ML19270F612
| ML19270F612 | |
| Person / Time | |
|---|---|
| Site: | Browns Ferry  |
| Issue date: | 01/31/1979 |
| From: | TENNESSEE VALLEY AUTHORITY |
| To: | |
| Shared Package | |
| ML19270F611 | List: |
| References | |
| TVA-TR79-01, TVA-TR79-1, NUDOCS 7902280320 | |
| Download: ML19270F612 (150) | |
Text
TVA-TR79-01 VERIFICATION OF TVA STEADY-STATE BWR PHYSICS METHODS QD q@4 Topical Report Tennessee Valley Authority January 31, 1979
TABLE OF CONTENTS Page ABSTRACT . . . . . .. . . . ... . . . .. . .. . . . . viii
- 1. INTL )UCTION . . . .. . .. . ... . . . . . .. .... 1-1
- 2. UNIT CELL PHYSICS .. . . . . . .. .. . . . . .... . 2-1 2.1 REACTIVITY COMPARISONS .. .. . .. . .. ... . . 2-1 2.2 REACTION RATE COMPARISONS . . . . .. .. . . ... . 2-4
- 2. 3 ISOTOPIC COMPARISONS .... . . . . . . . . . . . . 2-7
- 3. BUNDLE PHYSICS . .. .. . . .. .. . .. . .. .. .. . 3-1 3.1 REACTIVITY COMPARISONS . . .. . .. . . . . . .. . 3-2 3.2 LOCAL POWER DISTRIBUTION COMPARISONS . . . . .. . . 3-5 3.2.1 Unexposed Bundles ... . . . .. . . . .. . 3-5 3.2.2 E>. posed Bundles ... . .. . . . . . . . . . 3--24
- 4. CORE SIMULATION .. . . . . . ... . . . . . . . . . . . 4-1 4.1 QUAD CITIES COMPARISONS ... . . . . . . . .. . . . 4-2 4.1.1 Cold Xenon-Free Criticals .. . . . .. . . . 4-3 4.1.2 Hot Operating Reactivity . . . . . . . .. .. 4-5 4.1.3 TlP Comparisons During Cycles 1 and 2 .. . . 4-7 4.1.4 End-of-Cycle Camma Scan Comparisons . .. . . 4-39 4.2 BROWNS Fl.RRY UNITS 1 AND 2 COMPARISONS . . . ... . 4-51 4.2.1 Zero Power Xenon-Free Criticals . . . . .. . 4-57 4.2.2 Hot Operating Reactivity . . . . . . ... . . 4-59 4.2.3 Process Computer Comparisons . . . . . . .. . 4-61 4.3 BROWNS Fl'RRY UNIT 3 COMPARISONS . . . . . .. . . 4-64
- 4. 3.1 Zero Power Criticals . . . . . . .. . . . . . 4-73 4.3.2 Ilot Operating Reactivity . . . . .. . .. . . 4-73 4.3.3 Process Computer Comparisons . . . . . . . . . 4-76
- 5.
SUMMARY
. . . . ... . . . . ... . . . . .. . . . . . 5-1 5.1 LATTICE PHYSICS METHODS . .. . . . .. .. . .. . . 5-1 5.2 CORE SIMULATION . . . . . .. . . . . .. . .. .. . 5-3
LIST OF FIGURES Figure Title Page 2.3-1 Yankee-Rowe Cycle 1 U-235/U Ratio . . . . . . . . . . 2-8 2.3-2 Yankee-Rowe Cycle 1 Pu/U Ratio . . . . . . . . . . . . . . 2-9
- 2. 3- 3 Yankee-Rowe Cycle 1 Fissile Pu/Pu Ratio . . . . . . . . 2-10
- 2. 3-4 Yankee-Rowe Cycle 1 Pu-240/Pu-239 Ratio . . . . . . . 2-11 2.3-5 Yankee-Rowe Cycle 1 Pu-241/Pu-240 Ratio . . . . . . . . . 2-12
- 2. 3-6 Yankee-Rowe Cycle 1 Pu-242/Pu-241 Ratio . . . . . . . 2-13 3.2-1 Local Power Distribution for Quad Cities 1 Cycle 2 Central M02 Bundle at 40% In-channel Steam Voids . . . . . . . . 3-8 3.2-2 Local Power Distribution for a Type A Bundle at 0% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . 3-9 3.2-3 Local Power Distribution for a Type A Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . . . . . . 3-10 3.2-4 Local Power Distribution for a Type A Bundle at 80% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . 3-11 3.2-5 Local Power Distribution for a Type B Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . 3-13 3.2-6 Local Power Distribution for a Type C Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . 3-14
- 3. 2- 7 Local Power Distribution for a Type D Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . . 3-15 3.2-8 Local Power Distribution for a Type E Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . 3-17 3.2-9 Local Power Distribution for a Type F Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . . . . 3-18 3.2-10 Local Power Distribution for a Type G Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . . . . . 3-19 3.2-11 Local Power Distribution for a Type H Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . 3-20 3.2-12 Local Power Distribution for a Type I Bundle at 40% In-channel Steam Voids . . . . . . . . . . . . . . . . . . . . . . . 3-21 O
11
LIST OF FIGURES (Cont.)
Figure Title Page 3.2-13 EOC 2 Local Power Distribution for QC Bundle CX-214 at 57 Inches from Bottom of Core . . . . . . . . . . . . . . . . 3-26 3.2-14 EOC 2 Local Power Distribution for QC Bundle CX-214 at 129 Inches f rom Bottom of Core . . . . . . . . . . . . . . . 3-27 3.2-15 EOC 2 Local Power Distribution for QC Bundle CX-672 at 51 Inches from Bottom of Core . . . . . . . . . . . . . . . . 3-28 3.2-16 EOC 2 Local Power Distribution for QC Bundle CEB-159 at 51 Inches from Bottom of Core . . . . . . . . . . . . . . . . 3-29 3.2-17 EOC 2 Local Power Distribution for QC Bundle GEH-002 at IS Inches from Bottom of Core . . . . . . . . . . . . . . . . 3-30 3.2-18 EOC 2 Local Power Distribution for QC Bundle GEH-002 at 51 Inches from Bottom of Core . . . . . . . . . . . . . . . . 3-31 3.2-19 EOC 2 Local Power Distribution for QC Bundle GEH-002 at 129 Inches f rom Bottom of Core . . . . . . . . . . . . . . . 3-32 4.1-1 Average TIP Reading for QC 1 CY l at 247 MWD /T . . . . . . . 4-12 4.1-2 Average TIP Reading for QC 1 CY l at 646 MWD /T . . . . . . . 4-13 4.1-3 Average TIP Reading for QC 1 CY l at 800 MWD /T . . . . . . . 4-14 4.1-4 Average TIP Reading for QC 1 CY 1 at 1344 MWD /T . . . . . . . 4-15 4.1-5 Average TIP Reading for QC 1 CY l at 2031 MWD /T . . . . . . . 4-16 4.1-6 Average TIP Reading for QC 1 CY 1 at 2894 MWD /T . . . . . . . 4-17 4.1-7 Average TIP Reading for QC 1 CY I at 3480 MWD /T . . . . . . . 4-18 4.1-8 Average TIP Reading for QC 1 CY 1 at 3696 MWD /T . . . . . . . 4-19 4.1-9 Average TIP Reading for QC 1 CY 1 at 4297 MWD /T . . . . . . . 4-20 4.1-10 Average TIP Reading for QC 1 CY 1 at 4809 MWD /T . . . . . . . 4-21 4.1-11 Average TIP Reading for QC 1 CY l at 5471 MWD /T . . . . . . . 4-22 4.1-12 Average TIP Reading for QC .1 CY 1 at 5949 MWD /T . . . . . . . 4-23 4.1-13 Average TIP Reading for QC 1 CY 1 at 6175 MWD /T . . . . . . . 4-24 4.1-14 Average TIP Reading for QC 1 CY l at 6710 MWD /T . . . . . . . 4-25 111
LIST OF FIGURES (Cont.)
Figure Title llag 4.1-15 Average TIP Reading for QC 1 CY 1 at 6948 MWD /T . . . . . 4-26 4.1-16 Average TIP Reading for QC 1 CY 2 at 6625 L'D/T . . . . ... 4-27 4.1-17 Average TIP Reading for QC 1 CY 2 at 6833 E'D/T . . . . ... 4-28 4.1-18 Average TIP Reading for QC 1 CY 2 at 7225 E'D/T . . . . .. 4-29 4.1-19 Average TIP Reading for QC 1 CY 2 at 7641 ED/T . . . . ... 4-30 4.1-20 Average TIP Reading for QC 1 CY 2 at 79 73 L'D/T . . . . . . 4-31 4.1-21 Average TIP Reading for QC 1 CY 2 at 8293 L'D/T . . . . ... 4-32 4.1-22 Average TIP Reading for QC 1 CY 2 at 9229 L'D/T . . . . ... 4-33 4.1-23 Average TIP Reading for QC 1 CY 2 at 10195 MWD /T . . ... 4-34 4.1-24 Average TIP Reading for QC 1 CY 2 at 10827 MWD /T . . ... 4-35 4.1-25 Average TIP Reading for QC 1 CY 2 at 11973 MWD /T . . . ... 4-36 4.1-26 Average TIP Reading for QC 1 CY 2 at 12348 MWD /T . . . ... 4-37 4.1-27 Average TIP Reading for QC 1 CY 2 at 12466 MWD /T . . . ... 4-38 4.1-28 Thirty-one Assembi.y Averaged Axial La-140 Distribution from Quad Cities Unit 1 1974 Gamma Scan . . . . . . . . . . ... 4-42 4.1-29 Uncontrolled Assembly Axial La-140 Distribution f rom Quad Cities Unit 1 1974 Gamma Scan . . . . . . . . . . . . . ... 4-43 4.1-30 Controlled Assembly Axial La-140 Distribution from Quad Cities Unit 1 1974 Gamma Sean . . . . . . . . . . . .... 4-44 4.1-31 Assembly Average Radial La-140 Activity Distribution Comparison from Quad Cities 1 1976 Gamma Scan . . . .. . 4-48 4.1-32 Eighty-nine Assembly Averaged Axial La-140 Distribution from Quad Cities Unit 1 1976 Gamma Scan . . . . . .... 4-52 4.1-33 Axial La-140 Distribution for an Initial Core 7 x 7 UO,,
Central Assembly from Quad Cities 1 1976 Camma Scan . 7 .. 4-53 4.1-34 Axial La-140 Distribution for an Initial Core 7x 7 UO.,
Peripheral Assembly from Quad Citles 1 1976 Camma Scan' . . 4-54 4.1-15 Axial La-140 Distribution for a Reload 7 x 7 MO.,
Assembly from Quad Cities 1 1976 Gamma Scan '. . . .. . 4-55 iv
LIST OF FIGURES (Cont.)
Figure Title Page 4.1-36 Axial La-140 Distribution for a Reload 8 x 8 UO 2 Assembly from Quad Cities 1 1976 Gamma Scan . . . . . . . . . 4-56 4.2-1 Core Average Axial Power Distribution for BF 1 CY l at 2359 MWD /MT . . . . . . . . . . . . . . . . . . . . . . . 4-66 4.2-2 Core Average Axial Power Distribution for BF 1 CY l at 4026 MWD /MT . . . . . . . . . .. .. . . . . . . . . . . 4-67 4.2-3 Core Average Axial Power Distribution for BF 1 CY l at 6346 MWD /MT . . . . . . .. . . . . . . . . . . . . . . . 4-68 4.2-4 Core Average Axial Power Distribution for BF 1 CY l at 7698 MWD /MT . . . . . . . . . . . . . . . . . . . . . . . 4-69 4.2-5 Core Average Axial Power Distribution for BF 1 CY l at 9416 MWD /MT . . . . . . . . . .. . . . . . . . . . . . . 4-70 4.2-6 Core Average Axial Power Distribution for BF 1 CY l at 11994 MWD /MT . . . . . . . . . . . . . . . . . . . . . . . 4-71 4.2-7 Core Average Axial Power Distribution for BF 1 CY 2 at 3133 MWD /MT . . . . . . . . . . . . . . . . . . . . . . . 4-72 4.3-1 Core Average Axial Power Distribution for BF 3 Near Beginning-of-Cycle 1 . . . . . . . . . . . . . . . . . . . . 4-78 4.3-2 Core Average Axial Power Distribution for BF 3 Near Middle-of-Cycle 1 . . . . . . . . . . . . . .. . . . . . . . 4-79 4.3-3 Core Average Axial Power Distribution for BF 3 Near End-of-Cycle 1 . . . . . . . . . . . . . . . . . . . . . . . 4-80
- 4. 3-4 Core Average Axial Exposure Distribution for BF 3 Near End-of-Cycle 1 . . . . . . . . . . . . . . . . . . . . . . . 4-81 5.2-1 Reactivity of Combined Zero Power Criticals . . . . . . . . . 5-4 5.2-2 Reactivity of Combined Hot Operating Criticals . . . . . . . 5-5 v
LIST OF TABLES Table Title Page 2.1-1 LATTICE Results for Critical Experments . . . . . . . 2-2 2.2-1 Reaction Rate Comparisons . . . . . . . . . . . . . . . 2-6 3.1-1 Comparisons of k. at BOL as Calculated by LATTICE and ESP . . . . . . . . . . . . . . . . . . . . . . . 3-3 3.2-1 Comparison of Local Peaking Factors . . . . . . . . . . 3-23 3.2-2 Local Power Distribution Comparison for Exposed Bundles 3-25 4.1-1 Quad cities 1, Cycles 1 and 2, In-sequence Cold Criticals 4-4 4.1-2 Quad Cities 1 Local Cold Criticals at BOC 1 . . . . . . 4-6 4.1- 3 Quad Cities 1, Cycles 1 and 2, Hot Operating k-eff . . . 4-8 4.1-4 Quad Cities 1, Cycles 1 and 2, TIP Data Comparisons . . 4-10 4.1-5 Measured vs Computed Assembly Axial La-140 Activity Peak-to-Average Values from Quad Cities 1-1974 Gamma Scan . . . . . . . . . . . . . . . . . . 4-40 4.1- 6 Measured vs Computed Assembly Axial La-140 Activity Peak-to-Average Values f rom Quad Cities 1 -
1976 Gamma Scan . . . . . . . . . . . . . . . . . . . . 4-45 4.1-7 Comparison of 25 Highest Nodal La-140 Activities Quad Cities 1 - 1976 Camma Scan . . . . . . . . . . . . 4-47 4.1-8 Nodal Standard Deviations for the 12 Axial Planes from Quad Cities 1 - 1976 Gamma Scan . . . . . . . . . . . . 4-50 4.2-1 Zero Power Xenon-Free Criticals for Browns Ferry Units 1 and 2 . . . . . . . . . . . . . . . . . . . . . 4-58 4.2-2 Browns Ferry 1, Cycles 1 and 2, Hot Operating k-ef f . . 4-60 4.2-3 Browns Ferry 1, Cycles 1 and 2, Comparisons of CORE Code and Process Computer Peaking Factors . . . . . . . 4-62 4.2-4 Browns Ferry 1, Cycle 1 and 2, Comparisons of CORE Code and Process Computer Power Distributions . . . . 4-63 4.2-5 Browns 1erry 1, Cycles 1 and 2, Comparisons of CORE Code and Process Computer Radial Peaking Factors . . . 4-65 4.3-1 Zero Power Criticals for Browns Ferry Unit 3. . . . . . 4-74 vi
LIST OF TABLES (Cont.)
Table Title Page
- 4. 3-2 llot Operating Cases for Browns Ferry Unit 3 . . . . . . 4-75 4.3-3 Core Average Axial Peak-to-Average Power Ratios for Browns Ferry Unit 3 . . . . . . . . . . . . ... . . . 4-77 4.3-4 Radi:il Power Distribution for Browns Ferry Unit 3, Cycle 1 . . . . . . . . . . . . . . . . . . .. . . . . 4-83
- 4. 3-5 Nodal Power Distribution for Browns Ferry Unit 3. . . . 4-14
\
vii
ABSTRACT The Tennessee Valley Authority has developed the IATTICE program for the detailed physics analyses of fuel bundles and the CORE code for the simulation of light water reactor cores.
This report documents comparisons made to measured data and to results from more theoretically exact codes in order to verify the suitability of the models used in the CORE / LATTICE system for steady-state bolling water reactor analyses.
viii
- 1. INTRODUCTION This topical report is being submitted for NRC review concur-rently with two other topical reports:
TVA-TR78-02 METHODS FOR THE LATTICE PHYSICS ANALYSIS OF LWR's TVA-TR78-03 THREE-DIMENSIONAL LWR CORE SIMULATION METHODS The purpose of this report is to demonstrate that the methods described in TVA-TR78-02 and TVA-TR78-03 reflect the state of the art of boiling water reactor steady-state analysis methods. Because the lattice physics analysis method and the core simulation analysis method will be used as a system, a single verification report is being submitted. The verification data is presented in two main divisions, one for lattice physics and one for core simulation.
For the lattice physics analysis method (the computer code LATTICE),
comparisons to measured data are presented for the calculation of reactivity, local power distributions, and isotopics. Additional comparisons are presented against results from a Monte Carlo code for reactivity, local power distributions and reaction rates, and against results from a two-dimensional collision probability code for loca power distributions. For the core simulation method (the computer code CORE), comparisons are presented to measured data from eight cycles of four different BWR's, including the gamma scan measurements made at Quad Cities unit 1. These results together demonstrate that TVA core analysis methods reflect the current state of the art for BWR analyses.
1-1
- 2. UNIT CELL PHYSICS In order to demonstrate the validity of the basic components of the physics methods used in LATTICE, a set of 25 critical experiments was selected and analyzed. These experiments cover a wide range of hydrogen-to-heavy metal (H/M) atom ratios, fuel compositions, and lattice pitches. For 15 of the criticals, calculations were performed using a general Monte Carlo reactor analysis code, including detailed comparisons of absorption and nu-fission reaction rate distributions in space and energy.
To verify the correctness of the calculation of the buildup or depletion of uranium and plutonium isotopes, comparisons to the Yankee Rowe isotopic measurements are included.
2.1 REACTIVITY COMPARISONS The effective multiplication factor was calculated for each of 25 critical H 2 O moderated lattices of slightly enriched fuel rods using LATTICE unit cell physics parameters. The results show that LATTICE adequately predicts few group absorption, fission, and removal cross sections, and the corresponding diffusion coef ficients over a range of experimental configurations.
Table 2.1-1 describes the criticals that were analyz 4 The first 15 critical configurations were taken from the LEOPACD verification report (Reference 2-1). The lattices contained stainless steel clad UO r ds with enrichments that ranged from 2
2.70 to 4.02 weight percent U-235. The H/M atom ratios varied from 3.08 to 14.65. The critical k-effectives were estimated by correcting the LATTICE cell infinite multiplication factors for 2-1
TABLE 2.1-1 LATIICE Results fot citical Experiment s Lattice Critical Critical Lattice Enrichtent Pitch Buckling No ._ Reference Type
- H/M 'n't . % PPM Baron Clad Inches cm 2 n-eff 1 2-1 (case 9) S 3.08 2.70 0.0 SS r 405 0.004075 0.9978 2 2-1 (case 10) S 4.13 ?. 70 0.0 SS .435 0.005323 0.9931 3 2-1 (case 11) S 5.45 ).70 0.0 SS 0.470 0.006326 0.9866 4 2-) (case 12) S 9.92 2.70 0.0 SS 0.573 0.006564 0.9898 5 2-1 (case 13) S 11.99 2.70 0.0 SS 0.615 0.006007 0.9934 6 2-1 (case 14) S 14.65 2.70 0.0 SS 0.665 0.005292 0.9909 7 2-1 (case 15) S 3.53 2.70 0.0 SS 0.418 0.004750 0.9927 7
8 2-1 (case 17) S 3.53 3.70 0.0 SS 0.418 0.006880 0.9856 9 2-1 (case 18) S 6.37 3.70 0.0 SS v.493 0.009510 0.9705 10 2-1 (case 20) S 6.37 3.70 461 SS 0.493 0.007464 0.9770 11 2-1 (case 21) S 6.37 3.70 717 SS 0.493 0.006366 0.9310 12 2-1 (case 22) S 6.37 3.70 1275 SS 0.493 0.004099 0.9895 13 2-1 (case 23) S 6.37 3.70 1346 SS 0.493 0.003839 0.9899 14 2-1 (case 24) S 6.37 3.70 1489 SS 0.493 0.003338 0.9904 15 2-1 (case 26) S 3.60 4.02 3428 SS 0.595 0.001720 1.0022 16 2- 2 (L'0 2 ) S 5.27 2.459 2041 A1 0 640 0.0 0.9964 17 2-2 (pug 2) S 5.03 1.50** 2256 Zr 0.747 0.0 1.0065 15 2-3 (6bMIO S 13.07 1.9e** 1213 Zr i.0 v.0 1.0026 19 2-3 (8SC) S 12.87 2.0S** 1286 Zr 1.0 0.0 1.0042 20 2-3 (8BME) S 13.22 2.10** 1274 Zr 1.0 0.0 1.0030 21 2-4 (core 3) S 4.12 3.04 0.0 A1 0.531 0.009182 1.0055 22 2-4 (core 8) S 2.84 3.04 0.0 SS 0.4de 0.004747 1.0059 23 2-4 (core 10) S 2.89 3.04 0.0 A! 0.488 0.007076 1.0063 24 2-4 (core 11) T 2.27 3.04 0.0 A1 0.50 0.005538 1.0076 25 2-4 (c o re 13) T 1.32 3.04 0.0 A1 0.459 0.002436 1.0159 Average 0.9954 Standard Deviation 0.0107
- S: square lattice; T: triangular lattice
- P uo , in l' uO.3 + natural l'0 3 O O O
fast and thermal leakage using the age-diffusion equation eff " 7 3! 3 2 (2-D where T is the LATTICE value of neutron age to thereal, L is the LATTICE value of the thermal diffusion area, and B is the measured buckling. The k-effectives calculated using this method are listed in Table 2.1-1 for the appropriate criticals. The average value is 0.9887 with a standard deviation of 0.0079.
The criticcis numbered 16 through 20 in Table 2.1-1 (References 2-2, 2-3, and 2-12) were small lattices surrounded by a driver lattice and poisoned with soluble boron to a zero leakage configuration. Experiment 16 was aluminum clad UO with a U-235 enrichment of 2.46 weight percent. Criticals 17 through 20 were Zircaloy clad mixed-oxide pins with 1.5 to 2.1 weight percent pug The ll/M atom ratios varied from 5.27 to 13.22. Since 2
there was zero leakage, the LATTICE km was used as the calculated k-effective for each critical. For these five experiments, the average k-effective is 1.0025 with a standard deviation of 0.0038.
The remaining five experiments (Reference 2-4) were constructed in a near cylindrical configuration surrounded by an effectively infinite water reflector. The criticals had II/M atom ratios varying from 1.32 to 4.12. All were aluminum clad UO 2 rods with 3.04 weight percent enrichment, except for number 22, which was clad in stainless steel. For these five cases, LATTICE two group unit cell diffusion theory parameters were used in a one-dimensional diffusion theory code (Reference 2-5) with the experimental critical cylindrical radius and the measured axial buckling to calculate the 2-3
k-effcctive entered in Table 2.1-1. Group properties for the O
reflector region were also calculated using IaiTTICE. The average k-effective for these cases is 1.0082 with a standard deviation of 0.0044.
For all 25 critical experiments, the average calculated k-effective is 0.9954 with a standard deviation of 0.0107. However, if the criticals calculated using the less exact age-diffusion leakage correction are omitted, the average reactivity is 1.0054 and the standard deviation is reduced to 0.0049. This division of results into two groups is justified eince the age-diffusion correction is inaccurate for small, high-leakage lattices and because of the uncertainty in measured total bucklings. Note, however, that tases 1 through 15 which were calculated using the age-diffusion equation have an acceptable standard deviation. Thus, Loe results from the 25 criticals analyzed indicate that LATTICE correctly calculatt, physics parameters for unit cells.
2.2 REACTION RATE COMPARISONS Fifteen of the criticals selected for analysis with the lattice physics design method were also analyzed with the ESP Monte Carlo code (Reference 2-6). ESP is a full energy range reactor analysis code capable of using versions I through III of the ENDF/B neutron cross section data. For the present calculations, ENDF/B-III data was used except for natural zirconium, stainless steel, and hydrogen. ENDF/B-I neutron cross section data was used for natural zirconium and the components of stainless steel.
For hydrogen, a modification of ENDF/B-1 material 1001 was made 2-4
by setting the scattering cross section below 1.0 cv as a function of energy to the value obtained when the water scattering law data was processed with the FLANGE-Il (Refarence 2-7) computer code. Over 6000 neutron energy groups 5.ere used in ESP to represent the cross section data of the fuel media. All of the criticals were represented as single cells.
Comparisons of fractional reaction rates are summarized in Table 2.2-1. A thermal cutoff of 1.855 eV was used. The particular pa rameters prenented are k.., the neut ron source due to thermal neutrons (vE f2#2), the fraction of 'ast neutrons absorbed in the fuel (Ed4 '), the fraction of thermal neutrons absorbed in the fuel (E g2 4 fuel), and the fraction of thermal neutrons absorbed in the entire cell (Eg$ ). Following is a summary of hiases of LATT1('E relative to ESP and standard deviations:
Quantity Bias Standard Deviation km 0.00228 0.0108 vEg2c 0.000369 0.0130 E 1*1 -0.0239 6.0222 E
g t* 0.00452 0.0143 E 4" C
a2 2 0.00415 0.00734 The bias was calculated as [(7, b T/XESP)/ ]- .0, where X is the quantity of interest. The standard deviation is that of the rati bT/X ESP r e cases. De largest Mas is in the absorption in the fuel of neutrons with energies above 1.855 eV.
Because these systems are thermal, there is relatively little 2-5
/
TABLE 2.2-1 REACTION RATE COMPARISONS fuel fuel cell Cm bi No. Code k .,, " f2 2 al 1 a2 2 a2#2 1 ESP 1.1782 .0034 0.9420 0.3527 0.5288 0.6359 LAT 1.1710 0.9218 0.3595 0.5203 0.6264 2 ESP 1.20121.0027 0.9983 0.3098 0.5593 0.6782 LAT 1.2063 1.0022 0.2976 0.5638 0.6899 3 ESP 1.23231.0033 1.0674 0.2482 0.5969 0.7413 LAT 1.2273 1.0608 0.2450 0.5951 0.7439 4 ESP 1.2289!.0023 1.1234 0.1585 0.6264 0.8320 LAT 1.2187 1.1158 0.1534 0.023- 0.8375 5 ESP 1.2108!.0029 1.1204 0.1342 0.6244 0.8571 LAT 1.1979 1.1105 0.1306 0.6200 0.8607 6 ESP 1.18212.0025 1.1035 0.1147 0.6144 0.8765 LAT 1.1661 1.0928 0.1097 0.6096 0.8820 9 ESP 1.34132.0033 1.1653 0.2361 0.6281 0.7550 LAT 1.3322 1.1552 0.2339 0.6243 0.7557 15 ESP 1.04881.0031 0.7718 0.3462 0.4154 0.6280 LAT 1.0686 0.7833 0.3448 0.4234 0.6289 16 ESP 0.99331.0036 0.8273 0.2403 0.4700 0.7448 LAT 0.9964 0.8329 0.2355 0.4748 0.7467 17 ESP 0.98421.0039 0.8085 0.2553 0.5127 0.7225 LAT 1.0065 0.8358 0.2446 0.5341 0.7336 18 ESP 1.0008!.0035 0.9070 0.1221 0.5208 0.8624 LAT 1.0026 0.9162 0.1143 0.5298 0.8704 19 ESP 1.0022!.0036 0.9066 0.1217 0.5196 0.8626 LAT 1.0042 0.9148 0.1165 0.5283 0.8678 21 ESP 1.36372.0033 1.1426 0.3127 0.6305 0.6831 LAT 1.3766 1.1425 0.3096 0.632' O.6844 22 ESP 1.1856 .0025 0.9103 0.3929 0.5045 0.5942 LAT 1.1970 0.9052 0.3884 0.5038 0.5968 23 ESP 1.30762.0028 1.0302 0.3915 0.5701 0.6051 LAT 1.3253 1.0268 0.3896 0.5705 0.6042 2-6
absorption of fast neutrons and therefore greater statistical uncertainty in the Monte Carlo calculation. There is no apparent trend in cases 1 through 6, for which only the H/M ratio was varied. For k. and the thermal neutron reaction rates, the small biases and standard deviations demonstrate the acceptability of the besic physics methods utilized in the LATTICE code.
2.3 ISOTOPIC COMPARISON LATTICE results were compared to isotopic measurements made at the end of the first cycle of the Yankee-Rowe PL'R (Reference 2-8) .
The isotopics were calculated for a single pin in an asymptotic spectrum; input data was generated using design information in Reference 2-9. The calculatei concentrations and the experimental data were converted to isotopic ratios for the comparison. The results are plotted in Figures 2.3-1 through 2.3-6.
Agreement is excellent except that the Pu-242/Pu-241 ratio is underpredicted. This result has been reported by others (References 2-10 and 2-11) and is probably caused by an error in the ENDP Pu-242 cross section. Since Pu-242 is unimportant relative to the other fuel nuclides, the uncertainty in its cross section has insignificant effect on LATTICE calculations of physics parameters.
2-7
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O CHAPTER 2 REFERENCES
- 1. L. E. Strawbridge and R. F. Barry, " Criticality Calculations for Uniform Water-Moderated Lattices," Nucl . Sci. Eng.,
Vol. 23, pp. 58-73, 1965.
- 2. D. F. Newman, " Measurement of km, and Relative Reaction Rates in an li,0-Moderated UO,-Puo., Particulate Fueled Lattice,"
Nuc. Tech., Vol. 15, pp. 192-208, 1972.
- 3. M. N. Baldwin, et. al., " Physics Verification Program, Part 111, Tasks 2 and 3, Final Report," BAW-3647-16, 1970.
- 4. A. R. Boynton, et. al., "Ifigh Conversion Critical Experiments,"
ANL-7203, 1967.
- 5. D. C. Baller, "The FAIM Code, A Multigroup, One-Dimensional Diffusion Equation Code," AMTD-118, 1962.
- 6. S. N. Cramer, et. al., " ESP: A General Monte Carlo Reactor Analys is Code," ORNL-TM-3164, 1972.
- 7. H. C. Iloneck and D. R. Finch, " FLANGE II (Ve rsion 71-1): A Code to Process Thermal Neutron Data f rom an ENDF/B Tape,"
DP-1278, 1971.
- 8. J. Jedruch and R. J. Nodvik, " Experimentally Determined Burnup and Spent Fuel Composition of Yankee Core 1,"
WCAP-6071, 1965.
- 9. it . W. G raves , J r. , R. F. Janz, and C. G. Poncelet, "The Nuclear Design of the Yankee Core," YAEC-136, 1961.
- 10. W. J. Eich and M. L. Kennedy, "EPRI-CELL Isotopics Bench-marking," ARMP System Documentation, Part I, Chapter 3, Electric Power Research Institute, 1976.
- 11. C. L. Martin, "Lat t ice Physics Methods Verification,"
NEDO-20939, 1976.
- 12. M. N. Baldwin and G. T. Fairburn, " Physics Verification Program Part III, Tasks 5 and 6, Quarterly Technical Report, January-Ma rch 1971," BAW-364 7-21, 1971.
O 2-14
- 3. BUNDLE PIIYSICS For the verification of the lattice physics analysis method (computer code LATTICE) applied to typical BWR bundles, comparisons were made both to measured data and to results calculated by other computer codes which employ more exact physics models, geometric models, and cross sec. ion representations. Because of a lack of critical experiments in the public domain, reliance for verification of bundle reactivity is placed on comparisons to the ESP Monte Carlo reactor analysis code (Refere" e 3-1).
Of course, the best evidence that LATT1CE calculates bundle physics acceptably is the results obtained from the CORE simulator, which are discussed in Chapter 4. For local power distributions, comparisons are presented for one 8 x 8 bundle and three 7 x 7 bundles at a total of seven axial positions to the gamma scan measurements made at end-of-cycle 2 at Quad Cities unit 1 (Reference 3-2). The LATTICE calculation of the local power distribution for unexposed fuel is verified by comparison to results from the ESP Monte Carlo code and the CPM collision probability method code (Reference 3-31 Comparisons are given for eight 7 x 7 bundles and two 8 x 8 bundles. Results are presented only at 40 percent in-channel steam voids for most cases, but results are included at 0 and 80 percent in-channel steam voids for one of the 7 x 7 assemblies. Following is a description of the bundles for which comparisons are made against calculated data.
3-1
Type _ Description A 7 x 7 with an average enrichment of 2.5 weight percent. The first cut from the bottom of the bundle labelled Type 3 on page 6 of Reference 3-4.
B 7 x 7 with an average enrichment of 2.5 weight percent. The second cut from the bottom of the bundle labelled Type 3 on page 6 of Reference 3-4.
C 7 x 7 with an average enrichment of 2.5 weight percent. The third cut from the bottom of the bundle labelled Type 3 on page 6 of Reference 3-4.
D 7 x 7 with an average enrichment of 1.1 weight peretnt. The bundle labelled Type 1 on page 6 of Reference 3-4.
E Typical of 8 x 8 designs wit h one wat e r rod. Itas an average enrichment of 2.2 weight percent.
F Typical of 8 x 8 designs with two water rods.
Has an average enrichment of 3.0 weight percent.
G 7 x 7 with an average enrichment of 2. 3 weight percent. See page A-2 of Reference 3-5.
H 7 x 7 with an average enrichmant of 2.5 weight percent. The first cut from the hottom of the bundle labelled Type 2 on page 6 of Reference 3-4.
I 7 x 7 with an average enrichment of 2.5 weight percent. The second cut from the bottom of the bundle labelled Type 2 on page 6 of Reference 3-4.
J 7 x 7 mixed oxide bundle, labelled Assembly Type 5 on page A-6 of Reference 3-5.
3.1 REACTI/ITY COMPARISONS Monte Carlo calculations of beginning-of-life reactivity have been made for five 7 x 7 bundles and two 8 x 8 bundles at a total of 23 different conditions, using the ESP reactor analysis code. Reactivity differences were calculated as the logarithm of the ratio of L values. As can be seen from Table 3.1-1, the agreement is good. The average bias of IATT1CE relative to ESP 3-2
TABLE 3.1-1 Comparisons of k,at BOL as Calculated by LATTICE and ESP Fue' In-channel Reactivity Type Voids km (LAT) km (ESP) Difference A cold 1.1463 1.14691.0046 .0005 cold
- 0.9555 0.9541t.0055 .0015 0 1.1487 1.13751.0017 .0098 40 1.1315 1.1268f.0016 .0042 80 1.0855 1.0854!.0016 .0001 B 40 1.0700 1.06191.0039 .0076 C 0 1.0435 1.0216!.0049 .0212 40 1.0229 1.0105t.0050 .0122 80 0.9885 0.9662!.0058 .0228 D 0 1.0416 1.0385t.0038 .0030 20 1.0463 1.0445t.0043 .0017 40 1.0496 1.0518t.0035 .0021 60 1.0472 1.04751.0055 .0003 80 1.0351 1.0338 .0066 .0013 E O 1.0824 1.06401.0039 .0171 40 1.0688 1.0626t.0017 .0058 70 1.0430 1.0451t.0036 .0020 F 0 1.0771 1.0597t.0033 .0163 40 1.0596 1.05211.0017 .0071 80 1.0222 1.0228!.0038 .0006 1 0 1.1028 1.0829 .0051 .0182 40 1.0857 1.07411.0033 .0107 80 1.0477 1.0327!.0045 .0144 Bias = .0074 Standard Deviation = .0079
- controlled 3-3
is 0.0074 with a standard deviation of 0.0079. The reactivity ditterences for the 7 x 7 bundles show no apparent trend with in-channel water density. For the 8 x 8 bundles (Types E and F), the Monte Carlo code shows a slower variation with water density than does the I.ATTICE design method. Results for the Type J 7x 7 mixed oxide bundle at 40 percent in-channel i t e.e: voids have been obtained for a vendor's Monte Carlo code (1.0763?O.0014 I:e f e re n ce 3-6) and lattice physics design method (1.0884, Reference 3-6), and the CASMO code (1.077, References 3-7 cmd b8) . These results compare to 1.0857+0.0012 and 1.0873 1 rom ESP and LATTICE, respectively. This is excellent agreement for a c:txed oxide bundle heavily loaded with gadolinia.
Comparisons of the reactivity worth of the burnable poison calcul:ited by LATTICE and ESP were made for bundle Type E at cold conditions, and at 0, 40, and 70 percent in-channel voids.
The following results, expressed in percent, were obtained:
COLD 0 40 70 ESP 14.5 18.2 18.3 18.4 LAT 15.4 18.8 13.8 18.5 These results for bundle reactivity and for the worth of burnable poison demonstrate the adequacy of the LATTICE calculation of reactivity for clean bundles; results discussed in Section 2.3 and Chapter 4 demonstrate the adequacy of LATTICE depletion methods.
O 3-4
- 3. 2 LOCAL POWER DISTRIBUTION COMPARISONS Comparisons to demonstrate the adequacy of the LATTICE cal-culation of the local power distribution have been made against gamma scan measurements taken at end-of-cycle 2 of Quad Cities unit 1. Comparisons are presented in Subsection 3.2.2 for four bundles at a total of seven axial positions, at average in-channel voids ranging from 10 to 70 percent. Bundles were selected for benchmarking which did not exhibit large gradients across the bundle to facilitate direct comparison to single bundle, infinite lattice calculations. Additional evidence in the form of comparisons to results from more sophisticated codes are presented in Sub-section 3.2.1. These numerical comparisons are for unexposed fuel.
The LATTICE results were generated utilizing a standard BWR representa-tion including four neutron energy groups in the two-dimensional diffusion theory calculation of the local power distribution, with transport-corrected cross sections for the explicitly represented fuel pins and associated moderator regions.
3.2.1 Unexposed Bundles Beginning-of-life local power distributions calculated by LATTICE have been compared to distributions obtained f rom the ESP Monte Carlo reactor analysis code (Reference 3-1) and the CPM collision probability method code (Reference 3-3) which is distributed by the Electric Power Research Institute. ESP, which is essentially a continuous energy code, is capable of utilizing version I, II or III of the ENDF/B neutron crass section data. For these comparisons, over 6,000 neutron energy groups for the fuel media were used, with basic cross sections coming from ENDF/B-III for all materials except 3-5
natural zirconium and hydrogen bound in water. For natural zirconium, ENDF/B-I data was ured. For hydrogen bound in water, a inodification to the ENDF/B-I data for free hydrogen was used. This rnodi ficat ion was made by processing the ENDF/B-Il scattering law data for water us in g; FLANGE-II (Reference 3-9), and setting the scattering cross section below 1.0 eV for f ree hydrogen to the FLANGE-II values.
This was done at temperatures of 300 and 558'K. From 90,000 to 100,000 neutron histories were processed for each case for which local power distributions are given. CPM used 69 neutron energy groups in spectrum calculations and 20 groups (9 thermal) in the two-dimensional collision probability calculation of the local power distribution. Cross section libraries based on ENDF/B-III and distributed by EPRI were utilized. Comparisons are presented for t ;ht 7 x 7 fuel designs at 40 percent in-channel voids and for two e i 8 x 8 fuel designs at 40 percent in-channel voids. For the 7x7 Type A bundle, additional comparisons are given for 0 and 80 percent In-channel voids.
For the Quad Cities mixed oxide bundle (Type J in this report),
comparisons are made not only for LATTICE, ESP, and CPM, which were run by TVA, but also to results f rom a vendor's Monte Carlo code and lattice physics design code (Reference 3-6), and to CASMO (Reference 3- 7 ) .
The peak pin powers calculated by the various codes for this bundle are as follows:
CASMO 1.203 CPM 1.243 E ,P 1.201 Vendor Design Method 1.21 Vendor Monte Carlo 1.26 LATTICE 1.216 3-6
The pin-by-pin distributions for this bundle are presented in Figure 3.2-1. Even though this bundle is very different from conventional designs, the power distributions follow the same general trends. This comparison serves to strengthen the case for the use of CPM and ESP as benchmarks. The root-mean-square (RMS) differences of CPM relative to the other codes are 2.5, 3.1, 3.0, and 4.6 percent respectively. The RMS differences of ESP relative to the other codes are 2.4, 3.1, 3.6, and 4.8 percent respectively. The agreement of LATTICE with the other codes is good (3. 3, 4.4, 4. 2, 4. 2, and 4. 3 percent respectively) but this is fortuitous since LATTICE is primarily intended for analyses of standard design UG bundles, and a judicious choice of input 3
was necessary to obtain these results. This bundle, an island design with black burnable poison UO pins 1 c ted between black 2
mixed oxide pins and gray UO pins, has five different UO 2 2
enrichments and four different plutcnium concentrations, and is therefore a difficult bundle to analyze accurately. Figure 3.2-1 is presented nuinly to demonstrate the suitability of ESP and CPM as benchmark codes for calculating local power distributions at beginning of life. Reference 3-10 presents information supporting the CPM calculation of local power distribution.
Data presented in the remainder of this subsection confirms that I.ATTICE ralculates the local power distribution with acceptable accuracy for bundle designs typical of those commercially available.
Figures 3.2-2, 3.2-3, and 3.2-4 are comparisons of LATTICE local power maps to those calculated by ESP and CPM at 0, 40, and 80 percent in-channel steam voids for bundle Type A. The 3- 7
U-W l.165 CASMO 1.1 ~18 CPM l.171. ESP 1.19 Vendor Design Method 1.25 Vendor Monte Carlo 1.1/2 LATTICE 1.203 1.039 Figure 3.2-1 1.207 1.018 1.199 1.005 Local l'ower Distribution for the Quad Cities 1
- 1. 21 1.05 Cycle 2, Central Mixed Oxide Bundle at 40%
1.26 l.06 In-channel Steam Voids 1,215 1.061 1.u63 1.047 0.282 1.070 1.055 0.294 1.060 1.046 0.246 1.07 1.08 0.30 1.0d 1.08 0.30 1.uhl 1.085 0.223 L.ll4 1.172 1.053 0.544 1.050 1.119 1.175 1.055 0.535 1.091 i.llo 1.153 1.100 0.569 1.048 1,. l ? 1.19 1.07 0.55 1.00 1.12 1.19 1.05 0.56 0.99 1.110 1.216 0.986 0.598 1.010 1.104 1.158 1.032 1.050 0.239 1.106 1.155 1.037 1.091 0.241 1.085 1.129 1.067 1.087 0.204 1.10 1.17 1.05 1.05 0.25
- 1. 12 1.17 1.03 1.04 0.25 1.100 1.201 0.983 1.072 0.201 1.164 1.012 0.278 1.174 1.178 0.268 1.159 0.994 0.282 1.229 1.243 0.268
. . l!. n 0.986 0.242 1.201 1.201 0.232 1.lh 1.03 0.30 1.17 1.17 0.28 1.17 1.03 0.29 1.13 1.12 0.28 L.161 1.050 0.220 1.157 1.179 0.215 1.162 1.005 0.983 1.064 1.035 1.115 1.133 l.126 0.979 0.977 1.045 1.013 1.097 1.080 1.171 0.984 1.012 1.079 1.037 1.137 1.151 1.11 0.97 0.98 1.04 1.00 1.06 1.09 1.19 1.00 0.99 1.03 1.00 1.08 1.04 l.149 1.004 1.004 1.089 1.054 1.140 1.111 0
3-8
W-W Figure 3.2-2
. 079 CPM 1.114 ESP Lacal Power Distribution for a Type A Bundle 1.073 LATTICE at 0% In-channel Steam Voids 1.153 1.022 RMS(ESP-CPM) = 2.8%
1.113 0.976 RMS(ESP-LAT) = 3.1%
1.139 1.035 RMS(CPM-LAT) = 2. 4%
1.042 1.256 1.024 1.046 1.203 1.039 1.029 1.232 1.035 1.104 1.149 0.892 0.242 1.106 1.128 0.885 0.211 1.078 1.138 0.926 0.216 1.082 1.097 0.838 0.790 0.872 1.111 1.060 0.859 0.823 0.897 1.062 1.105 0.883 0.838 0.895 1.116 1.109 0.263 0.878 0.997 1.122 1.115 1.093 0.239 0.869 0.983 1.103 1.097 1.133 0.247 0.909 1.004 _
1.112 1.080 0.965 1.138 1.134 1.225 0.965 1.096 1.127 1.005 1.157 1.149 1.224 0.958 1.160 1.096 0.976 1.135 1.119 1.179 0.944 1.096 3-9
O W-W Figure 3.2-3 1.115 CPM 1.148 ESP Local Power Distribution for a Type A Bundle 1.107 LATTICE at 40% In-channel Ste.im Voids l.182 1.040 RMS(ESP-CPM) = 3.1%
1.170 1.039 RMS(ESP-LAT) = 3.9%
1.166 1.061 RMS (CPM-LAT) = 2.5%
1.059 1.271 1.030 1.054 1.210 1.002 1.042 1.253 1.049 1.115 1.158 0.900 0.287 1.095 1.114 0.893 0.256 1.080 1.149 0.936 0.258 1.092 l.108 0.844 0.780 0.840 1.103 L.077 0.861 0.789 0.845 1.061 1.114 0.886 0.829 0.870 1.129 1.123 0.317 0.863 0.955 1.066 1.133 1.112 0.290 0.848 0.924 1.039 1.098 1.146 0.297 0.896 0.976 1.076 1.088 0.966 1.136 1.107 1.175 0.920 1.044 1.148 0.996 1.198 1.145 1.191 0.932 1.105 1.100 0.972 1.123 1.088 1.137 0.911 1.063 0
3-10
W-W Figure 3.2-4 1.128 CPM 1.214 ESP Local Power Distribution for a Type A Bundle 1.085 LATTICE at 80% In-channel Steam Voids 1.191 1.055 RMS(ESP-CPM) = 4.1%
1.216 1.041 RMS(ESP-LAT) = 6.3%
1.150 1.077 RMS(CPM-LAT) = 3.7%
1.065 1.297 1.063 1.078 1.247 1.008 1.031 1.279 1.098 1.116 1.184 0.941 0.368 1.112 1.108 0.909 0.321 1.062 1.175 0.993 0.345 1.092 1.133 0.878 0.795 0.822 1.082 1.107 0.854 0.762 0.805 1.038 1.137 0.928 0.863 0.875 1.123 1.140 0.410 0.860 0.913 0.992 1.144 1.137 0.369 0.824 0.895 0.996 1.067 1.163 0.383 0.909 0.964 1.033 1.071 0.954 1.125 1.069 1.104 0.848 0.953 1.164 1.004 1.173 1.093 1.127 0.883 1.037 1.056 0.955 1.114 1.060 1.079 0.853 0.977 3-11
agreement lessens as the void fraction increases, as shown by the following table of RMS differences.
0% stm 40% stm 80% stm LAT-CPM 2.4 2.5 3.7 IAT-ESP 3.1 3.9 6.3 CPM-ESP 2.8 3.1 4.1 Figure 3.2-5 is a comparison of the local power map produced by LATTICE to that calculated by CPM for the Type B bundle design at 40 percent in-channel voids. The RMS difference is 3.3 percent. The siightly worse agreement is because Type B has one more gadolinia rod than Type A, and is therefore slightly more nonuniform. Since LATTICE somewhat underpredicts the power in the burnable poison rods, increasing the number of such rods increases the RMS difference.
LATTICE evidently does not significantly underpredict absorption in the burnable poison rods, since good agreement with Monte Carlo results is obtained (see Table 3.1-1) and since the core simulator well predicts core reactivity versus core average burnup (see Figures 5.2-1 and 5.2-2). Comparisons of the worth of the burnable poison rods in the Type E bundle are presented in Section 3.1.
Figure 3.2-6 is a comparison of the local power map calculated with LATTICE to CPM results for the Type C bundle design at 40 percent in-channel void fraction. The RMS difference is 3.7 percent. Again, Type C is slightly worse than Type B because of the addition of another gadolinia rod.
A comparison of the local power map f rom LATTICE to ESP results for the Type D bundle design at 40 percent in-channel voids is given in Figure 3.2-7. The Type D bundle, average 3-12
W-W Figure 3.2-5 1.019 CPM Local Power Distribution for a Type B Bundle 1.029 LATTICE at 40% In-channel Steam Voids 1.031 0.247 RMS(CPM-LAT) = 3.6%
1.051 0.258 0.977 1.078 0.932 0.982 1.134 0.993 1.097 1.119 0.887 0.297 1.069 1.131 0.935 0.269 1.121 1.128 0.869 0.823 0.899 1.083 1.138 0.914 0.866 0.917 1.187 1.173 0.341 0.920 1.027 1.151 1.142 1.194 0.313 0.946 1.036 1.146 1.157 1.029 1.218 1.195 1.277 1.003 1.141 1.153 1.022 1.185 1.153 1.209 0.972 1.136 3-13
O W-V Figure 3.2-6 1.097 CPM Local Power Distribution for a Type C Bundle 1.088 LATTICE at 40% In-channel Steam Voids 1.109 0.264 RMS(CPM-LAT) = 3.7%
1.I10 0.274 1.047 1.146 0.985 1.036 1.193 1.041 1.171 1.182 0.929 0.308 1.124 1.187 0.977 0.277 1.191 1.186 0.898 0.816 0.833 1.136 1.191 0.948 0.874 0.876 1.257 1.227 0.354 0.894 0.894 0.336 1.195 1.247 0.321 0.938 0.940 0.321 1.221 1.077 1.248 1.174 1.175 0.87/ 1.034 1.206 1.063 1.214 1.141 1.132 0.866 1.039 0
3-14
W-W Figure 3.2-7 0.996 ESP L cal Power Distribution for a Type D Bundle 0.916 LATTICE at 40% In-channel Steara Voids RMS(ESP-LAT) = 3.7%
f'. 38 2 1.333 1.149 0.608 1.292 1.140 0.644 1.274 0.663 0.621 0.605 1.257 0.658 0.634 0.569 1.234 1.049 0.599 0.590 0.642 1.251 1.107 0.631 0.622 0.619 1.255 1.087 0.610 0.603 0.612 0.994 1.280 1.128 0.638 0.627 0.624 1.065 1.404 1.204 1.150 1.171 1.097 1.160 1.333 1.361 1.216 1.150 1.122 1.119 1.143 1.218 3-15
enrichment 1.1 weight percent, was represented in the ESP run as one assembly in a 4-assembly module; the other three bundles were Type A bundles which have an average enrichment of 2.5 weight percent. The resulting RMS difference is 3.7 percent, demonstrating that the effee of having neighboring bundles of different composition was insignificant.
Figure 3.2-8 is a comparison of the local power distribution calculated by LATTICE to one frem ESP for the Type E bundle design at 40 percent in-channel void fraction. The RMS difference is 4.5 percent.
Figure 3.2-9 is a comparison of the IJ.TTICE and ESP local power distributions for the Type F bundle at an average in-channel void fraction of 40 percent. The dis difference between the distributions is 6,5 percent.
Figure 3.2-10 compares the LATTICE local power distribution to CPM results (Reference 3-8) for the Type G bundle at an average in-channel void fraction of 40 percent. The RMS difference between the maps is 3.0 percent.
IATTICE and CPM local power distributions are compared in Figure 3.2-11 for the Type 11 bundle at 40 percent in-channel voids.
The resulting RMS difference is 2.7 percent.
Figure 3.2-l' ; ccpparison of IATTICE and CPM local power distributio,. '
,ype 1 bundle at an in-channel void fraction of 40 percent. A MIS dificrence of 3.6 percent was obtained.
O 3-16
W-W Figure 3.2-8 1.152 ESP Local Power Distribution for Type E Bundle 1.107 LATTICE at 40% In-Channel Steam Voids 1.177 1.168 RMS(ESP-LAT) = 4.5%
1.173 1.200 1.046 0.995 1.052 1.055 1.048 1.094 1.210 1.158 0.901 0.246 1.183 1.174 0.941 0.276 1.189 1.061 0.836 0.797 0.0 1.141 1.111 0.891 0.831 0.0 1.202 1.061 0.251 0.818 0.805 0.249 1.153 1.106 0.283 0.852 0.849 0.279 1.047 1.192 0.980 0.945 0.918 0.922 1.019 1.012 1.221 1.009 0.953 0.934 0.943 1.072 1.184 1.162 1.046 1.222 1.190 1.184 1.056 1.001 1.111 1.133 0.997 1. 14 3 1.117 1.147 1.007 0.936 3-17
O W-W Figure 3.2-9 1.084 ESP Local Power Distribution for a Type F Bundle 1.057 LATTICE at 40% In-channel Steam Voids 1.129 1.127 RMS(ESP-LAT) = 6.5%
1.133 1.238 1.160 0.948 0.342 1.164 1.016 0.327 1.072 1.086 0.953 1.157 1.067 1.140 1.026 1.168 1.189 1.062 1.071 0.0 1.053 1.148 1.116 1.733 0.0 1.095 1.]31 0.339 0.918 1.008 0.962 0.857 1.113 0.322 1.061 1.041 0.998 0.938 1.237 1.089 0.264 0.997 0.986 0.256 1.018 1.180 1.124 0.281 1.035 1.011 0.272 1.063 1.233 1.128 1.202 1.169 1.139 1.141 1.196 1.238 1.145 1.067 1.163 1.091 1.061 1.061 1.070 1.040 0
3-18
W-W Figure 3.2-10 1.179 CPM Local Power Distribution for a Type G Bundle 1.149 LATTICE at 40% In-channel Steam Voids 1.163 1.072 RMS (CPM-LAT) = 3.0%
1.140 1.080 1.040 1.123 0.321 1.025 1.137 0.286 1.167 1.076 0.839 0.793 1.133 1.092 0.893 0.767 1.166 1.101 0.882 0.761 0.778 1.133 1.107 0.913 0.828 0.832 1.225 1.176 0.927 0.310 0.836 0.967 1.186 1.173 0.953 0.279 0.880 0.993 1.148 1.088 1.147 1.018 1.055 1.163 1.067 1.118 1.075 1.134 1.029 1.054 1.142 1.048 3-19
O W-W Figure 3.2-11 1.096 CPM Local Power Distribution for a Type H Bundle 1.090 LATTICE at 40% In-channel Steam Volds 1.155 O.989 RMS(CPM-LAT) = 2.7%
1.142 1.021 1.034 1.171 0.326 1.020 1.179 0.298 1.099 1.114 0.870 0.771 1.066 1.120 0.928 0.810 1.091 1.106 0.863 0.848 0.892 1.059 1.115 0.907 0.881 0.909 1.138 1.134 0.324 0.897 0.993 1.100 1.104 1.158 0.299 0.922 1.004 1.101 1.101 0.980 1.160 1.138 1.212 0.948 1.075 1.109 0.984 1.142 1.110 1.161 0.930 1.084 0
3-20
W-W Figure 3.2-12 1.150 CPM Local Power Distribution for a Type 1 Bundic 1.131 LATTICE at 40% In-channel Steam Voids 1.210 1.033 RMS (CPM-LAT) = 3. 6%
1.184 1.056 1.080 1.239 0.340 1.056 1. 2. 6 0.307 1.145 1.151 0.869 0.733 1.101 1.151 0.940 0.796 1.135 1.139 0.853 0.768 0.322 1.091 1.142 0.911 0.839 0.291 1.182 1.168 0.330 0.862 0.915 1.058 1.136 1.185 0.306 0.902 0.955 1.075 1.143 1.012 1.183 1.138 1.199 0.942 1.076 1.142 1.008 1.160 1.113 1.154 0.928 1.088 3-21
Table 3.2-1 compares peaking factors of the three codes LATTICE, ESP, and cpm. The bias of LATTICE relative to ESP is 0.1 percent, and the standard deviation is 2.2 percent. For LATTICE compared to CPM, the bias and standard deviation are ~2.1 percent and 1.6 percent.
Since 40 percent in-channel steam volds is most typical of core regions at peak power, the bias and standard deviation relative to both codes were calculated, with resulting values of -1.3 percent and 2.5 percent, respectively. All 7 x 7 cases were considered separately, yielding a bias of -1.1 percent and a standard deviation of 2.6 percent. For 8 x 8 bundles, values of -1.0 percent and 0.9 percent were obtained for the bias and standard deviation.
These RMS differences for local power maps and biases and standard deviations for peaking factors demonstrate that the LATTICE code adequately predicts local power distributions for typical BWR bundles at beginning of life. Comparisons to gamma scan measurements are presented in Subsection 3.2.2 to demonstrate that the LATTICE calculation of the local power is acceptable for exposed fuel.
O 3-22
TABLE 3.2-1 COMPARISON OF LOCAL PEAKING FACTORS Type Void Fraction LATTICE Ejij [ CPM A 0 1.232 1.224 1.256 A 40 1.258 1.210 1.271 A 80 1.277 1.247 1.297 B 40 1.209 -
1.277 C 40 1.247 -
1.257 D 40 1.383 1.428 -
E 40 1.221 1.222 -
E 70 1.219 1.238 -
F 0 1.221 1.236 -
F 40 1.238 1.238 -
F 80 1.236 1.263 -
G 40 1.186 -
1.225 H 40 1.179 -
1.212 1 40 1.216 -
1.219 3-23
.2.2 Exposed Bundles Local power maps generated by LATTICE have also been compared to rod-by-rod results from the 1976 Quad Cities unit 1 gamma scan (Reference 3-2). Table 3.2-2 lists the assemblies chosen for the analysis, covering a wide range of exposure and void f raction for several fuel designs. The exposures and exposure averaged void fractions were obtained from nodal edits of the Quad Cities end-of-cycle 2 CORE simulator case discussed in Subsection 4.1.4.
Figures 3.2-13 through 3.2-19 conpare the calculated and measured local power distributions. The measured powers were averaged for diagonally symmetric rods in order to further reduce experimental uncertainty. Root-mean-square (RMS) power differences and the bias in local peaking factors (maximum relative rnd powers) are also listed in Table 3.2-2. Ger.eral agreement is good except for the mixed oxide bundle which has a 4.9 percent RMS power difference.
The local peaking factor in this assembly is overpredicted by S.3 percent. LATTICE underestimates the local peaking factor in the UO2 bundles by an average of 1.2 1 1.5 percent relative to the gamma scan. The average RMS power difference is 2.4 percent for the UOy assemblies, which is comparabic to the 3 percent uncertainty in the measured data (Reference 3-2). The power in gadolina bearing rods was also accurately predicted with a bias of
-2.9 ! 2.6 percent.
O 3-24
TABLE 3.2-2 LOCAL POWER DISTRIBUTION COMPARISONS FOR EXPOSED BUNDLES Inches Percent Percent Bundle Core Fuel From Exposure In-channel LPF RMS Power Label Location Design Bottom (GWD/MT) Voids Bias Difference CX-214 33-34 7x7 57 20.606 37.8 -0.0056 2.7 Initial 129 13.106 63.3 -0.0341 3.5 2.12 enr CX-672 15-36 7x7 51 20.680 31.9 -0.0167 2.3 Initial Y 2.12 ent U
GEB-159 31-32 7x7 51 10.457 41.7 0.0532 4.9 Reload M0 2
GEH-002 13-36 8x8 15 10.823 7.3 0.0091 1.6 Reload 51 10.307 42.9 -0.0063 2.0 2.50 ent 129 6.199 69.8 -0.0168 2.5 Average * -0.0117 2.4 Standard Deviation 0.0145
- for UO bundles only 2
O W- W Figure 3.2-13 1.064 Gamma Scan EOC 2 Local Power Distribution for 1.017 LATTICE QC Bundle CX-214 at 57 Inches f rom Bottom of Core 1.000 0.997 0.963 0.999 RMS (SCAN-LAT) = 2. 7%
0.940 1.019 0.959 0.992 1.022 1.062 0.987 0.979 1.054 0.987 1.041 0.972 0.968 0.936 1.058 0.990 0.962 0.962 1.017 1.043 1.002 1.002 0.959 0.998 0.997 1.039 1.034 0.953 1.006 1.034 0.988 0.949 1.021 1.052 0.925 0.973 0.972 1.029 1.048 0.978 9
3-26
W-W Figure 3.2-14 1.114 Gamma Scan EOC 2 Local Power Distribution for 1.074 LATTICE QC Bundle CX-214 at 129 Inches from Bottom of Core 1.031 1.034 0.996 1.039 RMS(SCAN-LAT) = 3.5%
0.965 1.005 0.967 0.972 1.079 1.059 0.939 1.012 1.076 0.969 1.050 0.942 0.898 0.891 1.073 0.965 0.921 0.915 1.053 1.054 0.963 0.962 0.925 0.969 1.036 1.066 1.021 0.901 0.969 1.005 1.029 1.000 1.056 1.018 0.946 0.988 0.987 1.020 1.047 0.969 3-27
O W-W Figure 3.2-15 0.994 Gamma Scan EOC 2 Local Power Distribution for 1.008 LATTICE QC Bundle CX-672 at 51 Inches from Bottom of Core 0.935 0.944 0.955 0.992 RMS(SCAN-LAT) = 2.3%
0.919 1.039 0.953 1.012 0.981 1.072 0.989 0.973 1.053 0.988 1.075 0.985 0.982 1.057 0.993 0.967 0.984 1.049 1.033 1.019 0.990 1.010 0.992 1.039 1.037 0.961 1.012 1.039 0.963 0.947 1.028 1.043 1.020 0.966 0.969 1.032 1.050 0.976 9
3-28
W-W Figure 3.2-16 1.040 Gamma Scan EOC 2 Local Power Distribution for 1.007 LATTICE QC Bundle GEB-159 at 51 Inches from Bottom of Core 1.055 1.020 RMS(SCAN-LAT) = 4. 9%
1.023 0.878 1.028 0.801 1.022 1.108 0.948 0.987 1.167 0.924 1.064 0.931 0.992 0.506 1.087 0.949 1.092 0.581 1.035 0.999 0.863 1.069 1.074 0.769 1.015 1.011 0.762 1.085 1.151 0.708 1.054 0.990 1.070 1.080 1.048 1.010 0.951 1.067 1.115 1.055 3-29
O W-W Figure 3.2-17 1.008 Gamma Scan EOC 2 Local Power Distribution for O.981 LATTICE QC Bundle Gell-002 at 15 Inches from Bottom of Core 1.034 0.990 1.023 0.988 RMS(SCAN-LAT) = 1.6%
1.084 0.985 1.076 0.957 1.033 1.042 0.950 0.921 1.010 1.0 34 0.953 0.923 1.034 1.022 0.933 0.932 0.0 1.002 1.023 0.943 0.932 0.0 1.032 0.957 0.924 0.930 0.926 1.039 0.959 0.929 0.938 0.935 1.042 1.090 1.006 0.959 0.940 0.945 1.000 1.044 1.086 0.972 0.968 0.957 0.973 0.982 1.042 0.995 1.052 1.036 1.096 0.964 1.031 1.005 1.059 1.047 1.106 1.014 9
3-30
W-W Figure 3.2-18 1.055 Gamma Scan EOC 2 Local ?ower Distribution for 1.046 LATTICE QC Bundle Gell-002 at 51 inches from Bottom of Core 1.057 1.009 1.075 1.027 RMS(SCn3-LAT) = 2.0%
1.105 1.015 1.098 0.951 1.044 1.036 0.953 0.922 1.039 1.046 0.952 0.904 1.034 1.021 0.926 0.940 0.0 1.027 1.030 0.935 0.901 0.0 1.044 0.946 0.917 0.929 0.899 1.045 0.951 0.904 0.901 0.903 1.060 1.078 0.989 0.943 0.921 0.931 0.960 1.073 1.095 0.948 0.950 0.933 0.948 0.943 1.072 0.990 1.035 1.031 1.082 0.974 1.069 1.024 1.043 1.025 1.089 1.015 3-31
O W-W Figure 3.2-19 1.107 Gamma Scan EOC 2 Local Power Distribution for 1.070 LATTICE QC Bundle Gell-002 at 129 Inches from Bottom of Core 1.133 1.043 1.106 1.039 RMS(SCAN-LAT) = 2. 5%
1.126 0.994 1.114 0.940 1.086 1.062 0.942 0. 8t' 8 1.054 1.053 0.945 0.892 1.058 1.033 0.912 0.895 0.0 1.037 1.032 0.925 0.888 0.0 1.047 0.922 0.880 0.884 0.858 1.049 0.942 0.890 0.886 0.887 1.121 1.111 0.973 0.924 0.884 0.885 0.918 1.093 1.105 0.932 0.940 0.920 0.934 0.922 1.115 1.028 1.044 1.006 1.039 0.965 1.091 1.029 1.042 1.021 1.091 1.010 0
3-32
CllAPTER 3 REFERENCES
- 1. S. N. Cramer, et. al., " ESP: A General Monte Carlo Reactor Analysis Code," ORNL-TM-3164, 1972.
- 2. M. B. Cutrone and G. F. Valby, " Gamma Scan Measurements at Quad Cities Nuclear Power Station Unit 1 Following Cycle 2,"
EPRI NP-214, 1976.
- 3. A. Ahlin and M. Edenius, "The Collision Probability Module EPRI-CPM," ARMP System Documentation, Part II, Chapter 6, Electric Power Research Institute, 1975.
- 4. N. 11. Larsen, " Core Design and Operating Data for Cycles 1 and 2 of Peach Bottom 2," EPRI NP-563, 1978.
- 5. N . 11. Larsen, G. R. Parkos, and O. Raza, " Core Design and Operating Data for Cycles 1 and 2 of Quad Cities 1,"
EPRI NP-240, 1976.
- 6. R. L. Crowther, et. al., "GE/EPRI Quad Cities 1 Plutonium Recycle Nuclear and Fuel Performance Measurements," Trans.
Am. Nucl. Soc., Vol. 27, pp. 472-474, 1977.
- 7. A. Ahlin and M. Edenius, "CASMO - A Fast Transport Assembly Depletion Code for LWR Analysis," Trans. Am. Nucl. Soc.,
Vol. 26, pp. 604-605, 1977.
- 9. 11. C , lioneck and D. R. Finch, " FLANGE 11 (Version 71-1): A Code to Process Thermal Neutron Data from an ENDF/B Tape,"
DP-1278, 1971.
- 10. M. Edenius, "EPRI-CPM Benchmarking," ARMP System Documentation, Part I, Chapter 5, Electric Power Research Institute, 1975.
3-33
- 4. CORE SIMULATION The primary method of determining the accuracy of the CORE code (Reference 4-1) in BWR analyses is by comparison of its predictions to observed data from operating reactors. The operating reactors used for CORE comparisons have similar core design char-acteristics to those on which CORE will be used for reload analyses.
Comparison of calculated and measured reactor data provides a check not only on che core simulator program but also provides additional insight into the adequacy of the overall BWR analysis (including lattice physics methods and analysis procedures).
CORE code calculations will be compared to data recorded for the following reactor cores:
- 1. Quad Cities unit 1, cycles 1 and 2
- 2. Browns Ferry units 1 and 2, cycles 1 and 2
- 3. Browns Ferry unit 3, cycle 1 and beginning of cycle 2 The Quad Cities 1 reactor has a slightly smaller core than the Browns Ferry units (724 versus 764 fuel bundles), its flow rate at rated conditic..s is approximately 2 percent less, and the rated power is approximately 24 percent lower. The Browns Ferry units 1 and 2 and Quad Cities unit 1 initial cores were composed of 7 x 7 fuel bundles while the Browns Ferry unit 3 initial core and all reload cores contained 8 x 8 fuel bundles. The ave rage initial fissile enrichment of the bundles ranged from 1.10 to 2.74 weight percent. Each of the cores analyzed contained gadolinia in at least a portion of the fuel bundles.
4-1
4.1 .QUAD CITIES COMPARISONS Comparison of CORE calculations to observed critical configu-rations in Quad Cities unit 1 for both cold and operating conditions were performed to assess CORE's capability to calculate reactivity.
Comparisons to end-of-cycle gamma scan data were used to determine the accuracy of the calculated power distributions and comparisons to T rave rs inr, Incore Probe (TI P) measurement s were used to confirm the adequacy of the calculated power distribution during the cycles.
The design information on fuel bundles used in the Quad Cit ies analyses and t he core loading patterns are given in Reference 4-2. The lattice physics data utilized in CORE was generated as a function of control state, exposure, water density, and history effects using the IATTICE program (Reference 4-3).
ihe complete functional dependence of the lattice physics data for CORE is discussed in Reference 4-1. The dependence of individual bundle flows on the bundle power, power shape, core pressure, pressure drop, and inlet enthalpy was developed using the TilAS program as described in Reference 4-1 with the input values of the total form losa coefficients (and their two phase multipliers) adjusted to force agreement with vendor supplied data. The albedo boundary conditions used at the top, bottom, and sides of the reactor core were based on previous studies (analytical and fine mesh dif fusion theory calculations) performed for use in analysis of the Browns Ferry cores.
The CORE model for Quad Cit.ies employed a full-core description 42
with nodes for each 6-inch segment of each fuel bundle (and Jts associated water gaps) . The crit ical configurations of rod pattern, power, flow, pressure, and inlet subcooling throughout the first two cycles were taken f rom Reference 4-2 with error corrections and supplemental information obtained directly from EPR1.
Reference 4-2 also recommended the depletion steps used in this analysis.
4.1.1 Cold, Xenon-Free Criticals Reference 4-2 contains some of the cold, xenon-free, in-sequence critical configurations which occurred during cycles 1 and 2 for Quad Cities unit 1. Each of the eight cold criticals in Reference 4-2 were calculated with the CORE code; the results are summarized in Table 4.1-1. Since the CORE code uses lattice physics data represented as a continuous function of water density (and temperature) over the complete range encountered in BWR co re s, the calculations were performed at the recorded temperatures and no moderator temperature corrections were required. The calculated k-ef fectives were corrected for the reactivity equivalent of the measured reactor period, but nc other adjustments, corrections, normalizations or biases were employed. The average k-effective calculated by CORE was 0.9963 with a standard deviation of 0.0027.
One important use of the CORE code is shutdown margin calcula-tions. Shutdown margin calculations are performed at the most reactive core state (normally cold) with the highest worth control rod withdrawn. Verification of CORE's capability to accurately calculate cold reactivity is partially provided by comparisons to 4-3
TABLE 4.1-1 QUAD CITIES 1 CYCLES 1 AND 2,IN-SEQUENCE COLP CRITICALS Core Coc.lant Reactor Average Temperature Period Corrected
- Date GWD/MTM ( F) (Sec) k-eff 4/05/72 0.0 147 230 1.0018 2/08/73 2.866 160 ' -
300 0.9983 5/07/73 3.749 120 300 0.9972 8/07/73 4.940 120 45 0.9954 1/06/74 6.912 180 300 0.9948 10/06/74 8.277 185 100 0.9943 12/16/74 9.142 160 45 0.9954 5/04/75 10.604 190 130 0.9935 Average 0.9963 Standard Deviation 0.0027
- The corrected k-eff has the reactivity equivalent of the observed period subtracted from the calculated k-eff.
O 4-4
in-sequence criticals such as shown in Table 4.1-1. 1:owever, shutdown margin calculations involve a very localized area of high reactivity compared to normal in-sequence rod patterns and thus introduce very large neutron flux gradients. In order to verify the capability of CORE to predict very localized reactivity con-figurations, it is necessary to examine criticals employing rod patterns similar to the stuck rod configuration. A series of local (two or three adjacent rods withdrawn) criticals were per-formed during the startup testing of Quad Cities unit 1. Ten of these criticals were calculated using data obtained from the Commonwealth Edison Company; the results are given in Table 4.1-2.
The average k-effective value (corrected for the reactor period) from CORE was 1.0009 with a standard deviation of 0.0006.
The k-effective for the beginning-of-cycle 1 in-sequence critical was L.0018. Thus a bl.is of less than 0.1 percent reactivity between the localized and distributed criticals was obtained from CORE. This is strong evidence that CORE can accurately perform reactivity calculations for localized reactivity configurations and that comparisons to in-sequence criticals provide an accurate measure of the calculational error for such localized configurations.
4.1.2 llot Operating Reactivity Each of the data sets in Reference 4-2 (plus three additional data sets obtained f rom EPRI) represents a high-power critical reactor configuration which occ. red during the first two cycles of operation of Quad Cities unit 1. Each of these hot operating critical configurations was analyzed with CORE. Equilibrium xenon 4-5
O T/.BLE 4.1-2 QUAD CITIES 1 LOCAL COLD CRIT 1CALS AT BOC 1 Coo l m t Reactor Control Huds l'a r t ia l l y W i t lid rawn Teru]>e r.i t u re l'e r io d Corrected
- l'o l lj Wi t lui r awn Rod Notch .(*
_ JQ _ _ _ _( Sje )_ k-eff 30-47; 30-41 2 6 '+ 3 06 156 160 1.0011 40-47; 34-47 - -
158 45 1.0003 35-41; 35-47 30-4 3 On 158 60 1.0003 26-41; 26-41 30-43 06 157 148 1.0010 18- l'i , 22-35 18-31 06 159 238 1.0003 18-35; 18-39 22-35 08 158 25 1.0017 14-39; 18-39 - -
159 260 1.0005 14-35; I8- 35 18-31 06 159 350 1.0011
? !-11; 26-23 26-27 08 160 30 1.0018 i'-M; I4-39 - -
160 175 1.0013 Average 1.0009 Standard Deviation 0.0006
- The corrected k-eff has the reactivity equivalent of the observed period suhtracted from the calculated k-eff.
O 4-6
s concentration was assumed since Reference 4-2 (page 2) indicates that st eatly-st at e ope rat ion was iield at eacli configurat ion for at least 48 h.nin, before the data wan serorded. Table 4.1-1 lists the results of the CORC k-effective calculation for each of the 29 data sets. The tabulated k-effectives are the direct code output values without adj us tme n t . The average k-effective valu" nhtained l by CORE was 0.9980 with a standard deviation of 0.0044 lioweve r , i there is an obvious trend of higher predicted k-effective values '
for higher core average exposures. This trend is consistent with that reported in Reference 4-4 for gadolinia-bearing first cycles.
s The first cycle of Quad Cities unit 1 was terminated well before
- full power reactivity depletion; thus the second cycle has char-l acteristics much like the end of a normal first cycle. The average T *% , M,*.
A .
k-ef fective value from CORE for core average exposures less than N(s 10,000 MWD /MTU was 0.9961 with a standard deviation of 0.0027. \s IN kg The corresponding values for core average exposures above 10,000 s MWD /MTU were 1.0041 and 0.0027 respectively.
T 12Ryg\ }
4.1.3 TIP Comparisons During Cycles 1 and 2, For 27 of the 29 data sets in Reference 4-2, detailed incore detector measurements were available. This data consisted of 24 axial values in each of 41 Traversing Incore Probe (TIP) thimble locations. The data was normalized such that for each detector used, there resulted an average reading of 100 when inserted in the common thimble location (32-33). The simulated TIP readings calculated by CORE for each of the 27 data sets were normalized such that the average of all 24 x 41 segments was the same as the
, averaged measured value. Since the TIP reading is closely related
,y"
.,e Tv j' 4-7 e
O TABLE 4.1-3 QUAD CITIES 1, CYCLES 1 AND 2, HOT OPERATING k-eff Core Rod Data Average Notches Fraction of Rated: Calculated Set Date GWD/MTM Inserted Power Flow k-eff 1 6/29/72 0.273 1936 0.870 0.861 0.9904 2 8/ 30/ 72 0.712 2032 0.897 1.016 0.9960 3 9/11/72 0.882 2056 0.892 0.966 0.9942 4 11/01/72 1.471 2192 0.875 0.996 0.9961 5 12/26/72 2.239 2056 0.976 1. 'C0 0.9951 6 3/08/73 3.190 2156 0.961 0.i"' O.9950 7 5/lb/73 3.837 2436 0.875 0.968 0.9946 8 6/0n/73 4.075 2316 0.924 0.967 0.9961 9 7/17/73 4.738 2290 0.947 0.948 0.9950 10 8/30/73 5.301 2254 0.931 0.928 0.9947 11 11/01/73 6.031 2104 0.802 0.750 0.9940 1 .' L2/il/73 6.558 2064 0.886 0.999 0.9978 13 12/29/73 6.807 1892 0.880 0.961 0.9995 14 2/13/74 7.397 1924 0.903 0.976 0.9975 li 3/05/74 7.660 1840 0.871 0.997 0.9981 16 3/26/74 7.980 1688 0.878 0.979 0.9984 ll* 7/26/74 7.303 1788 0.567 0.503 0.9909 18 8/li/74 7.532 1408 0.865 0.855 0.9963 19 9/12/74 7.964 1202 0.859 0.898 1.0021 20 10/23/74 8.424 1332 0.835 0.837 0.9942
.' l 11/18/74 8.790 1164 0.960 0.994 0.9977 22 12/11/74 9.142 956 0.996 0.987 0.9997 23 4/03/75 10.l74 748 0.981 0.992 1.0021 24 6/19/75 11.239 36 0.985 0.980 0.9991 25 8/08/75 11.936 338 0.858 1.002 1.0038 26 10/20/75 12.897 32 0.682 0.960 1.0055 27 11/13/75 13.199 0 0.682 0.960 1.0053 28 12/19/75 13.612 0 0.616 0.977 1.0064 29 12/31/75 13.742 0 0.592 0.968 1.0068 Average 0.9980 Standard Deviation 0.0044
- First data set in cycle 2 O
4-8
to the power in the surrounding nodes, comparisons of measured and simulated readings can be utilized to evaluate the ability of the CORE code to calculate operating power distributions. Table 4.1-4 summarizes the results of these comparisons. The percent difference (D ) between measured (M ) and calculated (C ) T1P readings was determined by:
Di = 200*(M. - C.)/(M. + Ci) (4-1) i i i and the standard deviation computed by Equation 4-2:
n _
I (D - D),'
I a= (4-2) n- I where D is the average D value and n is the number of values.
Table 4.1-4 presents the standard deviation of the difference between individual 6-inch axial segment (nodal) readings as well as the standard deviation of the dif ference between axially integrated tiimble values. The combined standard deviation for all 27 data sets is 11.17 and 5.40 percent for nodal and integrated values respectively.
The TIP thimbles in the Quad Cities reactor have half-core symmetry about a diagonal line; the core loading patterns are also symmetric about this line. For fifteen of the data sets, the control rod pattern maintained reflective symmetry about the diagonal line of thimble symmetry, allowing comparison of measured TIP values from symmetric locations. From Table 4.1-4, the combined standard deviation of the differences between symmetric measured readings was 11.24 and 7.53 percent fo;; nodal and integrated values respectively. Thus the standard deviation of dif ferences 4-9
TABLE 4.1-4 O
NI'AD CITIES 1, CYCLES 1 AND 2, TIP DATA COMPARtSONS Core Measured - Calculated Symmetric Measurements luta Average Standard Deviation (%) Standard Deviation (%)
5 rt Date CWD/MTM Nodal Integrated Nodal Integrated 1 6/29/72 0.273 10.28 5.21 10.73 8.62 2 8/ 30/72 0.712 8.22 5.49 12.04 8.62 1 9/11/72 0.882 8.50 5.60 12.44 8.99 a 11/u1/72 1.471 8.60 5.73 - -
5 12/26/72 2.239 8.38 5.75 - -
s 3/08/73 3.190 8.95 6.02 12.50 8.75 7 5/16/73 3.836 9.55 6.04 - -
H ti/06/73 4.057 10.48 6.25 - -
9 //17/73 4.738 9.44 5.82 - -
10 8/30/73 5.301 10.82 5.85 - -
11 11/01/73 6.031 12.59 5.21 - -
12 12/11/73 6.558 10.62 5.62 12.16 8.37 13 12/29/73 6.807 10.70 5.44 13.05 8.50 14 2/13/74 7.397 10.43 5.46 - -
15 3/05/74 7.660 11.14 5.41 10.89 8.20 16 1/ ? ti/ 74 7.980 - - - -
17* 7 / .'6 / 7 4 7.303 13.37 4.38 11.25 5.91 18 H/15/74 7.532 13.49 5.11 12.33 7.49 19 9/12/74 7.964 11.66 4.78 10.88 6.28 20 10/23/74 8.424 ll.84 5.21 - -
21 11/18'74 8.790 11.03 5.04 - -
22 12/11/74 9.142 10.85 5.22 - -
23 4/03/75 10.174 11.30 5.76 10.11 6.34 24 6/19/75 11.239 12.78 4.79 - -
25 8/08/75 11.936 12.17 5.60 - -
26 10/20/75 12.897 - - - -
27 11/13/75 13.199 11./4 4.76 9.74 6.37 28 12/19/75 13.612 14.12 4.62 9.18 5.74 29 12/ 31/75 13.742 14.95 5.11 9.23 5.86 Combined 11.17 5.40 11.24 7.53
- First dat a net in cycle 2 4-10
between measured and calculated TIP readings was approximately the same as that for the symmetric measurements. For many of the data sets, the measured versus calculated standard deviation was less t:ian the symmetric measurements standard deviat lon. The only non-symmetrical effect in the calculated values was due to a slightly non-symmetric exposure accumulation occurring during depletion with rod patterns with rotational symmetry only. Thus the two s/mmetric calculated values were always very nearly the same and were otten bounded by the two symmetric measured readings.
The maximum values of nodal and integrated TIP readings from the CJRE simulation and measured data were also compared. On the a ve ra ge , CORE underpredicted the maximum measured nodal TIP reading for the 27 data sets by 4.04 percent with a standard deviation of 4.26 percent. The maximum integrated thimble readings from CORE averaged 3.55 percent lower than the maximit.a measured value, with a standard deviation of 4.00 percent.
In Figures 4.1-1 through 4.1-15, the average TIP reading versus axial position is plotted for each of the data sets in cycle 1. Figures 4.1-16 through 4.1-2/ present similar plots for each of the data sets in cycle 2. Comparison of calculated and measured average TIP readings veraus axial position yields a good indication of CORE's ability to calcu17tc gross axial power distributions. The agreement between the calculated and measured axial TIP distributions is excellent for both cycles. A slight deterioration in agreement occurred near end-of-cycle 1, and was worse 1: "ycle 2.
4-11
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DC1 C'T1: 800 MWD /T (9/11/72) DATA SETn03 y 150 -
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2 4 6 8 10 12 14 16 18 20 22 24 AXIAL NODE Figure 4.1-3 O O O
QC1 CY1: 1334 MWD /T (11/1/72) DATA SETnO4 y 150 7 N MEASURED
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QC1 CY1: 289L1 MWD /T (3/8/73) DATA SETn06 u_I 150 -
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OC1 CY1: 3480 MWD /T (5/16/73) DATA SETn07 m
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QC1 CYl: 3696 MWD /T (6/6/73) DATA SETn08 y 150 -
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QC1 CY1: 4297 MWD /i s //16/73) DATA SET =09 LLI 150 -
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DC1 CY1: 4809 MWD /T (8/30/73) DATA SETn10 bJ 150 -
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QC1 CY1: 5471 MWD /T (11/1/73) DATA SETull y 150 MEASUBED
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2 4 6 8 10 12 14 16 18 20 22 24 AXIRL NODE Figure 4.1-11 O O O
QC1 CY1: 59L19 MWD /T (12/11/73) DATA SETn12 y 150
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OC1 CY2 7641 MWD /T (11/23/74) DATASETn20 y 150 -
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QC1 CY2 8293 MWD /T (12/11/7L1) DATASETn22 y 150 -
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2 4 6 8 10 12 14 16 18 20 22 24 AXIAL NODE Figure -. 1-23 O O O
QC1 CY2 10827 MWD /T (8/8/75) DATASETn25 uJ 150 _
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2 4 6 8 10 12 14 16 18 20 22 24 AXIAL NODE Figure 4.1-27 O O O
4.1.4 End-of-Cycle Gamma Scan Comparisons The most precise information available for verification of power distributions predicted by CORE results from fuel assembly gamma scans. The gamma scan measures the relative La-140 activity distribution. La-140 is produced by decay of the fission product Ba-140 which has a half-life of approximately 13 days. Thus the La-140 distribution is proportional to the power distribution during the 40 to 60 days of operation prior to the scan. Since the power distribution may change during this time period, the CORE code maintains a calculated Ba-140 distribution by solving the dif ferential equation for Ba-140 production and decay for each node in the core.
The gamma scan measurement data from Reference 4-4 for Quad Cities unit 1 at end-of-cycle 1 was utilized to verify CORE's capability to predict axial peaking factors and axial power shapes.
Table 4.1-5 compares the calculated and measured axial peaking factors in each of 31 scanned bundles. For all 31 bundles CORE predicted an axial peaking factor which averaged 4.72 percent higher than the measured values; the standard deviation of the differences was 2.64 percent. Fourteen of the scanned bundles were adjacent to partially inserted control rods while the remain-der were uncontrolled. CORE overpredicted the uncontrolled bundle peaking factors by an average of 3.68 percent compared to 5.98 percent overprediction for partially controlled bundles. The standard deviation of the error between calculation and measurement was essentially the same for controlled and uncontrolled bundles.
4-39
TABLE 4.1-5 MEASURED VS COMPUTED ASSEh3LY AXIAL La-140 ACTIVITY PEAK-TO-AVERAGE VALUES FROM QUAD CITIES 1 - 1974 GAMMA SCAN Rod Location Gamma CORE Percent Notch XX - YY Scan Code Difference 48 39 - 58 1.2712 1.3210 -3.84 48 41 - 58 1.2125 1.3035 -7.23 48 41 - 56 1.2236 1.2594 -2.89 48 17 - 48 1.2870 1.3288 -3.20 48 55 - 42 1.1854 1.2579 -5.93 48 57 - 42 1.1913 1.2992 -8.67 48 57 - 40 1.2452 1.3154 -5.49 48 07 - 34 1.1763 1.2096 -2.79 48 09 - 32 1.1476 1.1944 -4.00 48 07 - 26 1.1696 1.1958 -2.21 48 09 - 24 1.1854 1.2338 -3.96 48 31 - 26 1.3543 1.3765 -1.63 48 47 - 18 1.2498 1.3135 -4.97 48 23 - 10 1.1784 1.2013 -1.93 48 25 - 08 1.2390 1.2286 0.84 48 31 - 10 1.1718 1.1935 -1.83 48 33 - 08 1.2212 1.2553 -2.75 38 39 - 56 1.2815 1.3353 -4.11 14 17 - 50 1.6087 1.7427 -7.99 38 15 - 48 1.2800 1.3285 -3.72 38 55 - 40 1.2688 1.3316 -4.83 08 09 - 34 1.4180 1.5151 -6.62 28 07 - 32 1.3225 1.4142 -6.70 08 09 - 26 1.3660 1.5130 -10.21 38 07 - 24 1.2313 1.2803 -3.91 14 49 - 18 1.6017 1.7366 -8.08 38 47 - 16 1.2829 1.3161 -2.55 08 25 - 10 1.3579 1.4936 -9.52 38 23 - 08 1.2512 1.2814 -2.38 08 33 - 10 1.3851 1.5044 -8.26 28 31 - 0 8 1.3693 1.4366 -4.80 Av rage i r nce = -4.72 FOR ALL 31 BUNDLES:
Standard Deviation = 2.64 Average DiCierence = -3.68 17 UNCONTRO' LED liUNDLES:
Standard l'eviation = 2.28 14 CONI Rol.l.1:D liUNDLLS: ^ # " E'" " *"" '
Standard Deviation = 2.56 O
4-40
The quoted reproducability of the gamma scan measurements was 2 percent (Reference 4-4).
Figure 4.1-28 displays the measured and calculated 31 bundle averaged axial La-140 distributions from tne Quad Cities unit 1 1974 gamma scan. The gross axial power shapes are in excellent agreement with the CORE code overestimating the axial peaking factor by 3.6 percent. Since many of the bundles were adjacent to partially inserted control rods during operation prior to the gamma scan, the measured axial distributions varied from bundle to bundle depending upon the nearest control rod position. Figures 4.1-29 and 4.1-30 show typical uncontrolled and partially controlled bundle axial La-140 distributions respectively, taken from Reference 4-4. The overall agreement between measurement and calculation is good for both bundles; however, there is a slight overprediction of the nodal powers immediately above the partially inserted control rod.
Following cycle 2 operation of Quad Cities unit 1, a large body of gamma scan data was collected. The 1976 Quad Cities gamma scan collected detailed data on the gross power distribution in one octant of the core and in additional bundles to test the degree of asymmetry. The 1976 Quad Cities gamma scan data presented in Reference 4-5 was utilized to verify several aspects of CORE's power distribution predictions. In Reference 4-5, the accuracy of the gamma scan data was given as approximately 3 percent considering measurement uncertainty and biases.
Table 4.1-6 presents the comparison of measured and calculated 4-41
QC1 197tl GAMMA SCAN 31 ASSEMBLY AVERAGE LA-1L10 2.0
>- ~
F--- -
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- 1.5 -
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0.0 6 8 10 12 14 16 18 20 22 24 2 14 AXIAL NODE Figure 4.1-28
- O e
QC1 1974 GAMMA SCAN ASSEMBLY 23-10 LA-140 2.0
~
~ HEASURED
~ 1.5 -
--- CORE F- ~
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I I I I I ! I I I I I I I I I I I I I I I I I 0.0 2 L1 6 8 10 12 ill 16 18 20 22 2t1 AXIAL NODE Figure 4.1-29: Typical Uncontrolled Assembly
QC1 1974 GAMMA SCAN ASSEMBLY 55-40 LA-140 2.0
~
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1 I I I I I i i I i I i l i I I I I I I I I 0.0 2 4 6 8 10 12 14 16 18 20 22 24 AXIAL NODE ri.gure 4.1-30: Typical Partially Controlled Assembly O O O
TABLE 4.1-6 MEASURED VS COMPUTED ASSEMBLY AXIAL La-140 ACTIVITY l'EAK 'lo-AVERAGE VAI,UES FROM QUAD CITIES I - 1976 GAMMA SCAN Location Gamma CORE Percent Location Gamma CORE Percent XX - YY Sean Code Diff. XX - YY Scan Code Diff.
33 - 44 1.1923 1.2181 -2.14 23 - 14 1.1946 1.2183 -1.97 31 - 32 1.1379 1.1642 -2.29 37 - 48 1.1852 1.2208 -2.96 31 - 30 1.1353 1.1639 -2.48 47 - 38 .1473 1.2126 -5.54 29 - 32 1.1335 1.1636 -2.62 09 - 48 1.3266 1.3401 -1.01 29 - 30 1.1302 1.1628 -2.84 05 - 36 1.2375 1.3176 -2.31 05 - 48 1.3518 1.3265 1.89 07 - 34 1.2445 1.2803 -2.83 31 - 34 1.1937 1.2049 -0.93 09 - 34 1.2285 1.2612 -2.63 33 - 32 1.1842 1.2096 -2.12 09 - 32 1.2341 1.2734 -3.13 07 - 48 1.3490 1.3748 -1.90 11 - 50 1.2933 1.3289 -2.71 05 - 46 1.3495 1.3167 2.46 13 - 32 1.2233 1.2487 -2.05 07 - 46 1.3333 1.3532 -1.48 27 - 34 1.1866 1.2090 -1.87 01 - 32 1.3311 1.3253 0.44 03 - 36 1.3468 1.3680 -1.56 03 - 32 1.3116 1.3580 -3.48 13 - 40 1.2187 1.2105 0.67 11 - 32 1.2263 1.2648 -3.09 23 - 38 1.1982 1.2244 -2.16 05 - 32 1.2785 1.3087 -2.33 03 - 40 1.3924 1.3893 0.22 47 - 06 1.3119 1.3031 0.68 15 - 46 1.1872 1.2276 -3.34 27 - 32 1.1802 1.2033 -1.94 21 - 32 1.1864 1.1933 -0.57 07 - 32 1.2420 1.2803 -3.03 09 - 46 1.3086 1.3149 -0.49 15 - 32 1.1990 1.2174 -1.52 15 - 38 1.2181 1.2175 0.05 19 - 32 1.1563 1.1846 -2.42 19 - 36 1.2103 1.2052 0.42 49 - 10 1.2911 1.3554 -4.86 05 - 38 1.3263 1.3308 -0.34 01 - 40 1.4128 1.3510 4.47 19 - 42 1.2039 1.2417 -3.09 13 - 36 1.1651 1.1948 -2.52 25 - 32 1.1932 1.2137 -1.70 23 - 34 1.1871 1.2067 -1.64 11 - 44 1.2169 1.2411 -1.97 17 - 42 1.2089 1.2282 -1.59 15 - 34 1.2006 1.2193 -1.54 09 - 40 1.2008 1.2141 -1.10 19 - 38 1.2237 1.2344 -0.87 07 - 42 1.3108 1.3087 0.16 13 - 46 1.2225 1.2416 -1.55 09 - 42 1.2586 1.2552 0.27 17 - 34 1.1857 1.1997 -1.18 07 - 40 1.2714 1.2692 0.18 09 - 36 1.1944 1.2176 -1.92 23 - 32 1.1975 1.2093 -0.98 17 - 36 1.1589 1.1895 -2.61 13 - 48 1.2107 1.2237 -1.07 13 - 44 1.1660 1.1977 -2.69 17 - 44 1.1664 1.2097 -3.65 21 - 36 1.1844 1.2038 -1.63 21 - 40 1.1861 1.2163 -2.51 17 - 32 1.1777 1.1915 -1.16 09 - 50 1.3328 1.3669 -2.52 09 - 38 1.2548 1.2318 1.85 41 - 18 1.2010 1.2293 -2.33 11 - 40 1.2054 1.2148 -0.78 17 - 40 1.2028 1.2321 -2.41 09 - 18 1.2007 1.2816 -6.52 15 - 42 1.1894 1.2063 -1.41 17 - 10 1.2137 1.2554 -3.38 15 - 40 1.2173 1.2303 -1.05 03 - 42 1.3827 1.3340 3.59 11 - 36 1.2028 1.2302 -2.25 01 - 34 1.3357 1.3295 0.47 15 - 36 1.1984 1.2134 -1.25 13 - 38 1.2103 1.2106 -0.02 13 - 34 1.2144 1.2364 -1.80 37 - 14 1.1634 1.2163 -4.45 25 - 36 1.1673 1.1863 -1.61 23 - 48 1.1941 1.2152 -1.75 25 - 34 1.1892 1.2059 -1.40 47 - 24 1.2168 1.2113 0.45 09 - 52 1.3590 1.3225 2.72 13 - 24 1.1558 1.2110 -4.67 05 - 44 1.3582 1.3061 3.92 FOR AI L 89 ASSEMBLIES: Average Difference = -1.47 Standard Deviation = 1.89 4-45
peak-to-average La-140 activity in each of the 89 scanned bundles.
The a g reemen t between measurement and calculation is excellent with the calculated peaking factor averaging 5 percent higher than raeasured with a standard deviation of 1.9 percent. A measure of the agreement on maximum nodal power was obtained by comparing the relative La-140 activity for the 25 highest measured and calculated values as shown in Table 4.1-7. For the 25 highest powered nodes, the CORE value averaged 1.4 percent higher than the gamma scan, with a standard deviation of 1.3 percent.
Ehe 1976 Quad Cities unit 1 gamma scan provided sufficient data to allow an excellent comparison of the calculated and measured r.idial distribution of bundle powers. Figure 4.1-31 shows the comparison of the relative radial I.a-140 activities obtained by averaging the nodal values in each assembly for the measured elevations. The standard deviation of the differences between measured and calculated radial powers was 3.82 percent.
The CORE code slightly underestimated (5.7 percent) the power in the peripheral fuel bundles, but no gross distortion in the radial power shape is evident. The maximum measured radial activity of 1.352 (at coordinate 29-30) occurred in a mixed-oxide bundle and was underestimated by 3.46 percent by CORE. CORE overestimated the maximum radial value, regardless of location, by 1.25 percent.
Table 4.1-8 presents the standard deviation of the differences between the 89 calculated and measured nodal values for each of the 12 axial planes with any axial bias removed. The average of the planar standard deviations is 4.85 percent and the maximum is 7.96 percent. A slight tendency for larger radial error exists 4-46
TABLE 4.1-7 COMPARISON OF 25 HIGliEST NODAL La-140 ACTIVITIES
- QUAD CITIES 1 - 1976 GAMMA SCAN Gamma CORE Percent Scan Code Difference 1.584 1.655 -4.423 1.567 1.643 -4.729 1.558 1.632 ~4.654 1.558 1.582 -1.519 1.547 1.564 -1.106 1.546 1.561 -0.995 1.531 1.560 -1.866 1.528 1.559 -1.994 1.528 1.555 -1.775 1.524 1.536 -0.794 1.523 1.529 -0.346 1.523 1.526 -0.187 1.519 1.522 -0.198 1.519 1.521 -0.157 1.511 1.518 -0.448 1.511 1.518 -0.462 1.511 1.518 -0.438 1.510 1.517 -0.426 1.505 1.517 -0.811 1.501 1.515 -0.897 1.501 1.514 -0.911 1.495 1.513 -1.237 1.485 1.513 -1.879 1.484 1.508 -1.569 1.484 1.507 -1.589 Average Dif ference -1.416 Standard Deviation 1.331
- The 1,068 nodal activities (12 planes where all 89 assemblies were measured) were normalized to an average of 1.0 4-47
(NOTE: SEE CONTINUATION FOR ADDITIONAL VALUES) 0 479 52 0.437 9.27 0.634 ! 0.789 i FOR ALL 89 MEASURED ASSEMBLIES:
50 0.685 f 0.825 j STANDARD DEVIATION OF DIFFERENCE = 3.82%
-7.83 ! -4.56 1 0.450 0.603 0.768 l l 1.223 48 0.389 0.658 0.818 I i 1.191 14.45 -8.78 ; 6.35 ' l 2.68 0.491 0.851 l 1.057 1.101 46 0.489 0.702 0.754 l 0.898 l ,
1.098 1.128 0.44 -7.02 -5.40 l ! -3.87 -2.43 0.584 i 1.041 j 1.344 1.326 -GAMMA SCAN 44 0.563 1.30" 1.369 +- CORE CODE l 1.068 3.62 1 -2.52 4 -3.18 +- % DIFFERENCE 0.484 0.863 0.988 . 1.137 1.166 1.138 42 0.437 0.885 1.019 i 1.151 1.169 1.140 y 10.19 -2.49 -3.08 ! -1.21 -0.23 -0.19
$ ! 0.389 0.596 0.926 1.265 1.115 I 1.102 1.106 ' 1.189 1.285 40 0.364 0.637 0.938 1.199 1.094 1.106 1.129 1.218 1.286 6.72 -6.57 ! -1.29 5.37 1.87 -0.32 -1.98 -2.42 -0.11 0.840 1.078 fi 1.092 f 1.108 '
1.103 1.068 38 0.854 1.075 j l 1.109 1.100 ' 1.094 1.066
-1.56 0.30 l l - 1.51 0.76 0.80 0.26 0.708 0.874 1.124 1.321 1.104 1.085 1.273 1.326 l 1.117 l 1.337 36 0.741 0.889 1.238 j 1.116 ' 1.278 1.113 1.292 1.098 1.077 1.246
-4.54 -1.68 6.93 1 0.07 4.57 0 99 2.27 0.56 0.74 2.13 0.500 0.981 1.057 1.094 1.110 1 1.098 i 1.071 1.078 1.082 1.094 1.081 34 0.493 0.991 1.059 1.0881 l 1.082 1.090 { 1.054 1.068 1.072 j 1.091 1.071 1.53 -1.00 -0.21 - 0.59 ! 2.57 0.74 i 1.56 0.96 0.84 - 0.25 0.95 0.510 0.732 0 865 0.942 1.013 l 1.051 i 1.057 I 1.083 1.088 j 1.068 1.047 1.046 1.071 1.110 i 1.349 l 1.339 1.080 32 0.501 0.765 0.886 0.971 1.025 1.047 l 1.058 ' 1.074 1.060 1.050 1.033 1.031 1.054 1.094 1.306 1.306 1.092 1.75 -4.29 -2.39 -3.05 -1.12 0.43 -0.09 0.84 2.58 1.70 1.38 1.42 1.65 1.46 ' 3.24 2.54 -1.17
, 1.352 1.331 30 9 1.306 1.306 t 1 3.42 1.89 Y
X- 01 03 05 07 09 11 13 15 17 19 21 23 25 27 29 31 33 FIGURE 4.1-31: ASSEMBLY AVERAGE RADIAL LA-140 ACTIVITY DISTRIBUTION COMPARISON FROM QUAD CITIES 1 1976 GAMMA SCAN O O O
BUNDLE LOCATION GAMMA CORE PERCENT LABEL XX - YY SCAN CODE DIFFERENCE CX 622 47 - 06 0.404 0.391 3.44 CX 711 49 - 10 0.619 0.685 -10.17 CX 445 41 - 18 1.145 1.171 -2.24 CX 359 37 - 14 1.087 1.131 -3.96 CX 398 23 - 48 1.076 1.128 -4.72 CX 401 47 - 24 1.103 1.113 -0.92 CX 318 13 - 24 1.123 1.108 1.33 CX 384 23 - 14 1.116 1.129 -1.17 CX 412 37 - 48 1.125 1.130 -0.42 CX 414 47 - 38 1.135 1.112 2.03 CX 096 09 - 18 0.974 0.967 0.73 CX 124 17 - 10 0.963 0.988 -2.54 FIGURE 4.1-31: Assembly Average Radial La-140 Activity Distribution Comparison from Quad Cities 1 - 1976 Gamma Scan (continued) 4-49
O TABLE 4.1-8 NODAL STANDARD DEVI ATIONS FOR TIIE 12 AXIAL PLANES FROM QUAD CITIES 1 - 1976 GAMMA SCAN Plane % Planar
_(Bo t t o m) Standard Deviatlon*
1 ....... . ................... 5.61 3 ........... ................ 4.04 5 ........ ................. 3.41 7 ... ...... .................. 3.79 9 ..... ....................... 4.09 11 ..... ................... ... 4.19 13 ......... ................... 4.15 15 ..... ............ .......... 4.51 17 ............................ 4.60 19 . ........ ... .............. 5.30 2l .......... .... ............ 6.59 23 .. .. ..... ... ............. 7.96 (Top)
- For each axial plane the 89 neasured (M) and calculated (C) nodal values were normalized to an average of 1.0 and the dif ference at each node calculated by:
D. =
200 * (M - C.)/(M. + C )
1 i t i i The standard deviation of the differences was calculated using the standard n:et hod:
I (D 1- D) 2 a=I i=1 _
t n-1
~~
where D is the average of the D values and n is equal to 89 0
4-50
near the top and bottom boundaries, but overall the planar results are consistent with the 3.82 percent standard deviation for bundle radial powers.
Figure 4.1-32 shows the comparison of the 89 bundle average axial La-140 activity for the Quad Cities 1976 gamma scan. The CORE code underpredicts the power at the ends of the core and overpredicts the power .n the center. The overall agreement is fair and is consistent with the axial TIP comparisons near end-of-cycle 2 presented in Section 4.1.3. The Quad Cities core was operated with all control rods withdrawn for a significant time prior to the 1976 gamma scan; therefore, the individual assembly axial comparisons are similar to the 89 assembly average, as shown in Figures 4.1-33 through 4.1-36 for typical bundles.
4.2 BROWNS FERRY UNITS 1 AND 2 C0FiPARISONS The Browns Ferry units 1 and 2 initial cores each consisted of 168 fuel bundles with an average enrichment of 1.10 weight percent and 596 bundles with an average enrichment of 2.50 weight percent. All of the bundles were of standard 7 x 7 design. The higher enrichment bundles contained gadolinia in some of the fuel rods for power shaping and supplemental reactivity control. Both units were refueled with 8 x 8 design fuel with an average enrich-ment of 2.74 weight percent (168 reload bundles for unit 1 and 132 fo r un i t 2). Details of the core designs are niven in References 4-6, 4-7, and 4-8.
The measured data used for comparisons to CORE was obtained f rom data collected by plant personnel for records and contractual 4-51
L.-
OC1 1976 GAMMA SCAN 89 ASSEMBLY AVERAGE LA-140 2.0
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DC1 1976 GAMMA SCAN ASSEMBLY 29-30 LA-140 2.0 t--- -
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QC1 1976 GAMMA SCAN ASSEMBLY 13-36 LA-140 2.0 HE9SURED
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purposes. The data consisted of observed critical configurations (rod pattern, core thermal power level, total core flow rate, reac*or pressure, core inlet temperature, and core average exposure) ami power distribution information. The power distribution informa-tion was obtained f rom the plant process computer. The CORE cc de calculations for these comparisons were generated as part of normal core follow work performed by TVA. The lattice physics data used by CORE was generated with the LATTICE program (Reference 4-3). A full core model consisting of 30 x 30 x 24 nodes (24 equal length axial segments in each fuel bundle) was employed in the core follow calculations. The core average exposure accumula-tion between operating configurations was determined from the process computer data and the average increase allocated to individual nodes ccording to the power dist ribution computed by CORE at the beginning of the interval. In a s imi l ia r manner, the water density and control histories were updated for the interval. Generally, the core average exposure increment between operating states was between 250 and 500 MWD /KrU.
4.2.1 Zero Power, Xenon-Frg Criticals As a normal part of plant operations, the critical coafiguration of the reactor core is recorded fo each startup. The critical configurations occurring after sufficiently long shutdowns to allow the xenon-135 concentration to reach negligible levels are shown in Table 4.2-1 for cycles 1 and 2 of Browns Ferry units 1 and 2. These criticals cover the range of core average exposures f rom zero to approximately 14,200 MWD /MTU and coolant temperatures ranging from 10l*F to 400*F. The rod patterns employed include 4-57
TABLE 4.2-1 ZERO POWER XENOS-FREE CRITICALS FCE EROWNS FERRY UNITS 1 AND 2 Core Rod Pattern Information Coolant Reactor Unit Cycle Average Rods Rod Moving Temp. Pe riod Corrected
- No. No. Date GWD/MTU Seq. Out Co-or Notch ( F) _ (Sec) k-eff 1 1 9/25/73 0.0 Test 11 38-39 08 101 125 0.99/3 1 1 9/25/73 0.0 A 52 46-35 20 112 140 0.9965 1 1 9/26/73 0.0 A , 56 22-11 22 140 141 0.9962 1 1 3/08/74 0.96; A 72 38-19 14 330 78 0.9907 1 1 4/12/74 1.313 A 66 30-03 42 182 105 0.9953
, 1 1 5/22/74 1.617 A 56 38-11 18 170 89 0.9947 4 1 1 6/29/74 1.906 A 49 14-35 22 140 142 0.9943 m 1 10/04/74 3.519 A 44 30-35 20 200 1 147 0.9911 1 1 11/24/74 4.354 Test 5 30-23 10 132 76 0.9999 1 1 11/24/74 4.354 A 44 30-35 14 132 137 0.9996 1 1 2/09/75 5. 759 A 32 10-23 30 215 76 0.9976 1 1 3/01/75 6.042 A 29 42-23 10 195 180 0.9979 1 1 9/14/76 6.345 A 29 42-23 12 185 112 0.9984 1 1 1/09/77 7.601 B 27 38-15 08 210 152 0.9942 1 2 1/13/78 9.730 B 24 42-31 12 150 79 0.9972 1 2 9/20/78 14.198 A 44 30-35 04 242 80 0.9954 2 1 7/20/74 0.0 Test 10 22-39 16 90 138 0.9977 2 1 8/03/74 0.0 A 54 46-19 16 124 125 0.9960 2 1 7/21/74 0.0 A 52 46-35 10 110 350 0.9968 2 1 8/27/76 2.486 A 48 34 -3 9 24 146 200 0.9958 2 1 4/21/77 5.937 A 45 26-27 16 410 85 0.9924 2 2 6/26/78 9.176 A 24 30-31 10 160 123 0.9971 Average 0.9960 Standard Deviation 0.0024
- The corrected k-ef f has the reactivity equivalent of the observed period subtracted from the calculated k-eff.
O O O
both normal (distributed) withdrawal sequences (A and B) as well as a special test withdrawal sequence which successively removes rods in the center of the core in a checkerboard pattern. The test sequence was used for shutdown margin determination during startup testing.
The effective multiplication factor obtained by CORE for each critical is also shown in Table 4.2-1. The CORE k-effective has been corrected by subtracting the reactivity equivalent of the observed reactor periad from the code output values. No other co rrec t ions, normalizations or biases were employed. The average k-effective obtained by CORE for the 22 critical configurations was 0.9960 with a standard deviation of 0.0024. There are no apparent systematic trends in predicted k-effective versus e .posure or control rod pattern. In particular, there is not a significant difference ir. the calculated k-effective for in-sequene; and the more localized test sequence criticals at the same core average exposure.
4.2.2 Hot Operating Reactivity Table 4.2-2 lists the critical configurations with equilibriun xenon and high reactor power for which comparisons were made for Browns Ferry unit 1 during cycles 1 and 2. The average k-effective calculated by CORE for the 20 configurations in Table 4.2-2 was 1.0041 with a standard deviation of 0.0040. However, there is a definite trend in the predicted k-effective versus exposure. The observed trend is similar to that observed in Reference 4-4 for first cycle gadolinia bearing cores. The tendency to predict 4-59
O
.a0LE 4.2-2 Bi10WNS FERRY 1, CYCLES 1 AND 2, liOT OPERATING k-ef f Care Fraction Average of Rated Calculated Date Cvele GWD/MTU Power k-eff 2/02/74 1 0.639 0.639 0.9966 6/21/74 1 1.852 0.982 1.0024 7/18/74 1 2.359 0.989 1.0010 10/29/74 1 3.942 0.972 0.9987 11/02/74 1 4.026 0.976 1.0006 1/15/75 1 5.389 0.931 0.9981 2/18/75 1 5.908 0.943 0.9987 3/22/75 1 6.346 0.985 1.0010 1/19/77 1 7.698 0.981 1.0068 2/22/77 1 8.296 0.957 1.0064 4/21/77 1 9.416 0.947 1.0083 6/13/77 1 10.370 0.942 1.0085 7/20/77 1 11.021 0.893 L.0091 8/09/77 1 11.378 0.819 1.0086 9/13/77 1 11.994 0.598 1.0084 4/14/78 2 11.281 0.967 1.0050 4/2h/78 2 11.521 0.978 1.0055 5/26/78 2 12.203 0.947 1.0059 6/29/78 2 12.798 0.966 1.0059 8/08/78 2 13.591 0.894 1.0056 Average 1.0041 Standard Deviation 0.0040 0
4-60
higher k-effectives near the end of the first cycle may have been accentuated in the Browns Ferry unit 1 comparisons due to the presence of boiling in the bypass region. All of the cycle 1 data in Table 4.2-2 for core average exposures greater than 7500 MWD /MrU was collected af ter plugging of the bypass flow holes in the core plare to eliminate instrument tube vibrations. Alternate flow paths were drilled into the fuel bundle lower tie plates af ter cycle 1 and significant bypass boiling did not occur in cycle 2.
For core average exposures less than 7500 MWD /MTU, the average calculated k-effective was 0.9996 with a standard deviation of 0.0019. For core average exposures greater than 7500 MWD /MTU, the calculated values were 1.0070 and 0.0015 respectively.
4.2.3 Process Computer Comparisons Table 4.2-3 contains a comparison of axial and total peaking factors f rom the Browns Ferry unit 1 process computer during cycles 1 and 2 to the peaking factors calculated by the CORE code.
For the 16 cases in Table 4.2-3, the core average axial peak-to-average power was overpredicted by CORE by 0.5 percent with a standard deviation of 4.3 percent. The total peaking factor (radial x axial x local) was overpredicted by 1.0 percent with a 5.6 percent standard deviation.
Table 4.2-4 summarizes the results obtained by comparing the relative power in individual nodes and fuel assemblies predicted by CORE to thei r values from the process computer. For the seven configurations considered, the root-mean-square (RMS) difference in process computer and CORE calculated relative powers was 7.0 percent for assemblies and 11.4 percent for nodes.
4-61
O TABLE 4.2-3 BROWNS FERR1 1, CYCLES 1 AND 2, COMPARISON OF CORE CODE AND PROCESS COMPUTER PEAKING FACTORS Core Core Avera3;e Axial Average Peak-to-Average Powe r Total Peaking Factor Date CWD/HrU P.C. CORE Z Diff P.C. CORE % Diff 2/02/74 0.639 1.27 L.27 0.0 2.39 2.44 -2.07 6/21/74 l.852 1.30 1.24 4.72 2.47 2.29 7.56 7/18/74 2.359 1.34 1.29 3.80 2.44 2.25 8.10 10/29/74 3.942 1.37 1.34 2.22. 2.61 2.53 3.11 11/02/74 4.026 1.36 1.31 3.75 2.58 2.43 5.99 1/15/75 5.389 1.40 1.48 -5.56 2.71 2.78 -2.55 2/18/75 5.908 1.32 1.43 -8.0 2.55 2.67 -4.60 3/22/75 6.346 1.27 1.35 -6.11 2.39 2.52 -5.30 2/22/77 8.296 1.27 1.28 -0.78 2.57 2.49 3.16 4/21/77 9.416 1.34 1.38 -2.94 2.52 2.70 -6.90 7/20/77 11.021 1.29 1.28 0.78 2.17 2.13 1.86 8/09/77 11.378 1.32 1.29 2.30 - - -
4/14/78 11.281 1.29 1.43 -10.30 2.29 2.52 -9.56 5/26/78 12.203 1.24 1.29 -3.95 2.15 2.29 -6.31 6/29/78 12.798 1.15 1.22 -5.91 2.02 2.11 -4.36 8/08/78 13.591 1.15 1.23 -6.72 2.05 2.12 ~3.36 Average -0.49 Average -L.02 Standard Deviation 4.27 Standard Deviation 5.53 The percent difference is calculated as:
% Diff = 200*(P.C. - CORE)/(P.C. + CORE)
O 4-62
TABLE w.2-4 BROWNS FERRY 1, CYCLES 1 AND 2, COMPARISON Ok CORE CODE AND PROCESS COMPUTER POWER DISTRIBUTIONS Core RMS Difference in Average Relative Powers Date Cycle GWD/HTU Assembly Nodal 7/18/74 1 2.359 8.43 11.50 11/02/74 1 4.026 6.52 11.54 1/19/77 1 7.698 5.75 8.37 6/13/77 1 10.370 5.45 9.87 8/09/77 1 11.378 6.45 10.42 4/26/78 2 11.521 7.37 13.73 6/29/78 2 12.7oo 8.17 13.50 Combined 6.96 11.42 The RMS difference between the process computer (PC) and core code (CORE) relative power distributions was calculated as:
D =
100*(PCf - CORE ) (percent) n RMS =l 1" (I D) i=1 where n is 764 for assembly comparisons and 18,336 for nodal comparisons.
4-63
A comparison of the radial peaking factors (maxir>un bundle relative powers) as determined by CORE and the Browns Ferry unit 1 process computer is shown in Table 4.2-5. The radial peaking f actors predicted by CORE during cycles 1 and 2 averaged 2.8 percent higher than the process computer values; the standard deviation of the differences was 3.2 percent. There is a slight tendency for CORE to underpredict the radial peaking factor early in the cycles and overpredict the values near the end of cycles relative to the process computer.
Figures 4.2-1 through 4.2-7 present comparisons of the core average relative power versus axial node for CORE and the process computer for several points in cycles 1 and 2 of Browns Ferry unit 1. The overall agreement between the axial distributions is good but CORE lightly underestimated the power in the bottom half of the core early in cycle 1. Iscar the end of cycle 1, CORE siightly overestimated the power in the bottom half of the core and this overestimation remained into cycle 2.
4.3 BRO'CS FERRY UNIT 3 COMPARISONS The Browns Ferry unit 3 initial core consisted of 764 fuel bundles of 8 x 8 design (one water rod and 146 inch active fuel length) with a bundle average enrichment of 2.19 weight percent.
Two bundle types with different gadolinia content were employed.
Details of the initial core design are given in Reference 4-6.
~i he reload bundles were of 8 x 8 design (2 water rods and 150 inch active fuel length) with a bundle average enrichment of 2.65 weight percent. The cycle 2 core design is described in Reierence 4-9.
O 4-64
TABLE 4.2-5 15ROWNS FERRY 1, CYCLF.S 1 AND 2, COMl'ARISONS OF CORE CODE AND PROCESS COMPUTER RAD!AL PEAKING FACTORS Core Average Maximum Bundle Power Percent Date Cycle GWD/MTU CORE P.C. Difference 7/18/74 1 2.359 1.295 1.346 3.86 11/02/74 1 4.026 1.322 1.367 3.35 1/19/77 1 7.698 1.336 1.333 -0.22 6/13/77 1 10.370 1.349 1.310 -2.93 8/09/77 1 11.378 1.296 1.273 -1.79 4/26/78 2 11.521 1.349 1.356 0.52 6/29/78 2 12.798 1.397 1.332 -4.76 Average -2.81 Standard Deviation 3.17 4-65 <
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- iO
The measured data utilized for comparisons to CORE was obtained as described for units 1 and 2. The CORE code input data and the exposure accumulation procedure were also as described for Browns Ferry units 1 and 2.
4.3.1 Zero Power Criticals Table 4.3-1 presents the zero power criticals calculated for Browns Ferry unit 3 comparisons. The xenon concentration is not negligible for three of these criticals due to the short length of time the plant was shutdown (less than 60 hours6.944444e-4 days <br />0.0167 hours <br />9.920635e-5 weeks <br />2.283e-5 months <br />). Iloweve r , for the criticals for which xenon is not negligible, the reactor was operating at a condition of equilibrium xenon prior to the shutdown and shutdown occurred rapidly. Thus the xenon concentration after shutdown was readily calculated utilizing the transient xenon capability in CORE. The corrected k-effective values are the direct code output with the reactivity equivalent of the observed reactor period subtracted from them. The average k-effective obtained for the Browns Ferry unit 3 zero power criticals was 0.9991 with a standard deviation of 0.0036.
- 4. 3. 2 Ilot Operating Reactivity The principal high power critical configurations occurring during cycle 1 operation of Browns Ferry unit 3 are described in Table 4.3-2 along with the eigenvalue obtained from CORE. A beginning of cycle 2 high power configuration is also presented.
Thc average k-effective for the 20 cases is 1.0015 with a standard deviation of 0.0033. The tendency to calculate higher k-effective values near the end of first cycles of gadolinia bearing cores is 4-73
TABLE 4.3-1 ZERO POWER CRITICALS FOR BRO'n'NS FERRY UNIT 3 Core Rod Pattern Information Coolant Reactor Average Rods Rod Moving Temperature Per13d Corrected ***
Date CVD/MTU Seg e Out Co-or Notch (*F) (Sec) iK-eff 8/03/76 0.0 B 28 3S-15 18 92 132 1.0023 3.599 45 26-27 12 212 162 1.0003 4/30/77 B 0.9980 4.492 44 30-35 22 335 49 6/19/77 A 7/10/77 4.755 A 45 38-27 14 455 140 0.9941 5.695 44 30-35 06 170 69 1.0027 e 9/05/77* A 0.9972 6.502 47 42-27 04 518 90 14 10/17/77 B 11/26/77 7.262 A 45 38-27 24 514 45 0.9937 1/29/78* 8.480 B 51 18-35 20 230 84 1.0021 3/20/78 9.425 A 45 38-27 14 300 65 0.9927 4/2./78 9.895 A 46 10-19 14 270 69 1.0020 7/14/78* 11.574 B 73 '
-35 10 230 59 1.0021 12.201 74 27 04 250 107 1.0010 8/21/78 h 0.9997 8.651 45 26 '7 12 150 45 11/22/78** B Average 0.9991 Standard Deviation 0.0036
- Calculated using the transient Xe option.
- Critical at beginning of cycle 2.
has the reactivity equivalent of the observed period
- Ihecorrectedk[becalculatedk subtracted fron* eff' O O O
TABLE 4.3-2 HOT OPERATING CASES FOR BROWNS FERRY UNIT 3 Co re Ave rage Fraction of Rated Calculated Date GWD/MTU Power Flow k-eff 11/08/76 0.454 0.847 0.981 0.9976 12/08/76 0.933 0.980 0.980 1.0000 1/11/77 1.544 0.997 0.951 1.0006 2/17/77 2.255 0.994 0.961 0.9989 4/05/77 3.197 0.937 0.912 0.9985 6/09/77 4.320 0.965 0.884 0.9980 8/10/77 5.196 0.967 0.998 0.9989 9/21/77 6.035 0.970 0.990 0.9994 10/26/77 6.675 0.963 1.022 0.9987 11/11/77 7.013 1.000 1.028 0.9992 1/04/78 7.993 0.952 0.984 0.9992 1/24/78 8.411 0.910 1.001 1.0006 3/31/78 9.628 0.969 0.996 1.0037 4/28/78 10.024 0.945 1.001 1.0040 5/24/78 10.569 0.962 0.984 1.0054 6/22/78 11.180 0.963 1.001 1.0072 7/31/78 11.866 0.939 1.003 1.0089 9,01/78 12.348 0.767 0.683 1.0019 9/08/78 12.460 0.770 0.804 1.0035 12/20/78* 8.984 0.992 0.959 1.0048 Average 1.0015 Standard Deviation 0.0033
- This case is near the beginning of cycle 2.
4- l'>
also present in the Browns Ferry unit 3 data. The average k-affe'aive for exposures less than 8,000 MWD /MTU is 0.9990 with a standard deviati. of 0.0008. The corresponding values for exposures greater than 8,000 MWD /MTU are 1.0044 and 0.0027 respectively.
4.3.3 Process Computer Comparisons Table 4.3-3 presents a com.arison of process computer and CORE code values of axial peak- to-average power for high power configurations in Browns Ferry anit 3. On the average, CORE overpredicted the axial peaking factor by 1.73 percent with a standard deviation of 6.50 percent. The core average axial power shapes near beginning-of-cycle, middle-of-cycle and end-of-cycle are shown in Figures 4.3-1, 4.3-2, and 4.3-3 respectively. The beginning-of-cycle power shapes are in good agreement, but CORE underpredicted the power in the bottom section of the core which had the highest gadolinia content. Ey the middle-of-cycle, the effect of the high gadolinia section had burned out and the power distributions from CORE and the process computer are in excellent agreement. During the latter part of the cycle the trend was reversed and CORE overpredicted the power in the bottom section of the reactor compared to the process computer as shown in Figure 4.3-3.
Figure 4.3-4 gives a comparison of core average relative exposure versus axial position for CORE and the process computer near the end of the first cycle. The excellent agrecment of the end-of-cycle relative exposure shapes indicates that the underprediction of power in the bottom of the CORE early in the cycle was effectively cancelled by the overprediction in the last half of the cycle.
4-76
TABLE 4.3-3 CORE AVERAGE AX1AL PEAK-TO-AVERAGE POWER RATIOS FOR BROWNS FERRY UNIT 3 Core Average CORE Process Percent Date GWD/MTU Code Computer Difference 11/08/75 0.454 1.276 1.239 -2.94 12/08/76 0.933 1.340 1.355 1.11 1/11/77 1.544 1.500 1.471 -1.95 2/17/77 2.255 1.387 1.430 3.05 4/05/77 3.197 1.255 1.313 4.52 6/09/77 4.320 1.419 1.450 2.16 8/10/77 5.196 1.317 1.255 -4.82 9/21/77 6.035 1.285 1.262 -1.81 10/26/77 6.675 1.236 1.293 4.51 11/11/77 7.013 1.147 1.244 8.11 1/04/78 7.993 1.239 1.267 2.23 1/24/78 8.411 1.193 1.316 9.80 3/31/78 9.628 1.302 1.157 -11.79 4/28/78 10.024 1.226 1.150 -6.40 5/24/78 10.569 1.294 1.135 -13.09 6/22/78 11.188 1.234 1.180 -4.47 7/31/78 11.866 1.309 1.211 -7.78 9/01/78 12.348 1.194 1.229 2.89 9/08/78 12.460 1.267 1.158 -8.99 12/20/78* 8.984 1.301 1.190 -8.91 Average -1.73 Standard D viation 6.50
- This case is near the beginning of cycle 2 4-77
3=3 CY1: L: 5L %Of f- (' './8/76)
~
P=2790 MWT 1, q _
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I i I i I i i l I I I I I I I I I I I I I I 0.0 I I 2 4 6 8 10 12 14 16 18 20 22 2 11 AXIAL NODE Figure 4. 3-1: Near Beginning-of-cycle 1 O O O
3 3 CY'.: 6035 PhJ/F-~ (9/21/77)
I* P=3193 MWT T .
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I 8 10 12 14 16 18 20 22 24 AXIAL NODE Figure 4.3-2: Near Middle-of-cycle 1
3=3 CY1: '.1866 MJ/F~ (7/ 3 '. / 78) b 1 P=3091 MWT 1.4 r : ec w _
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--- cme o
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2 4 6 8 10 12 14 16 18 20 22 24 AXIAL NODE Figure 4.3-3: Near End-of-cycle 1 O O O
3=3 CY'.: 11866 MWJ/M- (7/31/78) l' J l.4 C -
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Table 4.3-4 shows the comparison of radial peaking factors (naximum relative bundle power) and individual bundle ICIS power differences for CORE and the process computer. On the average, CORE underpredicted the maximum bundle relative power by 3.7 percent with a standard deviation of 1.76 percent compared to the process computer values. Comparison of individual bundle relative power differences results in an average IOfS dif ference of 4.46 percent between the precess computer and CORE. Comparison of individual process computer bundle relative powers in symrcmtric locations but based on different TIP thimbles resulted in a 101S difference of 3.5 percent.
Table 4. 3-5 presents a comparison of CORE and process computer total peaking f actors (maximum nodal times local value) and the 10tS dif ference between individual nodal powers. Since the local peaking f actors for CORE and the process computer are approximately identical, the total peaking factor comparison primarily reflects differences in the naximum nodal powers. On the average, CORE underpredicted the total peaking factor with respect to the process computer value by only 0.66 percent with a 5.04 percent standard deviation. However. chis was obtained by underpredicting the total peaking facts.r l'y 4.1 percent during the first part of cycle 1 and overpredi ct in:, the peak by 1.74 percent for the remainder of the cases. The average IO1S difference in individual nodal rela-tive power fot CORI: and the process coraputer was 12.49 percent for the 9 cases where detailed data was available. The letS dal difference for symmetric prccess computer locations was found to be approximately 4.5 percent.
4-82
TABLE 4.3-4 RADIAL POWER DISTRIBUTION FOR BROWNS FERRY UNIT 3. CYCLE 1 Core Radial Peaking Fac tor Percent RMS Average CORE Process Percent Bundle Power Date GWD/MTU Code Computer Difference Difference 11/08/76 0.454 1.311 1.355 3.30 4.436 12/08/76 0.933 1.286 1.348 4.71 4.019 1/11/77 1.544 1.263 1.340 5.92 -
2/17/77 2.255 1.267 1.330 4.85 -
4/05/77 3.197 1.286 1.360 5.59 -
6/09/77 4.320 1.260 1.323 4.88 4.652 8/10/77 5.196 1.319 1.370 3.79 -
9/21/77 6.035 1.300 1.329 2.21 4.274 10/26/77 6.675 1.361 1.419 4.17 4.498 11/11/77 7.013 1.367 1.420 3.80 -
1/04/78 7.993 1.378 1.435 4.05 4.543 1/24/78 8.411 1.351 1.410 4.27 -
3/31/78 L.628 1.382 1.398 1.15 4.18.
4/28/78 10.024 1.351 1.350 -0.07 -
5/24/78 10.569 1.225 1.310 6.71 -
6/22/78 11.180 1.249 1.257 0.64 4.301 7/31/78 11.866 1.197 1.230 2.72 -
9/01/78 12.348 1.265 1.315 3.88 5.240 9/08/78 12.460 1.183 230 3.90 -
Average 3.70 4.461 Standard Deviation 1.76 s 4-83
O TABLE 4.3-5 NODAL POWER DISTRIBUTION FOR BROWNS FERRY UNIT 3 Core Total Peaking Factor Percent RMS Average CORE Process Percent Nodal Power Date GWD/FRU Code Computer Difference Difference 11/08/76 0.454 2.241 2.173 -3.08 8.104 12/08/76 0.933 2.230 2.261 1.38 8.964 1/11/77 1.544 2.450 2.440 -0.41 -
2/17/77 2.255 2.176 2.332 6.92 -
4/05/77 3.197 2.079 2.311 10.57 -
6/09/77 4.320 2.281 2.482 8.44 11.306 8/10/77 5.196 2.449 - - -
9/21/77 6.035 2.050 2.151 4.81 6.991 10/26/77 6.675 2.272 2.228 -1.96 11.361 11/11/77 7.013 2.162 2.222 2.74 -
1/04/78 7.993 2.382 2.271 -4.77 19.838 1/24/78 8.411 2.207 2.321 5.04 -
3/31/78 9.628 -
1.995 -
16.083 4/28/78 10.^24 2.055 1.998 -2.81 -
5/24/78 10,5u9 1.907 1.820 -4.67 -
6/22/78 11.180 1.898 1.839 -3.16 13.681 7/31/78 11.866 1.836 1.727 -6.12 -
9/01/78 12.348 1.870 - -
16.108 9/08/78 12.460 1.743 1.690 -3.09 -
12/20/78* 8.984 2.323 2.356 1.41 -
Average 0.66 12.493 Standard Deviation 5.04
- This case is near th( beginning of cycle 2 0
4-84
CllAPTER 4 REFERENCES 1 S. l.. Forkner, G. 11. Mertwether, and T. D. lie u , "three-Dimensional I.WR Core Simulation Methods," TVA-TR78-03, 1978.
- 2. N. 11. Larsen, G. R. Parkos, and O. Raza, " Core Desir,n and Operating Data for Cycles 1 and 2 of Quad Cities 1," EPRI NP-240, 1976.
- 3. 11 L. Darnell, T. D. P>e u , and G. W. Perry, " Methods for the Lattice Physics Analysis of LWR's," TVA-TR78-02, 1978.
- 4. G. R. Parkes, "BWR Simulator Methods Verification," General Electric Company, NEDO-20946A, 1977.
- 5. M. B. Cutrone and G. F. Valby, " Gamma Scan Measurements at Quad Cities Nuclear Power Station Unit 1 Following Cycle 2,"
EPRI NP-214, 1976.
- 6. firowns Ferry Nuclear Plant Final Safety Analysis Report.
- 7. NEDO-24020, " General Electric Boiling Water Reactor Reload 1 Licensing Amendment for Browns Ferry Nuclear Plant Unit 1,"
May 1977.
- 8. NEJ0-24095, " Supplemental Reload Licensing Submittal for Browns Ferry Nuclear Plant Unit 2 Reload 1," December 1977.
- 9. NEDO-24128, " Supplemental Reload Licensing Submittal for Browns Ferry Nuclear Plant Unit 3 Reload 1," June 1978.
4-85
- 5.
SUMMARY
5.1 LATTICE PHYSICS MET 110DS Although a more meaningful indication of the adequacy of the physics methods used in the LATTICE code lies in the resolts obtained f rom the CORE simulator that were presented in Chapter 4, data was ' 'uded in Chapters 2 and 3 to demonstrate the overall suitability of the models used. Comparisons were presented to measurements and to calculated results from other codes with more detailed models.
In Section 2.1, values of k-effective for 25 critical experi--
ments were presented; the average was 0.9954 with a standard deviation of 0.0107. It was shown that by grouping similar experiments, considerably smaller standard deviations resulted.
In Section 2.2, reaction rate distributions in space and energy calculated by LATTICE and ESP, a general Monte Carlo reactor analysis code, were compared for 15 of the experiments analyzed in Section 2.1. The largest bias and standard deviation was for the absorption of fast neutrons in the fuel. Agreement was good for km and thermal reaction rates; the bias and standard deviation were 0.00228 and 0.0108 for km. Section 2.3 presented comparisons to measured data for the calculation of isotopic concentrations of uranium and plutonium as a function of burnup. Excellent agreement was obtained for all isotopic ratios except for the ratio of Pu-242 to Pu-241, which was underpredicted by approximately 35 percent at an exposure of 12,000 MWD /MDI. This discrepancy does not affect the ability of LATTICE to fulfill its intended function.
5-1
The comparisons given in Chapter 2 demonstrate that the basic models used in LATTICE accurately represent the neutronic phenomena important to light water reactor analyses.
Chapter 3 contains information which confirms the adequacy of the LATTICE calculation of important bundle physics parameters.
Comparisons to measured data were presented for the local power distribution of exposed bundles. For unexposed bundles, comparisons were made to reactivity and local power distributions calculated by more exact codes. The ESP Fonte Carlo code and the CPM collision prcbability code were used for these comparisons.
Table 3.1-1 exhibited km, values calculated for unexposed fuel for a variety of fuel types and water densities. For the 23 cases, the bias of LATT1CE relative to ESP was 0.0074 with a standard deviation of 0.0079. Good agreement for the calculated worth of the burnable poison in a particular bundle design was also discussed.
Comparisons of local power distributions were given in Section 3.2.
Beginning-of-life comparisons to ESP and/or CPM were presented in Figures 3.2-2 through 3.2-12. RMS differences ranged from 3.1 to 6.5 percent relative to ESP, and from 2.4 to 3. 7 percent relative to CPM. The RMS differences were statistically combined with a result of 4.0 percent. LATTICE predicted bundle peaking factors well compared to ESP, obtaining a bias of 0.1 percent and a standard deviation of 2.2 percent; relative to CPM there was a bias of
-1.8 percent with a standard deviation of 1.8 percent. Thus LATTICE adequately predicts local power distributions and peaking factors compared to two other codes using more exact theory.
5-2
Local power distributions for exposed fuel were compared in Figures 3.2-13 to 3.2-19 to gamma scan measurements taken at the end-of-cycle 2 of Quad Cities unit 1. RMS differences ranged from 1.6 to 4.9 percent. The statistical combination of the RMS differences for UO bundles was 2.4 percent. The power of the 2
burnable poison pins was in good agreement. For peaking factors of exposed fuel, the resulting bias and standard deviation were
-1.2 and 1.5 percent. Chapters 2 and 3 confirm the conclusion, reached by examining results from the CORE simulator, that LATTICE well predicts parameters of interest in commercially available BWR fuel bundles.
5.2 CORE SIMULATION The capability of TVA methods to accurately simulate the steady-state physics of boiling water reactor cores was verified by comparisons to measured data from Quad Cities unit 1 and all three Browns Ferry units. For zero power criticals, a total of 53 critical configurations was calculated. Figure 5.2-1 presents all of the k-effective values from CORE for the zero power criticals as a function of core average exposure. The average k-effective for all 53 points is 0.9977 with a standard deviation of 0.0025.
There is no apparent trend in the predicted k-effective for cold criticals versus core average exposure. Additionally, there was not a significant bias between the calculated k-ef f ective values for localized and in-sequence control rod patterns.
Calculated k-effective values were presented for a total of 69 high-power critical configurations. Figure 5.2-2 presents the calculated hot operating k-effectives versus core average exposure.
5-3
ZE90 30AE9 C9f~fCA S 1.015 _
6 QC1 CYl&2 O BF2 CY162 1.010 -
. e bFl CY162 X BF3 CY162 LtJ 1. 005 -
~ -
X w l-- y X X X 1 (_) o X uJ 1. 000 - x x bJ ii e 0* x 0 e G
d0.995 -
ee x *e X o
4
[ O x g e 0.990 -
0'985 O 2 ' ' ' ' 4' ' ' ' ' ' ' ' ' '6' ' ' ' ' ' ' ' ' ' '8 10 12 14 CORE AVG EXPOSURE (GWD/MT)
Figure 3.2-1 O O O
~ ~
0~ 0 3 E 9FT \G C9 ~CA _S 1.015 _
_ o QC1 CY1 A QC1 CY2 1.010 [ e nFi Cri e 3F1 Cv2 e
_ e e o%
X BF3 CY1 + BF3 CY2 e g q^*
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+
- 00 x x ^x O ^ ^ x m, H -
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x 0 e O X w 1.000 x x D .
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x e x x w -x ,o a y : % o o o o
o z 0.995 -
, e o , ,
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0.990 0.985 0
'''''2 4 6 8 10 12 14 CORE AVG EXPOSURE (GWD/MT)
Figure 5.2-2
The average k-effective for all 69 points is 1.0008 with a standard deviation of 0.0039. Ilowever, a trend toward higher predicted k-effective values for increasing core average exposures is evident.
For core average exposures typical of reload cores (greater than 10,000 MWD /MTU), the average k-effective value for 22 points is 1.0056 with a standard deviation of 0.0025.
Comparisons of simulated (by CORE) and measured T1P readings were performed for 27 operating points in Quad Cities unit 1 cycles 1 and 2. The standard deviation of differences between calculated and measured readings for 6-inch segments and integrated thimble values is approximately the same as the standard deviation of differences between symmetric measurements. The bundle axial peak-to-average values of La-140 activity from CORE were compared to gamma scan measurements for Quad Cities performed at the end of cycles 1 and 2. For the end-of-cycle 1 gamm. scan, CORE overestimated the axial peaking factor by 4.72 percent with a standard deviation of 2.64 percent. The end-of-cycle 2 values were overpredicted by 1,47 percent with a standard deviation of 1.89 percent. The average and individual bundle axial La-140 distributions were in good agreement with the measured data.
For the end-of-cycle 2 Quad Cities gamma scan measurements, CORE overpredicted the 25 highest nodal La-140 activities by 1.4 percent with a standard deviation of 1.3 percent. The radial power distribution (as indicated by bundle average La-140 activities) predicted by CORE was in good agreement with the measured data.
The standard deviation of differences for individual bundles was 3.82 percent.
5-6
Comparisons to process computer power distributions for the llrowits Ferry units confirm that CORE reliably predicts the the reactor power distribution throughout the operating cycle.
5-7