.00 1.02 ' $ 0.00 0.00 0.01 0.04
- $g g . . . . . . . . . . , . . . . . . . . . . !. . . . . . . . . . . : s y .
1.08 0.86 1.03 0.00 1.03 *
$ 1.10 0 87 1.02 0.00 1.02
'M m
g .02 .01 0.01 0.00 0.01 o
................. ... g 1.10 1.10 1.01 0.99 0.94 0.95 !
1.11 1.08 1.00 0 97 0 92 0.92
- l
.01 0 02 0.01 0.02 0.02 0.03
........... i 1.03 1.06 0.83 1.00 0.98 0.78 1.10 -
1.05 1.06 0 82 0.98 0.96 0.77 1.10
.02 T60- 0.01 0.02 U 02 0.01 0.00 I
0.99 0.96 0.97 1.15 1.13 1.05 0.99 0.99 1 02 0 98 0.97 1.13 1.11 1.04 0 98 1.01
- 03
.02 0.00 0.02 0.02 0.01 0.01 - 02 NARROW WATER GAP 1
1 4-132 i
l i Figure 4.2.1.12 l Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 8: Peach Bottom 8X8 Fuel Lattice With Gadolinium l Unrodded,40% In-Channel Voids WlDE VATER GAP 0.93 i ! i ! ! ! 0.97 -
.04 : : :
..............j. CASMO-1 Fission Rate * ......i lj @j i ; KENO-IV Fission Rote
- f
.03 .01 :
Delta ""! 1.06 0.95 1.06 - l 1.08 0.96 1.06_ :
- No rm alized to 1.0 0 i
.02 .01 0.00 : . . :
.... .. .......:..................... z g . . .
cc 1.12 1.01 1.03 1.06 : % 0 1.13 1.02 1.03 1 04 0.00
, l :$
$ .01 .01 0.02 : : g y .. ... ..:..................... a 1.10 1.10 0.87 0.87 1.04 0.00 0.00 1.01 0 96
.hm 1.02 . :
0.00 0.00 0.02 0.00 0.05 o E . : > 1.11 1.12 1.01 0.98 0.92 0.92 . 1.11 1.11 1.01 0.97 0.91 0.90 0 00 0.01 0.00 0.01 0.01 0 02 . 1.04 1.07 0.82 0.99 0.96 0.76 1.07 1.06 1.08 0.82 0.97 0.94 0.75 1.05 -
.02 .01 0.00 7.; .02 0.02 0.01 0.02 .
1.00 0.96 0.95 1.12 1.09 1.01 0.95 0.95 1 C4 0 97 0.96 1.10 1.07 0.99 0.95 0 96
- C4
. .01 - 01
. 0.02 0.02 0.02 0.00 - 01 NARROW WATER GAP l
4-133
l l l : Figure 4.2.1.13 ' , Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution I Case No. 9: Peach Bottorn 8X8 Fuel Lattice With Gadoliniurn Unrodded,70% In-Channel Voids i r 1 WIDE WATER GAP 0.96 ! ! ! ! ! ! 1.01 : :
.05 . : :
CASMo-1 Fission Rate * ......i 1
.;0 KENO-IV Fission Rate *
{
.03 .02 : : :
Delta '"'! 1.08 0.99 1.09 1.09 0.99 1.10 i
- Normalized to 1.00 :
.01 0.00 .01 : :
..............................:...........z 1 .>
cc 1.14 1.04 1.06 1.07
- : 2 O
J .16
.02 1.03 0.01 1.05 0.01 1.06 0.01 :
- g g
y 1.11 0.89 1.06 0.00 1.00
- M
$ 1.11 0.88 1.05 0.00 0.98 '
.m g 0.00 T Ul- 0.01 0 00 0.02 :
'o
.....................g 1.12 1 13 1.02 0.97 0.91 0.90 :
1.13 1.12 1.01 0.96 0.89 0.88 *
.01 0.01 0.01 0.01 TUT 0 02 .
1.04 1.08 0.82 0.98 0.94 0.73 i.03 i 1.06 1.09 _0.81 0 97 0.94 0.72 1.01 -
.02 .01 0.01 0.01 0 00 0.01 0 02 :
0.99 0.95 0.94 1.09 1.05 0.96 0.90 0.90 1 03 0 96 0.94 1 08 1.04 0 95 0.90 0.91
.04 .01 0.00 0.01 0.01 0.01 T).00 - 01 NARROW WATER GAP 4-134
{ Figure 4.2.1.14 { Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.10: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded, 0% In-Channel Voids f///////////////////////////////////////
/ / / .
WrDE WATER GAP
/
0.32 .'
/ 0.33 i i !
/
.01 -
/ .
/ .......... .............. CASMO-1 Fission Rote. ......j
/
/ 0.43 0.53 i i 0.44 0.54 KENO-IV Fission Rate * !
/ .01 EDT 7
/
0.52 0.66 0.89 DeIto """j 0.52 0.65 0 88 { /
/ 0.00 0.01 0.01
,No rm alized to 1.00
, /,- a ..........>................................z . [ /
/ 0 0.62 0 62_
0.78 0.79 0.99 0.99 1.17 1.13
'2 / $ 0.00 .01 0 00 0.04 : : :g / /
q g ....................,...........m
/
0.66 0.74 1.09 0.00 1.28
/ $ 0 65 0.75 1.08 0.00 1.24
* :M x
/ g 0.01 .01 0.01 0.00 0.04 : o
/ ..........:...........;
/p 0.74 1.01 1.11 1.20 1.21 1.25 :
/ 0.75 1.02 1.09 1.19 1.17 1.24 *
/
/
.01 .01 0 02 0.01 0.04 0.01 .
/
/ 0.79 1.05 0.95 1.24 1.29 1.03 1.51
/
/
0.83
.04 1.06
.01 0.95 0 00 1.24 0 00 1.27 1.04 1.51 i
0.02 0.01 T diT l L , 0.89 1.01 1.13 1.44 1.48 1.42 1.36 1.37 0 96 1.03 1 12 1.42 1.47 1.40 1.35 1.40
.07 .02 0.01 0.02 0.01 0.02 0.01 .03 NARROW WATER GAP 4-135
l Figure 4.2.1.15 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.11: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,40% In-Channel Voids
////////////////////////////////////////
s l
/
. ,/ WrDE WATER GAP
/ . . . .
/,/ 0.34 ! ! ! ! ! ! !
0.36 -
/
.02 : : : :
f :
..........!..........!... CASMO-1 Fission Rate *
/ @ j5 5 g.] ; ; KENO-IV Fission Rate
- j 0.00 0 00 *
/ ........;... Delta " !
0.54 0.64 0.87 - 0 53 0 65 0.88 : ' y/ 0.01 .01 .01 .
- No rm alize d to 1.0 0
'/ '
/ .........l........ .'.... !
.z
/ g
< 0.63
// O 0.65 0.77 0.77 0.97 0.98 1.14 1.11
. :m j/ .02 0.00
{ { ;$
$ .01 0 03 - -
g y j/
/ n . . . . . . . . . :. . . . . . . . . . : ....:u .>
// $
0.68 0.69 0.73 0.74 1.07 1.06 0.00 0.00 1.26 : :
.M 1.20 .m j/ g .01 .01 0.01 0.00 0.06 :
, c3
/ .
. . . . . . . . . . . ?;
/,
0 77 1.02 1.10 1.19 1.19 1.24
/ 0.78 1.02 1.11 1.16 1.18 1.20
/
/
.01 ~0 00 .01 0 03 0.01 0.04
/
/ 0.83 1.06 0.94 1.24 1.28 1.04 1.50 -
/
/
0 87
.04 1.08
.02 0 94 0 00 1.21 1.26 1.03 1.5D .
0 03 0 02 0.01 0 00 b .. . 0.94 1.02 1.13 1.43 3.47 1.40 1.35 1.36 1 00 1.05 1 15 1.41 1 44 1.38 1 35 1.39
.00 .03 .02 0.02 - 0.03 0.02 0.00 - 03 NARROW WATER GAP i
[ 4-136
l I Figure 4.2.1.16 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution 1 Case No.12: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,70% In-Channel Voids
///////////////////////////////////H//
/
/ . . . . . . . . . ..
Wl6E WATER GAP
/
/ 0.38 : .
l 0.40 *
- n
[ .02 .
.......... ......... ... CASMO-1 Fission Rate * .... 3
/ @$ @] ! : KEN o--IV Fissio n Rate * ;
.02 .02 . .
/ ......... ..
Delta 'i
! 0.56 0.64 0.85 0.57 0.65 0.85 *No rm alized to 1.0 0 0.00
/
/
.01 .01
/ wt
....................'.....................:z>
a M
/
/
3-0 72
.01 0 74
.01 1.05 0.00 0.00 0 00 1.20 0.04 .
.m c;
/
/
..........m
/
/
0.80 0.82 1.02 1.02 1.10 1.08 1.18 1.15 1.18 1.16 1.23 1.22
/
/
.02 0 00 0 02 0 03 0.02 0.01 .
/
/ 0.86 1.08 0.94 1.23 1.27 1.03 1.49
/
/
0 90
.04 1.09
.01 0.94 0.5T 1.20 0 03 1.25 0.02~
1.01 0 02 1.44 0 05
- Z 0.97 1.03 1.12 1.41 1.45 1.38 1.33 1.35 l 1.03 1.06 1.11 1.41 1.43 1.34 1.32 1.36
.06 .03 'v.01 0.00 0.02 0.04 0.01 .01
{ NARROW WATER GAP f ( 4-137
Figure 4.2.1.17 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.13: Peach Bottom 8X8 Fuel Lattice With Gadolinium
. Unrodded, 0% In-Channel Voids
{ WlDE VIATER GAP ( 1.05 i i i i i i l 1.09 :
.03 -
CASMO-1 Fission Rate * ......! . 1.14 1.19 i : ' 1.15 1.22 : : KENO-IV Fission Rate * -
.01 .03 . :
Delta "'"i 1.17 0.97 0.27 ' 1.16 1.00 0.29
- No rm alize d to 1.0 0 0.01 .03 .02 .
. i
..........,.................................Z
- a. .
< 1.03 1.10 0.95 1.21 -
- *I O 1.08 1.09 0.95 1.18 . . :"
0 00 0.01 0 00 q U 03- i i i :$ y ..........:....................c 1.17 1.05 1.14 0.00 1.17
$ 1.16 1.07 1.11 0.00 1.13_
- M
.m
, g 0.01 .02 0 03 - 0 00 0.04 i ,a
..................g 1.11 0.26 0 92 1.06 1.01 0.86 i !
1.11 0.28 0 93 1.04 0.99 0.86 : 0 00 .02 .0: 0 02 0 02 0.00 . : 1.22 1.04 0.25 1.01
- CO 0.25 1.05 1.23 1.07 0.28 1.00 1.00 0.27 1.08
- . 01 70T . 0.$ W' u ou .02 .03 1.20 1.10 1.19 1.15 1.14 1.13 1.18 1.17 1.21 1.11 1.18 1.13 1.12 1.13 1 16 1.16
- 01
.0 0.01 0 02 0.02 0.00 0.02 0.01 T
\ NARROW WATER GAP I 4-138
Figure 4.2.1.18 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No.14: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids k WIDE VIATER GAP / 1.10 i ! ! ! ! ! I 1.10 : : : 0 00 :
...... ...;.............. CASMo-1 Fission Rate * ......!
[ : : :
]$.01 1y
.01 j
j KENO-IV Fission Rate
- l Delta "'"i 1.19 1.00 0.32 : .
1.17 1.02 0.34 i
- No rm alized to 1.0 0 j 0 02 .02_ .02 : . . . :
..........,s.................... ............z a . . .
cc 1.08 1.12 0.96 1.19 : : : : 2 O 1.07 1.11 0.96 " 1.16 : y .O 0.01 0.01 0 00 0 03 i : jg y . . . . . . . . . . ; . . . . . . . . . . :. . . . . . . . . . . : s g . . .> 1.18 1.08 1.13 0.00 1.11
$ 1.17 1.08 0.00 1.08
- .M
- 1. 12_ _ : .m 5-0.01 0 00 0.01 0 00 0 0T .
- o>
....................v 1.13 0.32 0.93 1.03 0.97 0.85 i i 1.13 0.34 0.94 1.02 0.94 0.84 : .
U 00- .02 .01 0 01 0 03 0.01 . : 1.23 1.08 0.31 0.99 0.97 0.30 1.04 1.23 1.11 0 33 1.00 0.97 0.32 1.06 0.00 .03 .02 - 01 0 00- - 02
.02 1.20 1.10 1.17 1.11 1.09 1.08 1.13 1.11 1.21 1.09 1.17 1.10 1.06 1.07 1.11 1.11
.01 0.01 0 00 0 01 W 0.01 0 02 0 00 NARROW WATER GAP i
- <-n,
Figure 4.2.1.19
/
Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.15: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% In-Channel Voids WIDE VATER GAP 1.11 i i ! ! i i i 1.12 : : :
.01 : : : :
..........!..........!.... CASMO-1 Fission Rate * ......i
{ : : :
]:]9 )) j j KENO-IV Fission Rate
- j 0 00 0.01 . : :
..........{.... Delta "'"!
1.19 1.03 0.39 : : 1.16 1.04 0.41 i *No rmalized to 1.00 i 0 03 .01 .02 : . . . :
. . . . . . . . . . :. . . . . . . . . . . :. . . . . . . . . . .: . . . . . . . . . . .: z a . . .
cc O 1.08 1.14 0.98 1.19 : : : :m 1.06 1.13 0.99 1.15 : : :
$ 0 02 0.01 .01 0 04 i j i i:*$
q y
..........;....................: a 1.18 1.10 1.14 0.00 1.08 : : H
$ 1.17 1.12 1.13 0.00 1.05 : : :$
g 0.01 .02 0.01 0 00 M' j j
,a
..........,............p 1.14 0.38 0.96 1.01 0.94 0.84 i i 1.14 0.41 0.96 0.99 0.93 0.85 : : ,
0 00 .03 0 00 0 02 0 01 .01 : . 1.22 1.11 0.37 0.98 0.95 0.35 1.02 ! 1.22 1.15 0.39 0.97 0.95 0.37 1.05 : 0.00 .04 .02 0.01 U 0D- - 02
. .03 :
1.18 1.08 1.15 1.07 1.03 1.03 1.06 1.03 1.20 1.09 1.15 1.06 1.02 1.02 1.05 1.03
.02 .01 T05- 0.01 0.01 0.01 0.01 0.00 NARROW WATER GAP i
4-3.40
Figure 4.2.1.20 1 Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No.16: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded, 0% In-Channel Voids
/l//////////////////////////////////////
/ WIDE WATER GAP
/
/ 0.37
/ 0.37 i i i i i i
/
/ 0.00
/
CASMo-1 Fission Rote.
/
7 0.48 0.67
- i O.49 0.68 KENO-IV Fission Rate * !
/j .01 .01
/ ..........>...
! 0.57 0.65 Delta "i
/
/ 0.57 0.67 0.27 0 30 i
- ,No rm alize d to 1.0 0 0.00 i
/ .02 .03 g j
/
/ g ..........:...........:.....................z.>
0.58
/
O 0.85 0.95 1.37 * * ' 2
/ 0.58 0.84 0 96 1.34 h / g 0 00 0.01 .01 U BT i i
ig
/
/
q g . . . . . . . . . . ; . . . . . . . . . .i. . . . . . . . . . .! >u 1
/ 0.68 0.89 1.22 0.00 1.48
.M Y
/ g$
0 68 0.90 1.20 0 00 1.43 : : .m
/
/ =
0.00 .01 0.02 0.00 0.05 l jg i
/ .
......................o
/ 0.71 0.29 1.06 1.33 1.32 1.15
/ 0.72
.01
._.0 31
.02 1.08
.02 1.31 1 30 1.16 0 02 0.02 .01 : :
/p/
0.92
..........j 1.03 0.32 1.30 1.33 0.35 1.48 l /
/
0 93
.01 1.07
.04 0.34
.02 1.29 1.32 0.38 1.49
- j 0 01 0.01 . 03 ~ .01
.L :
l 1.09 1.17 1.42 1.49 1.54 1.57 1.13 1.67 1.66 1, 1 17 1.40 1.45 1.49 1.54
.04 1 65 1.65 !
0.00 0.02 0.04 0.05 0.03 0.02 0.01 NARROW WATER GAP 1 < i j 4-2 u
Figure 4.2.1.21 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.17. Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,40% In-Channel Voids f///////////////////////////////////////
/
/ W16E WATER GAP
/ . .
/
0.39 ! ! ! ! ! !
/ 0.40
/ .01 *
/ . . . . . . ; . . . . . . . . . . ;. . CASMo-1 Fission Rate * .....;
/ @j
/ @js l KENO-IV Fission Rate
- i 0.01 . 0 ". -
/ ............. .
Delta h ! 0.57 0.64 0.34 0.57 0.65 0.37
- N o rm alize d to 1.0 0 0.07 .01 .03
/ l . . .
/
/ m
......... 3.................. .:...........z
< 0.59 0.82
/ 0.92 '
1.31 : % 0 0.59 0.82 0.92
/ 0.00 0 00 0 00 1.28 : : $ / /
q 0 03 , ,
; :E
- . . . . . . . . . :s
/ y 0.70 / 0 70 0.88 1.17 0.00 1.42 : :
- M
// g$ U.00 0 88 0 00 1.13 0 C<
0 00 0 00 1.36 0.06 m o
/
..... . . . . . . . . . . . . ?;
/ / :
/
0.75 0 36 1.C6 1.29 1.28 1.15 : .
/ C 76 C.39 1.C8 1.25 1.24 1.15
/ .01 .03 - . 02 0.04 0.04 0.00 .
/
/ ...........
/ 0.96 1.07 0.39 1.29 1.32 0.42 1.50
) / 1.00
.04 1.11
.04 0.42
- 03 1.27 0.02 1.29 TOT 0.46 1.51 .
j,/
- 04
- 06 .
1.12 1.18 1.42 1.46 1.50 1.54 1.63 1.62 1.17 1.20 1.41 1.43 1.4~ 1.52 1.59 1.61
.C5 .02 0 01 0 03 0.03 0 02 0.04 0.01 NARROW WATER GAP j <-u 2
Figure 4.2.1.22 l Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No.18: Peach Bottom 8X8 Fuel Lattice With Gadolinium f Rodded,70% In-Channel Voids f///////////////////////////////////////
/
// ...........
W!6E WATER GAP
/
/ C.42 i i
0 43 - -
/ .01 .
//
CASMO-1 Fission Rate * ......: 0
/
/
KENO-IV Fission Rate *
.01 .02
/
/
Delta ~~. O.58 0.64 0.42
- 0 59 0 65
/
/ . 0 '. .01 C 45
.03
,No rm alize d to 1.0 0
/
.z
/ m< 0 59 3.....................:.........
/
/ C 63 0.63 j_82 0 69 0 91 1.25 1.20 .
'I i*
/ ]O . .01 .02 .02 0.05 -
- g
/ y .. ... ......... ....:.... :a>
/ M
/ 0 71 C.87 1.13 0 00 1.36
.$m
- f. / $ 0 72 C 89 1.12 0.00 1.29
/ g W
.0. .02 C.01 0.00 :
o
}.
/
/.
. . . . . . . . . . . . . . . . : 2;
/ 0 78 0 45 1.07
- 25 1.24 1.16
/ 0 60 _0.43 1 03 1.20 1.19 1.15 :
/ .02 .03 .01 0 OD O.03 0.01 . .
f
/ C 99 1.11 0.48 1.27 1.30 0.52 1.50 :
y /
/
1.C4
.Co 1.15
.04 0.52
.04 W 1.27 1.28 0.55 1.49 0 02 .03 0 01 Z -
1.15 1,18 1.40 1.41 1.45 1.50 1.59 1.56 1 20 1. 19 1.38 1.37 1 38 1.46 1 53
.C5 1.52
.01 v.02 C.04 ~C UT 0.04 0.06 0 04 h
NARROW WATER GAP ) 4-143 )
Figure 4.2.1.23 l Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No.19: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded, 0% In-Channel Voids WlDE V/ATER GAP 0.83 i ! ! ! ! 0.87 . i
.04 : : : : }
CASMo-1 Fission Rate * ......! [$ .04 ($.02 j j KENO-IV Fission Rate
- j Delta !
0.95 0.88 0.89 ', ; 0.97 0.89 0.89 : ,No rm alize d to 1.0 0
.02 .01 0.00 i
.:z a . .
< 0.89 0
0.99 0.94 1.12 : : : :% 0 91 0.98 0.94 1.11 : : :
; y .0T 0.01 ~ 0.00 'O.01 *o j j } }g y
y ..........:..................s 1.01 1.03 1.09 0.00 f 1.07 : :
- pm
$ 1.02 1.01 1.07 0.00 1.04 :
.01 0.01 0 02 0.00 0.03 3- : :
- o>
y .........,.........y 1.02 0.92 1.00 1.03 0.97 0.98 1.05 0.92 1.04 1.02 0.97 0.96 *
.03 0.00 T D2 0 01 0 00 0.02 :
i 1.07 1.11 0.86 1.C4 1.02 0.81 1.09 1.13 ) 1.11 0.86 1.03 1.00 0.80 1.12
.02 0 00 D.00~ 0.01 0.02 0.01 0.01 :
f 1.02 0.99 1.14 1.06 1.05 1.08 1.07 1.01 1 05 1.00 1.13 1.04 1.03 1.07
- 03 1.06 1.04
.01 0.01 0.02 0.02 0.01 0.01 - 03 NARROW WATER OAP f
4-144
Figure 4.2.1.24 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution ' Case No. 20: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids f r I WlDE $ VATER GAP / 0.87 O.93 .
. . 06 -
........i........!.... CASMO-1 Fission Rate * ......:
1 0.94 1.04 . : KENO-IV Fis:, ion Rote *
' 0.99 1.07 -
.05 .03 - -
Delta
""i 1 0.98 0.91 0.91 ,
1.00 0.92 0.92 : ,No rm alize d to 1.0 0 :
.02 .01 .01 : . .
g .........l...............................,>Z
< 0.9i 1.01 0.96 1.13 : : %
C 0.93 1.01 0 96 l 1.10 i : ; i* o
.02 0.00 0.00 0 03 {
)
3 :
- g ;
q _
. ; . . . . . . . c. . . . . . . . . . .; >a m 1.03 1.05 1.10 0.00 1.05 .' :M
$ 1 04 1.06 1.09 0 00 1.02
.m 3 .01 .01 0.01 0.00 0.03
- o
/
7 1.04 1.05 0 94 0.93 1.06 1.02 0.95 0.95 :: l 1.05 0.99 0.93 0.93 - I .01 0.01 0.01 0 03' O.02 0.02 . - 1.09 1.12 0.85 1.03 1.00 0.78 1.09
) 1.11 1.13 0.85 1.01 0.97 0.76 1.07 :
.02 .01 0.00 0.02 0 03 0 02 0 02 :
I 1.03 0.99 1.12 1.04 1.01 1.03 1.02 0.97 l 1.07 0.99 1.12 1 02 0.99 1.02 1 02 0.93 l
- 04 0.CO 0.00 0.02 0.02 0.01 0.00 .01 NARROW WATER GAP 1
l 4-145
Figure 4.2.1.25 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 21: Peach Bottom 8X8 Fuel Lattice With Gadolinium ( Unrodded,70% In-Channel Voids L WIDE WATER GAP i . : . : : ( 0.90 - ( 0.94 : : - - -
.04 . :
..........!..........i.... CASMO-1 Fission Rate * .....:
0
- j. f KENO-IV Fission Rate *
.03 .04 -
..........;... Delta ":
1 1.00 0.94 C.94 - 1.02 0.95 0 94 *No rmalized to 1.0 0
.02 .01 0 00 .
..........;.............................<z a . . .
< 0.93
- 04 0 99 1.15 :
M O O 94 1.05 0.93 I 13 . :
.01 J
q 0; 0.01 0.02 i j :k y 1.04 1.07 1.12 0.00 1.04
- : H
>:e
$ 1.04 1.07 1.11 0 03 1 00 .
g 0 JC O.00 0.01 0 00 0.04 j j ,o
.....................y 1.04 0.95 1.07 1.01 0.94 0 93 -
1.04 0.95 1.07 1.00 0.94 0.91 - 0 00 C.CO O 00 T0T" U 00 W -
.s 1.C9 1.13 0.85 1.02 0.98 0.76 1.06
) 1.11 1.13 0.86' 1.00 0.96 0.75 1.04 02 0.0) . 0 '. v.02 0.02 0.0i 'TIIT . I
" 03 0.98 1. 11 1.01 0.98 0.99 0.93 0.92 06 " CO 1.10 0 99 0 97 0 99 0 93 0 93
- 03
.02 0 01 0.02 0.01 0.00 0.00 .01 N A R R O'N 'N ATER G AP 4-146
Figure 4.2.1.26 C omparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution f Case No. 22: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded, 0% In-Channel Voids l //////////M/////M//MM//MM///
/
/
/
WI6E WATER GAP
/ .
O.29
/
/ 0.30
.01 : : : :
f
/
CASMo-1 Fission Rate * .
@f @j : . KENO-IV Fission Rate *
.01 .01 -
j
/
/ ..............
- i
!/
Delta " " * ) 0.48 0.61 0.76 -
// O 48 0 63 0.76 :
- No rm alized to 1.0 0
// 0.00 .02 0.00 -
/, .
l/
/
e
< 0.50 0.77 0.91 1.22
.............:z
- 2
) O O 50 0 78 )
/ 0.00 .01 0.90 1.20 0 02 j
$ 0.01
'/ : : : : g
/
/
q g . . . . . . . . . . ; . . . . . . . . . :. . . . . . . . . .:
/ 0.61 f 0.87 1.13 0.00 1.31
/ $ 0.61 0.87 1.13 0.00 1.27
'M m
/ g 0.00 0 00 0 00 u.00 0.04 ,
jg
.... .. ,.... .. .,p
/ 0.68 0.83 1.15 1.24 1.24 1.29 ;
/
/
0 63 0.uo 0 84
.01 1.13 0 02 1.21 0.03 1.21 u.03 W 1.26 '
- j
/ ,
/
/ 0.81 1.08 0.97 1.28 1.32 1.08 1.54 -
4 I ) / 0.84 1.09 0 9B 1 26 1.31 1.07 1 51 :
//
.03 .01 -0.I O 02 0 02 0 01 Wl . 1 1
j 1 I O.91 1.03 1.32 1.33 1.37 1.46 1.46 1.40 0 93 1.05 1.31 1.32 1.36 1.43 1.47 1.41 T - . 02 0.01 0.01 0.01 0 03 .01 .01 ( NARROW WATER GAP I ) I 4-147
l L Figure 4.2.1.27 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 23. Peach Bottorn 8X8 Fuel Lattice With Gadolinium l Rodded, 40% In-Channel Voids
/ / ////////////////////////////////////// / / WIDE WATER GAP / . /
0.32 i i i ! i
/ 0.34 - -
i !
/ : : -
.02 : :
/ . .
/
..........;..........:.... CASMO-1 Fission Rote. ... .:
/ [j @j j KENO-IV Fission Rote *
.02 .02
/
/
..........;.... 9,l,o ~.~.
/ 0.49 0.60 0.73 -
0.50 0.62 0.73 ,No rm alized to 1.0 0
/
/ .01 .02 0.00 i
/
/ w
. . . . . . . . . . :. . . . . . . . . . . . . . . . . . . . . j . . . . . . . . . . ; z 0.51
//
O 0.52 0.76 0 76 0.88 1.19
/ $ .01 0 00 0.89
.01 1.19 0 00 j
i
- g
//
q y . . . . . . . . . . . . . . . . . . . ;. . . . . . . . . . .; y
/
> 0.63 0.86 1.11 0.00 1.29 : : :
/ $ 0 63 0.87 1.10 0.00 1.25 : : :M m / -
3 0.00 .01 0.01 0.00 0.04 : :
- o f -
,/ 0.71 0.84 1.14 1.23 1.23 1.28
....................n
( f. 0 73 0 84 1.12 1.20 1 21 1.24 '
/ .02 0.00 0.02 0"03- 0.02 0.04 : / / / 0.85 1.09 0.97 1.28 1.32 1.07 1.53 l h / 0 90 1.11 0 96 1.24 1.27 1.06 1.52 : / .05 .02 0.01 0.04 d.05 0.01 0.01 ! l I
0.96 1.04 1.32 1.32 1.36 1.44 1.45 1.39 1 01 1 08 1 32 1.30 1.33 1.41 1.45 1.38
.05 .04 0.00 0.02 0.03 0.03 0.00 0.01 NARROW WATER GAP f
4-148
i l Figure 4.2.1.28 1 Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 24. Peach Bottom 8X8 Fuel Lattice With Gadolinium ( Rodded,70% In-Channel Voids f///////////////////////////////////////
/
l
/
/ .
WlbE WATER GAP l / 0.35 i i i i i i i
/
/ 0 36 . : :
.01 : : : :
/
/ :
....................[.... CASMo-1 Fission Rate * ...
3 0.44 0.58
/
/ 0 44 0 59 i
KENO-IV Fission Rate' : O 00 .01 : : :
/ ..........j.... g,n, ......;
! 0.51 0.60 0.72
/
0.52 0 61 0.72
- No rm alized to 1.0 0
/
/ .01 .01 M : . . . g'
/ ..........:............. . . . . . . . . . .: . . . . . . . . . .
/
/
g
< 0.53 0.75 0.86 1.16
- 2 O
$ /
j/ ,$ 0.53 0 00 0 76
.01 0.87
.01 1.12 0.04 i
j i$
- g g . . . . . . . . . . ; . . . . . . . . . . :. . . . . . . . . . .: e
/,/ , . .>
/ 0.65 0.86 1.09 0.00 1.28 : :
- M 0.66 0.88
/ $
g .02 1.08 0 01 0.00 0 00 1.23 0.03
- .m j/ .01
.g
/
/
1 l
/
/
0.74 0 77 0.84 0.86 1.14 1.12 1.21 1.19 1.22 1.18 1.26 1.25 l
/ - 0T
.02 u.02 0 02 0 04 0 01 .
y/ . . . . . . . . . . .
/ O.89 1.11 0.97 1.27 1.31 1.06 1.52 2 ) //
0 93
.04 1.13
.02 0.98
.01 1.26 0 01 1.28 TOT 1.02 0 04 W 1.49 .
'l 1.00 1.06 1.31 1.30 1.34 1.42 1.44 1.37 1 06 1.09 1 30 1.29 1.32 1 39 1.42 1.36 i
.06 .03 0.01 0.01 0 02 0.03 0.02 0.01 I NARROW WATER GAP
)
I 1 1 4-149 ; i i
l Figure 4.2.1.29i Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution ( Case No. 25. Vermont Yankee 8X8 Fuel Lattice With Gadolinium Unrodded, 0% In-Channel Voids WIDE' WATER GAP i : : : : : : :
,1.02
.04
.02 : : : :
..........}..........j.... CASM0-1 Fission Rate * ......i .
I 1.09 1.08 i i { 1.16 1.10 : : KENO-IV Fission Rote * !
.07 :
.02 : :
.........p... oelta "'!
i 0.99 0.94 0.97 : 1.02 0.96 0.99 j .03 i 'No rm alized to 1.0 0 i
.02 .02 :
i m . . . . . . . . . i. . . . . . . . . . . i. . . . . . . . . . i . . . . . . . . . . .! z
< 1.14 1.08 0.82 I
O 0.21 : : : : 5 1.16 1.09 0.82 0.21 : h $ .02 .01 0 00 0 00 i i i ig g
, . . . . . . . . . . ; . . . . . . . . . . i. . . . . . . . . . .! >s 1.11 1.02 0.77 0.77 0.00 :
- M 3 d2~ 0
)
.....................p 1.14 0.99 0.21 0.80 0.96 1.00 : :
1.12 1.04 0.23 0.83 0 96 1.05 : : 0 02 .05 .02 0"00 0.00 .05 : : 0.99 1.17 0.96 0.98 1.03 1.10 ) .0.98 1.20 0.93 0.95 1.21 ! _0.99 1.08 1.19 : 0.01 .03 0 03 0 03 0.04 0 02' O.02 : 1.12 1.14 1.02 1.23 1.24 1.31 1.15 1 15 1.13 1.07 1.04 1.18 1.22 1.24 1.14 1.05
.03 0.01 .02 0.05 0.02 0 07~ 0.01 0.02 NARROW WATER GAP i
TAnalysis performed by Yankee Atomic Electric Company. i Taken from Reference 7. 4-150
Figure 4.2.1.30i Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution 3 Case No. 26: Vermont Yankee 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids ) WIDE 1/ATER GAP 1.09 ! ! ! ! ! ! 1.15 : :
.06 : : .
..........i..........'....
CASMO-1 Fission Rate * ......!
];jj 1)l l i KENO-IV Fission Rate
- l
.01 .03 -
l i 1.03 0.98 Ddta '*! 1.01 ' 1.06 0.99 0.97 i
- No rm alized to 1.0 0 :
.03 .01 0.04 :
j a
..........s...............................
. z
< 1.17 l
I O 1.11 0.84 0.25 : : 'm 1.18 1.16 0 88 0.26 f $ .01 .05- .04 .01 i ! : ig y f 1.14 1.05 0.79 0.75 0.00 f $ 1.15 1.04 0.80 0.81 0 00
' .N
.m 3 .01 0.01 .01 .06 0.00 a
..................... g .
1.16 1.03 0.26 0.79 0.90 0.94 .' ! 1.14 1 05 0 27 0.78 0.86 0.92 * * ! 0 02 .02 .01 0.01 0.04 0.02 - : ) '
- l 1.01 1.19 0.96 0.95 0.98 1.04 1.15 1.04 0 96 !
) 1.20 0.94 0.99 0 99 1.13
.03 .01 0 00 'O 01 .01 0 05 0.02 '
I 1.13 1.14 1.00 1.18 1.18 1.24 1.08 1.01 1 14 1 15 1.00 1.14 1.14 1.20 1.03 0 97
- 01
.01 0.00 0.04 0.04 0.04 0.05 0.04
) l NARROW WATER GAP ) T Analysis performed by Yankee Atomic Electric Company. ) Taken from Reference 7. s 4-151
Figure 4.2.1.31i l Comparison of KENO-iV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 27: Vermont Yankee 8X8 Fuel Lattice With Gadolinium Unrodded,70% in-Channel Voids l l WIDEMATER GAP f 1.13 : i 1.18 - i i i i !
.05 : : .
l
..........!..........'.... CASMO-1 Fission Rate * ......:
) jj ] jj f l- KENO-IV Fission Rate *
.03 .03 f
l : Delta '"! ) 1.05 1.02 1.05 l 1.05 1.05 1.06 :
- No rm alized to 1.0 0 O 00 .03 .01 :
a ..........s................................ z
< 1.19 O
1.15 0.89 0.31 2 I 1.14 1.10 0.93 0.33 h $ 0 05 0 05 .04 .02 - i
- g q
> a ....................:...........:>, 1.15 1.08 0.82 0.77 0.00 I ) $ 1.16 1.05 0 83 0.79 0.00
- M
.m CY 5 .01 0 03 .01 0 00 g
............. D 1.17 1.07 0.32 0.78 0.87 0.90 1.16 1.08 0.33 0.79 0.85 0.89 '
O.01 .01 .01 .01 0 02 0 01 1.02 1.21 0.97 0.93 0.94 0.98 1.08 7 1.00 1.19 0.99 0.92 _0.96 0.97 1.12 ; O 02 0 02 .02 0.01 .02 0 01 .04 . 1.13 1.13 0.97 1.13 1.11 1.16 1.02 0.95 1 14 1.13 0.97 1.10 1.09 1.15 0 98
- 01 0.94 0.00 0.00 0.03 0.02 0.01 0.04 0.01 NARROW WATER GAP T Analysis performed by Yankee Atomic Electric Company.
l Taken from Reference 7. 4-152
Figure 4.2.1.32i l Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution t y Case No. 28: Vermont Yankee BX8 Fuel Lattice With Gadolinium l Rodded, 0% in-Channel Voids l//////////////////////////////////////
/ V/iDE WATER GAP
/
/ 0.35 i ! ! !
// 0.38 . :
.03 : : :
/! '
.........!..........:... CASMO-I Fission Rate * .....:
l
/
/ @j @p
; j KENO-IV Fission Rate * .
0 00 f
/
.02 ; .
! Delta '!
> / 0.47 0.62 0.78 : -
' 0.50 0.63 i
/ 0.79 i
- Norm alized to 1.0 0
.63
/ .01 .
l .01 : . . . : l / . . . . . . . . . . ; . . . . . . . . . . :. . . . . . . . . . .: . . . . . . . . . . .: z
/
/
m
< 0.59 0.80 0.74 0.24 2
O 0.61 0 79 i
/ 0.76 0.25 i '$
)
/ $ .02 0.01 .02 .01 :
- g
/ q ._
..........;..........i.... . . . . .: s
> /
/
n 0.63 0.82 0.77 0.91 0.00 ) : M
/ $ 0.63 0 82 0.82 0.94 0.00 : x
/
/
g 0 00 0.00 .05 .03 0 00 , g
/ . . . . . . . . . . . . . . . . ,
/ 0.73 0.73 0.87 0.89 0.25 0.27 1.00 1.01 1.25 1.23 1.34 1.30
/y/ 0 00
. .02 .02 .01 0 02 0 04 '
I p/ 0.78 1.16 1.11 1.24 1.37 1.50 1.69 - ) / 0.82 1.19 1.09 1.21 1.36 1.44 1.64
/ .04 - 03 0 02' O 03 O '01 - 0 06 0 05 L .
l 1.06 1.23 1.22 1.58 1.67 1.81 1.62 1.53 1 22 1 22 1.24 1.54 1 60 1.74 1.61 1.51
.16 0.01 - 02 0.CW 0.07 0 07 0.01 0.02 NARROW WATER GAP T Analysis performed by Yankee Atomic Electric Company, l
Taken from Reference 7. 4-153
t l l Figure 4.2.1.33i 1 l Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution l ( Case No. 29. Vermont Yankee 8X8 Fuel Lattice With Gadolinium ! l Rodded,40% In-Channel Voids
///////////////////////////////////////
/
/
/
WIDE WATER GAP [ 0.39 i i !
/
/ 0.43
.04 -
/
/
CASMO-1 Fission Rate * ......i 8$ j g% ; j KENO-IV Fission Rate
- 0.01 - 07 ; i
/ ..............
Delta "!
/ 0.48 0.61 0.76 -
0 50 0.62 0.75. ,N o rm alize ci to 1.0 0
/ .02 .01 0.01 y/
. . . . . . . . . . : . . . . . . . . . .:. . . . . . . . . .> . .: . . .l
//
a
< 0.61 0.78 0.74 0.30
*2 O '*
i I
/
/
O 61 0.00 0.81
.03 0.73 0.01 0.34
.04
$ : . : : q ;
/
/
q
=
..........:..........:.........: a>
{
/
/ $
0.66 0 68 0.82 0 83 0.77 0.81 0.89 0 89 0.00 0.00
*M m
/ -.02
/
g .01 .04 0.00 1 .00 ,
'g
/
/
0.77 0.89 0.32 0.99 1.20 1.29 '
/
/
0 79
.02 0 92 73-0.34
.02 1.02
.03 1.16 0 04 1.29 0 00 i
/, .. .......
/ 0.82 1.19 1.13 1.22 1.33 1.46 1.66
) /
/
0 85
.03 1.17 0.02 1.15
.02 1.18 0.04 1.29 0.04 1.41 0.05 1.66 0 00 1 l
1.12 1.25 1.21 1.55 1.63 1.77 1.58 1.50 1.14 1.27 1.19 1 53 1.59 1.71 1 58 1.44
.02 - 02 0.02 0.02 0.04 0.06 0.00 0.06 i l NARROW WATER GAP T Analysis performed by Yankee Atomic Electric Company. l Taken f rom Ref erence 7.
4-154
Figure 4.2.1.34i Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution Case No. 30. Vermont Yankee 8X8 Fuel Lattice With Gadolinium Rodded,70% In-Channel Voids 7/,/yy,/yyy//g//y//y//yy//////// l v/IDE WATER GAP y[ ........... .. ..... .... .... .............. .... ...... ....... .. . l [ 0.43 i i ! ! ! /
/ 0.47 :
.04 -
[ ..........!........'.... CASMo-1 Fission Rate * ......i 8j gj : . KENO-IV Fission Rote * [
.03 0.03
/
/ .............
cena ! 0.50
//
j 0.52 0.61 0.63 0.74 0.76 *No rm alize d to 1.0 0 l
.02 .02 .09 7
n / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .;>z
//
c.
< 0.63 0.77 0.73 0.39 0 0.70
/ ~ DT 0.80
.03 0.79
.06 0.41
.02 ig
/r
,/
q .........s...................... s g >
/ 0.69 0.83 0.78 0.89 0.00 .M
,/ 0.76 0 84 0.82 0.90 0.00 x g$
.0/ - 01 .04 0.00
,/
/
.01
,g
.......o
/ 0.81 0.93 0 98 0.41 0.93 1.16 1.25
{
/
,/
0 81
' O C0 .05 0 44
. 0.3 1 01
.03 1.15 0.01 1.21 0.04 9 . . . . . . . .
/ 0.86 1.21 1.14 1.20 1.30 1.42 1.61 l
) /
/
0 88
.02 1.18 OW 1.15
.01 1.19 0.01 1.27 0.03 1.33 0.09 1.54 0 07 '
1.17 1,26 1.19 1.50 1.57 1.70 1.53 1.46 1 15 1 26 1.20 1.41 1.53 1.64 1.47 1 37 0.02 0.00 .01 0.09 0.04 0.06 0.06 0.09~ 1 NARROW WATER GAP 6 T Analysis performed by Yankee Atomic Electric Company. I Taken from Reference 7. 4-155 i
Figure 4.2.1.35i Comparison of KENO-IV and CASMO-1 Fuel Pin Fission Rate Distribution i Case No. 31: Vermont Yankee 8X8 Fuel Lattice With Gadolinium Unrodded. 0% In-Channel Voids l l WlDE WATER GAP O.92 i i i ! i i i l 0.91 : : : 0.0T : : : :
..........[,..........].... CASMO-1 Fission Rate' ......i
@j 8'99 ; f KENO-IV Fission Rate
- f
.01 0 00 :
9g ......
\
0.90 0.89 0.98 0.88 0 91 1.00 l 'No rmalized to 1.0 0 f 0.02 .02 .02 : . . :
.........,s..... . . . . :. . . . . . . . . . .: . . . . . . . . . . .; z a . . .
.)
< 1.06 1.05 0.92 0.50 : : : : 2 0 1.03 1 10 0.95 0 91 l l l j$g
$ 0.03 .05 .03 .01 i i !
y .
' . . . . . . . . . . i . . . . . . . . . . j. . . . . . . . . . .j >s
( 1.04 1.03 0.92 0.93 0.00 : :
- M
$ 1.05 1 03 0.92 0 91 0.00 : : :x g .01 0.00 0.00 0.02 0 00' i ig 3 .
.T 1.07 1.06 0.94 0.92 0.95 0.94 : :
1.08 1.09 0.94 0 90 0.93 0.93 : : { .01 .03' 0 00 0.02 0.02 0.01 : 0.92 1.14 1.01 0.97 0.97 0.99 1.08 i
) 0 93 1.13 1.01 0 96 0.93 0.93 1.07 :
.01 0.01 0 00 0.01 0.04 DT 0.01 :
I 1.03 1.06 0.96 1.14 1.13 1.17 1.01 0.94 1 05 1 08 0.97 1.13 1 15 1 16 1.02 0.93 1
- 02
. .02 .01 0.01 .02 T.01 .01 0.01 l
i NARROW WATER GAP l l I TAnalysis performed by Yankee Atomic Electric Company. Taken from Reference 7. l 4 4-156 !
Figure 4.2.1.36i Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 32: Vermont Yankee 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids l WIDE 1/ATER GAP O.98 i i i i i i i 0.99 : : :
.01 : : : :
..........i..........i.....
CASMO-1 Fission Rate * ......i . 1.04 1.05 i i ! 1.07 1.09 : : KENO-IV Fission Rate * { :
.03 .04 : : :
Delta '""! 0.94 0.92 1.01 i O 93 0 91 1.02 : , N o r m ali.'.e d t o 1. 0 0 i 0.01 0.01 .01 :
~. .
g . . ..... . ..y ... .......;..... ......;... ...... . ; >z
< 1.09 1.08 0.93 0.89 . : : 2 0
l 1 07 CI67 1.10 0 95 0.93 : : : l 3 .02 .02 .01 i i iE y . . . . . . . . . . ; . . . . . . . . . . i. . . . . . . . . . .: a y . ( 1.07 1.05 0.92 0. 93 0.00 : .
- M
$ 1.07 1.05 0.92 0.89 _0.00 : : :m 0.00 0.00 0 00 0 CO 0.01 : c>
3- : :
.....................p ) . :
1.09 1.08 0.93 0.89 0.9' O.90 . 1.10 1 09 0.94 0.92 0 90 0.92 : :
.01 .01 .01 .03 0.01 .02 :
0.94 1.16 1.01 0.95 0.93 0.96 1.04
) 0.95 1.14 1.02 0.91 0.90 0 93 1.03 : ,
.01 0 02 .01 0.04 0 03 0 03 0.01 -
! 1.04 1.07 0.94 1.11 1.09 1.12 0.97 0.90 1 09 1 08 0 96 1.08 1.07 1.10 0.96 0.83
.05 .01 .02 '0.03 0.02 0.02 0.01 0.02 NARROW WATER GAP 1
l l T Analysis performed by Yankee Atomic Electric Company. I Taken from Reference 7. 4-157 l i l l
! Figure 4.2.1.37i l Comparison of KENO-IV and CASM0-1 Fuel Pin Fission Rate Distribution Case No. 33: Vermont Yankee 8X8 Fuel Lattice With Gadolinium ) Unrodded,70% In-Channel Voids l WIDE WATER GAP 1.02 i i i i i i i 1.04 : : :
.02 : : : :
.........i.........l.... CASMO-1 Fission Rate * .....i 1 08 g ].}@ KENO-IV Fission Rate
- i 0.01 0 00 -
0.97 0.96 1.04
..........}....
DeIta """I ' 1.01 0.98 1.04 :
- No rm alize d to 1.0 0 i
.04 .02 0 00 -
a . . . . . . . . . . } . . . . . . . . . .]. . . . . . . . . . l . . . . . . . . . . .] z 1.11 1.11 0.96 0.90 . : : 'm 0 1.12 1.14 0.96 0.87 :
.01 .03 0.C0 0 03
$ i j ,g y
\ y '........'.........]...........!>g l 1.03 1.08 0.93 0.90 0.00 : :
$ 1.11 1.06 0 94 0.88 0.00 *
- :N ::o 3-
.03 0.02 .01 0.6T 0 00 :
- o
..............n 1.10 1.10 0.94 0.88 0.88 0.87 : :
1.11 1 11 0 93 0 90 0 89 0 87 ) .01 .01 0.01 .02 .01 0.C0 . . 0.95 1.17 1.01 0.93 0.91 0.93 1.00
) 0 97 1.17 0.99 0.92 0.88 0.92 1.02
- 02 TDT 0 02 0 . 0'i~ 0 03 0.01 .02 1.05 1.06 0.93 1.07 1.04 1.07 0 93 0.86 1.04 1 06 0.92 1.07 1.02 1.05 0 94 0.84 0.01 0.00 0.01 0.00 0.02 ~6.02 .01 0.02 NARROW WATER GAP 1
i 1 T Analysis performed by Yankee Atomic Electric Company. Taken f rom Ref erence 7.
, 4-158
l 4.2.2 Comparisons Between PDQ-7-E and CASMO-1 Puel Pin Pission
- Rate Predictions
\ PDQ-7-E fuel pin fission rate predictions have been benchmarked to CASMO-1 results at various fuel exposure, void fraction and control condit Lons. To accomplish this, the PDQ-7-E calculations mod, led an infinite lattice geometry consisting of a sii.gle assembiv with reflection symmetry (i.e., zero c.rrent) boundary conditions. Distinct regions were used in the PDQ-7-E model to represent each fuel pin cell and water rod cell, as well as the channel, inter-assembly water gaps and control rod (Figure 4.2.2.1). The physical dimensions and layout of these regions were nearly identical to those used in the CASMO-1 single assembly model. Four energy group cross sections for each of the PDQ-7-E compositions assigned to these regions were likewise generated by CASMO-1, and processed into PDO-7-E format by COPHIN. The cross section collapsing and averaging procedure used the CASMO-1 converged flux solution to perform the volume and flux weighted
)
integrations. Because of differences between diffusion { and transport theories, it was necessary to adjust the nuclear data input to PDQ-7-E in those cases involving the presence of heavy absorbers (gadolinium and/or control rods). This procedure effectively matched the assembly reactivity predictions between CASMO-1 and 4-159
l PDQ-7-E so that proper account of reactivity effects could be achieved in the PDQ-7-E multi-assembly model. Figures 4.2.2.2 to 4.2.2.25 cont ain comparisons between CASMO-1 and PDQ-7-E fuel pin fission rate predictions for a typical Peach Botton 8x8 fuel lattice at various exposure, void fraction, and control rod conditions. Table 4.2.2.1 provides a summary of the single assembly local pin peaking factors and RMS difference statistics derived from these results. From the figures it may be observed that an increased bias occurs in the PDO-7-E fuel pin power results for the rodded lattice case. This bias occurs for the fuel pins adjacent to the narrow water gaps, and causes the PDQ-7-E fuel pin powers at these locations to be underpredicted when compared to the same CASMO-1 results. In defense of the model, however, the following points are noted: (1) The bias is restricted primarily to coincident high fuel burnup and high in-channel void conditions. ) Rodded nodes at these conditions are probably non-existent, and certainly non-limiting for actual I steady-state reactor operations. (2) The bias has a small effect on the local peaking factor results. CASMO-1 local peaking factor predictions are in good agreement with those from i l 4-160 l
)
i I l PDQ-7-E for all fuel burnup, void, and control ; conditions studied. (3) The rodded assembly PDQ-7-E bias would tend to conservatively predict the local peaking factor in neighboring unrodded fuel assemblies. Since PDQ-7-E tends to underpredict the rodded assembly fuel pin relative powers adjacent to the narrow water gap, fuel pin relative powers adjacent to the wide water gap in neighboring unrodded assemblies should tend to be slightly overpredicted by PDQ-7-E in the multi-assembly geometries. The flux gradient produced by the control rod will tend to locate the peak pin power in a neighboring unrodded assembly near one of these wide water gap locations. In consideration of the above, the PECo PDQ-7-E model can be used for the accurate prediction of local peaking factors in multi-assembly geometries at all fuel burnup, in-channel void, and control rod configuration conditions. As displayed in Table 4.2.2.1, the average I RMS percent difference between PDQ-7-E and CASMO-1 fuel pin fission rate predictions is 3.3%. Likewise, the RMS percent difference between PDQ-7-E and CASMO-1 local peaking factor predictions is 2.2%. I 4-161
TABLE 4.2.2.1 COMPARISDN OF PDQ-7-E/ HARMONY AND CASM0-1 FUEL PIN FISSION RATE DISTRIBUTIONS Case Lattice Control Void Exposure Figure RMS PDQ CASMO LPF No. No. Rods 1%1 GWD/MTU Numbe.- %Diff. LPF LPF %Diff. I 1 No 0% 0 4.2.2.2 1.8% 1.255 1.279 -1.9% 2 11 4.2.2.3 1.4% 1.116 1.116 0.0% 3 21 4.2.2.4 1.5% 1.128 1.105 +2.1% 4 32 4.2.2.5 1.8% 1.123 1.089 +3.1% 5 40% 0 4.2.2.6 2.1% 1.247 1.273 -2.0% 6 11 4.2.2.7 1.6% 1.100 1.095 +0.5% 7 21 4.2.2.0 2.0% 1.096 1.087 +0.8% 8 32 4.2.2.9 2.5% 1.090 1.073 +1.6% 9 70% 0 4.2.2.10 2.8% 1.230 1.271 -3.2% 10 11 4.2.2.11 2.2% 1.133 1.128 +0.4% 11 21 4.2.2.12 2.7% 1.104 1.081 +2.1% 7 12 32 4.2.2.13 3.5% 1.090 1.065 +2.3% o' 13 1 YES 0% 0 4.2.2.14 2.2% 1.607 1.632 -1.5% S3 14 10 4.2.2.15 2.3% 1.499 1.476 +1.6% 15 21 4.2.2.16 2.4% 1.542 1.501 +2.7% 16 32 4.2.2.17 2.7% 1.539 1.487 +3.5% 17 40% 0 4.2.2.18 3.4% 1.547 1.593 -2.9% 18 10 4.2.2.19 3.4% 1.460 1.442 +0.8% 19 21 4.2.2.20 3.7% 1.503 1.476 +1.8% 20 32 4.2.2.21 4.3% 1.509 1.470 +2.7% 21 70% 0 4.2.2.22 4.7% 1.481 1.543 -4.0% 22 10 4.2.2.23 4.9% 1.407 1.443 -2.5% 23 21 4.2.2.24 5.7% 1.448 1.470 -1.5% 24 32 4.2.2.25 6.6% 1.459 1.500 -2.7% Average RMS % Difference 3.3% Average LPF % Difference 0.2% RMS LPF % Difference 2.2%
l F!GURE 4.2.2.1 PDQ-7-E 8X8 SINGLE ASSEMBLY MODEL GEOMETRY DESCRIPTION l A
/
./////;/-4MCONTROL RODV/Y/p/hl NII
' s-++__a i l i l l ! l l ; ( l l 1 I l l I I l
, I1 1 I I I I I WATER G AP I I ! I I i 11 I l' , I I I I I I i i l l I i i I i I I I i 1
, e i e i , , , e e e i CL&INNCE WAI f
]
I I ! I l 1 1 I I _ _ - -p- + -g. .l.. l_ _ _p +_ _q _q 1 Eo. _ _1-l _J_ l l l l_ . L_ 1-l _J l
- _l _
l - - -l _J O- 1 i ! I I I i 1 1 0: ---
, . . . . i -,
J: __ 1_ J - _I - 1 I _1_ _J_ _ _I _ __J C) i I I I I I I I I
.e ___
__q _ _' _ _]_ ' ' ' _j_ _ _l - _ _,' _h_ 7ggL _
.u- =- ' '
PIN -
-='
._ _ _'_ _ '_ _ '_ _ CELLS _ _'_ _' _ _ '_ _ _
I I I I I I I I
/l, - _ p -+- _p_
I 9- .i_. ._l +_ q _4 l I I i 1 1 I I
'~~~ I
~~~
t i i l I i i i l I ____ _L_ _1_ J_ ._i_. _ i_ _ _L_ _1_ _J. __J
./ I I I I I I I I i T.---- . i . , i . . i -7 LLL_ _ _L_ _1_ _J . _1_ L_ _L_ _1_ _J_ _J l I i l I i l i l I 1 l
- re*__-
t s s _ _ _ ., 1 1 I M M --s __s I 1 I i1 I i l I i ! I I I I I I I I i 1 l l l I I I 1 1 1 i WATER G AP l I I I I I 11 I L L L J J _ L _f 1 L J L l 1 L J _ L J 1 !_ J L L _ J i l I i !. 4-163
Figure 4.2.2.2 Comparison of CASM0-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.1. Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,0% In-Channel Voids, Exposure = OM WIDE W'ATER GAP 1.020 i ! ! ! ! ! ! 1.020 : : : 0 000~ . : : :
..........i...
PDQ-7-E Fission Rate * .....i . 1.051 0.268 i i 1.042 0.227 : : CASMO-1 Fission Rate * :
- 0. 009~ tit 4T :
Delta ""! 1.129 0.906 1.067 : 1.138 0 895 1.061
- No rm a:lzed to 1.0 0 i
.009 0.011 0 006 . . . :
.........y... . . . . . :. . . . . . . . . .: . . . . . . . . . .; z a . . .
< 1.214 0.995 1.068 1.155 : : : 'm O 1.228 0 982 *
.014 0 013 1.066 0.002 1.175
.020
$ i ! ! !g y ... ..
g . . . . . . . . . . . . . . . . . . . . i >e 1.163 0.293 1.011 0.000 1.118 : :
- M
$ 1.169 0.256 1.019 0.000 1.146 : :x 3 .006 0 037 .005 0 000 .028 .
- o
.,............g 1.253 1.105 O.974 1.024 0.982 O.859 ! !
1.265 1.097 0 970 1 052 0.992 0.846 :
.012 0 003 0.004 - 6hT .010 0 013 : :
1.239 1.142 0.292 0.999 0.975 0.277 1.045 i 1.232 1.128 0.257 0.997 0.978 0.249 1.050 : 0.007 0.014 0 035- 0 C02 .003 TDIEI - 005 . 1.220 1.128 1.048 1.256 1.225 1.089 1.100 1.158 1 212 1 123 1 049 1 279 1.250 1.113 1.116 1 171 6.008 0 005 - 001
.023 .025 .024 - 016
- 013, 1
NARROW WATER GAD 4-164
Figure 4.2.2.3 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No. 2: Peach Bottom 8X8 Fueli.attice With Gadolinium Unrodded,0% In-Channel Voids, Exposure = 11$$ WIDE WA'TER GAP 0.901 i ! ! ! ! ! ! 0.903 : : .
.002~ : : : :
J..........i..........!.... PDQ-7-E Fissic n Rate * ......i . 0.962 0.949 ! 0.963 0.926 : CASMO-1 Fission Rate' !
.0DT 0 023 : : :
. . . . . . . . . . ;. . . Delta """i 1.000 0.941 1.034 - l 1.On2 0.950 1.037 :
- No rm alize d to 1.0 0 l
.002 - 15GI
.003 : . . i
..........y..........:...........:...........: 2:
a . . .
< 1.063 0.992 1.033 1.039 :
- : 2 0 1.059 1.003 1.026 1.059 : : : :
0 004' $
$ .011 'D UD7 ; 020-i : ! ig y . . . . . . . . . ; . . . . . . . . . . i. . . . . . . . . . .i s D 1.051 0.934 1.035 0.000 1.007 : :
- M
$ 1.053_ 0 904 1.045 0.003 1.033 : : :m 3 .002 N .010 0 000 .02o .
.o
..........,............m 1.062 1.098 1.028 0.993 0.956 0.954 i 1.057 1.095 1.026 1.003 0.961 0 966 : .
Ti3DF 0 DDT CI057 .010 .005 .012 0.998 1.059 0.902 1.015 0.993 0.850 1.105 0 998 1. C49 0.871 1.014 0 995 0.815 1.083 :
.000 0 010 0 031 0 001 .002 TDIF 'DD2T :
0.954 0.945 0.955 1.117 1.096 1.034 0.963 0.957 0 962 _0 957 0 977 1 116 1.100 1.033 0.977 0.971
.008 .012 .022 0.001 .004 0.C01 - 014
. - 014 NARROW WATER GAP l
l 4-165 i
I l Figure 4.2.2.4 Comparison of CASM0-1 and PD0-7-E Fuel Pin Fission Rate Distribution l Case No. 3. Peach Bottorn 8X8 Fuel Lattice With Gadoliniura Unrodded,0% In-Channel Voids, Exposure = 21M WIDE WXTER GAP 0.866 i i i i ! ! 0.866 : . .
.0C0 : : : :
- .........i..............
PDO-7-E Fission Rate * ......i
@$ @p l i CASMo-1 Fission Rote
- f N
O 016 : : 1 Delta ""'i 0.956 0.940 1.048 : 0.946 0 946 1.051
- No rm allz.7d to 1.00 0 010 . 006 .003 i . . .
j g ..........y..........:..........:...........,>z
< 1.016 0 992 1.064 1.063 :
0 1.001 1 007 1.053 1.074 : : : :"
$ 0 015 T.DiT t 011 .011 i ! ! !$
g
, . . . . . . . . . . ; . . . . . . . . . i. . . . . . . . . . .! >s 1.010 0.960 1.067 0.000 1.035 : :
- M
$ 1.003 0 940 1.067 0.030 1.057 : : :m
~5 557 0 020 .C00 0 OM .022 : : e; D .
- : :p
......................g 1.017 1.091 1.064 1.029 0.993 1.0C4 ! i 1.003 1.091 1.059 1.038 1.011 1.022 :
0 014 N N .009 .013 .018 : 0.956 1.C43 0.944 1.050 1.033 0.916 1.128 i 0 949 1.032 0.921 1.050 1.039 0.893 1.100 : T6D7 0.011 N . 0N .006 ' TIDE TUN : 0.906 0 918 0.942 1.107 1.092 1.038 0.948 0.926 0 916 0 934 0 972 1.105 1.099 1.037 0 977 0 952
- 010
.016 .030 0.002 .00/ 0.001~ .029 - 026 NARROW WATER GAP i
I 4-166 1 t
Figure 4.2.2.5 Cornparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 4: Peach Bottorn 8X8 Fuel Lattice With Gadolinium Unrodded,0% In-Channel Voids, Exposure = 329% WIDE V/ATER GAP O.900 ! ! ! ! ! ! i 0 9c4 : : :
.004 : : : :
..........!..........:.... PDQ-7-E Fission Rote * ......i 0.905 0.885 i !
0.897 0.876 : : CASMO-1 Fission Rote' ! 0 008 0 009 : : :
..........;.... Delto '""i 0.938 0.932 1.047 : :
0.922 0.939 1.051 :
- N o rm alize d to 1.0 0 :
0.016 .007 .u04 i . . . !
..........;...........:...........;...........2:
g . . .
< 0.985 0.932 1.086 1.082 : : : : 2 0 0 961 0.999
$ 0 024 .017 1.070 0'016-1 083
.001 i
i i ig Q ...............................E g . . .> 0 982 0.963 1.088 0.030 1.060
$ 0 %7 0 952 1.079 0.0C0 1.077
* :M
- :a g 0 015 0 011' N N .017 j i !o
........,............m 0.987 1.063 1.038 1.058 1.036 1.043 i !*
O . %5 1.066 1.079 1.067 1.057 1.065 : N .003 M . 0>3 '.021 ' .022 0.941 1.014 0.963 1.073 1.060 0.958 1.123 i 0 930 1.003 0.947 1.073 1.070 0.937 1.089 : 0.011 0.011 0.016~ -
.C00 .010 0.021- 0 034 .
0.906 0.908 0 931 1.035 1.075 1.031 0.933 0.913 J 0 921 0 927 0.967 1 079 1.031 1.028 0.972 0.950
.015 - 019 036 TE .006 0.003 .039 ' 037 NARROW W ATER GAP 4-167
Figure 4.2.2.6 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Disttibution Case No. 5: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids, Exposure = Ou% WIDE WATER GAP 1.044 i i i i ! ! ! 1.070 : : :
.026 : : : :
...,i
. . .! PDQ-7-E Fission Rate * .
1y
.006 0.044 f
f CASMO-1 Fission Rate
- f
' '!
- Delta 'i 1.145 0.943 1.086 : :
1.169 ,0 928 1.074 i
- No rm alize d to 1.0 0 :
.024 0 015 0.012 : . . . :
i g
. . . . . . .:.>z
< 1.222 1.027 1.066 1.119 :
- m O 1 248 1.003 1 061 1 139 -
l .S
.026 0.019 0.005 o
$ .020 i : j ig i j .... ;5 y . >
1.176 0.350 1.012 0.000 1.064 . :
- A
$ 1.191 0 309 1.012 0 000 1.038
- *x g
.015 0 041 0.0v0 0 COL .024 ,
; ;o
.g 1.243 1.i33 0 937 0 996 0.952 0.864 i :
1.273 1.123 0 972 1.013 0 951 O 633 *
. 0 !b 0 Olb 0 0i5 .017 0.00i 0 031 . .
1.220 1.155 0.345 0.992 0 962 0.325 1.036 i 1 235 1. 144 0 308 0 978 0 953 0.295 1.035 :
- 016
. 0 011 7 037 0.014 0.C09 ED37 0 001 :
1.192 1 109 1.031 1.216 1.179 1.053 1.050 1.039 ! 1 209 1 113 1 032 1 234 1 196 1 C'O 1 C64 1 111
- .ui, .C04 0.005 .015 -- 0 C - .0 17 - 014
. - 022 1
N ARR0 N WATER G AP i l 4-168 r I
Figure 4.2.2.7 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 6. Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids, Exposure = 11$$$ WIDE V/ATER GAP 0.965 . ! ! ! ! ! ! 0.979 -
.014 : : :
..........!..........l.... PDQ-7-E Fission Rote * ......i 1.016 0.972 i i 1.018 0 955 : :
CASMo-1 Fission Rate * !
.002 TUTT :
..........;.... Delta "*"i 1.045 0.963 1.045 : ;
1.046 0 974 1.047 i *No rm allred to 1.0 0 i
.001 .011 .C02 : . . . :
g ..........y..........:...........;...........;>z
< 1.093 1.006 1.038 1.031 : : : : 2 0 1 093 1.015 1.026 1.050 : :
M 2.009 .019
$ 'O 012~ i ! j ig y '..........;..........'...........!>s 1.078 0.932 1.027 0.C00 0.978 : :
- M
$ 1 081 0 905 1.036 0 000 10'4 . : :x 3-
.003 TUIT -29 0 000 .0~2T : : c3
..... 4
,..............p 1.088 1.100 1.019 0 968 0.924 0.916 :
1 085 1 095 1.012 0.977 0 926 0 920 ' TUDT M TD37 .009 -7007 .004 . : 1.026 1.062 0.886 0.992 0.961 0.812 1.062 ! 1.031 1.051 0.853 0.935 0 956 0.773 1.034 :
.005 0.011 TQ3I TD37 TD3F TD37 'O 028 :
0.983 0.959 0.951 1.093 1.068 1.008 0.937 0.938 1 007 0.976 0 976 1 094 _1 069" 1.003 0 959 0.970
- 024
. - 017
.025 EN .001 TUP 5 .022~ - 032 NARROW WATER GAP 1
l 4-169
Figure 4.2.2.8 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No. 7: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids, Exposure = 21M WIDE WATER GAP 0.935 ! : ! ! ! ! O M7 : : :
.012 : : : :
PDQ-7-E Fission Rate * ..i 0.971 0.934 i i 0 963 0 924 :
' CASMO-1 Fission Rate' !
0.008 0 010 : ,' i Delta ! 1.008 0 953 1.044 : 0 995 0 955 1.048 ,N o rm alize d to 1.0 0 0 013
.012 .004 .
g :
.:z .>
cc 1.059 0 997 1.060 1.053 : : 0 1 040 1 011 1 041 1.062 -
$ 0.019 .014 0 019 .039 :
.$g Q .
i ...
= ,
, >G 1.045 0.954 1.051 0.000 1.003 d 1 037 0 935 1 049 0 000 1.027 :
' 'R x
g 0 008 0 019 0 002 0.000 .024 , ; .o 1.052 1.052 1.045 0 995 0.956 0.956 - 1 033 1 031 1.035 1 005 0 967 0 959 ' ' 0 014 0 001 TUi6 .010 .011 .013' : l 0.994 1.042 0 926 1.019 0.993 0.879 1.087 : 0 991 1.031 0 930 1.011 0 992 0.848 1.05) 0.003 0 011 0 026 Td6E O 001 0 031 0 036 : 0 945 0.941 0 942 1.096 1.071 1.024 0 933 0 973 0 922 0 962 0 933 1 037 1 073 1.018 0 972 0 972
- 028
- 021
.02 F009 .002 0.006 - 042 .
- 0$0 NARR0 N WATER G AP 4-170
Figure 4.2.2.9 Comparison of CASM0-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 8: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,40% In-Channel Voids, Exposure = 32$$$ WIDE W'TER A GAP 0.958 ! ! ! ! ! ! 0 976 : : :
- .018 :
. } . . . . . . l. . , PDO-7-E Fission Rate * ...l
@j j $} f !
CASMO-1 Fission Rote * ! 0.011 3N :
- Delta '
0.993 0.941 1,034 i j 0 970 0.953 1.042 -
,N o rm alize d to 1.0 0 -
TU2T -- 012 .003 i . . !
- . . . . . . . .: .. . . . . . . . . . .: z a . .
< 1.033 0.932 1.078 1.072 : : : : 2 l 0 1 032 0 031-1 000
.018 1.052 TDTo" 1 072 TDM i i j
'$g Q ... . j . . .j ..
j>E 1.022 0.953 1.069 0.000 1.027 : :
- M
$ 1 004 0 941 1 058 0 000 1.050 : :m
,q 0.018 0 012 0.011 TDU .023 j ; ;g
.a 1.023 1.053 1.064 1.019 0.935 0.934 :
1 033 1.056 1.050 1.031 1.006 1.005 . 0 DIF .003 0 014 .012' .021 .0f1- . 0.931 1.014 0.944 1.040 1.016 0.922 1.090 l 0.972 1.004 0.922 1.030 1.018 0.889 1.046 : 0.C09 0 010 0.022 0 010 -.002 TU3T o 044 : 0.940 0.932 0.935 1.087 1.066 1.031 0.921 0.911 0 974 0 958 0 932 1 073
- 068 1 020 0 978 0 976
.034 026 ~- 557 0.014 - 002 0.011 .057 - 065 NARROW WATER GAP i
1 l l \ 4-171 l 1
Figure 4.2.2.10 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No. 9: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% In-Channel Voids, Exposure = 0$$ ; WIDE WATER GAP 1.047 i ! ! i i ! ! 1.105 :
.058 : : : :
i PDQ-7-E Tission Rote
- i 1.106 0.386 :
1.13e 0.340 CASMO-1 Fisslon Rote
- l 76RI O 046' :
i' Delto i 1.150 0.980 1.115 i 1.191 0 965 1.101 : ,No rm alized to 1.00 i
.041 0 015 0 014 : :
m . !. i.Z>
< 1.220 1.061 1.078 1.105
. : : 2 O 1.261 1 039 1.073 1.127 : : :
y TUTI M
.041 .022 i i i !g Q -
g .
!>E .
i 1.179 0.J15 1 027 0.000 1.033 : :
- M
$ 1 202 0 371 1 019 0.000 1.047 .
- x 3-
.023 3.044 'O 008 N - 014
- o
- 7 1.230 1.167 1.008 0 985 0.939 0.876 . ! i 1 271 1 149 0 934 0 939 0 921 0.825 .
l
.041 0 018 0.024 . 0M 0 018 0 051 .
I : 1.184 1.160 0 405 0.991 0.956 0.379 1.022 : 1 1.223 1.155 0.365 0.963 0 931 0 347 1 013 : -
.03 6 N ON N O 025 0 032 0 009 -
}
l 1.146 1.080 1.024 1.179 1.136 1.016 1.000 1.015 l 1 18 9 1 093 1 012 1 187 1 140 1.023 1 004 1 033 i
- 043
. - 013 0.012 - 008
.004 - 007
. - 0M
. - 023 l
, l NARROW WATER GAP l
l l
\
4~172 l
Figure 4.2.2.11 : Cornparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No.10: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% In-Channel Voids, Exposure = 11$ WIDE W'TER A GAP 1.026 ! ! ! ! ! ! ! 1.063 : : :
-.037 : : : :
... . i . . I. .
PDQ-7-E Fission Rate *. .. 1.069 0.936 i ! ! 1.07e 0.931 : : CASMO-1 Fission Rate * : .
.006 0 005 j
- '" Delta i 1.089 0.980 1.057 i 1 092 0 997 1.061 ,No rm alize d to 1.0 0 -
.003 .07 .004 i . . !
- z 0 1.133 1.019 1.049 1.036 O 1 128 1 023 1 034 1.056 : : : ,
$ 0 005' x.009 TJiT ; .020' :
- i :$:s E
l lg d 1.106 1.1C9 0.928 0 904 1.026 1.035 0.003 0 000 0.959 0 982,.
- A
'x M
.00T C 024 .009~ O'000 .023, -
o
- : 7 1.113 1.093 1.014 0.949 0.893 0.834 . i 1 113 1.092 1.002 0.955 0 893 0 873 : :
.0C0 'O 006 0 012 .006 0 005 0 011 1.050 1.059 0.866 0.970 0.931 0.773 1.015 1.063 1.048 0 832 0 955 0 914 0 726 0.973
' 013 0.011 0 034 0 015 EdI7 W 'D DTT : ,
i 1.CO6 0.971 0 949 1.083 1.043 0.933 0 908 0 911 1 055 0 992 0 973 1 069 1 035 0 969 0 964
.049 .621 .024 0.014 0.C03 0.014 "0 GT5.uT 2 - 051 NARRON WATER GAP l i
)
l l 4-173 1
Figure 4.2.2.12 Comparison of CASM0-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.11: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% In-Channel Voids, Exposure = 21$$$ WlDE WATER GAP 1.005 ! ! ! ! 1.039 . : .
.034 :
PDO-7-E Fission Rate * . i 1.035 0 944 i ! ! 1.028 0 944 : : CASMO-1 Fission Rote
- TDDT N :
i Delta "i 1.064 0 960 1.033 i 1.048 0 979 ' 046 -
,No rm alized to 1.0 0 -
0.016
.015 i. T M i e
- z
< 1.104 0 999 1.060 1.050 .
- : 2 0 1 081 1 014 1.034 1 059 : :
$ T075 .01b T57f .009 l l l :g$
y - o 1.032 i>u 0 945 1.039 0.000 0 978 . . :
$ 1 073 0 929 1 037 0 000 1 032 : . :Nx M
0.009' O 016' 0 002 0 000~ .024 :
. c)
....y 1.083 ;
1.070 1.029 0 965 0 919 0.912 1.074 1 068 1 013 0 974 0 925 0 917 *
- 0.014 T03T 0 016 .009 - 006
. .005 : :
1.020 1.033 0.905 0.991 0.956 0.843 1.041 i 1 034 1.024 0 877 0 971 0.943 0. 8N 0 996 :
.004 TdDF TJTJ 0 023 0 Oi3 TOTT 0.04 3 .
1 0.920 0 961 0.943 1.033 1.052 1.012 0.938 0.933 ' 1 037 0 939 0 935 1 067 1 045 0 994 _0 960 0.937 .
- 057
.023 - 042 0.021 0.007, 0.018 .052 - 079 N ARROW WATER G AP 4~174
Figure 4.2.2.13 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.12: Peach Bottom 8X8 Fuel Lattice With Gadolinium Unrodded,70% In-Channel Voids, Exposure = 32u% WIDE W4TER GAP 1.022 i
- i :
1.065 .
.043 :
[. PDO-7-E Fission Rate * ; l-@y 8 90 . CASMo-1 Fission Rate
- j 0.012 .005 -
Delta 1.055 0.944 1.018 : 1.026 0.965 1.031 -
*No rm alized to 1. 0 0 ;
0.029 .021 .013 . . :
.. .. z a . . < 1.089 0.981 1.072 1.067 'I O 1.050 C.999 1.036 .$
1.065 - 3
. 0.039 - 018 0.036 0.002 -
- E t-E 1.069 0.939 1.051 0.000 0.996 M
$ 1.048 0.929 1.039 0.000 1.022 m n 0.021 0.010 0.012 0.000 .026 o 1.073 1.039 1.041 0.930 0.935 0.927 .
1.047 1.041 1.022 0.993 0.954 0.941 0.026 .002 0.019 .013 .019 .014 1.023 1.007 0.920 1.007 0.972 0.881 1.048 1.020 1.000 0.893 0.983 0.962 0.836 0 993 - 0.003 0.007 0.027 0.024 0.010 C C45 0.055 - 0.975 0.957 0.939 1.090 1.055 1.031 0 903 0 933 1.041 0 991 0.995 1 062 1.048 1,006 0 977 1 005
- 066
. - 034
. - 056
. 0.028 0.007 0.025 .074 - iO2 NARROW WATER GAP 4-175
l Figure 4.2.2.14 j Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.13: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,0% In-Channel Voids, Exposure = Ou%
///////////////////////////////////////
Wid'E WATER GAP
/ / 0.346 ! / / 0.374 -
i
.028 -
f
/
PDQ-7-E Fission Rate * ......; 0.458 0.208
/ / 0.454 0.194 :
CASMO-1 Fission Rate * : 1 004 0.014 7
/ ... . ...
Delta '- f 0.586 0.676 0.968 f 0.566 0.665 0.966 ,No rm alized to 1.0 0 - 0.020 0.011
/ /
0.002 ;
....... . . . . . . ....... 2
/ a
< 0.693
/
/ O O 662 0.812 0 788 1.075
_1._077 1.285 I 1.319_ ,$
/ /
q 0.031 0.024 .002 .034 , g
..s...... / w
- >s
/ $
0.711 0.291 1.095 0.000 1.376 -
.M / g 0.675 0.264 1.115 0.000 1.413 .m / /
0.036 0.027 .020 0.000 .037 ,o
/ . .. / 0.848 1.021 1.085 1.246 1.249 1.127 / /
0 827 0.021 1.009 0.012' 1.084 O.001 1.280
.034 1.255
.006 1.099 0 028
/
/
/ 0.964 1.112 0.348 1.247 1.268 0.375 1.434
/
0.970 1.118 0.309 1. 25.' . 274 0 330 1.443
/ .006 .C06 0.039 .01C .006 0 045 .009 '
b . . 1.102 1.168 1.217 1.575 1.608 1.477 1.518 1 139 1.609 1 192 1.233 1.605 1.632 1.491 1.519 1 611
-.037 - 024
.016 .030 - 024.
.014 .001 .002 '
NARROW WATER GAP 4-176
Figure 4.2.2.15 l Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.14: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded, 0%.In-Channel Voids, Exposure = 10 $$
/,///////////////////////////////////////
/
I j/ . . .. Wl6E WATER GAP
/ 0 an - - - :
/
/ 0 342
.03,
. i f .. ... . . . . . ..... PDQ-7-E Fission Rate * .
/ 0 426 0.565 -
- // 0 431 0.551
CASMo-1 Fission Rate * ! /- .005 0.014 * . / - ' ' Delta '
'i l !/ 0.521 0.676 0.902 0 504 0 668 0.892 ,No rm alized to 1.0 0 0.017 0.008 0.010
/
l 7 . . . ... . . ......... .........z O. 0.615 0.795 1.010 1.137 '
/ 0 0 584 0 786 *
/ 0.994 1.160
/ y 0.031 0.009 7
0.016 .023 - g j//
.. ...s.. . .. .. .
.g 0.659 0.793 1.087 0.000 1.233 :
M l $ 0.634 0 754 1.090 0.000 1.268 .
- o j/ g 0.025 0.039 .003 0.000 .035 o 1
//
Q
/ 0 733 0 714 1.016 1.123 1.192 1.206 1.235
/ T 019 1.003 1. 121 1.208 1.214 1.249 *
//
0 013 FDD2 .016 .008 .014
/
/ 0 791 1.C47 1.000' 1.250 1.281 1.093 1.500
/
/
0 806
.015 1.051
.004 0.972 0.028 1.256
.006 1.288
007 1.048 0 050 1.476 0.024 .
I O 881 0.997 1.117 1.402 1.441 1.398 1.333 1.340 0 926 1.032 1.153 1.412 1.453 1.396 1.352 1 365
.C45 - 035
.036 .010 .012 0.C02 .019 .025 l
NARROW WATER GAP l l I l 4-177
l Figure 4.2.2.16 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No.15. Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,0% In-Channel Voids, Exposure = 21GW g f///H////////////////////////////////// WIDE WATER GAP 0.293 ! '. ! [/[ 0.325 ' - *
.032 c /
/ . .. . . .. .. .. PDQ-7-E Fission Rate * . ..
j% jy CASMO-1 Fission Rate *
/ .005 0.006
/ '
- ' Delta '
0.486 0.660 0.894 0.468 0.551 0 824
/ 3.018 0.009 0.010
- No rm alized to 1.0 0
/-
' ... .... ....... . . . . . . . . .. ....... 2 e >
/,/
< 0.575 0.779 1.023 1. 14 6 . W O 0 774 "
f
/ O 542 0.033 0.005 1.002 1.156 , ,O
/p/ $
0.021 .010 - g q .. .... .... a
/
/ s:
0.622 0.818 1.109 0.000 1.260
// g$. 0 593 0 787 1.096 0.000 1.287 *$ m 0 027 0.031 0.013 0.000 .027 j/ ,
o
/ . . .. .
/
/
0.6 93 0.667 0.995 0.984 1.155 1.145 1.231 1.240 1.263 1.275 1.317 1.333
/
/
0.023 0.011 0.010 .009 .012 .016 .
/
/ 0.744 1.016 1.063 1.292 1.338 1.228 1.544
/
/
0 755
.011 1 020
.00T 1.045 0.018 1.293
.001 1.347
.009 1.189 1.501 0.039 0.043 0.819 0.952 1.089 1.380 1.432 1.405 1.308 1.287 0 267 0 992 1 136 1.383 1.440 1.398 1.342 1 324
.048 - 040
- 047
.003 - 003 0.007 .034 .037 NARROW WATER GAR 4-178 r
( Figure 4.2.2.17 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.16. Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,0% In-Channel Voids, Exposure = 325} f///////////////////////////////////////
/ . . . . . . . .
WIDE WATER GAP
/[p 0.305 OM i
/ .035
- f .. ..;... . ... ..
PDO-7-E Fission Rate * .. t
/ @j @y ,
CASMO-1 Fission Rate * .
.006 0.003 .
/
Delta 0.477 0.650 0.883 0 457 0.641
/
/ 0.020 0.009 0.873 0.010 -
,No rm alized to 1. 00 .
/ ... .... ....... . ....
z
/ /
o.
< 0.556 0.765 1.033 1.157 / O' O.522 0 761 1.005 1.154 y / $ 0.034 0.004 0.028 0.003 o / y .:.. ;...... u
- E
/ :g / /
0.603 0.575 0.815 0 790
- 1. 12 1 1.096 0.000 0.000 1.287 1.307 'Nc
/ g$ 0.028 0.025 0.025 0. 00Cf .020
,o
/ . .. . .
g T
/ /
0.6e9 0.644 0.964 0.955 1.174
- 1. 158 1.262 1.309 1.368 1.269 1.330 1 388
/ ,[
0.025 0.009 0.016 .007 .021 .020
/ 0.731 0 983 1.079 1.318 1.374 1.287 1.540 / /
0 739
.008 0 986
.003 1.068 0.0:1 1 317 1 384 1.251 1.487 :
0 001 .010 0 036 0 053
/-
f 0.816 0 870 0.939 1.073 1.351 1.410 1.398 1.291 1.274 0 931 1 126 1 348 1.416 1 386 1.333
-.054 1.324
- 042
- 053 0 003 -.006 0.012 .047 .050 NARROW WATER GAP i
L 4-179
l Figure 4.2.2.18 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No.17: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,40% In-Channel Voids, Exposure = 0y% { f///////// ////////////////////////////// WIDE WATER GAP
/ . . . ... . .. ... .. ... . . / / 0.393 .
0.408
/ .015 . .
PDQ-7-E Fissio n Rate * .. .
'50 4 CASMO-1 Fission Rate
- 0.022 0.015 -
/ Delta ! 0.618 0.685 0.943 .
0 580 0 655 0 925
- No rm alize d to 1.0 0 0.038
/ /
0 030 0.018
. .. .. . ... ..' .... 2 ! O 0.727 0.819 1.034 1.209
- O
/
/ g O 676 0.051 0 774 Q.C46 1.029 0.005 1.249
.040 $
g
/ q '
's>
/
/
g 0.760 0.357 1.068 0 000 1.299
/
f g$ 0 703 0.257 0.329 0.028 1 080
.012 0.000 0.000 1.350
.051
- d o
/ . ..
f
/
0.892 C 557 1.C51 1 023 1.084 1.075 1.199 1 236 1.205 1.214 1.132 1 097 )
/ /
0.035 0 028 0 009 Ed37 .009 0 035
/ / 0.996 1.133 0.418 1.230 1.248 0.446 1.425 / /
1 001
.005 1.13'
.0C4 O.380 0.038 1.246
.016 1.260 0 402 1.457
.012 0.044 .032 1.117 1.160 1.204 1.522 1.548 1.430 1.454 1.519 1.172 1.194 1 224 1 572 1.594 1 467 1 489 1 572
.055 .034 - 020
.050 .046 .037 .035 - 053 NARRO N WATER GAP 4-180
Figure 4.2.2.19 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.18: Peach Bottom 8X8 Fuel Lattice With Gadolinium l t Rodded,40% in-Channel Voids, Exposure = 10$ ) l {///////// ////////////////////////////// WibE WATER GAP > / [ ' 0.362 l : 5 !
- 0.384
[/
.022 . .
.. .... .!.. .... ... . PDO-7-E Fission Rate * .
04 f : CASMO-1 Fission Rate * , p/ 0.011 0.026 ,
/ //
Delta ': ) 0.561 0.676 0.880 , l
'/ 0 526 0 652 0.857 ,N o rm alize d to 1.0 0 // 0.035 0.024 D 023 : -
k/ 1
.'........{z
< 0.656 0.790 0.935
[
// C 0.606 0 766 0 958 1.102 1.126
'I l [ 0 050 0.024 0 027 .024 E
/l :
/ q .... . ... . . .......s
/
// 3:
0.706 0.787 1.060 0.000 1.196 ) $ 0 662 0 741 1.056 0.000 1.245 m j/ g 0.044 0.046 0.004 0.000 .049 o
/ ' / 0.790 0 754 1.019 1.105 1.159 1,170 1.197 /
0.995 1.098 1.183 1.186 1.211
- b
/ /
0.036 0 024 D DD7 .024 .016 .014 .
/ ... / 0.854 1.060 0.934 1.225 1.248 1.065 1.461 / 0.862 1.061 0.959 1.234 1.260 1.018 1.449 /
L
.008 .001 0.025 .009 ' 012
. 0 047 0.012 .
0.944 1.025 1.119 1.387 1A16 1.378 1.313 1.329 1 C08 1.070 1 167 1.408 1.443 1.392 1 366 1 4C5
.C64 - 045
.048 .021 .027 .014 - 053
-- 076 NARROW WATER GAP 4-181
Figure 4.2.2.20 Comparison of CASM0-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No.19: Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,40% In-Channel Voids, Exposure = 21u%
// /////////////////)////////////////////
j/ . . . . . . . . W:3E WATER GAP
; / 0.345
/ 0.369 :
. i ! -
.024~ . . *
/ .... ... .>. .. . . PDQ-7-E Fission Rate, .. .
0.438 0.537
/ 0 426 0.517 CASMo-1 Fission Rate * -
0 012 0.020 7 *
/
9 ,lgc .. . 0.530 0.656 0.862 l 0 491 0.632 0 837 0.039 No rm alize d to 1.0 0
/ /
0.024 0.025 .
/ a . ..
. ... z
/ O< 0.621 0.769 0.991 1.111 %
/ 0.566 0.747 0 953 1.118 ,$
f y 0.055 0.022 0.038 00) : .g
/ ;g / ......... .... . ..........a / $ 0.673 0 807 1.073 0.000 >
1.221
/ 0 626 *M 0 765 1.052 0 000 1.265 m I / g 0 047 0.C42 0.021 0.000 044 a / . .. .
j
/ 0.752 0.993 1.127 1.188 1.213 1.262 '. / 0 709 0 966 1.ill 1.207 1.23' 1.29] / 0.043 0.024 0.016 .019 .024 .028 / / / 0.815 1.026 1.042 1.258 1.294 1.190 1.504 / 0 814 1.026 1.027 1.261 1.311 1.161 1.477 / /
0 C01 0 000 0.016 .003 .016 0.029 0.027 0.892 0 992 1.093 1.376 1.416 1.402 0 957 1. JJO 1.299 1.041 1 162 1 38' 1.441 1.410 1.378 1 396 C65 - C49 - C64 .011 .025 .006 - 097
. 078~ .
NARROW WATER GAP / 4-182 /
Figure 4.2.2.21 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 20. Peach Bottom 8X8 Fuel Lattice With Gadolinium l Rodded,40% In-Channel Voids, Exposure = 325
///////////////////////////////////////
W
. . . . . . . . . . .' D E W AT E ............. R G A P.. ... .............
f
/
0.355 l
/
/
0.38, .
.026 f ..... ......
.. . PDO-7-E Fission Rote * ..
/ C.435 0.517
^
CASMo-1'Fis sion Rate
- 0 423 0 493 - -
f 0.012 0.018
/ ..... ......
Delta * '
/ 0.521 G.644 0.846 C . 4 80 0.620 0 821 ,No rm alized to 1.00 f 0.041 0 024 0.025
/ .... . .'......... .... . ... ....... 2
/ e . >
/ < 0.605 0.753 0 997 1.123 *I
/ ,$O O 546 0 C59 C 732 G.021 C 949 0.048 1.115 $
/
/ q#
C.CCS E
.: s>
/
/ 0 657 C 8^1 1.083 0.CCC 1. 2%
- M
)
/ W{ 0 606 C 762 1.048 0 COO 1.285 m
/
/
O.C51 C L39 0.C35 C.CCG .039 ,o m l
/ 0 734 0 958
/ 1.140 1.211 1.247 1 293
/ C 656 0.936 1.117 1.231 1.283 W
1.335
/
/
0.G46 0.U22 Ti J23- .62u .036
/
/ 0 802 C 995 1.C58 1.279 1.323 1.247 1.510
/ C 798 C 994 ..C46 1.279 1.342 1.217 1.471
/
I O OC4 L CLI L.012 L.Lcv .019 TU37 II'D37 . \ 0.655 0.9S2 1.086 1.361 1.408 1.412 1.289 1.287 0 957 1.034 1.16C 1.365 1.432 1.415 1 333 1.4C6
.072 - 054
. .0/4 .CC4 .C24 .Cd3 .099 - ils i
NARROW WATER G AP 4-183
Figure 4.2.2.22 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 21. Peach Bottom 8X8 Fuel Lattice With Gadolinium ! Rodded,70% In-Channel Voids, Exposure = Ou% f///////////////////////////////////////
/
/
WIDE WATER GAP !
/ . .
/ 0.447 :
.' i
/
[ 0. au . 0.0?3 : : :
..........;,.......... PDO-7-E Fission Rate * .....; / 0.550 0.333 ;
CASMo-1 Fission Rate
- l
/p 0.513 0 311 0.0A] 0. 0 '. 9 / .............
g ,i ,,
! 0.654 0.702 0.927
/ 0.597 0.650 0.888 *No rmalized to 1.C 0
/ T UST 0.052 0.039 7
/
( 7 m
.................... ..................... 2
< 0.764
/
/ O C 693 0 231 C 766 1.003 0 985 1.145 1.185 : l 0.07i ).C6b 003
/
/
q
.040 -
g i
...... ...:..... .... .......a / /
0.8C9 0 434 1.047 C.000 1.235 * 'j 0 733 0.405 .M ,
/ g$
1 C50 0 000 1.295 m l
/ C 076 0.029 .003 0 CCO .C60 g ! / / . .. . .... . ., / / /
G.933 0 286 1.079 1.040 1.033 1.C63 1.162 1.196 1.170 1.178 1.136 1.093
/ TNT 0.039 0.01b N ..cGe T03F / 1.016 1. 14 5 0.493 1.210 1.226 0.525 1.401 / /
1.C29
.013 1.153
- IC7 0 463 CT35' 1.230~
.02c 1.244
.015 0 487 TG3s 1.461
.c6c -
1.112 1. 140 1.183 1.461 1.481 1.375 1.354 1.419 1 193 1.186 1 207 1.526 1.545 1.434 1.448 1 517
.05T C46~ .C23 - CE5
. .C64 .059 -.L64 - 093 NARROW WATER GAP l l,
4-184 i
1 i Figure 4.2.2.23 Comparison of CASMO-1 and PD0-7-E Fuel Pin Fission Rate Distribution Case No. 22. Peach Bottom 8X8 Fuel Lattice With Gadolinium Rodded,70% In-Channel Voids, Exposure = 10 M f////// ////////////////H//H////////// Wide WATER GA?
/ / ' ' '
C.428 i
/
/ 0.437 -
.Cc9 .
f . . . . . . . . . ;, . . ...'... PDQ-7-E Fission Rate * .....; C.522 0.584 : CASMO-1' Fission Rote
- j C . 493 U.032 0 545 0.039 7
/ ............. .
Delta "'"
!/ /
C.611 0.682 0.863 : - 0 554 0.641 0 823
/
/ C.057 C.041 C.G4C -
.N o rm alize d to 1.0 0
/ ..................... ................. . 2
/
/
e
< 0.708 0.791 0.963 1. C72 C 0 635 0 749 / g T7i7T 0.042 0.922 1.093 ' $ / / q 0.C41 .021 E / .........;..................;>s //
C.761 0.696 0.782 0 729 1.C34 1.C24 C.000 0 GCC 1.161 1.223 M x
/ g 0.C65 :.053 C.G IC D.0C0 -.062 o / / .... . . ..... . . . , //
0.853 0.799 1.C23 0 937 1.C86 1.075 1.125 1.155 1.133 1.154 1.158 1.17C
//
0.Cb4 0.036 0 011 ~ .0JO
.021 - .012 7 . / /
Ct913 0 923 1.C68 1.C68 0.961 0.941 1.193 1.2C6 1.208 1.227 1.024 0.933 1.4C8 1.417
/23 .Utb W C.02C - .C l3 .019 0.041 .C09 l
1 1.CC4 1.C51 1.119 1.367 1.386 1.351 1.255 1.3C6 1 C93 1. ICS 1. 176 1.396 1.427 1.332 1.377 1.445 l
. .094 .t57 - C57
.C29 .C41 - 031
.092 139 '
l NARROW WATER GA? 4-185
Figure 4.2.2.24 1 1 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution. j Case No. 23: Peach Bottom 8X8 Fuel Lattice With Gadolinium l Rodded,70% In-Channel Voids, Exposure = 21M
///////////////////////////////////////
/ ' # '
. . . . . . . . . . . . . . . . . . . . . ?.^I.E R G A P
/
/
0 414 ' *
/ /
C 424 -
.C no . !/ ... ......:.............. PDQ-7-E Fission Rate * .....:
l/
/' O.493 C.549 / / O 462 0 513 CASMO-1 Fission Rate
- C.036 C.036 *
/
. . . . . . i. . .
Delta "', , 0 586 C.657 0.833
// /
C 522 G C64 C 616 C C41 0 793 0.040 .
,No rm alized to 1. 0 0
/
/ c.
......................................z
< C.678
/
/ O C.597 C.734 C.722 C 96G C.904 1.076 1.C78 .
3 0 081 0.05a
/ /
y 0.042 .002 - -
.........................'a E / /
7 0 734 0.793 1.C37 0 COO 1.179 *$
/ /
g C 662 C.L72 0.744 O L54 1.COS G.023 0.0C0 0.000 1.240
.C61 m
g;
/ / / C S23 0.985 1.095 .141 1.159 1.201 . / /
0.753 G.06b 0 949 G.036 1.075 0 020 1.17C
.029 1.195
.u36 1.240
.039
/
/ ..... .
/ 0.891 1.031 1.015 1.216 1.243 1.144 1.449
/ 0 884 N
1.029 1.005 1.220 1.266 1.127 1.443
/ 0 LO2 0 Gio .004 .023 0.01) 0.006 0 963 1.031 1.105 1.357 1.396 1.395 1.283 1.297 1.C65 1.092 1.183 1 383 1.434 1.418 " 410
. 1.473
.uS7 .C61 . u /8 .016 -.035 .023 .127 .i/6 l
NARROW WATER GAP l l L 4-186 '
Figure 4.2.2.25 Comparison of CASMO-1 and PDO-7-E Fuel Pin Fission Rate Distribution Case No. 24. Peach Bottom 8X8 Fue! Lattice With Gadolinium { Rodded,70% In-Channe! Voids, Exposure = 32y %
~ f///////////////////////////////////////
/
/ W'6E WATER GAP
/
/ 0.423 .' ! i
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. .. .....;.. ........... PDO-7-E Fission Rate * . .. .
0.496 0.530 CASMo-1 Fission Rate
- p/ 0.45e 0 038 0.495 0.035
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.u20 1.173 0.L22 1.441 0 0.9 -
l l Z l d 0.962 1.026 i.093 1.367 1.399 1.421 1.27 1.292 1 CES 1.092 1.192 1.374 1.437 1.436 1.438 1.5r4
. iC6 - C66 - 094
. LO7 .038 .L15 - .161 - 212 l
N ARRC W WATER GAP 1 1 4-187 l l I l
1 4.2.3 Qualification of Multi-Assembly Geometry Methods f Results from a four energy group, fine mesh PDQ-7-E multi-assembly geometry model have been used by PECo to qualify the use of approximate flux reconstruction techniques for prediction of local peaking factors. In order to accomplish this, three 2x2 assembly configurations from Peach Botton 2 cycle 7 were modeled by PECo using PDQ-7-E. The PDQ-7-E predicted relative fuel pin fission rate distributions were then compared to analogous results derived from the PINUP computer code, which is based on flux reconstruction methods. The PDQ-7-E model geometry used in this application is portrayed in Figure 4.2.3.1. The geometry consists of a fine mesh 4x4 assembly region, composed of the fuel lattices under study, surrounded by a buffer zone representative of the reactor nominal cross section conditions. Reflector assumptions were imposed on the outside boundaries. Fuel lattice cross section data l used in the multi-assembly model were identical to those used in the single assembly qualification. Puel burnup 1 was modeled by the use of BARMONY depletion steps, I together with a re-initialization process intended to represent core shuffling between cycles. Relative fuel pin fission rate distributions were ultimately edited for each of the four fuel assemblies in the central 2x2 l region. 4-188
k The three 2x2 assembly configurations used as the basis for the multi-assembly methods qualification are i depicted in Figure 4.2.3.2. PDQ-7-E results for each assembly configuration were edited at: (1) three cycle exposure points: / E = 0.0 GWD/MTU (beginning of cycle), E = 4.5 GWD/MTU (middle of cycle), E = 9.0 GWD/MTU (end of cycle), i (2) three void conditions: V=0%, 40%, 70%, and t (3) six control rod configurations: M=5, 6, 9, 10, 11, 12. ( This yielded a total of 162 different PDQ-7-E multi-assembly geometry cases making up the study. Typical PDQ-7-E 2x2 assembly geometry relative fuel pin fission rate predictions, as obtained from this analysis, are contained in Figures 4.2.3.3, 4.2.3.4, and 4.2.3.5. f The same set of multi-assembly geometry cases was also analyzed by the PECo-developed flux reconstruction , code, PINUP. This code basically determines the flux l f distribution, 4, for the multi-assembly geometry by perturbing the single assembly flux solutions, $o, associated with each of the individual assemblies. The } basic equation solved is: ) I ! 4-189 )
L _
$ (L,i',j') = (o (L,i',j') + f *i'*A$1 L L
+ fJ *j'*ATJ + fIJ*1'*j'*ATIJ where:
(l',j') = Coordinate location of a fuel pin cell as measured from the center of assembly L, l and expressed in units of pin pitch. AII = Change in the average flux for laterally neighboring assemblies along the b' 1 coordinate direction. ATJ = Change in the average flux for laterally neighboring assemblies along the A j' coordinate direction. ATIJ = Change in the average flux for diagonally } neighboring assemblies along the i A A (l' + j') direction. L L L f I, fJ, f1J = Empirically-derived cou ling constants along eachoftherespectivei',$',and A A (l' + j') directions. Figu're 4.2.3.6 portrays a geometrical description of this j equation. f
/
4-190
i l PINUP requires the following input data: 1 (1) For each of the four central assemblies (L=1,2,3, l l and 4), single assembly relative fuel pin fission j i t rate distributions, po(L). These originate '
)
from single assembly PDQ-7-E solutions for the I purpose of qualification to multi-assembly PDQ-7-E solutions. Alternately, the po(L) distributions are taken f rom single assembly CASMO-1 so:Istions in the production use of PINUP. l (2) Assembly-averaged fission power densities, P(L), for each of the 16 fuel assemblies in the 4x4 assembly geometry. These originate from PDQ-7-E ! l multi-assembly geometry solutions for the purpose l of qualifying PINUP to multi-ascembly PDQ-7-E solutions. Alternately, the P(L) data are taken from SIMULATE-E nodal power solutions in production use of PINUP. (3) [g and K[f fission cross section data for each fuel pin cell, and averaged over each assembly. These are used for the flux conversion of the above j data. [g and K[f data originate from CASMO-1 cross section files. l I l 4-191
1 l l PDQ-7-E and PINUP fuel pin fission rate results from the multi-assembly geometry interqualification study are summarized in Table 4.2.3.1. This table displays the RMS differences between PDQ-7-E and PINUP fuel pin fission rate predictions for each of the central four assemblies in the multi-assembly 1 l geometry. Also displayed are the percent t I differences in the local peaking factor predictions i 1 of the two codes. The general agreement between ! PDQ-7-E and PINUP predictions is very good. The 1 overall RMS difference between PDQ-7-E and PINUP fuel pin fission rate predictions is 0.028 for the entire data base of 40,176 (162 cases x 4 assemblies / case x 62 fuel pins / assembly) fuel pins analyzed. Likewise, the average percent difference (bias) in the local peaking factor predictions from both codes is 0.6% for the entire database of 648 individual assembly peak fuel pins analyzed. It ! l should be noted that on the average, PINUP slightly i overpredicts the peaking factors as compared to j 1 PDQ-7-E. The overall RMS difference between the I peak fuel pin fission rate predictions from both codes is 2.0%. i
)
l l l 4-192 ( ! 1
1 l l TABLE 4.2.3.1 COMPARISON OF PDQ-7-E AND PINUP FUEL PIN FISSION RATES l ASSEMBLY LOCATION (L) CASE FUEL CYCLE ROD L=1 L=2 L=3 L=4 NO. CONF EXP VOID CONF RMS PK RMS PK RMS PK RMS PK l (%) (M) (%) (%) (%) (%) l l 1 04 BOC 00 05 0.05 2.6 0.04 ~5.3 0.03 -1.4 0.05 2.6 2 04 BOC 00 06 0.03 0.9 0.04 -1.2 0.04 0.0 0.03 0.9 3 04 BOC 00 09 0.04 -0.3 0.03 2.6 0.03 -1.4 0.04 -0.3 4 04 BOC 00 10 0.05 2.8 0.03 1.3 0.03 0.8 0.03 -3.1 5 04 BOC 00 11 0.04 -3.7 0.03 -2.2 0.03 2.4 0.04 -3.7 6 04 BOC 00 12 0.02 -2.2 0.02 -0.3 0s02 -0.7 0.02 -2.2 7 04 MOC 00 05 0.05 5.4 0.05 -2.9 0.02 2.0 0.05 5.3 8 04 MOC 00 06 0.03 -0.4 0.03 -1.7 0.04 1.4 0.03 -0.4 9 04 MOC 00 09 0.04 0.2 0.03 2.2 0.03 0.0 0.04 0.2 10 04 MOC 00 10 0.05 5.0 0.04 1.4 0.04 0.9 0.03 0.1 11 04 MOC 00 11 0.02 -2.6 0.03 -3.2 0.01 1.2 0.02 -2.6 12 04 MOC 00 12 0.03 2.2 0.02 0.2 0.01 2.1 0.03 2.2 13 04 EOC 00 05 0.05 5.1 0.05 -1.9 0.04 4.4 0.05 5.1 14 04 EOC 00 06 0.03 -1.2 0.03 -1.0 0.04 2.4 0.03 -1.2 15 04 EOC 00 09 0.03 -0.2 0.03 2.0 0.04 0.8 0.03 -0.2 16 04 EOC 00 10 0.05 1.8 0.04 1.0 0.05 1.4 0.03 3.8 17 04 EOC 00 11 0.02 2.1 0.03 -3.0 0.01 -0.2 0.02 2.1 18 04 EOC 00 12 0.03 2.7 0.02 0.9 0.03 4.1 0.03 2.7 19 04 BOC 40 05 0.04 1.3 0.03 -5.1 0.03 -3.6 0.04 1.3 20 04 BOC 40 06 0.02 0.1 0.04 -0.2 0.04 -0.1 0.02 0.1 21 04 BOC 40 09 0.03 -0.8 0.02 0.3 0.03 -2.3 0.03 -0.8 22 04 BOC 40 10 0.03 0.2 0.02 0.5 0.03 -0.1 0.02 -1.7 23 04 BOC 40 11 0.03 -2.4 0.03 -2.1 0.03 2.1 0.03 -2.4 24 04 BOC 40 12 0.02 -0.8 0.01 -0.8 0.02 0.1 0.02 -0.8 25 04 MOC 40 05 0.04 2.6 0.03 -3.3 0.02 -1.3 0.04 2.6 26 04 MOC 40 06 0.02 -1.8 0.04 -0.6 0.04 0.9 0.02 -1.8 27 04 MOC 40 09 0.03 -0.1 0.02 1.7 0.03 -1.2 0.03 -0.1 28 04 MOC 40 10 0.04 2.2 0.03 -0.3 0.03 -0.1 0.02 2.6 29 04 MOC 40 11 0.02 -1.5 0.03 -2.9 0.01 0.8 0.02 -1.6 30 04 MOC 40 12 0.01 1.2 0.01 -0.6 0.01 0.8 0.01 1.2 31 04 EOC 40 05 0.04 2.6 0.04 -2.7 0.03 -1.1 0.04 2.6 32 04 EOC 40 06 0.02 -2.4 0.04 -0.4 0.04 1.7 0.02 -2.4 33 04 EOC 40 09 0.03 -0.2 0.02 1.5 0.03 -0.6 0.03 -0.2 34 04 EOC 40 10 0.04 -0.3 0.03 -0.6 0.03 0.2 0.02 3.4 35 04 EOC 40 11 0.02 2.4 0.03 -2.8 0.01 -0.3 0.02 2.4 36 04 EOC 40 12 0.02 1.9 0.01 0.2 0.02 2.4 0.02 1.9 37 04 BOC 70 05 0.03 -0.2 0.02 -4.4 0.02 -3.4 0.03 -0.2 38 04 BOC 70 06 0.03 -0.7 0.04 -0.8 0.04 0.1 0.03 -0.7 39 04 BOC 70 09 0.02 -0.8 0.01 0.4 0.03 -2.3 0.02 -0.8 40 04 BOC 70 10 0.03 -0.4 0.02 -0.2 0.02 -1.0 0.02 2.2 41 04 BOC 70 11 0.03 0.7 0.03 -1.9 0.01 -1.2 0.03 0.7 42 04 BOC 70 12 0.01 -0.8 0.00 0.0 0.00 -0.3 0.01 -0.8 4-193
TABLE 4.2.3.1 (Continu;d) COMPARISON OF PDO-7-E AND PINUP FUEL PIN FISSION RATES ASSEMBLY LOCATION (L[ CASE FUEL CYCLE ROD L=1 L=2 L=3 L=4 NO. CONP EXP VOID CONP RMS PK RMS PK RMS PK RMS PK (%) (M) (%) (%) (%) (%) 43 04 MOC 70 05 0.03 0.8 0.03 -3.6 0.02 -2.0 0.03 0.8 44 04 MOC 70 06 0.03 -2.5 0.04 -0.4 0.04 0.8 0.03 -2.5 45 04 l MOC 70 09 0.02 -0.4 0.01 0.0 0.03 -1.9 0.02 -0.4 ; 46 04 MOC 70 10 0.03 0.8 0.02 -0.8 0.02 -0.9 0.02 1.2 l 47 04 MOC 70 11 0.02 -0.3 0.03 -2.6 0.01 -1.3 0.02 -0.3 l 48 04 MOC 70 12 0.01 1.2 0.01 -0.7 0.00 -0.2 0.01 1.2 I 49 04 EOC 70 05 0.04 0.8 0.03 -2.8 0.02 -2.0 0.04 0.8 l 50 04 EOC 70 06 0.03 -2.8 0.04 -0.3 0.04 1.4 0.03 -2.8 ! 51 04 EOC 70 09 0.02 -0.5 0.01 0.1 0.03 -1.5 0.02 -0.5 I 52 04 EOC 70 10 0.03 -0.9 0.02 -0.9 0.02 -0.8 0.02 0.9 53 04 EOC 70 11 0.01 1.8 0.03 -2.6 0.01 -1.6 0.01 1.8 1 54 04 EOC 70 12 0.01 1.2 0.01 -0.7 0.01 0.4 0.01 1.2 55 09 BOC 00 05 0.04 3.5 0.04 -1.5 0.02 -0.8 0.04 3.5 56 09 BOC 00 06 0.04 4.5 0.03 -0.2 0.03 0.7 0.04 4.5 57 09 BOC 00 09 0.04 4.9 0.02 2.3 0.03 -0.5 0.04 4.9 58 09 BOC 00 10 0.04 2.5 0.04 3.7 0.03 1.5 0.04 6.6 59 09 BOC 00 11 0.02 0.8 0.03 -2.7 0.01 1.2 0.02 0.8 60 09 BOC 00 12 0.03 3.9 0.01 -0.4 0.01 1.0 0.03 3.9 61 09 MOC 00 05 0.05 5.2 0.04 1.4 0.03 2.0 0.05 5.2 62 09 MOC 00 06 0.03 0.4 0.03 -1.3 0.03 1.1 0.03 0.4 63 09 MOC 00 09 0.04 5.1 0.02 2.0 0.03 -0.3 0.04 5.1 j 64 09 MOC 00 10 0.05 4.9 0.04 3.2 0.04 1.7 0.03 6.4 65 09 MOC 00 11 0.02 3.7 0.03 -3.1 0.01 0.7 0.02 3.7 66 09 MOC 00 12 0.03 4.2 0.02 0.3 0.02 2.4 0.03 4.2 l 67 09 EOC 00 05 0.04 4.1 0.04 -0.8 0.03 3.7 0.04 4.1 68 09 EOC 00 06 0.03 1.4 0.03 -0.5 0.03 1.5 0.03 1.4 69 09 EOC 00 09 0.03 2.4 0.02 1.7 0.03 0.1 0.03 2.4 70 09 EOC 00 10 0.04 0.5 0.04 2.9 0.05 2.4 0.03 4.8 71 09 EOC 00 11 0.02 3.5 0.03 -2.5 0.01 -0.3 0.02 3.5 72 09 EOC 00 12 0.02 2.1 0.01 -0.2 0.03 3.8 0.02 2.1 73 09 BOC 40 05 0.03 1.3 0.03 -2.1 0.02 -1.5 0.03 1.3 74 09 BOC 40 06 0.03 3.5 0.03 -0.3 0.04 0.7 0.03 3.5 75 09 BOC 40 09 0.03 4.1 0.02 2.0 0.03 -1.3 0.03 4.1 76 09 BOC 40 10 0.03 -0.4 0.03 3.0 0.02 -0.3 0.03 5.1 1 77 09 BOC 40 11 0.02 2.0 0.03 -2.6 0.01 0.3 0.02 2.0 l 78 09 BOC 40 12 0.02 2.0 0.01 0.2 0.00 -0.2 0.02 2.0 79 09 MOC 40 05 0.04 2.7 0.03 0.6 0.02 -1.6 0.04 2.7 80 09 MOC 40 06 0.03 -0.9 0.03 -0.6 0.04 0.9 0.03 -0.9 81 09 MOC 40 09 0.03 3.7 0.02 2.4 0.03 -1.2 0.03 3.7 82 09 : TOC 40 10 0.04 2.5 0.03 2.3 0.03 0.1 0.02 4.6 i 83 09 MOC 40 11 0.01 3.3 0.03 -2.9 0.01 0.4 0.01 3.3 84 09 MOC 40 12 0.02 2.7 0.01 0.6 0.01 1.4 0.02 2.7 l 85 09 EOC 40 05 0.04 2.1 0.03 0.9 0.03 -1.9 0.04 2.1 86 09 EOC 40 06 0.02 0.2 0.03 -0.2 0.04 1.2 0.02 0.2 87 09 EOC 40 09 0.03 2.9 0.02 2.2 0.03 -0.9 0.03 2.9 88 09 EOC 40 10 0.03 -0.9 0.03 2.0 0.03 0.7 0.02 3.8 4-394
TABLE 4.2.3.1 (Continund) COMPARISON OF PDO-7-E AND PINUP FUEL PIN FISSION RATES ASSEMBLY LOCATION (L) CASE FUEL CYCLE ROD L=1 L=2 L=3 L=4 NO. CONF EXP VOID CONF RMS PK RMS PK RMS PK RMS PK (%) (M) (%) (%) (%) (%) l 89 09 EOC 40 11 0.02 3.9 0.03 -2.5 0.01 0.0 0.02 3.9 90 09 EOC 40 12 0.01 1.8 0.01 -0.1 0.02 2.4 0.01 1.8 91 09 BOC 70 05 0.03 0.0 0.02 -2.2 0.02 -2.8 0.03 0.0 l 92 09 BOC 70 06 0.03 -0.1 0.05 -0.2 0.03 0.2 0.03 -0.1 93 09 BOC 70 09 0.02 2.2 0.01 2.2 0.03 -2.8 0.02 2.2 i 94 09 BOC 70 10 0.03 0.4 0.02 0.4 0.02 0.5 0.02 1.8 95 09 BOC 70 11 0.03 4.8 0.03 -1.7 0.01 -0.4 0.03 4.8 96 09 BOC 70 12 0.01 0.6 0.00 0.5 0.01 0.8 0.01 0.6 97 09 MOC 70 05 0.03 1.2 0.02 0.7 0.02 -1.6 0.03 1.1 [ 98 09 MOC 70 06 0.03 -2.1 0.04 -1.1 0.04 0.8 0.02 -1.4 99 09 MOC 70 09 0.02 2.8 0.02 2.3 0.03 -1.7 0.02 2.7 100 09 MOC 70 10 0.03 1.4 0.02 1.6 0.02 -1.3 0.02 3.1 101 09 MOC 70 11 0.01 3.0 0.03 -2.8 0.01 -1.8 0.01 3.1 102 09 MOC 70 12 0.01 1.5 0.01 0.8 0.01 0.1 0.01 1.5 103 09 EOC 70 05 0.03 0.7 0.02 0.0 0.02 -2.2 0.03 0.7 104 09 EOC 70 06 0.02 -0.9 0.03 -0.5 0.04 1.2 0.02 -0.9 105 09 EOC 70 09 0.02 2.3 0.01 1.9 0.03 -1.5 0.02 2.3 106 09 EOC 70 10 0.03 -1.0 0.02 2.4 0.02 -0.7 0.02 2.8 107 09 EOC 70 11 0.01 3.2 0.03 -2.6 0.01 -1.4 0.01 3.2 108 09 EOC 70 12 0.01 1.2 0.01 0.7 0.01 0.7 0.01 1.2 109 11 BOC 00 05 0.04 0.6 0.04 -1.2 0.02 -1,1 0.04 0.6 110 11 BOC 00 06 0.03 2.5 0.05 2.4 0.03 0.7 0.03 2.5 111 11 BOC 00 09 0.04 4.5 0.03 -1.0 0.03 0.0 0.04 4.5 112 11 BOC 00 10 0.03 -0.9 0.04 -1.8 0.03 3.2 0.02 5.4 113 11 BOC 00 11 0.02 2.0 0.04 2.3 0.02 0.1 0.02 2.0 114 11 BOC 00 12 0.02 1.7 0.02 -1.6 0.01 1.4 0.02 1.7 ( 115 11 MOC 00 05 0.04 0.6 0.03 -3.6 0.03 -1.5 0.04 0.6 116 11 MOC 00 06 0.03 1.6 0.05 2.3 0.03 1.2 0.03 1.6 117 11 MOC 00 09 0.03 2.4 0.02 -0.1 0.03 0.1 0.03 118 2.3 11 MOC 00 10 0.03 -0.5 0.03 -1.2 0.03 2.7 0.03 2.3 119 11 MOC 00 11 0.02 1.7 0.04 2.5 0.01 0.6 0.02 1.7 120 11 MOC 00 12 0.01 1.2 0.01 0.2 0.02 2.4 0.01 121 1.2 11 EOC 00 05 0.04 0.8 0.03 -1.5 0.03 -0.9 0.04 0.8 ( 122 11 EOC 00 06 0.03 -1.5 0.04 1.3 0.04 1.1 123 0.03 -1.5 11 EOC 00 09 0.03 1.7 0.02 2.1 0.03 -0.2 0.03 124 11 1.7 EOC 00 10 0.03 -0.7 0.03 -0.4 0.03 1.5 0.03 1.8 125 11 EOC 00 11 0.03 1.9 0.03 -1.2 0.01 0.9 0.03 1.9 126 11 EOC 00 12 0.01 -0.9 0.01 0.2 0.01 1.9 127 11 0.01 -0.9 BOC 40 05 0.03 0.2 0.03 0.2 0.02 -1.5 0.03 0.2 128 11 BOC 40 06 0.02 0.9 0.03 0.3 0.03 0.5 0.02 0.9 129 11 BOC 40 09 0.03 3.5 0.02 0.3 0.03 -1.1 0.03 130 3.5 11 BOC 40 10 0.03 -1.4 0.03 -0.3 0.02 1.1 0.02 3.7 131 11 BOC 40 11 0.02 1.8 0.03 -1.0 0.01 0.3 0.02 1.8 132 11 BOC 40 12 0.01 1.6 0.01 -1.0 0.01 0.5 0.01 1.6 ) 133 11 MOC 40 05 0.04 0.5 0.03 -2.7 0.02 -1.8 0.04 0.5 134 11 MOC 40 06 0.02 1.2 0.04 0.8 0.03 0.9 0.02 1.2 ! I 4-195 i
TABLE 4.2.3.1 (Continutd) COMPARISON OF PDQ-7-E AND PINUP FUEL PIN FISSION RATES ASSEMBLY LOCATION (L) CASE FUEL CYCLE ROD L=1 L=2 L=3 L=4 NO. CONF EXP VOID CONF RMS PK RMS PK RMS PK RMS PK (t) (M) (t) (t) (t) (t) l 135 11 MOC 40 09 0.03 2.0 0.02 0.9 0.03 -0.9 0.03 2.0 l 136 11 MOC 40 10 0.03 -1.2 0.03 -0.4 0.03 1.4 0.02 3.7 137 11 MOC 40 11 0.02 1.2 0.03 0.2 0.01 0.7 0.02 1.2 138 11 MOC 40 12 0.01 1.0 0.01 -0.2 0.01 1.5 0.01 1.0 139 11 EOC 40 05 0.04 0.5 0.03 -2.9 0.02 -1.7 0.04 0.5 100 11 EOC 40 06 0.02 0.6 0.04 0.2 0.04 0.8 0.02 0.6 10 1 11 EOC 40 09 0.02 1.3 0.01 1.8 0.03 -1.2 0.02 1.3 142 11 EOC 40 10 0.03 -1.4 0.02 -0.4 0.03 0.7 0.02 3.2 143 11 EOC 40 11 0.02 1.3 0.03 -1.7 0.01 0.8 0.02 1.3 144 11 EOC 40 12 0.01 0.1 0.00 0.5 0.01 1.3 0.01 0.1 14S 11 l10G 70 05 0.04 -0.4 0.03 0.2 0.02 -3.0 0.04 -0.4 146 11 boc 70 06 0.02 -1.0 0.03 -0.7 0.04 0.8 0.02 -1.0 147 11 BOC 70 09 0.02 2.5 0.02 2.3 0.03 -1.8 0.02 2.5 148 11 BOC 70 10 0.03 -1.8 0.03 0.5 0.02 -0.8 0.01 2.6 149 11 BOC 70 11 0.01 1.5 0.03 -0.2 0.01 -1.4 0.01 1.5 150 11 BOC 70 12 0.01 0.9 0.01 -0.3 0.00 -0.2 0.01 0.9 151 11 MOC 70 05 0.04 -0.4 0,03 -2.3 0.02 -1.9 0.04 -0.4 152 11 MOC 70 06 0.02 -0.3 0.03 -0.1 0.04 1.1 0.02 -0.3 153 11 MOC 70 09 0.02 2.2 0.01 0.8 0.03 -1.6 0.02 2.2 154 11 MOC 70 10 0.03 -1.8 0.02 0.0 0.02 -0.1 0.01 2.8 55 11 MOC 70 11 0.02 2.0 0.03 0.1 0.01 -1,1 0.02 2.0 156 11 MOC 70 12 0.01 1.2 0.00 0.8 0.01 0.4 0.01 1.2 157 11 EOC 70 05 0.04 0.0 0.03 -2.7 0,02 -2.9 0.04 0.0 158 11 EOC 70 06 0.02 -0.8 0.03 -0.5 0.04 0.8 0.02 -0.8 159 11 EOC 70 09 0.02 1.9 0.01 0.9 0.03 -1.7 0.02 1.9 160 11 EOC 70 10 0.03 -2.1 0.02 -0.2 0.02 -0.4 0.02 2.5 161 11 EOC 70 11 0.02 2.4 0.03 -2.2 0.01 -1.2 0.02 2.4 162 11 EOC 70 12 0.01 1.0 0.00 0.1 0.01 0.3 0.01 1.0 Overall RMS Difference = 0.028 Average PKt Difference = 0.58% Overall PK RMSt Difference = 2.02% NOTES: (1) In this table RMS values represent the absolute RMS difference between PINUP and PDQ-7-E fuel pin fission rates in assembly L (L=1,2,3,4). (2) PK values represent the percent difference in peak fuel pin fission rates in assembly L. Positive values indicate PINUP predictions are higher than those from PDQ-7-E. l l 1 4-196 I l l l J
1 1 FIG URE 4.2.3.1 l PDQ-7-E MULTI-ASSEMBLY MODEL GEOMETRY DESCRIPTION 1 l I l REFLECTOR BUFFER REGION LAT.y4 LAT./3 LAT.#4 LAT. 3 EXP.#4 EXP.p3 EXP.g4 EXP. 3 V0lD#4 V0lD#3 V0lD#4 VOID 3 z LAT.p2 LAT.pl LAT.#2 LAT.#1 , o EXP.#2 EXP.#1 EXP.#2 EXP.g1 c:
$ 5 V0lD#2 VOIDjl V0lDg2 V0lDg1 a A G e 9 ? $ = x R $ $ LAT.p3 LAT.j3 LAT.14 LAT.p3 U h g EXP.#3 EXP.#3 EXP.#4 EXP.#3 g V0lDi3 V0lDp3 V0lDg4 V0lDy3 LAT.g3 LAT.g3 LAT.p2 LAT.#1 EXP.#3 EXP.p3 EXP.#2 EXP.#1 V0lDp3 V0lDp3 V0lDp2 V0lD#1 1
BUFFER REGION
)
1 REFLECTOR 1 4-197 L l
1 FIGURE 4.2.3.2 PDQ-7-E MULTI- ASSEMBLY GEOMETRY CONFIGUR ATIONS* l l CO NFIGU R ATIO N d4 3.18n/o 3. 0 3 */c l EXP=0H3 EXP-12M3 3.0 3 w/o 3.18*/o l EXP=18H3 EXP=0H3 CO N flGU R Ail 0N ill CO NflGU R ATION # 9 3.19w/o 3.13*/o 319n/o 319w/o E X P-9 H3 EXP=0H3 EXP=0H3 EXP=9H l 3.0 3 w/o 3.19 w/o 3. 0 3 w/o 3.19n/c l EXP-16H3 EXP=956 EXP=19Hi EXP=0H3 l
- CENTR AL 2X2 ASSEMELY EDIT REGION. EXPOSURES REPRESENTATIVE OF PEACH BOTTOM 2 BEGINNING OF CYCLE 7. ENRICHMENTS ARE BOL LATTICE AVERAGES.
4-198
l FIG URE 4.2.3.3 PDQ-7-E MULTIPLE ASSEMBLY GEOMETRY RELATIVE PIN POWER DISTRIBUTION, j FUEL CONFIGUR ATION #4 ) BOC,0% VOID, ROD CONFIGUR ATION #9 1 WIDE WATER G AP 1
.15 1.18 1.27 1.M 1.26 1.36 1.43 1.42 1.03 1.09 1.07 1.07 0.97 1.04 1.02 0 99 l 1 1.14 0.20 1.09 1.18 0.19 1.21 1.27 1,43 0.98 1.12 0.97 1.09 1.07 0.98 1.11 1.02 l 1.17 1.04 1.09 1.07 1.03 1.02 0 32 1.31 1.07 0.85 1.07 1.13 1.02 0.98 0.98 1.04 1.15 1.C8 1.03 1.13 0 00 1.04 1.04 1.35 0.98 1.00 1.01 0 00 1.14 1.02 1.0- 0 97 1.05 O.67 0.94 0 00 1.08 0 97 0 99 1.29 0.93 0.95 0.95 1.04 0.00 1.13 ' 09
.. 1.07 1.07 0 98 0 87 0 94 0.94 0 82 0.28 1.12 0.92 0.73 0 SC 0.95 1.01 1.07 0.97 1.07 g 1.05 0 95 0.26 0 88 0.88 0 26 1.00 1 08 0.90 0.98 0 73 0.95 1.00 0 85 1.12 1.09 3 o O C'
(" i O.96 1.01 0 97 1.07 1.08 0 99 1.02 1.12 0.83 0 93 0 92 0 93 0 98 1.07 0 98 1.03 g i
~ >
j NARROW WATER GAP y x a 0 97 1.07 1.33 1.34 1 38 1.47 1.50 1.42 a.12 1.08 1.11 1.29 1.35 1.31 1.43 1 42 o l B;--
> 1 v 1 0 82 1.09 1.10 1.32 1.57 1.26 1.62 1 50 1.02 1.03 0 28 0 99 1.04 0 32 1.27 1.43 l l
0 65 0 89 1.15 1.22 1.26 1.33 1.26 1.47 0.99 0 26 0 82 0 97 1.04 1.02 1.21 1 36 6 0 55 0 $1 1 07 0 00 1.23 1.26 1.37 1.32 1.08 0 88 0 91 1.08 0 00 1.03 0.19 1.26 0 45 0 "'O O 87 1.11 0.00 1.22 1.32 1.34 1.07 0 88 0 94 0 00 1.13 1.07 1.18 1.X 0 41 0 55 0 74 0 87 1.07 1.15 1 10 1.33 0.97 0 26 0 87 0 94 1.03 1.09 1.09 1.27 0 33 0 48 0 55 0 70 0 81 0 89 1.09 1.07 1.01 0 95 0.98 0 67 1.08 1.04 0 20 1.18 0 25 0 33 0 41 0 45 0 55 0 65 0 82 0 97 0 96 1 05 1.07 1.05 1.15 1.17 1.14 1.15
-WIDE WATER GAP L AIIlCE 1 L AIIiCE 2 Exp = 0.00 Exp = a 76 4x4 Assrus LY POWER oisTale uTio N Mcx Pin = i.4 3 M ax Pin = 1.14 1.120 1 280 1.270 E620 0 995 0 905 1 160 1.270 L s, : T!Cc 1 0.531 0.540 0 E5 1 250 LA i i 91-3
- t. x p = i7 b, Exp = 0.0 0 0.470 0 531 0 996 1 120 Max P;n = 1.62 Max o n = 1.4 3 4-199
l i l FIGURE 4.2.3.4 PDQ-7-E MULTIPLE ASSEMBLY GEOMETRY RELATIVE PIN POWER DISTRIBUTION, FUEL CONFIGURATION #9 BOC,40% VOID, ROD CONFIGUR ATION #11 WIDE WATER G AP t.00 1.06 1.07 1.10 1.04 1.00 0.29 0.80 s.24 1.01 0 78 0 62 0.58 0.51 0 J3 0 29 1.06 1.01 0.98 1.00 0.83 1.01 0 93 0 79 1.43 1.13 0 99 0.17 0 79 0.66 0 43 0 33 1.10 1.00 1.08 1.04 1.00 0 94 0 70 0 83 1.47 0 35 1.03 1.03 0 95 0.86 0 66 0 $1 1.17 1 OS 1.08 1.07 0 00 0 94 0 93 0 97 1.66 1.24 1.18 0.00 1.16 0 95 0 79 0 58 1.16 0 93 1.08 0.00 1.01 0 91 0 93 0 98 1.70 1.27 1.20 1.29 0.03 1.00 0 17 0 62 1.20 1.19 1.08 1.03 0 96 0 93 0 63 0 94 1.$8 02 1.11 1.20 1.18 1.03 0 98 0.78 g 1.15 1.18 0 87 1.06 1.01 0 73 1.04 0 92 1.64 1.51 0 38 1.27 1.24 0 35 1.13 1.01 3 o C y 1.13 1 79 1.07 1.23 1.17 1.06 0 98 0 96 1.79 1.64 1.58 1.70 1.66 1.47 1.43 1.24
"{ N ARR0 N WATER GAP p u
- e 0 99 0 35 1.08 0 93 0 96 0 96 0 92 0 84 0.96 0 92 0 94 0 98 0 97 0 $3 0 79 0 $3 o R 7 1.05 1.10 0 93 1 02 0 9B 0 82 1 03 0 92 0 93 1.04 0 69 0 90 0 90 701 0 93 0 83 1 03 1.02 1.C8 1.02 0 97 0 94 0 82 0 96 1.06 0 73 0 93 0 91 0 94 0 94 ' 01 1.03 1 03 1 07 1.12 0 03 1.03 0 97 0 98 0 96 1.17 1.01 0 96 1.01 0 03 1.00 0 83 1.04 0 94 1.04 1.01 1.'2 0 00 1.02 1.02 0 93 1.23 1.06 1 03 0 33 1.07 1.04 1.03 1.10 1.00 0 96 1 02 1 01 1.12 1.08 0 93 1.08 1.07 0 87 1.08 1.08 1.08 1 08 0 98 1.07 1
0 97 1.06 , 96 1E 1.07 1.02 1.10 0 95 1.09 1.15 1.19 0 93 1.06 1.03 t.0i 1.06 1 0 94 0 97 1.0? O 94 1 03 1 03 1.05 0 98 1.13 i.15 1 20 1.16 1.17 1.10 1 26 1.03 WIDE N ATER G A A I i L ATTiCE 1 L ATTiCE 2 l f.i#P C X" Pi n =i.c. p = 0 00 I
.,z ..i c x Pin = 1.7 9 4x4 AssEveLy oo NEP OisTP!s uTioN 1.200 0 973 0.539 0 522 l 1.080 1.040 0 559 0 529 L ATTICr 3 t ATT,Cr 1 12}3 1 00 G3 0 973 t.x p =.-
200 b
- t. x p = 7. 7 3 1.410 1.2 93 1.050 1.200
'iOx
. 0;n = 1 i2 '.i c x o;n = 1.2 3 1
4-200
FIGURE 4.2.3.5 PDQ-7-E MULTIPLE ASSEMBLY GEOMETRY RELATl.' , 5 f'OWER DISTRIBUTION, FUEL CONFIGUR ATION #9 BOC,70% VOID, ROD CONFIGUR ATl1N 112 WIDE WATER GAD 1.06 1.i2 1.16 1.24 1.19 1.24 1.19 1.15 1.03 1.07 1.13 1.11 1.14 1.09 1.07 1.03 1.11 0 39 0 99 1.07 0 42 1.18 1.17 1.08 0 99 1.07 1.11 0 89 1.02 0.98 0 99 1.07 1.15 0 98 1.12 1.09 1.04 1.02 0 41 1. 33 0.96 0 83 1.01 1.02 1.05 1 06 0 98 1.09 1.22 1 06 1.08 1.11 0 00 0 99 1.00 1.19 1.09 0 97 0.95 0 00 1.04 1.05 1.02 1.14 1.17 0 41 i 03 0 03 1.04 0 94 0 96 1.14 1.04 0 92 0 93 0 96 0 00 1.02 0 89 1.11 1.21 1.15 1 00 0 98 0 94 0 88 0 38 1.02 0 98 0.73 0.87 0 93 0 95 1.01 1.11 1.43 1.16 1.14 0 40 0 98 0 95 0.38 0 91 0.73 0 92 0 97 0.83
$ 1.02 1. 1.01 1.07 1 07 3 a - a rm 1.i2 1.06 1 01 1.16 1.13 i.01 0 99 1.0; 0 92 0 91 0 98 1.C4 1.C9 0 96 0 99 1.03
]
H g { N ARRC N WATER G AD
~
p m a i.04 1 00 s.13 1 C3 1 00 1.02 1.04 0 95 i 01 1.00 1.02 1.14 1.19 1 03 1.08 1 15 o p \ 3: c ! 1 07 1.06 0 93 1.02 0 98 0 87 1.07 1 04 0 93 1.02 0 38 0 96 1.03 0 41 1.17 1.19 l 1 03 0 98 1 06 1. X 0 95 0 94 0 87 1 C2 1.0i 0 38 0 38 0 94 0 99 1.02 1.18 1.24 1 02 1 00 i 08 0 03 1.00 0 95 0 98 1.00 1.13 0 95 0 94 1 04 0 00 1.04 0 42 1.i9 , I O 93 0 98 0 98 1 08 0 OJ 1.00 i 02 1.03 1.16 0 98 0.98 0 CO 1.i1 1.09 1.07 1.24 l 0 99 0 93 0 95 0 95 L 08 1.06 0 93 1.12 1.01 0 40 1.00 1.03 1.08 1.i: . 99 1.is j l 0 95 0 99 0 93 0 93 1 00 0 9' 1 06 1.03 1.06 1.14 1.15 0 41 1.06 0 98 0 39 i . .: I 1 0 97 0 95 0 99 0 93 1.02 1 03 1.07 1 04 1.12 1.16 1.21 1.17 1.22 s.15 1.11 1# g
#1DE WATER G AP L ATTICE 1 L ATTiCE 2
*Pc" x0 Pi 9' Okn = s .24 fJ *a x *Pi n = 1.14 P 4X4 A S S E S,8 9 LY DO NED DISTolB UTiON h.i 3.03) ;,033 o 933 o 940 0 965 1.0;0 1 110 0 95J 3--..- 0 939 0 973 i 010 i . 3J L. ".- M. , -
t xp =2 0. 37 b ' ' ' c" l tap = 0.0 0 0 909 0 939 0 965 1.050
'.10 x o.n = 1.i3 '1cx C;n = 1.24 4-201
{ FIGURE 4.2.3.6 1 1 PINUP CODE GEOMETRY DESCRIPTION l lL-11 lL-21 5, i' (Is+bf
)
C'. I' s x,,, Y (F,taf,) ( F, + 4 f,,) I I L- 31 l L- 41 l l
,(m, i' r) = e(1, i: l') + ft i' a 6,
+ ft l' a 6, + ??, i' l' a 6,,
4-202
l 4.2.4 Overall Local Peaking Factor Statistical Evaluation l The total PINUP to measurement uncertainty in the prediction of local peaking factors can now be derived by combining the uncertainties from: (1) CASMO-1 predictions of local peaking factors compared with measurements, (2) PDQ-7-E predictions of local peaking factore compared with CASMO-1 predictions, and, i (3) PINUP predictions of local p9s'ing factors compared with PDQ-7-E predictions. This yields the overall uncertainty, cPINUPe in the PINUP code local peaking factor prediction: OPINUP (OCASMO/ MEAS + OPDQ/CASMO + OPINUP/PDQ)
=
{2.02 + 2.22 + 2.02)W
= 3.6%
It should be noted that the overall bias in the PECo local peaking factor methodology is in the conservative sense, i.e., PEco methods on the average, tend to overpredict local peaking. The local peaking factor bias is therefore conservatively ignored. 1 4-203 l y
1 l l l
)
4.3 Benchmarking of Reactivity Parameters ! l BWR safety knalysis methods rely on the steady-i state physics models for the determination of Doppler, void, and control rod reactivities. The predictive accuracy of the PEco 3-D physics model, as demonstrated in the calculations of core k-effective and power distribution, provides an indirect qualification of the steady-state methods used to calculate reactivity parameters. PEco has, however, conducted additional benchmark studies to establish a more direct qualification, and to determine the statistical biases and uncertainties associated with the model's prediction of these reactivity parameters. In the cas( of Doppler reactivity, accurate experimental data for the U-238 resonance integral and Doppler coefficient exist. Comparisons to this data have therefore been used to qualify the PECo CASMO-1 lattice physics Doppler methodology, as presented in Section 4.3.1. CASMO-1 predictions of void and control rod reactivities, on the other hand, have been benchmarked by PECo via comparisons to higher order Monte Carlo calculations. These comparisons are l presented in Sections 4.3.2 and 4.3.3. 1 l l l 4-204 ' i
4.3.1 Benchmarking of Doppler Reactivity Calculations 4.3.1.1 Lattice Physics Benchmarks Experimental measurements of the U-238 resonance integral and Doppler temperature coefficient hsve been conducted by a number of laboratories, including A.B. Atomenergi(NO. These tests primarily employed Np-239 activation techniques, using in-pile capsules holding either UO2 or metallic-U fuel rods. The~ test capsules typically contained an electrical heating element with a thermocouple to control and monitor the fuel temperature, as well as a cadmium liner to separate epithermal and thermal neutron absorptions. The induced Np-239 activity was cross-calibrated against the activation of a known standard isotope, such as Au-197(24, Isolating four tests involving exclusively UO2 fuel, the Reference 26 study performed a best fit of the data I to derive the U-238 resonance integral equation at ; room temperature, To. 1 RIo = 5.60 + 26.3 * ( S/M)1/2, where S/M is the surface to mass ratio of the fuel rod I 1 2 expressed in cm / gram. l l
)
The Doppler temperature coefficient, no, is expressed in terms of the variation of the U-238 l resonance integral with temperature: 4-205
RI(T) - 6 = (RI(To) - 6)*(1 + ao (T1/2 _ yo /2)) ,l where in the above equation, 6 is the 1/v contribution to the resonance integral above 0.55 ev: i Em f _1/E1 1 1.558 barns 6 = f".dE O 55 E The most quoted expression for the Doppler coefficient, no, is based on the original Swedish data measured in f the heavy water reactor, Rl(27); a0 = (0.58 + 0.5 S/M) *10-2 Independent theoretical investigations have been conducted by both EPRI and AB Atomenergi which compare CASMO-1 resonance absorption predictions to the results from the empirically derived cor relations (2s)(s) . The EPRI study cited results from the CPM (3) lattice physics code, which uses the same resonance absorption methods contained in CASMO-1. Comparisons of calculated and
' measured' (i.e., empirically derived) Doppler ,
l coefficients obtained by both studies are displayed in Table 4.3.1.1. It should be noted that the 002 pellet geometry with radius 0.52 cm has approximately the same radius as found in Peach Bottom BWR 8x8 fuel assembly designs. 1
;-206 l l
l l The 0.52 cm pellet radiun cases from both ! investigations demonstrate, on the average, a slightly more negative CASMO-1 Doppler coefficient prediction relative to the measured data. The mean and standard deviation difference statistics for these cases, when expressed as percentages are: pE -6.6% (CASMO-1 Doppler Coefficient More Negative Tnan Measurements) oE 1.9% Consideration of the quoted uncertainty (110%) in the measured Doppler coefficient data, yields the overall mean bias and uncertainty inherent in CASMO-1 Doppler coefficient predictions: p DOP ; -6.6% (Mean CASMO-1 Doppler Bias) o DOP ; 10.2% (CASMO-1 Doppler Uncertainty) i l 4-207
~
TABLE 4.3.1.1 DOPPLER COEFFICIENT COMPARISONS CASMO-1 PREDICTIONS VS. EMPIRICAL CORRELATIONS DERIVED FROM SWEDISH D A REACTOR MEASUREMENTS UO 2 ASSIMED FUEL PELLET FUEL TEMPERATURE PREDICTED MEASURED
- PERCENT INVESTIGATOR CHANGE ("K) DOP. COEFF. DOP. COEFF. DIFFERENCE
------ ----- RADIUS (CM)------ _. __
EPRI (REF. 28) 0.52 300 to 900 -0.00806 -0.0077 -4.7 1.04 300 to 900 -0.00697 -0.0067 -4.1 STUDSVIK (REF. 29) 0.52 300 to 1000 -0.00835** -0.0077 -8.5 1.04 300 to 1000 -0.00695** -0.0067 -3.8
- The ' Measured' Doppler Coefficient Is Inferred From The Empirically Derived Equation: i a0 = (0.58 + 0.5 S/M) X 10-2
** Extrapolated Slightly From keference 29 Data Using Actual Resonance Integral Correction Factor in CASMD-1.
l
4.3.1.2 NORGE-B Cross Section Pit Analysis i l SIMULATE-E Doppler predictions depend upon the i accuracy of the late.ica physics code, CASMO-1, as well , as a proper representation of the Doppler effect as generated by the cross section processing code, NORGE-B. Doppler model biases and uncertainties which are ( attributable to the NORGE-B methodology are now derived 1 based 6n the following presentation. l NORGE-B represents the nodal Doppler effect as a linear relationship between the fast group absorption partial cross section and the square root of the nodal fuel temperature. This results in a Doppler worth representation of: (AK/K) pop = Koop * ( Tg /2 1 - TBASE )e where Koop is a constant which is evaluated independently at each set of nodal exposure and void conditions in the unrodded state. Differentiating this expression yields the equivalent NORGE-B representation for the Doppler coefficient: O ~E DOP DOP = dk/k
=
dTp 1/2 14Koop ( Ty1 /2 - TBASE ")e 4-209
The accuracy of this representation was evaluated by i performing a separate CASMO-1 Doppler worth sensitivity study. In this study, fuel temperature and control state l conditions were intentionally perturbed from those originally used by NORGE-B in its derivation of the actual SIMULATE-E Doppler cross section representation. , The results of this sensitivity study are summarized in Table 4.3.1.2. In this table results from three sets of CASMO-1 Doppler calculations are compared. The ' Base Method' results consist of Doppler coefficients inferred from CASMO-1 unrodded k-infinity calculations which are actually used by NORGE-B to generate the Doppler representation in SIMULATE-E.
' Alt. 1 Method' results consist of Doppler coefficients inferred from CASMO-1 unrodded k-infinity calculations which used a different Doppler fuel temperature to calculate the Koop parameter in the Doppler worth correlation. Since all other nodal dependencies are modeled explicity in SIMULATE-E, differences between the Alt. 1 Method and the Base Method were used to infer the NORGE-B cross section fit uncertain.ty for the unrodded nodes. When evaluated over the representative set of exposures found in Table 4.3.1.2, this RMS difference was demonstrated to be 3.6%.
4-210
' Alt. 2 Method' results consist of Doppler coefficients inferred from CASMO-1 rodded k-infinity ^
calculations which are not used by NORGE-B to represent Doppler dependencies in SIMULATE-E. Thus the mean of the ( differences for this set is used to infer the NORGE-B Doppler bias in the representation of the rodded nodes in SIMULATE-E. Likewise, the standard deviation about this mean is interpreted as the NORGE-B Doppler uncertainty for the rodded nodes. When evaluated over the same set of exposure conditions, the NORGE-B Doppler model bias and uncertainty for rodded nodes were thus demonstrated to be 11.7% and 1.0%, respectively. ) 4-211 i
._ - x ,
TABLE 4.3.1.2 CASMO-1 DOPPLER COEFFICIENT SENSITIVITIES BASE METHOD ALT. 1 METHOD ALT. 2 METHOD UNRODDED UNR00DED R000E0 NODAL DOPPLER DOPPLER ALT. 1 DOPPLER ALT. 2 EXPOSURE COEFF.* COEFF.** METHOD COEFF.*** METHOD (GWD/MTU) (AK/K/ K0 IN) (AK/K/ K0 3R) % DIFF. (AK/K/ K3#) %DIF 0 -1.442 x 10-3 -1.432 x 10-3 -0.7 -1.588 x 10-3 10.1 5 -1.311 x 10-3 -1.210 x 10-3 -3.2 -1.462 x 10-3 11,5 { 10 -1.342 x 10-3 -1.308 x 10-3 -2.6 -1.510 x 10-3 12.5 15 -1.433 x 10-3 -1.363 x 10-3 -5.1 -1.592 x 10-3 11,3 21 -1.473 x 10-3 -1.409 x 10-3 -4.5 -1.645 x 10-3 11.7 32 -1.470 x 10-3 -1.413 x 10-3 -4.0 -1.665 x 10-3 13.3 RMS % DIFF. (UNRODDED NODE UNCERTAINTY) ...... 3.6% MEAN % DIFF (R000ED NODE BIAS) ........................................ 11.7% S.D. % DIFF (RODDED NODE UNCERTAINTY) ........................................ 1.0%
- Base Method Unrodded Doppler Coefficients Were Derived Using The Cross-Section Representation Actually Used in SIMULATE-E.
** Alt. 1 Method Unrodded Doppler Coefficients Were Derived Using fuel Temperature Conditions Different From Those Used In The Base Method.
*** Alt. 2 Method Rodded Doppler Coefficients Were Derived Using the Same Base Method fuel Temperatures. But In the Rodded State.
4.3.1.3 Overall Doppler Reactivity Statistics r N < Combining the NORGE-B Doppler fit statistics with those observed in the CASMO-1 lattice physics benchmarks results in an overall statistical evaluation of the nodal Doppler reactivity as modeled in the SIMULATE-E program. Algebraically combining the NORGE-B and CASMO-1 Doppler reactivity biases in this manner results in an overall Doppler bias of: p DOP
= -6.9% for unrodded nodes, and E -6.9% + 11.7% = 4.8% for rodded nodes.
The sign of these values is such that negative biases I indicate the predicted nodal Doppler coefficient to be more negative than expected measurement values. Likewise, determining the overall standard I deviation of the individual NORGE-B and CASMO-1 Doppler j reactivity uncertainties results in an overall nodal Doppler uncertainty of: oDOP E ( (10. 3 )? + ( 3. 6 ) ?) 1/2 = 10.9% for unrodded nodes, and E ((10.3)2 + ( 1. 0 ) 23 1/2 = 10.4% for rodded nodes.
)
4-213 /
4.3.2 Benchmarking of Void Reactivity Calculations 4.3.2.1 Lattice Physics Benchmarks PEco has benchmarked CASMO-1 predictions of void ! reactivity via comparison to Monte Carlo calculations generated with the KENO-IV computer code. The PECo l KENO-IV model used the 27 group ENDP/B-IV cross section 4 library which had been previously benchmarked by Oak Ridge National Laboratories (ORNL) using data from seventy critical experiments (30 Of these, twenty-six of the lower enriched (2.35 U-235 w/o) criticals are representative of Peach Bottom fuel lattices. Table 4.3.2.1 contains a summary of these twenty-six critical experiments, together with the associated KENO-IV k-effective predictions. The mean and standard deviation in the KENO-IV critical k-effective predictions derived from this data yield a one-sigma i confidence interval of: KENO KCRIT = 0.993 i .004 Using this nuclear cross section library, PECo developed a KENO-IV model for the Peach Bottom BWR 8x8 fuel lattice geometry portrayed in Figure 4.3.2.1. The KENO-IV model developed for this study used, to the greatest extent practical, the same BWR 8x8 fuel i ! assembly geometry, material specifications, and temperature related input parameters employed in PECo's 4-214 i
CASMO-1 model. Since KENO-IV does not internally model ( thermal expansion effects, CASMO-l's thermal expansion model was used to derive input parameters to KENO-IV. Some minor adaptations of the actual fuel assembly geometry were required to allow a KENO-IV input description for the problem. In these cases, the same \' adaptations were made to the CASMO-1 input description. This ensured a consistent benchmark test for both models, and thus provided a proper basis to evaluate CASMO-l's predictive capabilities. It should be noted that no attempt was made to either normalize the results of one model to the other, or to impose any other modeling assumption used in one code to the other code. Instead, an objective comparison was attempted, with the goal of quantifying true differences between the predictions from both models. k The sequence test chosen as the basis for the CASMO-1 void reactivity benchmark consisted of k-infinity predictions for a total of 33 cases, representing operating states and fuel lattices typical of Peach Bottom design analysis conditions. Twenty-four of these cases were performed by PEco using the KENO-IV and CASMO-1 models described above, while nine cases were quoted from a similar study performed previously at Yankee Atomic Electric CompanyU). The 33 k-effective predictions were based on three different BWR 8x8 fuel lattices, containing various gadolinia loadings, both in ! 4-215 l r
l rodded and unrodded control states. Three steam void conditions (0%,40%,70%) were modeled for each l r combination of gadolinia loading and control state l selected. The 33 CASMO-1 and KENO-IV k-infinity predictions thus produced 22 void reactivity comparisons for the two void ranges: 0+40% and 40+70%.
; Void coefficient comparison results are displayed in Table 4.3.2.2. The resulting CASMO-1 and KENO-IV predictions of the void coefficient are in excellent agreement. The mean void coefficients from the two codes differ by approximately 1.6% in overall magnitude.
The standard deviation of the differences between CASMO-1 and KENO-IV predicted void coefficients is approximately 7.3% of the mean KENO-IV value. l l l l 1 I 4-216
TABLE 4.3.2.1 KENO-IV CRITICALS BENCHMARK
- CALCULATED EXP. PLA1E PLATE ARRAY PLATE-TO-CENTER CRITICAL SEPARATION K-EFFECTIVE NO. MATERIAL THICKNESS SIZE CLUSTER GAP BETWEEN CLUSTERS 27-GROUP NOFB4 (cm) (cm) (cm) 15 20 x 17 11.92 0.992 t 0.004 5 -- --
20 x 16 -- 8.39 0.990 t 0.004 27 SS304L 0.302 20 x 16 0.645 7.42 26 0.999 i 0.004 SS304L 0.302 20 x 16 4.042 7.76 1.004 i 0.004 28 SS304L 0.485 20 x 16 0.645 6.68 29 0.991 1 0.004 SS304L 0.485 20 x 16 4.042 7.51 0.991 1 0.004 24 6061 AI 0.625 20 x 16 0.645 8.67 0.996 i 0.005 48 6061 Al 0.625 20 x 16 4.042 8.78 0.992 1 0.004 46 Zircalloy-4 0.652 20 x 16 0.645 8.79 6 47 Zirca11oy-4 0.990 1 0.004 0.652 20 x 16 4.042 8.78 0.994 t 0.004 O 31 Copper 0.646 20 x 16 0.645 6.62 0.987 i 0.004 O 12 Copper 0.646 20 x 16 4.442 7.51 43 Copper 0.992 i 0.004 0.337 20 x 15 0.645 6.88 0.995
- 0.004 44 Copper 0.337 20 x 15 4.042 7.00 4I 0.986 1 0.004 Cu (0.989 Cd) 0.357 20 x 15 0.645 5.15 0.992 1 0.004 36 Cd 0.061 20 x 17 0.645 6.74 37 0.991 + 0.004 Cd 0.061 20 x 17 4.042 9.37 0.996 i 0.004 50 Cd 0.0291 20 x 17 1.482 7.87 54 0.991 1 0.004 Cd 0.061 20 x 17 1.482 7.60 0.987 i 0.004 52 Cd 0.0901 20 x 17 1.482 7.54 0.989 i 0.004 20 Boral 0.713 20 x 17 0.645 6.34 0.997 i 0.004 16 Boral 0.713 20 x 17 4.442 9.03 0.986 i 0.004 32 SS304L (1.058) 0.298 20 x 17 0.645 7.56 0.994 1 0.004 33 SS304L (1.058) 0.298 20 x 17 4.042 9.62 0.996 i 0.004 38 SS304L (1.628) 0.298 20 x 17 0.645 7.36 0.992 1 0.004 39 SS304L (1.628) 0.298 20 x 17 4.042 9.52 0.994 1 0.004 MEAN KENO-IV CRITICAL K-EFFECTIVE PREDICTION = 0.993 STANDARD DEVIATION A800s MEAN = 10.004
- From Reference 31. Results Are Quoted For 2.35 W/0 Enriched 002 Fuel, Having A Square Pin Pitch of 2.032 cm.
And No Reflectors.
TABLE 4.3.2.2 CASMO-1 VS. KENO-IV VOID COEFFICIENT COMPARISON LATTICE NO., W/0 CONTROL VOID KENO-IV CASM0-1 NO. GAD RODS RODS CilANGF (%) AK/AV (AK/%V) AK/AV (AK/%V) 4 1 7 9 4 W/0 NO O + 40 -6.32 x 10-4 (PECo) 40 + 70 -9.02 x 10-4 -6.34 x 10 4 YES 0-. 40 -1.52 x 10-3 -9.29 x 10 3 40 -+ 70 -2.02 x 10-3 -1.51 x 10 3 NO GAD NO O -+ 40 -5.64 x 10-4 -2.05 x 10 4 40 - 70 1l.19 x 10-3 -4.89 x 10 3 YES 0-. 40 -1.01 x 10 3 40 + 70 -1.s4
-3.13 xx 10'3 10- -1.97 x 10 3 2 7 @ 4 W/0 NO O -+ 40 -5.29 x 10-4 -2.% x 10 4 (PECo) 40 -. 70 -8.82 X 10-4 -5.77
-8.74 X x 10 10-4 7 YES 0-. 40 -1.45 x 10-3 -1.49 x 10-3 w 40 -+ 70 -2.04 x 10-3 -2.00 x 10-3
$ N0 GAD NO O + 40 -5.14 x 10-4 -4.62 x 10-4 40 - 70 -1.19 x 10-3 -9.76 x 10-4 YES 0 - 40 3 3 40 - 70 -2.03
-2.97 x 10- < 10 3 -1.% x 10 3 3 3 9 4 W/0 NO O + 40 -4.00 x 10-4 -2.%
-3.75 xx 10 10-4 (YAEC) 40 + 70 -8.67 x 10-4 -9.33 x 10-4 YES 0 -. 40 -1.68 x 10-3 -1.78 x 10-3 40 -. 70 3 3 NO GAD NO O -+ 40 -2.63 x 10 4 -2.53 x 10 4 40 - 70 -2.50
-5.33 xx 10 10-4 -1.75
-7.67 xx 10 10-4 VOID COEFFICIENT STATISTICS: MEAN VOID COEFFICIENT -1.36 x 10-3 -1.34 x 10-3 MEAN DIFFERENCE (CASMO-KENO). 2.2 x 10-5 ggfgy STD DIFFERENCE: 9.9 x 10-5 ggfgy MEAN DIFFERENCE x 100 1.6%
MEAN STD DIFFERENCE x 100 7.3% MEAN
1 FIGURE 4.3.2.1 l l PECO KENO-IV BX8 SINGLE ASSEMBLY MODEL GEOMETRY DESCRIPTION l l l qwxnmwawmnrm ; WATER G AP l C H A N N C L/I N N C R W Af(R G A P l
!$ 99999999 l W 99999999 l il 99999999 l B ! 9 9 9 9 0 99 9 !l i
s i S 9 9 0 9 99 9 i! if 99999999 ! M 99999999 l l 9 9 99 9 9 9 9 l , I l
, WATER G AP
. u___________________________________i ! l l I 4-219
1 l I : 4.3.2.2 NORGE-B Cross Section Pit Analysis . l (A) Uncontrolled Nodes The instantaneous void dependence of each unrodded cross section is accurately represented by NORGE-B. This is accomplished by the use of either explicit cross section tables, or quadratic polynomial functions, each dependent upon the instantaneous relative moderator density, U. The instantaneous void cependence is determined by NORGE-B based on CASMO-1 unrodded branch void calculations performed at different exposure and void history depletion conditions. As a final QA check, NORGE-B performs a comparison of the cross section fits with the original CASMO-1 results for all cross , sections, as well as for k-infinity and migration area (M2). These comparisons generally indicate an absolute error of 0.3%AK or less in the k-infinity versus instantaneous void fit. In order to quantify the uncertainty in the void coefficient predictions attributable to the NORGE-B representation, the following statistical evaluation is presented. At each exposure and void history condition, assume l 1 1 I a quadratic dependence exists between k-infinity and the I instantaneous void, V: !
- K.(V) = (V-40)(V-70) K.(V=0 ) - V(V-70) K.(V=40) + V(V-40) K.(V=70) ,
2800 1200 2100 i l l 4-220 1
{ ! Note that such a representation is exact at void conditions V=0%, 40% and 70%. Using this relationship, the void coefficient at any void condition, V, may be determined by differentiation: dK. = (V-55) K.(V=0) - (V-35) K.(V=40) + (V-20) K.(V=70) dV 1400 600 1050 Assuming the accuracy in the predictions to be independent of void conditions, the variance between the , CASMO-1 and NORGE-B void coefficient predictions can now be determined as: VAR (dK./dV) =,'V-552 VAR (K.(V=0)) + IV-352 VAR (K.(V=40)) 0400 L 600 , l
+FV-2d2 VAR (K.(V=70))
L1050J l l where VAR (K.(V=0)) = VAR (K.(V=40)) = VAR (K.(V=70)) is the variance between CASMO-1 and NORGE-B k-infinities determined from instantaneous void branch restart cases. To calculate this variance, K. differences between CASMO-1 and NORGE-B have been analyzed in the unrodded state for a typical Peach Bottom fuel assembly design. The k-infinity differences as edited by NORGE-B are listed in Table 4.3.2.3 as a function of exposure (E), void history (VH), and instantaneous void (V) conditions. From this table, the variance between the CASMO-1 and NORGE-B inferred k-infinities is computed to be: VAR (K.) = 1.0 x 10-6 4-221
l I i Substituting this k-infinity variance into the above equation yields the NORGE-B void coefficient fit uncertainty for the uncontrolled state. At core average void conditions, (V=40%), this is evaluated as: ogid g ,odded = (VAR (dF./dV)}h4 = 2.34 x 10-5 AK/K/%V. Since the core average void coefficient as evaluated by SIMULATE-E is typically 1.1 x 10-3 AK/K/tV, the above represents approximately a 2.1% NORGE-B fit uncertainty in the calculated void coefficient. (B) Controlled Nodes The controlled nodes in SIMULATE-E are represented by an additional set of exposure and void dependent control rod partial cross sections. These partial cross sections are generated by NORGE-B based on differences , l between results from rodded and unrodded CASMO-1 cases i at various exposure and instantaneous void conditions. The additional void dependence introduced by the control rod cross sections causes the void coefficient to be more negative in the rodded state, an effect which is accurately modeled by the NORGE-B cross section l representation. To assess the accuracy of the NORGE-B l void coefficient methodology for rodded nodes, a j sensitivity study was performed using the results from , 4-222 I l
k ( additional CASMO-1 void branch cases in the rodded condition. At each exposure condition, the void I coefficient derived in the rodded state was compared to l the sum of the corresponding unrodded void coefficient f plus the change in void coefficient caused by the change in rod worth at different voids. This is analogous to the method used by NORGE-B to model the cross section void dependencies for the rodded nodes. The results from this sensitivity study are summarized in Table 4.3.2.4. Statistical analysis of this data indicates that the NORGE-B void coefficient fit uncertainty for rodded nodes is approximately: o ed
=
4.8 x 10-5 AK/K/W This represents approximately a 4.4% uncertainty in the calculated void coefficient for the rodded nodes when compared to the typical core average void coefficient as determined by SIMULATE-E. 4-223
0
. . . . . 0 .
= O 0 0 0 0 0 0 V -
4 4 3 3 3 3
% % 0 0 0 0 0 0 0 0 1 1 1 1 1 1 -
+
4 . -
= O x x x x x x
=
M 8 9 0 0 0 0 S V V T 2 9 2 2 2 2 I - - - - - - F E V R U 5 C 0 7 . . . . . . . B O 0 0 0 0 0 0
- =
E G V R O N D 5 4 3 3 3 3 N - - - - - - 6 A 0 0 0 0 0 0 - 0 1 1 1 1 1 1 1 % 1
- 0 . x x x x x x x O O M = 0 0 5 6 6 5 0
S A V 3 8 1 1 1 1 1 C 3 N = m 2 E 7 E 0 % 3 3 W T 4 0 4 6
/
e. u 4 E = . . . . . . . 2 B = O 0 0 0 0 0 0 K E H A L S V V B E 1 A C 3 = 1 N E 0 3 3 3 3 3 6[i
- R - - - - - - = w E 0 0 0 0 0 0 F
F 0 1 1 1 1 1 1 K I 7 . x x x x x x A D O
= 0 3 4 6 5 3 R Y A T
I V 5 1 2 2 2 2 V _ N - I F - N _ I . K % 0 - D . . . . . . . - E = O 0 0 0 0 0 0 _ L _ L V - O R T N 5 4 3 3 3 3 O % - - - - - - C 0 % 0 0 0 0 0 0 N 7 0 1 1 1 1 1 1 U 4
= x x x x x x
= .
H O 0 4 7 7 6 4 V V 6 9 1 1 1 1 0 7
= 0 0 O 0 0 0 0 V
)
T _
/
D 0 5 1 2 W G 0 1 5 1 1 2 3 ( . E _
TABLE 4.3.2.4 CASMO-1 RODDED NODE VOID COEFFICIENT STUDY NORGE-B METHOD CASMO-1 SENSITIVITY STUDY EXPOSURE UNR000ED DELTA-ROD WORTH RODDED R000ED (PWD/T) , DELTA-VOIDS "y "y CASE 1: VOID CHANGE FROM 0 4 70% 0 -6.31 x 10-4 -8.40 x 10-4 -1.47 x 10-3 -1.47 x 10-3 1 -5.70 x 10-4 -8.81 x 10-4 -1.45 x 10-3 -1.44 x 10-3 5 -4.79 x 10-4 -1.08 x 10 -3 -1.56 x 10-3 -1.53 x 10-3
. 10 -6.00 x 10 -4 -1.16 x 10-3 -1.76 x 10-3 -1.80 x 10-3 5 15 -6.70 x 10-4 -1.14 x 10-3 -1.81 x 10-3 -1.85 x 10-3 21 -6.75 x "-4 -1.11 x 10-3 -1.79 x 10-3 -1.80 x 10-3 32 -6.43 x IG-4 -1.09 x 10-3 -1.73 x 10-3 -1.68 x 10-3 CASE 2: VOID CHANGE FROM 40 h 70%
0 -9.05 x 10-4 -1.07 x 10-3 -1.97 x 10-3 -1.99 x 10-3 1 -8.43 x 10-4 -1.16 x 10-3 -2.00 x 10-3 -1.98 x 10-3 5 -8.26 x 10-4 -1.37 x 10-3 -2.20 x 10-3 -2.21 x 10-3 10 -1.07 x 10-3 -1.44 x 10-3 -2.51 x 10-3 -2.63 x 10-3 15 -1.16 x 10-3 -1.45 x 10-3 -2.61 x 10-3 -2.68 x 10-3 21 -1.14 x 10-3 -1.41 x 10-3 -2.55 x 10-3 -2.59 x 10-3 32 -1.07 x 10-3 -1.38 x 10-3 -2.45 x 10-3 -2.39 x 10-3 p = Core Average SIMULATE-E Vold Coefficient 2 -1.1 x 10-3 ggfgfgy a= UNCERTAINTY IN apD = 4.80 x 10-5 3gfgfgy (c/p*100) = % UNCERTAINTY IN a R00DED = 4.4%
I 4.3.2.3 Overall Void Reactivity Statistics Combining statistica derived from the CASMO-1 l lattice physics benchmarks with those obtained from the NORGE-B curve fit studies results in the following overall nodal statistics for the void reactivity calculation. For the uncontrolled nodes: CASMO-1 CODE NORGE-B CODE TOTAL p(Bias) 1.5% 0% 1.5% a(Uncertainty) 7.3% 2.1% 7.6% Por the controlled nodes: CASMO-1 CODE NORGE-B CODE TOTAL p(Blas) 1.5% 0% 1.5% a(Uncertainty) 7.3% 4.4% 8.5% The relatively small overall bias and uncertainty in the nodal void reactivity calculation provides a basis of confidence in the PEco methodology used to calculate this parameter. It is further noted that although the l computed bias between CASMO-1 and KENO-IV is small, the l l CASMO-1 void reactivity predictions on the average underpredict the magnitude of the void reactivity by 1.5%. l 1 ,I 4-226 I
4.3.3 Benchmarking of Control Rod Reactivities 4.3.3.1 Lattice Physics Benchmarks As in the case of the void coefficient, PECo has benchmarked CASMO-1 predictions of control rod worth to Monte Carlo calculations generated with the KENO-IV computer code. The KENO-IV rodded fuel assembly model contained the same input description used in the unrodded case, except for additional input specifications associated with the control rod regions. Again, some small adaptations of the actual control rod geometry were required to allow a KENO-IV input description for the problem. As much as practical, the same adaptations were made to the CASMO-1 input description. This ensured a consistent benchmark test for both models, and thus provided a proper basis to evaluate CASMO-l's predictive capabilitieu. The test sequence chosen as the basis for the CASMO-1 control rod reactivity benchmark consisted of k-infinity prediction for a total of 32 cases, representing operating states and fuel lattices typical of Peach Bottom design analysis conditions. Twenty-four of these cases were generated by PEco while eight are t quoted from a nimilar study performed previously at Yankee Atomic Electric CompanyU). The 32 k-effective predictions were based on results from four different BWR 8x8 fuel lattices, containing various gadolinia l I 4-227 l l
( loadings, and at three steam void conditions (0%, 40%, 70%). The 32 CASMO-1 and KENO-IV k-infinity predictions thus produced 16 control rod worth comparisons between CASMO-1 and KENO-IV. These results are displayed in [ Table 4.3.3.1. The resulting CASMO-1 and KENO-IV predictions of control rod worth are in excellent agreement. The mean control rod worths from the two codes differ by approximately 0.5% in overall magnitude, while the standard deviation of the differences between CASMO-1 and KENO-IV predicted control rod worths is approximately 2.0% of the mean value. 1 5 i 4 I I I l l 1 I I 4-228
\
TABLE 4.3.3.1 CASMO-1 VS KENO-IV CONTROL ROD WORTH COMPARISON LATTICE NO., W/O RENO-IV CASMO-1 NO. CAD RODS VOID (%) AK(CR) AK(CR) 1 (PECO) 7 9 4 W/O O 0.1971 0.1966 40 0.2328 0.2316 70 0.2664 0.2652 NO GAD 0 0.2660 0.2613 40 0.3211 0.3206 70 0.3791 0.3791 2 (PECO) 7 9 4 W/O O 0.2091 0.2077 40 0.2460 0.2440 70 0.2809 0.2778 NO GAD 0 0.2593 0.2560 40 0.3203 0.3157 70 0.3737 0.3752 3 (YAEC) 3 0 4 W/O O 0.219 0.227 40 0.270 0.283 70 0.323 0.331 4 (YAEC) 5 9 3 W/O 40 0.253 0.264 CONTROL ROD WORTH STATISTICS: MEAN 0.2761 0.2772 MEAN DIFFERENCE (CASMO-KENO) 1.18 x 10-3 AK STD DIFFERENCE 5.59 x 10-3 AK I MEAN DIFFEREldCE
---- gggg------ X 100 0.43%
STD DIFFERENCE t
----- gggg----- X 100 2.02%
i 4-229 l
4.3.3.2 NORGE-B Cross Section Pit Analysis i Control rod worths are represented in SIMULATE-E by a set of enposure and void dependent partial cross sections which are assigned to the rodded nodes. These partial cross sections are generated by NORGE-B using the differences between results from rodded and unrodded CASMO-1 cases at various exposure and instantaneous void conditions. Since the void history dependence is not explicitly modeled, the major uncertainty in this representation involves potential differences in the control rod worth which might occur if the instantaneous void and the void history conditions were unequal. To assess the accuracy of the NORGE-B control rod worth methodology, a sensitivity study was performed using results fro.1 additional CASMO-1 rodded branch cases at different void and void history conditions. The control rod worth derived using variable void history conditions at a constant instantaneous void level was then compared to the control rod worth derived using the NORGE-B method I as applied in SIMULATE-E. The results of this sensitivity study are summarized in Table 4.3.3.2. The NORGE-B control rod worth model uncertainty is derived i by evaluating the RMS of differences between the rod worth predicted by the NORGE-B model and those from the CASMO-1 sensitivity study: , 4-230
1 l l 0 = ([ ( AKc r - AKcr) ) / = 0.0021 AK 421/2 l 1 Since the average control rod worth in this table is l l p = 0.2431AK, the percent uncertainty in the NORGE-B control rod model is defined to be: 0.0021 o
- 100 = ----
- 10 0 % = 0. 9 %
I 4-231 l
- -- - - - - . - - - , _ . . , ,,- - , , ~ , . .
i
TABLE 4.3.3.2 CASMO-1 CONTROL ROD WORTH (AKer) STUDY VOID HISTORY (VH) (GWD/T) VB = 0% VH = 40% VH = 70% l CASE 1: INSTANTANEOUS VOIDS = V=0% l 0 0.1910* 0.1910 0.1906 1 0.1914* 0.1917 0.1918 5 0.2079* 0.2091 0.2096 10 0.2238* 0.2222 0.2207 15 0.2146* 0.2133 0.2122 21 0.2026* 0.2022 0.2018 32 0.1826* 0.1848 0.1861 CASE 2: INSTANTANEOUS VOIDS = V=40% 0 0.2251 0.2246* 0.2243 1 0.2265 0.2266* 0.2270 i 5 0.2499 0.2512* 0.2512 l 10 0.2724 0.2702* 0.2674 l 15 0.2618 0.2603* 0.2586 l 21 0.2476 0.2472* 0.2463 32 0.2235 0.2262* l 0.2275 i l CASE 3: INSTANTANEOUS VOIDS = V=70% I 0 0.2576 0.2572 0.2566* 1 0.2603 0.2608 0.2614* l 5 0.2913 0.2925 0.2924* t 10 0.3202 0.3170 0.3133* l 15 0.3080 0.3060 0.3038* 21 0.2914 0.2906 0.2895* i 32 0.2631 0.2660 0.2675* i 1 l l l
- Cases where V=VH are used in SIMULATE-E control worth methodology.
4-232
i 4.3.3.3 Overall Control Rod Worth Statistics
~ Combining statistics derived from the CASMO-1 lattice physics benchmarks with those obtained from the NORGE-B curve fit studies results in the following overall nodal statistics for the control rod worth calculation:
l CASM0-1 CODE NORGE-B CODE, TOTAL p (BIAS) 0.5% 0.0% 0.5% o (UNCERTAINTY) 2.0% 0.9% 2.2% The relatively small overall bias and uncertainty in the nodal control rod worth calculation provides a basis of confidence in the PEco methodology used f.o calculate this parameter. I t- is also noted that although the 'l computed bias between CASMO-1 and NENO-IV is small, the : CASMO-1 rod worth predictions on the average tend to overpredict the rod worth by 0.5%. i 1 I l 1 l 4-233
4.4 Benchmarking of Isotopics Calculations 1 1 As discussed in Reference 24, isotopic concentrations calculated by the CASMO-1 program have been compared to experimental data obtained from Yankee RowE Core I and Saxton Core II exposed fuel assemblies to validate the accuracy of CASMO-l's fuel depletion calculation. These studies ultimately identified a number of small differer.ces between the CASMO-1 burnup model and the experimental data. To quantify the effect of these isotopics differences on overall lattice reactivity, PEco has performed a series of CASMO-1 sensitivity calculations, the results of which are reported in this section. A brief discussion of the original CASMO-1 isotopics benchmark is also undertaken here for background information. 4.4.1 CASMO-1 Isotapics Benchmark Summary Yankee Rowe Core I CE) consisted of 76 fuel assemblies, each loaded with either 304 or 305 fuel rods set in a square lattice, for a total of 23,142 rods (each assembly had one center fuel rod removed from the lattice to provide a space for the insertion of a flux wire thimble). Each fuel rod was composed of approximately j 150 fuel pellets, each with an enrichment of 3.4 w/o U-235 (20,908 kgs of uranium in the total core). The nominal length and diameter of the pellets were 0.6 inch and 0.294 inch, respectively. The active core fuel l 4-214
k length was 91.89 inches and the equivalent core diameter was 75.1 inches. The cladding was composed of 0.021 inch thickness stainless steel with an outer diameter of 0.340 inch. This design resulted in a unit cell water-to-uranium ratio (W/U) of 2.67. Yankee Rowe Core I operated from 8-16-60 (initial criticality) to 5-18-62 (final shutdown). The Cycle 1 core average burnup was 8,470 MWD /MTU and the average power level during 1 generation was 119 MWe (including coastdown). Sampled l assembJies were loaded in central locations. Most of the samples were taken from axial positions representative of asymptotic flux conditions, midway between local i i perturbations resulting from stainless steel spacer discs and axial expansion voids. Figures 4.4.1 through 4.4.3 contain a graphical comparison of CASMO-1 isotopics predictions and Yankee Rowe Core I experimental data. Saxton Core II(3@ was a partial plutonium core l consisting of nine central mixed oxide fuel assemblies 1 and twelve peripheral UO2 assemblies. The mixed oxide fuel contained 6.6 W/O PuO2 in natural 002 (the plutonium contained 8.6% Pu-240).(}O U02 fuel was enriched to 5.7 W/o U-235. Thirty of the plutonium fuel rods were clad with 304 stainless steel and distributed in the central plutonium region to meet specific irradiation objectives. The remainder were clad with zircaloy-4. The plutonium rods had a fuel 4-235
l l 1 pellet diameter of 0.3374 inches (in pelletized rods) i uith an outer cladding diameter of 0.391 inches (23 mil clad thickness for the zircaloy and 15 mils for the stainless steel clad) and an overall fuel length of 36.6 inches. The core was operated from 12-6-65 (initial criticality) to 10-18-68 (Core II end-of-life). The l average operating power was 21.3 MWt and the peak plutonium rod average burnup was m approxi'ately 21,000 l MWD /MTU. i I Experimentally derived spent fuel icotopic data for the two cores were obtained by a variety of methods. Analyses included mass spectrometry for (1) the main chain uranium and plutonium isotopes (U-234, U-235, U-236, U-238, Pu-?39, Pu-240, Pu-241, and Pu-242), and (2) Pu-239/U-238 and Nd-148/U-238 atom ratios (Saxton only). Alpha spectrometric analyses were employed in the determination of Pu-236, Pu-238, Cm-242 and Cm-244 isotopic abundances; radiochemical analyses were used to evaluate the Np-237, Am-241, Am-242, Sr-90 and Cs-137 isotopes. The Yankee Rowe study also utilized x-ray spectrographic analysis for Pu/U mass ratios. In the case of the Saxton investigation, the mass spectrometric data were verified by comparing the values of total fissions determined by two independent methods - the Nd method, from the concentration of the Nd-148 fission product, and the Heavy Element method, based on conservation of heavy nuclei. 4-236 h
Measured and calculated isotopic concentrations for the mixed oxide fuel irradiated in Saxton Core II are compared in Table 4.4.1. The most important uranium and plutonium isotopes as well as americium and curium show good agreement. The Np-237, Pu-238 and Pu-242 concentrations appear to be somewhat underestimated. 4.4.2 CASMO-1 Isotopic Sensitivity Study f As previously mentioned, PEco has performed a series of sensitivity calculations to demonstrate the effect the CASMO-1 to experimental isotopics differences have on overall fuel assembly reactivity. CASMO-3 restart cases ( were executed for a typical Peach Bottom fuel assembly at 21,000 MWD /MTU burnup, where individual isotopic weight percents were varied by the observed CASMO-1 to ( experimental deviation for each of the prir.ary isotopes: U-235, U-238, Pu-239, Pu-240, Pu-241. Eigenvalue solutions were then compared to the base case (unperturbed isotopic concentrations) k-effective to determine the sensitivity of assembly reactivity to isotopic composition. Results as reported in Table 4.4.1 demonstrate a maximum reactivity effect of less than 0.07% AK/K due to the experimental to calculational percent difference in any isotopic concentration. The RMS of the reactivity differences over all five isotopes investigated was less than 0.05% AK/K. These results provide a basis for confidence in the CASMO-1 lattice depletion calculation. 4-237
_ _-m - -s - - - - - _ TABLE 4.4.1 CASM0-1 IS0 TOPICS QUALIFICATION USING SAXTON CORE II DATA EXPERIMENTAL CASMO-EXP DELTA-K NUCLIDE EXPERIMENI UNCERTAINTY *100 -(%)
% EXP K
--- _ 015-----___ ___
U-234 0.00465 28.7 +15.9 N/A** U-235 0.0547 0.9 -0.3 -0.04534 U-236 0.0355 5.6 +2.8 N/A** U-238 99.386 0.0 0.0 0.0 Pu-238 0.109 2.2 -11.4 N/A**
, Pu-239 73.77 0.0 -0.3 -0.02968 A, Pu_240 19.25 0.2 +1.6 -0.06898 g Pu-241 6.29 0.3 +0.4 0.01153 Pu-242 0.579 0.9 -16.0 N/A**
ATOM RATIOS NP237/U-238 1.14 x 10-4 15.0 -26.4 Pu-239/U-238 0.04383 0.7 +0.2 Pu-238/Pu-239 1.75 x 10-3 0.4 -9.8 i ' An-241/Pu-239 0.0123 15.0 -10.6 Cm-242/Pu-239 1.05 x 10-4 10.0 0.0 Cm-244/Pu-239 1.09 x 10-4 20.0 0.0 DELTA-K K-INFINITY (R.I.) - K-INFINITY (P.I.)
}*
K K-IRFIRIT-{i[IJ R.I. - Reference Isotopics - CASMD-1 Generated P.I. - Perturbed Isotopics - CASMO-1 Generated Using Isotope w/u Perturbed to Maximum Range of Error
** N/A Indicates Isotopic Sensitivity Was Not Analyzed With CASMO-1
FIGURE 4.4.1 Yankee Rowe Core 1 Pu-239 / Pu-240 Isotopic Ratlp CASMO-1 versus Experiment 9.0 ,
,gn CASMO-1 Results Experimental Results
-7. 0
?
= : .,
-6.0 -
k
- b a b 5.0 \
E
.l. 0 s,
3.0 N _ 8 s 0.0 5.0 10.0 15.0 20.0 25.0 3CD 5 ! F. R v,el. wgt. number density x 10 , O 10 00 30 mwd /kgU , *From Reference 24, STUDSVIK/RF-78/6293 4-239 _ _ _ _ ~
[ l l FIGURE 4.4.2 [ Yankee Rowe Core 1 [ Pu-240 / Pu-2411sotopic Ratig CASMO-1 versus Experiment [
' 8. 0 i
[ - CASMO-1 Results 7.0 Experimental Results 6.0 - { o [ . .
-5.0 5 '
E
~
k l. 0 . 2 , , 3.0 [ 2.0 4 c s % . .. . . . . . . . f 0.0 50 10.0 15.0 20.0 25.0 30.0 L E P. vol. wgt number density x 10 3 I I I i 0 10 20 30 mwd /isgu L k
*From Reference 24, STUDSVIK/RF-78/6293 4-240 '
i FIGURE 4.4.3 Yankee Rowe Core 1 Pu-241/ Pu-242 Isotopic Ratig CASMO-1 versus Experiment ! 1 10.0 ,, l 9.0 l 1
-80 3 -7.0 R ,
f
-60 _.
x ..
- 5.0 ~'
. \
\s CASMO-1 Results
- l. 0 Experimental Results b
0.0 5.0 10.0 15.0 20.0 25.0 30.0 5 F. P. vol. wgt. number density x 10 I I i i i ! 0 10 20 30 mwd /kgU
*From Reference 24, STUDSVIK/RF-78/6293 4-241
4.5 Qualification of Delayed Neutron Kinetics Parameters The accurate prediction of regionally averaged c effective delayed neutron fractions (beta-effective) and associated decay constants is essential to the s determination of the BWR transient neutron flux response. For PECo applications, six group beta-effectives and decay constants are calculated with the CASMO-1 lattice l physics program using the ENDP/B-V(35) delayed neutron data library. Quantification of the uncertainties in CASMO-1 generated delayed neutronics data is undertaken here. The application of delayed neutron parameters to the reload core design and licensing process is discussed in Section 5.7. ENDP/B-V delayed neutronics data for isotopes of interest in the analysis of 002 fueled cores are reported in Table 4.5.1. Fractional group yields, decay constants and their respective measurement uncertainties as reported by Tuttle(36), as well as the ENDP/B-V values for the overall delayed neutron fractions have been included for each fissionable isotope. When evaluated in conjunction with results from CASMO-1 calculations, this information was used to determine the expected uncertainty in CASMO-1 beta-effective which is f attributable to the ENDP/B-V library. [ ( f l 4-242
4 To this end, CASMO-1 calculations were performed for a typical Peach Bottom reload fuel lattice over a comprehensive set of fuel exposure, in-channel void, and control state conditions. A statistical evaluation of the resultant CASMO-1 total delayed neutron (beta) predictions, when averaged over all fissionable isotopes and reactor operating conditions, resulted in an overall beta predictive uncertainty (la) of approximately I 2.2% (percent of total beta). F Decay constant (A) statistics were developed in an analogous manner. CASMO-1 lambda predictions for the six-delayed neutron groups were averaged a'nd statistically analyzed over the same set of conditions chosen for the beta study. The overall one sigma uncertainty in the CASMO-1 lambda predictions was in this way calculated to be approximately 3.7% (percent of average lambda). f The relatively small uncertainties associated with the ENDP/B-V delayed neutronics data, Seff and A, provides a basis for confidence in the CASMO-1 predictions of these parameters. x l l l 4-243
TABLE 4.5.1 ENDF/B-V DELAYED NEUTRONICS DATA FRACTIONAL GROUP
- DECAY CONSTANT
- ISOTOPE BTOTAL GROUP Ag (Sec-1)
YIELD at i 1 .038 i .004 .0127 i .0003 2 .231 i .007 .0317 1 .0012 U-235 .0068535 3 .188 i .024 .115 1 .004 4 .407 1 .010 .311 i .012 5 .128 i .012 1.40 i .12 6 .026 i .004 3.87 i .55 1 .013 i .001 .0132 i .0004 ,, 2 .137 i .003 .0321 i .0009 4 U-236 .01823 3 .162 i .030 .139 i .007 a- 4 .388 i .018 .358 i .021 5 .225 i .019 1.41 i .10 6 .075 i .007 4.02 i .32 1 .013 i .001 .0132 i .0004 2 .137 i .003 .0321 i .0009 U-238 .01823 3 .162 i .030 .139 i .007 4 .388 i .018 .358 i .021 5 .225 * .019 1.41 i .10 6 .075 i .007 4.02 i .32 1 .038 i .004 .0129 i .0003 2 .280 1 .006 .0311 i .0007 Pu-239 .00223 3 .216 i .027 .134 i .004 4 .328 i .015 .331 i '.018 5 .103 i .013 1.26 i .17 6 .035 i .007 3.21 i .38 i
- TAKEN FROM REFERENCE 36, TUTTLE.
4 TABLE 4.5.1 (Continued) ENDF/B-V DELAYED NEUTRONICS DATA FRACTIONAL GROUP
- DECAY CONSTANT
- ISOTOPE O TOTAL GROUP YlELD ai Ai (Sec-l) i 1 .028 i .004 .0129 1 .0006 2 .273 i .006 .0313 i .0007 Pu-240 .00321 3 .192 i .078 .135 i .016 4 .350 i .039 .333 i .046 5 .128 i .027 1.36 .30 6 .029 i-.009 4.04 1 1.16 s
E 1 .010 i .003 .0128 i .0002 i
*; 2 .229 i .006 .0299 i .0006 l Pu-241 .00549 3 .173 i .025 .124 i .013 1 4 .390 i .050 .352 .018 5 .182 i .019 1.61 .15 6 .016 i .005 3.47 1 1.7 1 .004 i .001 .0128 i .0003.
2 .195 i .032 .0314 i .0013 Pu-242 .00811 3 .161 i .048 .128 i .009 4 .412 1 .153 .325 i .020 5 .218 i .087 1.55 i .09 6 .010 i .003 3.70 i .44
- TAKEN FROM REFERENCE 36 TUTTLE.
e l l
1 5.0 MODEL APPLICATIONS IN CORE DESIGN AND LICENSING l Section five describes and demonstrates the L applicability of PEco's steady-state physics methods to a series of essential BWR core design and licensing related calculations. In some instances, demonstration calculations have been performed and compared to l available plant data and/or fuel vendor licensing analysis results. Biases and uncertainties inherent in these calculations have been demonstrated here, or referenced from other sections of this report. 5.1 Prediction of Maximum Average Planar Linear Heat Generation Rate (MAPLHGR) The prediction of Maximum Average Planar Linear Heat Generation Rate (MAPLF M) is required to monitor the average fuel pin segment power at each node relative l to plant Technical Specification limits. Exposure dependent MAPLHGR operating limits are specified by the fuel vendor to ensure that in the event of a erst case l Loss of Coolant Accident (LOCA), the fuel's peak cladding temperature would not exceed 22000 Parenheit. To this end, the PECo SIMULATE-E program has been f upgraded to include a MAPLHGR algorithm. The calculation is nearly identical to that found in the Peach Bottom plant process computer software. ) 5-1
1 5.1.1 MAPLHGR Uncertainty Based on the MAPL 8GR equation found in the process computer software, it may be 'shown that the percent uncertainty in the SIMULATE-E MAPLHGR prediction is equivalent to the program's point-wise . nodal power , percent uncertainty. In Section 4.1, this statistic was 1 demonstrated to be 6.9%. It may therefore'be concluded that an overall uncertainty of 6.9% exists in the-SIMULATE-E calculation of MAPLHGR. PECo will continue to monitor the accuracy of SIMULATE-E MAPLHGR predictions to assure the appropriate application of the
~
model to design and licensing calculations. Additionally, a comparison study was performed to validate the process computer to SIMULATE-E MAPLHGR software conversion. For a Peach Bottom 3 cycle 7 statepoint, nodal values of relative power and MAPLHOR were edited from the process computer for a quadrant of the core. The relative power distribution was subsequently transferred to SIMULATE-E. The program was then used to calculate nodal MAPLEGR values given the l process computer power shape. SIMULATE-E and process I computer MAPLHGR edits are for all practical purpose in identical agreement, exhibiting a mean differenca of 0.02% with an RMS difference of less than 0.1%. I s 5-2
L / 5.2 Prediction of Peak Pin Linear Beat Generation Rate (PPLHGR) As in the case of the MAPLHGR calculation, PECo has installed a Peak Pin LHGR correlation into SIMULATE-E which represents the PPLHGR at each node as being proportional to the product of the average fuel pin segment power and the local pin peaking factor. PPLHGR j calcu'.ations are necessarily performed to demonstrate adequate margin to the fuels' Technical Specification l LHGR limit for steady-state operating conditions. Operating limits as determined by the fuel vendor are specified to ensure that cladding circumferentill plastic strains will not exceed 1% during core wide anticipated operational transients. 5.2.1 PPLHGR Uncertainty As previously noted, nodal peak pin LHGR is , proportional to the product of the nodal relative power and the local peaking factor. Therefore, the 6.9% RMS uncertainty in the SIMULATE-E nodal power distribution / calculation, as reported in Section 4.1, is inherent in the PPLEGR prediction. Similarly, the 3.6% RMS error in PECo's local peaking factor calculation, as reported in f Section 4.2, must also be accounted for in the ) evaluation of PPLHGR uncertainty. Combining these ) statistics yields an overall PPLHGR uncertainty of: ) S-3
l 2 g2 PPLHGR = (o Power + LPF)1/2
= (6.92 + 3.62)l/2 = 7.8%
As in the case of the MAPLHGR calculation qualification, the SIMULATE E PPLHGR correlation was validated via comparison to the Peach Bottom process computer for a typical reactor statepoint. For / consistency, process computer local peaking factors and 3-D nodal power distribution were used in both models. , SIMULATE-E PPLHGR's were in good agreement with proces,s computer values, exhibiting an RMS difference of only 1.0%. l The accuracy of PECo's PPLHGR model, including the affects of nodal power and local peaking factor uncertainties, will be assessed on an ongoing basis. i h j ) ) ) 5-4
l 5.3 Prediction of Minimum Critical Power Ratio (MCPR) The Critical Power Ratio is defined to be the factor by which a given bundle power must be increased in order to cause the onset of transition boiling at any node in that bundle. Evaluation of this parameter is essential to the BWR analysis process to ensure that in the event of a limiting anticipated operational transient the fuel would not experience a significant departure from the nucleate boiling regime and a resultant overheating of the pins. For this reason, PECo has installed the General Electric Company CPR correlation, GEXL, into SIMULATE-E. GEXL is in l expirically based correlation which was derived from extensive data generated at the ATLAS test loop l facility. A detailed description of GEXL is omitted due to the GE propriety nature of the correlation. GEXL coefficients and R-factors are supplied by GE as part of PECo's current fuel contracts. 5.3.1 MCPR Uncertainty ( As previously defined, Critical Power Ratio is evaluated as a function of assembly integral power I level. In order to determine the uncertainty in the GEXL correlation due to uncertainties in the SIMULATE-E power distribution, a series of sensitivity calculations I were performed. Results of this study are report in Tables 5.3.1 and 5.3.2, and are displayed graphically in ) 5-5
i Figure 5.3.1. As anticipated, MCPR was shown to exhibit a linear response to assembly integral power level over
/
the SIMULATE-E power uncertainty range studied. Based on a least square fit of the more conservative statepoint #1 curve, MCPR sensitivity to assembly power may be expressed as: AMCPR =
-1.23554 (AP/Po) - 0.00144 MCPR o Given this equation, the 4.1% RMS error in the SIMULATE-E assembly integral power calculation, as determined in Section 4.1, will propagate into a 5.1%
~
uncertainty in the prediction of channel MCPR.
)
Using the same procedure as executed in the MAPLHGR and PPLBGR qualifications, a comparison was performed between SIMULATE-E and Peach Bottom process computer MCPR edits for a typical reactor statepoint. Once again
; SIMULATE-E MCPR values were in good agreement with the process computer, exhibiting an overall RMS difference of 1%, and on the average conservatively underpredicting MCPR by 0.4%. These statistics are attributed to s.ull differences between the SIMULATE-E and process computer j hydraulic solutions (2% RMS on channel flows).
Combination of this 1% RMS difference with the 5.1% uncertainty associated with the SIMULATE-E Integral J assembly power calculation indicates a 5.2% uncertainty ) in the overall SIMULATE-E MCPR prediction. As in the 1 5-6
l cases of MAPLHGR and PPLHGR, PECo will continue to 1 monitor the accuracy of the SIMULATE-E MCPR calculation. l l 1 L t l 1 ) i I L l 5-7
TABLE 5.3.1 l RELATIVE CHANGE IN MINIMUM CRITICAL POWER RATIO AS A FUNCTION OF RELATIVE CHANGE IN ASSEMBLY INTEGRAL POWER (PEACH BOTTOM 3 CYCLE 7 - STATEPOINT #1) l l BUNDLE POWER MCPR DELTA-MCPR PERTURBATION (%) __ (%) 1 0 (BASELINE) 1.263 ---
+1.4 1.244 -1.9 +3.5 1.217 -4.6 +7.0 1.174 -8.9 +10.5 1.133 -10.3 STATEPOINT #1 OPERATING CONDITIONS Power =
3293. MWTH (100%) Flow = 87.124 MLB/HR (85%) Subcooling = 16 BTU /LBM Pressure = 1020 PSIA (Rated) l Cycle Exposure = 0.0 (BGC) MCPR Operating Limit = 1.260 h 1 1 l l I I l S-8 l
l l TABLE 5.3.2 RELATIVE CHANGE IN MINIMUM CRITICAL POWER RATIO AS A FUNCTION OP RELATIVE CHANGE IN ASSEMBLY INTEGRAL POWER (PEACH BOTTOM 3 CYCLE 7 - STATEPOINT #2) l BUNDLE POWER MCPR DELTA-MCPR l PERTURBATION (t) (%) 0 (BASELINE) 1.410 ---
+1.5 1.389 -2.1 +3.7 1.358 -5.2 l +7.5 1.310 -10.0 +10.0 1.273 -13.7 l +11.2 1.264 -14.6 +14.9 1.222 -18.8 STATEPOINT #2 OPERATING CONDITIONS t
Power = 3293 MWTH (100%) Flow = 102.5 MLB/HR (100%) Subcooling = 26.14 BTU /LBM (Rated) Pressure = 1020. PSIA (Rated) Cycle Exposure = 0.0 (BOC) MCPR Operating Limit = 1.260 1 1 i l I 5-9 l
-_. -_-l
! FIGURE 5.3.1 Relative Change in Critical Power Ratio As a Function of Relative Change in Bundle Power 0.15 0 u .
0.12 5 - ----------:----------:----------:----- CO RRELATION: - -- - m = -1.236 p- y .0014 i Oi. i E o.ioo _ ..............;...............g..........;..............:.............3.............. un O .- . i i 1 - - - - - N 0.075 - ---------i------------i--------------------j--------------{------------ 5 o_ . . . . .
<1 : : : : :
0.050- ------------i- -- -- - -j-- --- - - i--- - - - --- l-
----{
A Statepoint #1 i i i
- 0.025- - --
---+-&------'------
0 Statepoint #2 j j ; 0.000 i i ; i i a
- 0.15 0 - 0.125 - 0.10 0 - 0.075 -0.050 -0.025 0.000 AMCPR MCPR O j .
5.4 Prediction of Doppler Reactivity As A Function Of Fuel Temperature The functional relationship between Doppler reactivity and fuel temperature is a necessary input to the BWR reload safety evaluation process. Safety calculations can utilize either one-dimensional space-time kinetics (RETRAN-02 1-D) or point kinetics (RETRAN-02 0-D) options in the analysis of the various limiting transients evaluated for plant licensing. The PECo Reload Safety Evaluation (RSE) hethods Report will describe the techniques employed in the derivation of radially-averaged, axially dependent cross section data for linkage to the RETRAN-02 1-D model. The PECo RSE ) Methods Report will be submitted to NRC separately. Generation of core average Doppler reactivity versus the core average fuel temperature for use in the
, RETRAN-02 point kinetics model is performed with the PECo SIMULATE-E program. The PECo procedure used to execute the SIMULATE-E program for generation of point kinetics Doppler reactivity data consists of the following steps:
(1) The cycle is depleted to each cycle exposure point of interest using a Haling power shape or controlled depletion steps. Control rod patterns in the latter case are based on cycle design projections. > 5-11 )
(2) At each cycle exposure point, a SIMULATE-E converged power distribution solution is calculated using reactor conditions (e.g., thermal power, core flow, subcooling, and control rod pattern) consistent with cycle design projections. This is referenced as a ' base case' in later fuel temperature perturbation cases. (3) Fuel temperature perturbation calculations are performed at each cycle exposure point using the thermal power distribution from Step 2. The fuel temperature is varied at each node by incrementing and decrementing the core thermal power. All other plant conditions are held constant. SIMULATE-E is executed at each of these fuel temperature perturbation conditions, assuming no moderator
) density feedback effects. SIMULATE-E edits of converged k-effective and core average fuel temperature are tabulated for each case executed.
(4) The SIMULATE-E k-effective data at each core average fuul temperature, T, are used to determine the Doppler reactivity as referenced to the base case k-effective derived from the nominal core i 1 average fuel temperature, TBASE:
~
1 2)DOP _ _ __ BASE { K(T)*K(TBASE) 5-12
As an illustration, SIMULATE-E calculhtions of the core average Doppler reactivity, (AK/K K2)DOP, 1 for Peach Bottom 3 Cycle 7 are plotted in Figure 5.4.1 as a function of the core average fuel temperature, T. From this data, the 3-D model Doppler coefficient plots were also derived as shown in Figure 5.4.2. For application to safety analyses, the statistical bias and uncertainty as demonstrated in Section 4.3.1 of this report will be considered so as to ensure a conservative evaluation of each anticipated operational transient. i i i k i 5-13 l 1
l i l l FIGURE 5.4.1 3-D DOPPLER REACTIVITY AS A FUNCTION OF CORE AVERAGE FUEL TEMPERATURE PEACH BOTTOM 3 CYCLE 7 m 0.015 . c2 . . . . M -- 0.0104 ---- ----- + - --------- + -- ---- .
+ --------- - ;------ - -- + - ---- -----
3d - N y 0.005- ---
-- -- - --- -- -----:-------- - - o -- --------- : --
------ v ----
<l 9ooo- ............
5..............g..... 5.............. v . . . b -0.0 05 - - ---- --- + -- - - -b------+---:------+----- e, 3 _o o39- .............f.............. .........e............i..............i............
. o .
) . . . . .
e - 0.015 - ------- ---- :--- - - --- g 3 t -0 020- ---------:;--------------------:----- , m . .
~~
0- -0 005-A B O C = 10.6 GWD T - ---i: - ----- - --: ---- - -
--5---------
O_ o -0'030- -- -- : -- - - --- ; - - -- ----;- --. -- - o O EOC = 18.6 GWD T . .
. ]
! -0.0 35 j i i i i i 548.6 1105.0 1661.4 2217.8 2774.2 3330.6 3887.0 Core Average Fuel Temperature (deg F) m____ _ _ _ . _ . _ _ _ _ _ _ _ _ _ . _ _ _ _ . _ . . _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _____m _ _ - _ _ _ _- - _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _
_ m m i- , - - - FIGURE 5.4.2 3-D DOPPLER COEFFICIENT AS A FUNCTION OF CORE AVERAGE FUEL TEMPERATURE PEACH BOTTOM 3 CYCLE 7
- 0.7 .
. ]
. . . . s.
nn _. 0 . 9 - ------------j----------f----------~------------~------- .-------------- j,j _ b_ . . . e_ . w C G . . . . . e e
.-- 1. 3 - ----- - -
.o O
+x so-y - 1. 5 - --- ---- --{ --- - -
-l---
--{------ -------l-------
----l -- - - - ---
eN -
~
oM : : : : (,,) y l.7_ ........... _. .........................................-........... ................ v . : : : : u . m jg_ . . CL - - - , i o_ ! ! ! A BOC = 10.6 GWD/T l 0 -2.1 -g - g . . 0 EOC = 18.6 GWD/T l l
-2. 3 a .
i i i i l 548.6 1105.0 1661.4 2217.8 2774.2 3330.6 3887.0 l Core Average Fuel Temperature (deg F)
[ 5.5 Prediction of Void Reactivity As A Function Of Moderator Density The functional relationship between void reactivity and moderator density is another necessary input to the BWR reload safety evaluation process. Safety calculations can utilize either one-dimensional space-time kinetics (RETRAN-02 1-D) or point kinetics 1 (RETRAN-02 0-D) options in the analysis of the various limiting transients evaluated for plant licensing. The PECo Reload Safety Evaluation (RSE) Methods Report will describe the techniques employed in the derivation of radially-averaged, axially dependent cross section data for linkage to the RETRAN-02 1-D model. The PECo RSE Methods Report will be submitted to NRC separately. Generation of core average void reactivity versus the core average moderator density for use in the RETRAN-02 point kinetics model is performed with the PECo SIMULATE-E program. The PECo procedure used to generate point kinetics void reactivity data consists of the following steps: ! I (1) the cycle is depleted to the cycle exposure point I of interest using a Haling power shape or i controlled depletion steps. Control rod patterns in the latter case are based on cycle design 1 projections. 5-16
L (2) At each cycle exposuie point, a SIMULATE-E r converged power distribution is calculated using reactor conditions (e.g. thermal power, cora flow, subcooling, and control rod pattern) consistent with cycle design projections. This is referenced as the ' base case' in later moderator density perturbation cases. (3) Moderator density perturbation calculations are performed at each cycle exposure point using the thermal power distribution from Step 2. The moderator density i.s varied by incrementing and decrementing the core inlet enthalpy. All other plant conditions are held constant. SIMULATE-E is executed at each of the specified moderator density perturbation conditions, assuming no thermal power feedback effects. SIMULATE-E edits of converged K-effective and core average in channel moderator density, p, are tabulated for each case. (4) The SIMULATE-E void dependent K-eff3ctive data are ( l then converted to reactivit.i.es as follows: K(p) - K(p ^
-'-----~~~ -
)
(AK/K K1 2) Void K(p)*K(pBASE) { The above equation uses the reference case K-effect ve. K(0 BASE), derivisd for the referenced S-17
~ N initial core average in-channel moderator density, BASE-As an illustration, SIMULATE-E calculations of core average void reactivity, (AK/K K1 2)yoid, for Peach Bottom 3 Cycle 7 are plotted in Figure 5.5.1 as a function of core average in-channel moderator density, t
- p. In this plot, the reference case value of core
( average moderator density (pBASE = 28.73 lb/ft3) corresponds to the rated full power core average in-channel void percentage (VBASE = 39.6%). Converting the core average in-channel moderator density (p) to the core average-in-channel void percentage (V) yields a secondary plot of void worth, AKyoid, as a function of V(%), as displayed in Figure 5.5.2. Differentiating this last curve yields a SIMULATE-E prediction for the 3-D void coefficient, r i av E -1.09 x 10-3 AK/%AV as evaluated at the reference case core average void f condition (VBASE = 39.6%V). [ For application to safety analyses, the statistical L bias and uncertainty as demonstrated in Section 4.3.2 of r this report will be considered so as to ensure a conservative evaluation of each anticipated operational transient. i i ( 5-18 r
~ ~ ~'~ m. . r-m .?m rt r- w rm v m n 73 _ r-FIGURE 5.5.1 3-D MODEL VOID REACTIVITY AS A FUNCTION OF CORE AVERAGE MODERATOR DENSITY PEACH BOTTOM 3 CYCLE 7 0.05 . . . . .
n - ca : : . : : : y :
~
M
~
0.03- '------- --- N --------'-------------------'------------------------l------ Y ! ! ! b ** i
<1 : : : : , :
v : : : : . : 0.01-- ---------------.------------------------ - ------ --- --- -- ---- -- i > _+_-
._ Q , Q } -
y .........................*.. , ...... .
...........~............r...........~............
o : : m : : : : CD : : . : : E : i 3 a -003- - ------- --------- ------ ---- "------- -- -
~
C) <
- i i A BOC = 10.6 GWD/T -
- : l y .
i . .: O EOC = 18.6 GWD/T
-0.05 i i i i i i 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 I
Core Average Mod. Density (Ib m ft3)
FIGURE 5.5.2 3-D MODEL VOID WORTH AS A FUNCTION OF CORE AVERAGE PERCENT IN-CHANNEL VOID PEACH BOTTOM 3 CYCLE 7 CALCULATIONS 0.05 . . . . . . . s 6 : s . . . . s . . . . s s:~ VOID COEFFICIENT: 0.03- -; ;; - '-------?-------.---- A : 's : : a = - 1. 0 9 x 10 - 5"'n M : 's . : m v
- 's -
- 4 -
AT REFERENCE CONDITIONS: 0 01 --- ---- ----- -- Vuu = 39.4% V u c : .
- t+ _ . . .
c3 _o.o3 ................. _ 5.........?....... 9..... .........?.......5.........;........
. O_
_ . . . . .s s O . . . . . . .
. . . . s . .
s.-
. s
-003- A BOC = 10.6 GWD 'T - :.-- ------': -- ----- --- '----- -- - =--------
- 's : -
/ .
s . ,.
. .s s .
's s.
O EOC = 18.6 GWD/T !
. s
-0.05 i i i i i i e' O.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 Core Average Void (%V)
[ S.6 Prediction of Control Rod Scram Reactivity As A Function Of Rod Insertion Distance ( The prediction of control rod scrare reactivity as a function of rod insertion distance is another necessary input to the BWR reload safety evaluation process. Safety calculations can utilize either one-dimensional space-time kinetics (RETRAN-02 1-D) or Doint kinetics ( (RETRAN-02 0-D) options in the analysis of the limiting transients evaluated for plant licensing. The PECo Reload Safety Evaluation (RSE) Methods Report will describe the techniques employed in the derivation of radially-averaged, axie'1.y dependent cross section data ( for linkage to the RETRAN-02 1-D model. The PECo RSE Methods Report will be submitted to NRC separately. Control rod scram reactivity values as a function ( of rod insertion length for use in the RETRAN-02 point kinetics model are generated with the PECo SIMULATE-E ; program. The PECo procedure used to execute the SIMULATE-E program in this application consists of the following steps: ( 1. ) The cycle is depleted to the cycle exposure point of interest using a Baling power shape or controlled depletion steps. Control rod patterns ( in the latter case are based on cycle design projections. ( 5-21
k [ (2) At each cycle exposure point, the SIMULATE-E F L converged power distribution is calculated using reactor conditions (e.g., thermal power, core flow, subcooling, and control rod pattern) obtained from cycle design projections. This is referenced as { the ' base case' in later control rod step insertion I cases. ( (3) Control rod step insertion calculations are performed at each cycle exposure point using the ( thermal power distribution from Step 2. The control rods are inserted into the reactor core in linear increments. All other plant conditions are [ held constant. SIMULATE-E is executed at each of the control rod step insertion conditions, assuming ( no thermal power feedback effects. ( (4) The SIMULATE-E k-effective data for each control rod step insertion length, L, are converted to r L control rod reactivities as follows:
=
K(L) - K(BASE) (AK/K K1 2) --- The reference k-effective in this calculation is derived using the base case initial reactor ( conditions. I L I 5-22 ___d
[ [ As an illustration, SIMULATE-E calculations of the ( scram reactivity, (AK/K K1 2)CR, for Peach Bottom 3 End of Cycle 7 are plotted in Figure 5.6.1 as a function of the rod insertion length, L. The base case rod configuration for this calculation was conservatively { set to all-rods-out (ARO). For application to safety [ analyses, the statistical bias and uncertainty as demonstrated in Section 4.3.3 of this report will be considered so as to ensure a conservative evaluation of each anticipated operational transient. ( { l 1 ( { l { [ { { 5-23
1 / L m i i m # i m , s i i r i r i i1 ii r N r t n J - t n i 1 F FIGURE 5.6.1 SCRAM REACTIVITY A8 A FUNCTION OF CONTROL ROD INSERTION PEACH BOTTOM 3 CYCLE 7
^ 28.0 c .
M_ 26.0- = EOC = 18,632 MWD MT i ! ! !
. ! ]
Y 7f, Q _ .......g......z.......:.......y......g......j......f.......}.......f......j......f..... M 22.0_ .
. t, o 20.0_ ...... ... .......... ........................... ............................... ...
1 sn v 18.0 _ . 0 16.0 - - - + --- + --- + --- +
. . . . -- +. - +. - +. ---- +. ---- +. ---- ------
14.0 - .
-+-- . . . . .
*n n .... ..... ... .... ..~...... .........
.............a...............~.................
O l4. U _ . O 10.0_ q) . . . . . . . . . . T 8. 0 _ ....... .............
- 6. 0 _
E 0 4. 0 - - - t - - :----- --- + 1 - - + * ; - ;- - - + -- -; -- --- u . o 2. 0 _ . m (n . m D 0.0 ,a , c- e m ~ - . - . . y 1 1 i i i i i i i
- 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.010.011.012.0 Control Rod Insertion (feet) l l
--i--.--- _ _____________m.
L l 5.7 Prediction of Delayed Neutron Kinetics Parameters i l As noted in Section 4.5, delayed neutron kinetics parameters are required input to the RETRAN-02 thermal-hydraulics transient analysis program. Three-dimensional nodal values of six group beta-effective fractional yields and decay constants as generated by CASMO-1 are processed by the SIMTRAN-E code for use by RETRAN-02 in the determination of the neutron flux response to system transients. A brief discussion of ( delayed neutronics generation and processing follows. [ The equations used by CASMO-1 in the determination of delayed neutron fractions Jg are as follows: Ng * [ Sm am,g [ PRODs ,g a 9 [ where: PROD a ,g = vag,1,m,g Vi $1,g Ni,a 1 = delayed neutron group, 15156 m = fissionable nuclide
=
Sa total fraction of delayed neutrons from nuclida n am,1 = the fraction of delayed neutrons from [ nuclide a related to delayed neutron group 1 i = fuel region index { g = micro group index V = volume N = number density L 5-25 W
L The effective delayed neutron yields, Segg,g are derived by further multiplying the Sg values by a factor to account for the reduced leakage probability associated with the delayed fission spectrum. Figures 5.7.1 and 5.7.2 graphically depict the relationship between beta-effective, exposure, and void level for a typical 8x8 Peach Bottom reload lattice in the uncontrolled and controlled states, respectively. For application to safety analyses, the statistical bias and uncertainty as demonstrated in Section 4.5 will be ( considered so as to ensure a conservative evaluation of each anticipated operational transient. [ CASMO-1 predictions of delayed neutron kinetics ( parameters are written to an external computer file which is subsequently accessed by SIMTRAN-E. Nodal beta-effective values are then represented in SIMTRAN-E for each lattice in the core as a function of exposure, in-channel void history, and control rod state. Nodal data is ultimately collapsed to either a one-dimensional or point reactor representation and functionalized for ( application in the RETRAN-02 program. A detailed description of the techniques employed by the SIMTRAN-E [ program will be undertaken in Philadelphia Electric Company's Reload Safety Evaluation (RSE) Methods Report to be submitted to the NRC at a later date. ) 5-26
,. __,- ~ % ,
FIGURE 5.7.1 CASMO-1 EFFECTIVE DELAYED NEUTRON FRACT ONS AS A FUNCTION OF EXPOSURE. UNRODDED STATE NOMINAL PEACH BOTTOM 8X8 RELOAD FUEL LATTICE 7.4 5 . i i ! i i iA 0% Void m 7. 0 - ; ; ; ; ; ; O
- : o 40% Void
- 6. 6 - . . . . .
x l . j j j j o 70% Void q) 6.2 - :
= , *~
u . . . . . . . Q },8 - ..........*...........*............... ........... 2..........*...........;.......... u , a) : : : . : : :
+ : : : : : : % C LJ J.A_
t . I . . . . . . 0
+-
5.0 - - - - ; - u) : : : : : : .
))
! CD : :
- 4. 6 - .
. s )
e l 4.2 i i i i i i i 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Exposure (GWD MTU)
v _ em ,. 1 i
)
l l FIGURE 5.7.2 CASMO-1 EFFECTIVE DELAYED NEUTRON FRACTIONS AS A FUNCTION OF EXPOSURE RODDED STATE NOMINAL PEACH BOTTOM 8X8 RELOAD FUEL LATTICE 6.6 . ( : A 0% Void n . . . . .
' 6 2 -t ~---- -- - '- - ---- -- ~----- ----- =-- -- --*- + -------- =--- -
o .
- i i
o 40% Void f _
.........r ..,....... :
.......i............i............i.s.. o 70% Void .
q) . v,i y .
*~ -----l------------i-----------i-----
2 () 5.4 - --- - -- -i---------- .. a)
+ : :
L.I 5. 0 - - - - - - - i - -- -
-i ------ ---i---- ----- -
I
- - .b - - - - - - - - - i - - - - - - - - .:
O
+- : : : : . :
no . . . . . . m 4. 6 _ ........................-....................... ........... 4.2 i i i i i i 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 Exposure (GWD MTU)
5.8 Prediction of Prompt Neutron Velocities Two-group prompt neutron velocities are edited by CASMO-1 based on flux-weighted integrals evaluated separately over the fast and thermal energy regions. [ The equations used by CASMO-1 for this purpose are: [ geh +g Og
- 0.454546 x 10-5 sec/cm,
~
(1/v)h = ----------- [ gch $9 where: h = 1 or 2, for each of CASMO-1 fast and thermal energy group edits. (g = spatially averaged neutron fluxes in each of the 25 CASMO-1 microgroups, g. og = microscopic cross section for a unit (1/v) absorber. (1/v)h = uverage inverse neutron velocity in group h The two-group average inverse neutron velocities so derived are writtr' to an external computer file at each fuel burnup step, 1-channel void condition, and control rod atate routinely analyzed with the PECo CASMO-1 model. Further processing of this data is performed by the linkage code, SIMTRAN-E, in order to ultimately provide input parameters for the PECo RETRAN-02 BWR system transient model. SIMTRAN-E calculates a racial (x-y) flux-weighted average of the three-dimensional I neutron velocity arrays at each axial node. It then derives an equivalent set of one-dimensional, axially dependent neutron velocities to be used in the RETRAN-02 L S-29 i .
L [ one-dimensional sp}}