ML20028H085
| ML20028H085 | |
| Person / Time | |
|---|---|
| Site: | Surry, North Anna  |
| Issue date: | 07/31/1990 |
| From: | Randy Hall VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.) |
| To: | |
| Shared Package | |
| ML18153C381 | List: |
| References | |
| VEP-NAF-1, NUDOCS 9010090077 | |
| Download: ML20028H085 (344) | |
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s 9 9 I I I I. I I I I I I I I 1-I I I I
i f$- VEP NAF-1 THE PDQ TWO ZONE MODEL
-BY R. A. HALL I NUCLEAR ANALYSIS AND FUEL DEPARTMENT
-- , NUCLEAR ENGINEERING SERVICES VIRGINIA ELECTRIC AND POWER COMPANY
=
RICHMOND, VIRGINIA
- . ( July, 1990 I'
I Recommended for Approval:
.J ]
k Dziado d
~ Supervisor, Nuclear Core Design
='
Approved: 1 xx-R. M. Berryman Manager, Nuclear Analysis and Fuel I i
I CLASSIFICATION /DISCLAI!iER I . The data and analytical techniques described in this report have been prepared specifically for application by the Virginia Electric and Power Company. The Virginia Electric and Power Company makes no claim as to the accuracy of the data or techniques contained in this report if used
.g'
-g by other organizations. Any use of this report or any part thereof must .
I have the prior. written approval of the Company. ginia Electric and Power. j l g-lI I t I l
.1 I
o l. LI l 3 a ul< 1 1
Il ABSTRACT i l l The Virginia Electric and Power Company (Virginia Power) - has developed a coarse inesh (i.e. , five non-uniform mesh per assembly), three dimensional, two neutron energy group diffusion-depletion calculational model designated as the PDQ two zone model. . The model uses the Virginia Power computer codes SHUFL, PDQV2, RECON, I
'l and PCF codes, as well as input from the EPRI ARMP-02 CELL 2 and Nt' PUNCHER codes, the EPRI ESCORE code, and the SCALE 3 package from ORNL (including
)
KENO V.a). The purpose of the model is to provide power distribution data for axially dependent vessel fluence calculations and to predict physics characteristics of t.h e Virginia Power Surry and North Anna nuclear W reactors. The accuracy of the two zone model is demonstrated L through comparisons with measurements taken at the Surry and North Anna Nuclear
~
Power Stations. " I I I, Il I IL 11 I I
I ACKNOWLEDGMENTS I The author would like to thank Mr. D, Dziadosz who conceived and supported this project, and Mr. A11 Abbasi, Mr. Walter Peterson and Mr. Jeff McElroy for assistance in performing the compcter calculations and
=
. data preparation required for this rcport. The author . also wishes to express his appreciation to the people who reviewed and provided comments on this report. i I
I: I I I I: I 1 I I I I) 111
9 i TABLE OF CONTENTS I.' Page CLASSIFICATION / DISCLAIMER , i
.. ,, ............ .. . j AESTRACT . . . . .. . . .. ... ........... .. . . 11 ACKNOWLEDGMENTS . . . . . .. . .. ............ .. . iii TABLE OF CONTENTS . . . . .. . .. ............... iv LIST OF TABLES . . . . . .. ... ............... v -
I LIST OF FIGURES . . . . . ... ............... . . vi SECTION 1 - INTRODUCTION . .. . . ... ............ 1-1 SECTION MODEL DESCRIPTION . .. ........... . . . .. 2-1 ; 2.1 Introduction . . .. ..... ... . . . . . . . . 2-1 2.2 Model Geometry . . . .............. . 2-7 I 2.3 Cross Section Generation . .... ..... . . . 2-17 2.4 PDQ Quarter Core Cycle Calculations .. . .. . . 2-26 2.5 Pin Power Reconstruction . . ....... ... . 2-?! SECTION 3 - RESULTS . . . . . . . , ....... ..... .. . 3-1 , 3.1 Introitetion . . .. ............ . . . 3-1 g. ga 3.2 Analytical Calculations ..... ...... . . 3-1 i 3.3 Measurement Data . . . ... ... ...... . . 3-4 - 3.4 Results . . . . . . .. ..... ... ... . . 3-10 l-I i 1-SECTION 4 -
SUMMARY
AND CONCLUSIONS . .... ....... . . . 4-1
- 1. ;
i SECTION 5 - REFERENCES . .. . .. ....... ...... . . 5 - l' _ i 1: LV I
I LIST OF TABLES Table Title Page l 1-1 Surry Nuclear Power Station Operating History . . . . . 16 l 1-2 North Anna Nuclear Power Station Operating History . 1-7 2-1 Nuclides Included in the PDQ Two Zone Depletion Chains . 2-28 1 3 Axial Geometry For Power Distribution Comparisons l I 3-7 3-2 Summary of Nuclear Reliabi'.ity Factors . . . . . . . . . 3-18 3-3 Power Distribution Statistics . . . . . . . . . . . . . 3-19 3-4 Flux Map Database Listing . . . . . . . . . . . . . . . 3-21 3-5 Reactivity Parameter Statistics . . . . . . . . . . . . 3-24 3-6 Reactivity Computer Induced Bias Error Estimate . . . . 3-25 l 5 I I I ., I. I < I LI
- I V
'I
l
' I' ,
LIST OF FIGURES Figure Title Page 2-1 ' PDQ Two Zone Model Flowchart
. . . . . . . . . . . . . . 2-5 2-2 Pin' Power Reconstruction F)ow Chart . . . . . . . . . . 2-6 ,
2-3 PDQ Two Zone Axial Mesh Structurc . . . . . . . . . . . 2-10 24 4 Surry Fuel 15 x 15 X-Y Pin Orientation . . . . . . . . 2-11 , 2-5 Surry Fuel Two Zone X-Y Mesh Structure . . . . . . . . . 2-12 2-6 North Anna Fuel 17 x 17 X-Y Pin Orientation . . . . . . 2-13 l 2-7 North Anna Fuel Two Zone X-Y Mesh Structure . . . . . 2-14 2-8 IAEA 2-D Benchmark Problem j PDQ 6 X 6 Uniform Mesh Results . . . . . .. . . . . . . 2-15 - l- 2-9 IAEA 2-D Bonchmark Problem PDQ Two Zone 5 X 5 Non-uniform Mesh Results g
. . . . . . 2-16 g 3-1 FULL CDRE MONITORED ASSEMBLY LOCATIONS . .. . . . . . . 3-8 .
l 3-2 CONTROL ROD BANK LOCATIONS . . . . . . . . . . . . . . . 3-9 3-3 N1C1 P(Z) COMPARISdN HZP, O MWD /T CYCLE BURNUP . . . 3-26
'3-4 N1C1 P(Z) COMPARISON HFP, 881 MWD /T CYCLE BURNUP . . . 3-27 3-5 NIG1 P(Z) COMPARISON HFP, 8405 MWD /T CYCLE BURNUP . . . 3-28 l
3-6 N1C1 P(Z) COMPARISON HFP, 14070 MWD /T CYCLE BURNUP . 3-29 I 3-7 NIC2 P(Z) COMPARISON HZP, O MWD /T-CYCLE BURNUP . . . 3-30 3-8 N1C2 P(Z) COMPARISON HFP, 305 MWD /T CYCLE BURNUP , . . 3-31 3-9 N1C2 P(Z) COMPAr.ISON HFP, 3277 MWD /T CYCLE BURNUP . . . 3-32 l 3-10 NIC2 P(Z) COMPARISON HFP, 8109 MWD /* CYCLE BURNUP . . . 3-33 3-11 NIC3 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-34 3-12 NIC3 P(Z) COMPARISON HFP, 487 MWD /T CYCLE BURNUP . . . 3-35 3-13 N1C3 P(Z) COMPARISON HFP, 6883 MWD /T CYCLE BURNUP . . . 3-36 vi I :
..~A . 4 - a m x- n. M+<- .aM>. , ,-w .
I I m S1 0F F1eURES I
~
r > E-- m i- e-3-14 NICS P(Z) COMPARISON HFP, 11434 MWD /T CYCLE BURNUP . . . 3-37 - 3-15 NIC4 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-38 3-16 NIC4 P(Z) COMPARISON HFP, 305 MWD /T CYCLE BURNUP , . . 3-39 3-17 N1C4 P(Z) COMPARISON HFP, 5521 MWD /T CYCLE BURNUP , . . 3-40 3-18 NIC4 P(Z) COMPARISON HFP, 10170 MWD /T CYCLE BURNUP . . . 3-41. 3-19 NICS P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP , . . 3 3-20 NICS P(Z) COMPARISON HFP, 225 MWD /T CYCLE BURNUP , . . 3-43 3-21 NIC5'P(Z) COMPARISON HFP, 6831 MWD /T CYCLE BURNUP . . . 3-44 1 3-22 N1CS P(Z) COMPARISON HFP, 12983 MWD /T CYCLE BURNUP . . . 3-45 3-23 N1C6 P(Z) COMPARISON HFP, 379 MWD /T CYCLE BURNUP . . . 3 ; 3-24 NIC6 P(Z) COMPARISON HFP, 6690 MWD /T CYCLE BURNUP , . . 3-47 3-25 NIC6 P(Z) COMPARISON HFP, 14340 MWD /T CYCLE BURNUP . . . 48 3-26 N1C7 P(Z) COMPARISUN HFP, 1062 MWD /T CYCLE BURNUP . . . 3-49 3-27~ N1C7 P(Z)' COMPARISON HFP, 4995 MWD /T CYCLE BURNUP . . . 3-50 3-28 N2C1 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-51 3-29 N2C2 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . 52 I. 3-30 N2C2 P(Z) COMPARISON HFP, 3225 MWD /T CYCLE BURNUP , . . 3-53 3-31 N2C2 P(Z) COMPARISON HFP, 6751 MWD /T CYCLE BURNUP . . . 3-54 3-32 N2C3 P(Z) COMPARISON fiZP, O MWD /T CYCLE BURNUP . . . 3-55 3-33 N2C3 P(Z) COMPARISON ITP, 1566 MWD /T CYCLE BURNUP , . . 3-56 3-34 N2C3 P(Z) COMPARISON HJP, '674
< MWD /T CYCLE BURNUP , . . 3-57 3-35 N2C3 P(Z) COMPARISON HFP, 13040 MWD /T CYCLE BURNUP . . . 3-58 l
3-36 N2C4 P(Z) COMPARISON HZP, [ O MWD /T CYCLE BURNUP . . . 3-59 I: vii 8
4 a a =- -. e.v - -- v# a LIST OF FIGURES Fli Title Page 3 N2C4 P(Z) COMPARISON HFP, 1060 MWLVT CYCLE BURNUt . . . 60 3-38 N2C4 P(Z) COMPARISON HFP, 6610 MWD /T CYCLE BURNUP . .. . 3 3-39 N2C4 P(Z) COMPARISON HFP, 11267 MWD /T CYCLE BURNUP . . . 3-62 3-40 N2C5 P(Z) COMPARISON HFP, 250 MWD /T CYCLE BURNUP . . . 3-63 : 3-41 N2C5 P(Z) COMPARISON HFP, 6075 MWD /T CYCLE BURNUP . . . 3-64 , 3-42 N2C5 P(Z) COMPARISON HFP, 13671 MWD /T CYCLE BURNUP'. . . 3-65 ' i l 3-43 SICI P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-66 3-44 SIC 2 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-67 3 45 . SIC 2 P(Z) COMPARISON HFP, 1100 MWD /T CYCLE BURNUP . . . 3-68 3-46 SIC 2 P(Z) COMPARISON HFP, 4050 MWD /T CYCLE BURNUP . . . .3 ' 3-47 SIC 3 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP , . . 3-70 - 3-48 SIC 3 P(Z) COMPARISON HFP, 250 MWD /T CYCLE BURNUP . . . 3-71 3-49 SIC 3 P(Z) COMPARISON HFP, 7175 MWD /T CYCLE BURNUP , . . 3-72 3-50 SIC 4 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-73 3-51 SIC 4 P(Z) COMPARISON HFP, 930 MWD /T CYCLE BURNUP . . . 3-74 3-52 SIC 4 P(Z) COMPARISON HFP, 8400 MWD /T CYCLE BURNUP . . . 75 h h 3-53 S1CS P(Z) COMPARISON HZP, O MWD /T CYCLE'BURNUP , . . 3-76 3-54 S1CS P(Z) COMPARISON HFP, 1300 MWD /T CYCLE BURNUP . . . 3-77 3-55 SICS P(Z) COMPARISON HFP, 7411 MWD /T CYCLE BURNUP , . . 3-78 3-56 ~ SICS P(Z) COMPARISON HFP, 10758 MWD /T CYCLE BURNUP . . . 3-79 3-57 S1C6 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-80 3-38 SIC 6 P(Z). COMPARISON HFP, 973 MWD /T CYCLE BURNUP . . . 3-81 3-59 SIC 6 P(Z) COMPARISON HFP, 7518 MWD /T CYCLE BURNUP . . . 3-82
.111 1:
E.
LIST OF FIGURES Figure Title Page 3-60 SIC 6 P(Z) COMPARISON HFP, 13207 MWD /T CICLE BURNUP 3-83 3-61 SIC 7 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . 3-84 ,
~ ' '
3-62 SIC 7 P(Z) COMPARISON HFP, 807 MWD /T CYCLE BURNUP 3-85 3-63 SIC 7 P(Z) COMPARISON HFP, 4329 MWD /T CYCLE BURNUP 3-86 3-64 SIC 7 P(Z) COMPARISON HFP, 7630 MWD /T CYCLE BURNUP 3-87 - 3-65 SIC 8 P(Z) COMPARISON HZP, 0 MWD /T CYCLE BURNUP 3-88 3-66 SIC 8 P(Z) COMPARISON HFP, 925 MWD /T CYCLE BURNUP 3-89 3-67 SIC 8 P(Z) COMPARISON HFP, 3737 MWD /T CYCLE BURNUP 3-90 . 3-68 SIC 8 P(Z) COMPARISON HFP, 80C1 MWD /T CYCLE BURNUP 3-91 3-69 SIC 9 P(Z) COMPARISON HFP, 240 MWD /T CYCLE BURNUP 3-92 3-70 SIC 9 P(Z) COMPARISON HFP, 8460 MWD /T CYCLE BURNUP 3-93
^
3-71 SIC 9 P(Z) COMPARISON HFP, 14606 MWD /T CYCLE BURNUP 3-94 3-72 S2C1 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP 3-95 [ 3-73 S2C1 P(Z) COMPARISON HFP, 2030 MWD /T CYCLE BURNUP 3 96 3-74 S2C1 P(Z) COMPARISON HFP, 7310 MWD /T CYCLE BURNUP 3-97 3-75 S2C1 P(Z) COMPARISON HFP, 12770 MWD /T CYCLE BURNUP 3-98 3-76 S2C2 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP , 3-99 3-77 S2C2 P(Z) COMPARISON HFP, 730 MWD /T CYCLE BURNUP 3-100 ' 3-78 S2C2 P(Z) COMPARISON HFP, 3750 MWD /T CYCLE BURNUP 3-101
. 3-79 S2C3 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP 3-102 3-80 S2C3 P(Z) COMPARISON HFP, 3127 MWD /T CYCLE BURNUP 3-103 . *
" ~
3-81 S2C3 P(Z) COMPARISON HFP, 9025 MWD /T CYCLE BURNUP 3-104 3-82 S2C4 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP 3-105 m - iX e . R . _ _ . _ _ _
.l l _
LIST OF FICURES l l Figure Title Page
~
3 83 S2C4 P(Z) COMPARISON HFP, 1186 MWD /T CYCLE BURNUP . . 3-106 { 3-84 S204 P(Z) COMPARISON HFP, 8250 MWD /T CYCLE BURNUP . . . 3-107 =t 3-85 S2C5 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . 3-108 3-86 S2C5 P(Z) COMPARISON HFP, 1830 MWD /T CYCLE BURNUP , . . 3-109. - i 3-87 S2C5 P(Z) COMPARISON HFP, 11320 MWD /T CYCLE BURNUP . . . 3-110 us - 3-88 S2C6 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP , . 3-111 , l 3-89 S2C6 P(Z) COMPARISON HFP, 1116 MWD /T CYCLE BURNUP . . . 3-112 3-90 S2C6 P(Z) COMPARISON HFP, 7390 MWD /T CYCLE BURNUP . . . 3-113 3-91 S2C6 P(Z) COMPARISON HFP, 13900 MWD /T CYCLE BURNUP . . . 3-114 I 3-92 S2C7 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP , , . 3-115 l 3-93 SOC 7 P(Z) COMPARISON HFP, 1647 MWD /T CYCLE BURNUP . . , 3-116 3-94 S2C7 P(Z) COMPARISON HFP, 5781 MWD /T CYCLE BURNUP . . . 3-117 h' 3 95 S2C7 P(Z) COMPARISON HFP, 13122 MWD /T CYCLE BURNUP . . . 3-118 3-96 S2C8 P(Z) COMPARISON HZP, O MWD /T CYCLE BURNUP . . . '3-119
. 3-97 S2C8 P(Z) COMPARISON HFP, 2423 HWD/T CYCLE BURNUP . . 3-120' 3-98 S2C8 P(Z) COMPARISON HFP, 6525 MWD /T CYCLE BURNUP . . . 3-?21 l
3-99 S2C8 P(Z) COMPARISON HFP, 12391 MWD /T CYCLE BURNUP . .. 3-122 B;'.,
'3-100 'S2C9 P(Z) COMPARISON.HFP, 1072 MWD /T CYCLE BURNUP . . . 3-123 3-101 S2C9 P(Z) COMPARISON HFP, e887 MWD /T CYCLE BURNUP . . . 3-124 3-102 NIC1 RPD COMPARISON HZP, O MWD /T BURNUP D-228 . . . 3-125 3-103 NIC1 RPD COMPARISON HFP, 11070 MWD /T BURNUP D-220 . . . 3-126 3-104 N1C2 RPD COMPARISON HZP, O MWD /T BURNUP D-228 . . . 3-127 1-3-105 N1C2 RPD COMPARISON HFP, 300 MWD /T BURNUP D-228 . . . 3-128 '.
X I i
^ I, i
W' LIST OF FIGURES .; Figure Title Page 3-106 N1C2 RPD COMPARISON HFP, 3277 MWD /T BURNUP D-222 . .. '3-129 3-107 NIC2 RPD COMPARISON HFP, 8109 MWD /T BURNUP D-210 . . . 3-130 l 5 3-108- NIC3 RPD COMPA'tISON HZP, O MWD /T BURNUP D-220 . . . 3-131 l 3-109 NIC3 RPD COMPARISON HFP, 6883' MWD /T BURNUP D-213 . . .- 3-132 3-110 NIC3 RPD COMPARISON.HFP, 11434 MWD /T BURNUP D-216 . . . 3-133 3-111 NIC4 RPD COMPARISON HZP, O MWD /T BURNUP D-228 . .. 3-134 L 3-112 NIC4 RPD COMPARISON HFP, 305 MWD /T BURNUP D-221 . . . 3-135 1 3-113 NIC4 RPD COMPARISON HFP, 5520 MWD /T BURNUP D-216 . . . 3-136 3-114 N1C4 RPD COMPARISON HFP, 10170 MWD /T DURNUP D-226 . . . 3-137 , 3-115 NICS RPD COMPARISON HZP, O MWD /T BURNUP D 228 . . ~ . 3-138 I 3-116 N1CS RPD COMPARISON HFP, 225 MWD /T BURNUP D-224 . . . 3-139 I
- i. 3-117 NICS RPD COMPARISON HFP.' 6831 MWD /T BURNUP D-224 . . . 3-140 3-118 N1CS RPD COMPARISON'HFP, 12983 MWD /T BURNUP D-228 . . . 3-141 3-119 N1C6 RPD COMPARISON HFP- 378 MWD /T BURNUP D-219 . . . 3-142 ?
3-120' NIC6~RPD COMPARISON HFP, 6690 MWD /T BURNUP D-228 . . . 3-143 3-121 NIC6 RPD COMPARISON HFP, 14340 MWD /T BURNUP D-228 . . . 3-144
'3-122 N2C2 RPD COMPARISON HZP, O MWD /T BURNUP D-228 . . . 145 3-123 N2C2 RPD COMPARISON HFP, 3225 MWD /T BURNUP D-224 . . . 3-146-3-124 N2C2 RPD COMPARISON HTP, 6751 MWD /T BURNUP D-218 . . . 3-147 3-125 N2C3 RPD COMPARISON HZP, 0 MWD /T BURNUP 'D-211 . . . 3-148 3-126 N2C3 RPD COMPARISON HFP, 1566 MWD /T BURNUP D-212 . . . 3-149 3-127 N2C3 RFD COMPARISON HFP, 7647 MWD /T BURNUP D-217 . . . 3-150 3-128 N2C3 RPD COMPARISON HFP, 13040 MWD /T BURNUP D-221 . . . 3-151-
.g XI i
~ ~
g y , i
' f1 iIST OF FIGURES ,
3 Figure 4 Title Page
.3-129 N2C4 RPD COMPARISON HZP, O MWD /T BURNUP D-211 . . . 3 152 L
3 130 N204 RPD COMPARISON HFP, 6610 MWD /T BURNUP D 220 . . . 3-153 3-131 N2C4 RPD COMPARISON HFP, 11267' MWD /T BURNUP D-228 . . . 3-154 3-132 NW 9PD COMPARISON HFP, 250 MWD /T BURNUP D-228 . . . 3-155
?
t 3-133 N2C5 kPD COMPARISON HFP, 6075 MWD /T_BURNUP D 228 . . . 3-156
' ~ '
3-134 N2C5 RPD COMPARISON HFP, 13671 MWD /T BURNUP D-228 . . . 3-157. 3-135 S1C2 RPD COMPARISON HZP, O MWD /T BURNUP D 214 . . 3-158 3-136- SIC 2 RPD COMPARISON HFP, 1100 MWD /T BURNUP D-222 . . . 3-159 3-137 SIC 2 RPD COMPARISON HFP, 4050 MWD /T BURNUP D-223 . . . 3-160 - 3-138 S1C3 RPD COMPARISON HFP, 250 MWD /T BURNUP. D 212 . . . 3-161 , 3-139 S1C3 RPD COMPARISON HFP, 7175 MWD /T BURNUP D-225 . . . 3-162- . 3-140 SIC 4 RPD, COMPARISON HZP, O MWD /T BURNUP D-220 . . . 3-163 3-141 SIC 4 RPD COMPARISON HFP, 930 MWD /T BURNUP D-215 . . . 3-16. !
'3-142 SIC 4 RPD COMPARISON HFP, 8400 MWD /T BURNUP D-206 . . . 3-165 3-143 SICS RPD COMPARISON HZP, O MWD /T BURNUP D-218 . . . 3-166 3-144 SICS RPD COMPARISON HFP, 1300 MWD /T BURNUP D-220 . . . 3-167 ;
3-145 SICS RPD COMPARISON HFP, 7411 MWD /T BURNUP D-224 . . 3-168-3-146 SICS RPD COMPARISON HFP, 10758 MWD /T BURNUP D-226 , . . 3-169
~
3-147 SIC 6 RPD COMPARISON HZP, O MWD /T BURNUP D-201 . . . 3-170 _ 3-148 SIC 6 RPD COMPARISON HFP, 973 MWD /T BURNUP D-217 . . . 3-171 3-149 S1C6 RPD COMPARISON HFP, 7518 MWD /T BURNUP D-228 . . . 3-172 ;
- 3-150 SIC 6 RPD COMPARISON HFP, 13207 MWD /T BURNUP D-222 . . . 3-173 I?
xii I ' E.
LIST OF FIGURES Figure' Title Page 3-151' SIC 7'RPD COMPARISON HZP, O MWD /T BURNUP D 221 . .. 3 174 3-152 SIC 7 RPD COMPARISON HFP, 807 MWD /T BURNUP D-228 . .. 3-175 3-153 SIC 7 RPD COMPARIS0N HTP, 4329 MWD /T BURNUP D 228 . .. 3-176 3-154 SIC 7 RPD COMPARISON HFP, 7630 MWD /T BURNUP D-228 . .. 3-177-
^ I 3-155 SIC 8 RPD COMPARISON HZP, O MWD /T BURNUP D-212 . .. 3-178 j I 3-156 3 157 SIC 8 RPD COMPARISON HFP, SIC 8 RPD COMPARISON HFP, 900 MWD /T BURNUP D-228 .
8081 MWD /T BURNUP D-227 . 3-179 3-180
)
l 3-158 SIC 8 RPD COMPARISON HFP, 13212 MWD /T BURNUP D-212 . .. 3'-181 3-159 SIC 9 RPD COMPARISON HFP, 240 MWD /T BURNUP D-220 . . . 3-182 3-160 SIC 9 RPD COMPARISON HFP, 7295 MWD /T SURNUP D-222 . . . 3-183-3-161 . SIC 9 RPD COMPARISON HFP, 14606 MWD /T BURNUP D-217 . .. 3-184 3-162 S2C1 RPD COMPARISON HZP, O MWD /T BURNUP D-200 . .. 3-185 3-163 S2C1RPDCOMPARIS0k'HFP, 2030 MWD /T BURNUP D-203 . . . 3-186 3-164 S2C1 RPD COMPARISON HFP, 7310' MWD /T BURNUP .D-215 . .. 3-187 3-165 S2C2 RPD COMPARISON HZP,_ 0 MWD /T BURNUP D-199 . .. 3-188 3-166 S2C2 RPD COMPARISON HFP, 730 MWD /T BURNUP D-210 . . - . 3-189 - 3-167
~
S2C2 RPD COMPARISON HFP, 3750 MWD /T BURNUP D-216 . .. 3-190 3-168 S2C3 RPD COMPARISON HFP, 3127 MWD /T ,BURNUP D-221 . .. 3-191 ! 3-169 S2C3 RPD COMPARISON HFP, 8688 MWD /T BURNUP D-224 . .. 3-192 1 3-170 S2C4 RPD COMPARISON HZP, O' MWD /T BURNUP' D-228 . .. 3-193 3-171 S2C4 RPD COMPARISON HFP, 1186 MWD /T BURNUP D-223 . .. 3-194 3-172 S2C4 RPD COMPARISON HFP, 8250 MWD /T BURNUP D-201 . .. 3-195 3-173 S2C5 RPD COMPARISON HZP, O MWD /T BURNUP D-216 . .. 3-196 xiii
Il LIST OF FIGURES Figure Title Page
]
3-174 S2C5 RPD CJMPARI',0N HFP, 1690 MWD /T BURNUP D-217 . . . 3-197-3-175- 'S2C5 RPD COMPARISON HFP, 11320 MWD /T BURNUP D 220 . .. 3-198 3-176 S2C6 RPD COMPARISON HZP, O MWD /T BURNUP- D-223 . . . 3-199 - 3-177 S2C6 RPD COMPARISON HFP, 1116 MWD /T BURNUP D-228 . . . 3-200 .
, '4 3-178 S2C6 RPD COMPARISON HFP, 7390 MWD /T BURNUP D-228 . . . 3-201 i 1
3-179 S2C6 RPD COMPARISON HFP, 13900 MWD /T BURNUP' D-227 . . . 3-202' j 3-180 S2C7 RPD COMPARISON HZP, O MWD /T BURNUP D-211 . . . 3-203 3-181 S2C7 RPD COMPARISON HTP, 1647 MWD /T BURNUP D-226 . . . 3-204 3-182 S2C7 RPD COMPARISON HFP, 5781 MWD /T BURNUP D-226 . .. 3-205 3-183 S2C7 RPD COMPARISON HFP, 13122 MWD /T'BURNUP D-223 . 3-206
)
3-184 S2C8 RPD COMPARISON HZP, O MWD /T BURNUP ~D-228 . . . 3-207 3-185 S2C8 RPD COMPARISON HFP, 2423 MWD /T BURNUP D-228 . .. 3-208 3-186 S2C8 RPD COMPARISON'HFP, 6525 MWD /T BURNUP D-218 . . . 3-209 3-187 S2C8 RPD COMPARISON HFP, 12391 MWD /T BURNUP D-221 . .. 3-210 3-188- S2C9 RPD COMPARISON HFP, 1072 MWD /T BURNUP D-208 . . . 3-211 3-189 S2C9 RPD COMPARISON HFP, 6887 MWD /T BURNUP D-223 . . . 3-212 3-190 N1C3 RPD COMPARISON HZP, O MWD /T. BURNUP, D-2, C-130 . . 3-213 3-191 N1C6 RPD COMPARISON HZP, 0 MWD /T BURNUP, D-25, . . . ,, 3-214 3-192 S1CS RPD COMPARISON HZP, 0-MWD /T BURNUP, D-0, C-219 . . 3-215 ' 3-193 S2C4 RPD COMPARISON HZP, O MWD /T BURNUP, D-0, . . . . . 3-216 L 3-194 S2C5 RPD COMPARISON HZP, O MWD /T BURNUP,.D-228 B-33 . . 3-217 3-195 HZP CRITICAL BORON CONCENTRATION DIFFERENCES . ... . . 3-218 3-196 INTEGRAL CONTROL ROD WORTH DIFFERENCES . . . . .. . . . 3-219 xiv I
1 i LIST OF F10i'RES . i Figure Title Page 3-197: NICS B-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-220 3-198 NICS B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-221 1 3-199 NIC6 B-BANK INTEGRAL WORTH COMPARISON VS. POCITION . . .- 3-222' 3 200 N106 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-223 3-201 NIC7 B-BANK INTEGRAL WORTH COMPARISON'VS. POSIT!ON . . . 3-224 ' 3-202 NIC7 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . J-225 3-203 N2L2 B-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-226 o m 3-204 N2C2 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION , 3-227 ., 3-205 N2C5 B-BANK INTEGRAL WORTH COMPARISON VS. POSITION . 3-228' l 3-206 N2C5 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-229 _ l 3-207 N2C6 B-BANK INTEGRAL WORTH COMPARISON VS. POSITION , . . 3-230 3-208' N2C6 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-231
~
3-209 S1C2:D-BANK INTEGR5'L WORTH COMPARI!ON VS. POSITION . . . 3-232 3-210 SIC 2 D-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-233- 1 3-211 SIC 2 C-BANK INTEGRAL WORTH' COMPARISON VS.. POSITION . . . '3-234~ 3-212 SIC 2 C-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-235 "3-213 SIC 3 D-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-236 3-214 S1C3 D-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-237 3-215 S1C3 C-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-238 3-216 S1C3 C-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-239 a 3-217 S1C4 D-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . 3-240 I 3-218 SIC 4 D-BANK DIFFERENTIAL WORTH COMPARISON VS, POSITION . 3-241 3-219 SIC 4 A-BANK INTEG'tAL WORTH COMPARISON VS. POSITION . . . 3-242 LI XV
LIST OF FIGURES Figure Title Page -
.3-220 SIC 4 A-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-243 3-221 S2C8 B-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-244 3-222 S2C8 B BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 3-245 3-223 S2C9 B-BANK INTEGRAL WORTH COMPARISON VS. POSITION . . . 3-246 .
s 3-224 S2C9 B-BANK DIFFERENTIAL WORTH COMPARISON VS. POSITION . 247 3-225 PREDICTED.VERSUS MEASURED DIFFERENTIAL BORON WORTH . . . 3-248 - 3-226 HFP ARO BORON LETDOWN CURVES FOR N1C1 AND N2C1 . . , . . 3-249 3-227- HFP ARO BORON LETDOWN CURVES.FOR N1C2 . . . . . . . . . 3-250 3-228 HFP ARO BORON LETDOWN CURVES FOR NIC3 . . . .. .- . . . 3-251 3-229 HFP ARO' BORON LETDOWN CURVES FOR NIC4 . . . . . . . . . 3-252 3-230 HFP ARO-BORON LETDOWN CURVES FOR N1C5 . . . . . . . . . 3-253 j l 3-231 HFP ARO BORON LETDOWN CURVES FOR N1C6 . . . . . . , . . 3-254 'I q 3-237. HFP ARO BORUN LETDUWN CURVES FOR N1C7 . . . . . . . . . 3-255 3-233 HFP ARO BORON LETDOWN CURVES FOR N2C2 . . . . . . . . .- 3-256 ! 3-234- HFP AP.0 BORON LETDOWN CURVES FOR N2C3 . . . . . . . . . 3-257 3-235 HFP ARO BORON LETDOWN CURVES FOR N2C4 . . . . . . . . . 3-258- <
\ .. 3-236 HFP ARO BORON LETDOWN CURVES FOR N2C5 . . . . . . . . . 3-259-3-237 HFP ARO BORON LETDOWN CURVES FOR N2C6 . . . . . . . . . 3-260 l 3-238 HFP ARO BORON LETDOWN CURVES FOR SIC 2 . . . . . . . . . 3-261 3-239 HFP ARO BORON LETDOWN CURVES.FOR SIC 3 . . . . . . .. . . 3-262 3-240 HFP ARO BORON LETDOWN CURBS FOR SIC 4 . . . . . . . . . 3-263 3-241 HFP ARO BORON LETDOWN CURVES FOR S1C5 . . . . . . . . . 3-264 3-242 HFP ARO BORON LETDOWN CURVES FOR SIC 6 . . . . . . . . . 3-265 ,
xvi n.
I , igi
.g LIST OF FIGURES e i , Figure Title Page 3-243 HTP ARO BORON LETDOWN CURVES FOR S1C7 . . . . . . . . . 3-266 3-244 HFP ARO BORON LETDOWN CURVES FOR S1C8 . . . . . . . . . 3-267 3-245 HFP ARO BORON LETDOWN CURVES FOR SIC 9 . . . . . . . . . 3-268 ,
3-246 HFP ARO BORON LETDOWN CURVES FOR S2C2 . . . . . . . . . 3-269 ! i W: 3-247 HFP ARO BORON LETDOWN CURVES FOR S2C3 . . . . . . . . . .3-270 3-248 HFP ARO BORON LETDOWN CURVES FOR S2C4 . . . . . . . . . 3-271 3-249 HFP ARO BORON LETDOWN CURVES FOR S2C5 .. . . . . . . . 3-272
; 3-250 HFP ARO BORON LETDOWN CURVES FOR S2C6 . . . . . . . . . 3-273 3-251 HFP ARO BORON LETDOWN CURVES FOR S2C7 . . . . . , . . . 3-274 g.
5 3-252 HFP ARO BORON LETDOWN CURVES FOR S2C8 . . . . . . . . . 3-275 3-253 HFP ARO BORON LETLOWN CURVES FOR S2C9 . . . . . . . . . 3-276 3-254 PREDICTED VERSUS MEASURED HZP ISOTHERMAL TEMPERATURE l COEFFICIENTS . . . . . . . . . . . . . . .. . . . . . . 3-277 1 1 4 I l I , I 1
- I I
I l I xvil l u l
SECTION 1 - INTRODUCTION > ;
'I The Virginia Electric and Power Company (Virginia Power) is updating-and - increasing ' the scope of its capability to perform nuclear utility reactor analyses for the Surry and North Anna nuclear power stations'.
The objective of this topical report is 1) to describe one of the' - computational models developed at Virginia Power for the purposes of reactor physics analyses and fuel management evaluations and 2) to demonstrate the accuracy of this model by comparing analytical results l generated with the model to actual measurent ts from Surry and North Anna. Units No. I and 2. The computational model to be described is a coarse mesh- (five
. non-uniform mesh per fuel assembly), three-dimensional (26 non-uniform axial mesh), two neutron energy group diffusion-depletion (with thermal-hydraulic feedback) , calculational package and is designated as the PDQ two zone calculational model. The "two zone" designation refers .
to the use of two separate material zones to represent each fuel assembly in the X-Y dimension - one zone where no lumped burnable poison rods or
; control rods exist and one. zone in which the poison rods or control rods are homogenized with the fuel materials. The PDQ two zone model uses the I Virginia Power computer. codes SHUFL and PDQV2, as well as input from the EPRI ARMP-028 CELL 2 8 '8 and NUPUNCHER' codes, the Virginia Power ETHIL code, the EPRI ESCORE' code, and the SCALE 3' package from ORNL (including KENO-V.a'). SHUFL is an update of the SHUFFLE 7 code ' developed by Babcock and Wilcox and adapted by Virginia Power. PDQV2 is an update to the PDQ7V2s code modified for use by Virginia Power. In addition, pin power ! ) .
distributions and instrument thimble fluxes are reconstructed using 1-1
A I pointwise flux and block nuclide. concentration files in conjunction with- -the Virginia Power computer _ codes PCF' and RECON. A detailed-description of the input / output,-. functioning, and physical models of the I above computer codes can be obtained from the referenced computer code manuals. The above computer codes are maintained by Virginia Power. The-EPRI computer codes are updaged through contractual arrangements between ; Virginia Power and EPRI. The SCALE 3 code package is updated periodically . through notification by the ORNL Radiation Shielding Information Center. ' The PDQ two zone model was designed to provide a three dimensional reactor physics analysis capability which combines the three dimensional j benefits of the Virginia Power FLAME'8 3-D nodal model with isotope deplation capability, cross section modeling complexity, more optimized mesh structure, and.more reliable reflector modeling available with PDQ. l i In addition, the cross section representation has been improved through gj use of CELL 2 with the ENDF/B-V option, through the use of KENO-V.a W {j benchmarking calculations, and through the addition of multiple G-factor l capability in the Virginia Power version of PDQ. . The 3-D two zone model requires more computer usage than the Virginia Power FLAME model or PDQ discrete (2-D pin by pin) model'*. However, use - of the two zone model provides the following:
- 1. Local power distributions for vessel fluence calculations _ l at any axial core elevation.
- 2. Benchmarking of the CELL 2/PDQ system without axial buckling assumptions.
g W
- 3. A modeling benchmark for the faster but less detailed 3-D g nodal code (FLAME). g i
- 4. A modeling benchmark for 2-D axial buckling verification. g g i
- 5. A single base model from which inputs for the Virginia Power NOMAD 1-D axial model can be obtained.
1-2 R . 5 ,
In addition, a 2-D collapsed version of the 3-D two zone model has , been developed to replace the Virginia Power PDQ one zone model s Benefits of the replacement will be an improved mesh structure, more l detailed cross section representation through the use of multiple G-factors, improved cross section data through use of CELL 2 with KENO V.a benchmarking, verified axial buckling inputs by direct comparison with 3-D model results, and pin power reconstruct.lon capability. Computer I requirements should be comparable to those of the one zt. model. The types of calculations that can be performed by the two zone model include:
- 1. Reactor Physics Analysis
- a. Three-dimensional assembly average radial power distributions ,
I relative radial peaking factors (FXY(Z)), enthalpy rise hot channel factors (FAH(X,Y)), assembly average axial power distr aution, core average axial power distribution (P(Z)), and heat flux hot channel factor (Fq (X,Y,Z))
- b. Critical soluble boron concentrations
- c. Nuclide concentrations
- d. Integral and differential control rod bank worths
- e. Abnormally positioned control rod bank worths
=
- f. Moderator and Doppler coefficients and defects
- 2. Fuel Management Analysis
- a. Batch power and burnup sharing
- b. Fuel isotopics as a function of burnup
- c. Scoping studies for the evaluation of alternative future cycle designs and fuel loadings These calculations are currently performed with other core models.
However, the benchmarking data presented in this report shos that the 3-D PDQ two zone model is a capable alternative. Of the above types of 1-3
.. _ ........ _ - =_
i Il calculations,. the ones' ~ that are of primary interest are thhse which-l- > require the greatest degree of 3-D modeling detail where computer use is o, not limiting. For example, vessel fluence calculations require a consistent model so that predictions which have been benchmarked to I I
' capsule measurements - for early cycles can be reliably extrapolated through future cycles. Calculation of the critical rod position for I ,:,
startups following a trip or extended outage- requires that both the l reactivity impact of isotope decay, the axial flux redistribution, and 3 ' the partially inserted control rod worth bc ' accurately predicted. Use of part length flux suppression rods to reduce vessel fluence requires a model which can predict the reactivity, power distribution, peaking and ~ 5'l depletion effects in three dimensions. Scoping studies involving axial ~ zoning, axial blankets or reduced length burnable poisons can also be I performed with the 3-D two zone. Comparison of two zone model predictions l wit': FLAME predictions has , provided a basis for identifying modeling improvements for the nodal model. Similar improvements in the 1-D NOMAD ii 1 l model cay be an additional benefit. All of these examples represent i possible reasons for choosing to use the 3-D PDQ two zone model. Il The Surry Nuclear Power Station and the North Anna Nuclear Power : Station, each consisting of two operating units, have been selected as ) i the operating ' system to be modeled for verification of the PDQ two zone model. The Surry Units Nos. 1 and 2 are identical Westinghouse designed . l three coolant loop pressurized water reactors with thermal ratings of 2441 - ' Mwt. Initial criticality was achieved for Surry Unit No. 1 on July 1, 1972 and for Surry Unit No. 2 on March 7,1973. Cycle operating summaries l for the Surry units are listed in Table 1-1. - 1-4 I I ,
a ~ \- The North Anna Units Nos.1 and 2 are identical Westinghouse designed
- three coolant loop pressurized water reactors with thermal ratings of 2893 Mwt (initially rated 2775 Mwt). Initial criticality was achieved for v North Anna Unit No. ' on April 5,1978 and for North Anna Unit No. 2 on June 6, 1980. Cycle operating summaries for the North Anna units are listed in Table 1-2. ,
[ The remainder of this report describes the Surry and North Anna versions of the PDQ two zone mode), the purpose and interrelationships of the'various computer cooes which comprise the PDQ two zone model,-and the comparison of cal'culated results with selected reactor measurements from all completed and operating North Anna and Surry cycles. 1-5
- _ m-----
I I TABLE 1-1 SURRY NUCLEAR POWER STATION OPERATING HISTORY UNIT / CYCLE ON LINE
, ? TE OFF LINE CYCLE BURNUP CORE RATING g DATE (MWD /MTU) (MWT) 3 SIC 1 09/12/1972 10/24/1974 13547 2441 -
S1C2 02/03/1975 09/26/1975 6915 2441 S103 12/08/1975 10/17/1976 8944 2441 S1C4 01/.4/1977 04/22/1978 13107 2441 SICS 07/09/1978 09/14/1980 14390 2441 SIC 6 07/06/1981 02/07/1983 16491 2441 SIC 7 05/30/1983 09/26/1984 11984 2441 SIC 8 12/26/1984 05/10/1986 14040 2441 S1C9 07/12/1986 04/09/1988 16073 2441 S1C10 07/14/1988 2441 S2C1 03/19/1973 04/26/1975 14870 2441 S2C2 06/19/1975 04/22/1976 9054 2441 S2C3 06/10/1976 09/10/1977 9422 2441 S2C4 10/12/1977 02/04/1979 13678 2441 S2C5 08/19/1980 11/07/1981 13971 2441 I S2C6 12/31/1981 06/30/1983 76006 2441 S2C7 09/25/1983 03/20/1985 14802 2441 S2C8 06/27/1985 10/04/1986 13359 2441 S2C9 11/30/1986 9/10/1988 15710 2441 S2010 0'/16/1989 2441 ! I 16 I Bi
1 I ! l TABLE 1-2 NORTH ANNA NUCLEAR POWER STATION OPERATING HISTORY I UNIT / CYCLE ON LINE DATE OFF LINE DATE CYCLE BURNUP (MWD /MTU) CORE RATING (MWT) 4 N1C1 04/23/1978 09/25/1979 15590 2775 NIC2 01/24/1980 12/28/1980 10711 I 2 7 7.". NIC3 04/10/1981 05/17/1982 13335 2775 NIC4 11/18/1982 05/12/1984 13478 2775 N1CS 09/25/1984 11/04/1985 13398 2775 NIC6 12/23/1985 04/19/1987 15705 2775/2893 , N1C7 06/29/1987 02/25/1989 16891 2893 N1C8 07/15/1989 2893 , I N2C1 N2C2 10/23/1980 03/07/1982 06/02/1982 04/02/1983 14494 8436 2775 2775 N2C3 05/29/1983' 08/02/1984 14717 2775 N2C4 11/02/1984 02/20/1986 15f34 2775 N2C5 04/01/1986 08/24/1987 17467 2775/2893 N2C6 11/03/1987 02/20/1989 17044 2893 N2C7 05/07/1989 2893 I I I I I 1-7 I
1 I
.I '
SECTION 2 - MODEL DESCRIPTION I I
2.1 INTRODUCTION
1 I lI The PDQ two zone model incorporates a few group, diffusion-depletion theory model, with thermal-hydraulic feedback, to perform spatial neutron
- flux and nuclide concentration calculations in three dimensions l throughout the reactor core. This calculation is performed at each mesh point represented in the geometry of the reactor core. Furthermore, each fuel cssembly la represented by a specified array of mesh blocks formed by the intersection of the mesh lines in the x and y directions (i.e. .
mesh points). Each mesh block is used to represent a material composition I whereas the neutron flux is calculated at each mesh point. 1 { 1 With the exception of burnable poison rods (BP) or control rods, the material compositions of each assembly are initially homogenized so that ! each mesh block within c.n ,ssambly represents an equal concentration of fuel rods, guide tubes, etc. Therefore, the concentrations of the various ' nuclides (non-BP or control rod) are initially the same in all mesh blocks t 1 I within a fresh fuel assembly. For reasons detailed in section 2.2, the control rod and BP related concentrations are segregated into only that 1
- 1. part of the assembly over which they exert the most influence. There are
{ l therefore two possible initial concentration zones for each assembly. ' I As the assembly undergoes depletion with power operation, however, the material compositions change in each mesh block according to the neutron flux associated with that mesh block. 2-1 1 l
'1 i
Il l Il The two zone model performs calculatioa.s in several steps. First, a fine group neutron flux spectrum and the appropriate cross sections as l a func*. ion of neutron energy are calculated for each material composition I with the cross section generating code CELL 2. The fine group flux g gi spectrum is then used to spectrum weight and collapse the fine group cross sections into two neutron energy groups (denoted as the fast and thermal , groups). The spectrum weighted two group cross sections associated with ; each material composition including the baffle and reflector are then used to perform an iterative diffusion theory calculation of the neutron flux ' as a function of spatial position. Solution of the diffusion theory equations consists of estimating an initial source distribution and eigenvalue, computing the flux in each group at each mesh point, and then [ recomputing the source and eigenvalue. This process is repeated until the change in flux and/or eigenvalue between successive iterations meets a predetermined convergence criterion. From the converged neutron flux and cross sections, the core power distribution is determined, and subsequently the fuel and moderator temperature distributions are ' calculated. Thermal feedback effects are included in the diffusion theory calculation by recalculating the neutron cross sections, flux and power distribution, and fuel and moderator temperature distribution iteratively until both the required nuclear and thermal convergence criteria are met. The neutron flux in the core is not only a function of energy and position but is also a fonction of changes in the nuclide concentrations and cross sections which vary with burnup. The initial nuclide depletion calculation is performed with the initial two group fluxes and 2-2 I'
I : I microscopic absorption and fission cross sections for the nuclides in each i mesh block that vary with burnup. The neutron flux is then recalculated ! based upon these new values of nuclide concentrations and cross sections. This process is repeated over an interval of depletion stcps until the ' desired burnup is achieved. Because in a 3 D model this process can lead l .g W to axial xenon concentration oscillations, an equilibrium xenon option I is of ten used for depletion cases. The equilibrium xenon concentration is calculated in an iterative manner similar to the thermal feedback. Thermal and xenon feedback convergence parameters are chosen to assure stability and convergence of the final solution. Following execution of the PDQ code, pin powers are reconstructed in 3 D to determine peaking I factors. Several interrelated computer codes are used to perform the , calculations outlined above. The computer codes comprising the PDQ two I . zone model and their interrelationships are presented in the flow chart of Figure 2-1. The PDQ computer code itself is the principal reactor analysis calculational tool in the PDQ two zone model and is used to perform the two group, two-dimensional dif fusion theory calculations. The other codes provide either input data, data manipulation, or use the PDQ code output. As indicated in Figure 2-1, the CELL 2 computer cod s is I used to calculate the required two group spectrum-weighted c.oss sections. The ETHIL computer code formats these cross sections for use in the PDQ code (as HARMONY tablesets). NUPUNCHER reads CELL 2 output files to provide cross sections for the lumped fission product representat bn. The KENO V.a Monte-Carlo code is used to provide benchmark eigenvalues as a basis for adjusting the HARMONY tableset input 2-3 I
\ I-so that closer agreement between KENO and PDQ is obtained. KENO V.a also provides the cross sections and worths for preparing and verifying the PDQ control rod cross section tables. The EPRI ESCORE code and XSDRNPM f rom the SCALE 3 package are used to provide the average fuel temperature as a function of burnup and power. The SHUTL computer code is a data manipulation code that takes appropriate end-of-cycle nuclide concentrations from the PDQ computer code and shuf fles this data in the reactor core according to a specified scheme which duplicates calculationally the actual replacement and movement of fuel assemblics in the reactor core as the result of a refueling. Figure 2-2 shows the calculations involved in pin power reconstruction. A database of reconstruction data is developed using PDQ single assembly models to represent each unique fuel type in the core. The data is calculated and stored by the PCF code. The RECON code is used to reconstruct in 3-D each pin power in the core to determine peaking factors and to prodtice data to be used with the PDQDK and INCORE ' codes. 8 INCORE is used to determine the measured core power distribution. I Section 2-3 describes in greater detail the functioning of each of the computer codes used in the PDQ two zone model. I I I 2-4 Il-
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I i FIGURE 2-2 ; PIN POWER RECONSTRUCTION FLOWCHART 2 I. PURPOSE I: PDQ TWO PDQ Deplete assembly models for each ZONE DISCRETE type of fuel / history combination. ' SINGLE SINGLE Major effects are control rods, BP, ASSEMBLY ASbMBLY depleted BP, burnup, BP history. I < PCP Calculate and store pef's, thimble flux multipliers for each fuel type. l
=
BUILD Write stored PCF data to a direct I' access file for RECON. 3D PDQ Write flux and concentration files. l FILES W I' RECON Read direct access file, 3D PDQ flux and concentration files, user input to calculate quarter core 3D peaking , factors and data for PDQDK/INCORE. PDQDK Read average power file and PDQDK I e input data written by RECON. Write 3 INCORE input data decks. g INCORE Read PDQDK and measured flux map data. Calculate measured power and peaking factors. I
,., I I
s ~ 2.2 MODEL CEOMETRY l The assembly geometry for the PDQ two zone model was selected based on the conflicting needs of minimum computer usage and maximum power l distribution accuracy. The primary dif ficulty of a coarse mesh dif fusion i theory model occurs et locations of rapidly changing neutron flux. This i problem can be overcome to a great degree at the core boundaries by adjusting the coarse mesh reflector constants to better match a fine mesh diffusion theory solution or transport theory solution. The problem is not as severe for assemblies away from the core boundaries except when burnable poisons or control rods are involved. The presence of a discretely positiorad strong neutron absorber depresses the flux in the vicinity of the absorber and creates a flux profile which rises away f rom the absorber. The current at the interface of a fuel assembly containing burnable poison (BP) rods and a non-BP neighbor of similar fuel characteristics will be directed inward at the poisoned assembly. The impact is an in-leakage of flux (and therefore power) from the non-BP assembly into the assembly with BP. If this current is not adequately calculated the relative power distribution among neighboring assemblies will not be accurate. In conventional diffusion theory (with no discontinuity factors) there are two requirements for maximizing the accuracy of power distribution calculations: First, the mesh structure should be finest near important boundaries, and second, the lumped poison rods or control rods must not be homogenized over the entire assembly. The first consideration was the primary factor in the selection of the 26 mesh axial 2-7
structure shown in Figure 2-3. Both considerations were important in the l selection of the X Y mesh structure. The pin by pin orientation for Surry , (15x15) fuel is given in Figure 2 4 Figure 2-5 shows the two zone X-Y "[ geometry model chosen to represent the 15x15 assembly. The corresponding North Anna (17x17) pin by pin orientation is given in Figure 2 6 and the I two zone representation is shown in Figure 2-7. The 5x5 mesh is coarse enough to reduce computer requirements by a factor of 10 versus a discrete m pin by pin representation. The variable mesh size improves the ability E to calculate the flux gradient with respect to either a core boundary or a neighboring assembly versus a fixed mesh model. The two zone feature, which segregates the control rods or poisot. uloser to their region of influence within the assembly, also provides a mesh block beyond the poison region over which the flux can rise. This better represents the ' flux gradient in a poisoned assembly versus a model in which the poison is homogenized over the entire assembly (such as the Virginia Power PDQ one zone model). Because the PDQ option of point depletion is used, all 25 mesh blocks are used in the representation of assembly surnup , gradients. Ei A stande.rdized probles designed to test the ef fectiveness of model geometry is the 2-D IAEA benchmark". This quarter core problem has a li i fixed set of neutron macroscopic cross sections for each fuel assembly and for the reflector region and a well defined solution for the assembly I average power distribution. Figure 2-8 presents a power distribution map l comparin3 the PDQ and benchmark solutions for a uniforn 6x6 PDQ nesh structure similar to that used in the Virginia Power PDQ one zone model. Figure 29 shows the same comparison based on a 5x5 non uniform nesh 2-8 l Bl
l f s 1
=
structure similar to that ured in the two zone model. Even though there are only 25 mesh blocks per assembly versus 36 per assembly in the 6x6 model, the non-uniform 5x5 power distribution errors are only half as large. A factor of two increase in power distribution accuracy is obtained while reducing computing time by 237.. Note that the power 1 I distribution differences in Figure 2-9 are largest at the core boundary ] l and exhibit an in out tilt in both sign and magnitude. Adjustments to the baf fle and reflector representation can be made to remove much of the ' tilt. The adjustment process will be discussed further in Section 2.3.6. I The axial mesh structure was selected using the same argument that l a finer mesh near the core boundary will maximize power distribution l accuracy and minimize computer run time. Although no benchmark results I are presented here, the process normalizing the axial reflector representation to a very fine mesh dif fusion model is described in Section 2.3.6. Axial power distribution plots comparing PDQ two zone and measured f data, as well as differential control rod worth comparison plots, will be presented in Section 3 to verify the accuracy of the axial structure, I r I I I :
- I I 2-9 I
i PDQ TWO ZONE AXIAL MESH STRUCTURE i I g
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FIGURE 2-4 l l SURRY FUEL 15 X 15 X-Y PIN ORIENTATION I I i 2 I ' 4 X l I 5 X X 6 X X 7 I 9 10 X X 11 X X 12 X 13 X X I X X 14 I FUEL PIN CELL I x rossleLE e ,oo e, con 1,el eco Loc m e, e INSTRUMENT THIMBLE I 2-11 t I
f FIGURE 2 5 SURRY FUEL TWO ZONE X-Y MESH STRUCTURE I
.X....
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, .. .X.
I 2 .. . .. . . . . .X. . . . .. .... .
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4 . . . . . . .. . .. . . . . . ... ..
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5 I ZONE 1 - HOMOGENIZED FUEL , I
.X. ZONE 2 - HONOGENIZED MIXTURE OF FUEL AND BP OR CONTROL ROD NOTE : BP and instrument thimble locations are shown.for reference only.
2-12 I
l I FIOURE 2 6 h I NORTH ANNA FUEL 17 X 17 X-Y PIN ORIENTATION I I 2 2 I 3 X X X i 1 4 X X 5 6 X X X X X l 1 7 l 8 J I 0 9 X X X X ; 10 I 11 i 12 X X X X X 13 l 14 X X 15 X X X 16 I 17 I X POSSIBLE BP R0D OR CONTROL ROD LOCATION O INSTRUMENT THIMBLE t 2 13 l .l
I IF: .. f FIGURE 2 7 i NORTH ANNA FUEL TWO 7.0NE X-Y MESH STRUCTURE : I i I.P i 1
. . .. .. X.....X.. . . .X . .. ... .
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i r ZONE 1 - HOMOGENIZED FUEL I
.X. ZONE 2 '.30MOGENIZED MIXTURE OF FUEL AND BP '
. . . OR CONTROL ROD NOTE : BP and instrument thimble locations g, are shown for reference only. 5 2 14 I
, , , - -- . . - - , - e -n e"- * '
v I i FIGURE 2-8 l I IAEA 2-D BENCHMARK PROBLEM I X) 6 X 6 UNIFORM MESH RESULTS , I O.746 1.310 1.454 1.211 0.610 0.935 0.934 0.750 I 0.728 2.413 1.24 3
-5.115 1.394
-4.127 1.160
-4.211 0.s10 0.000 0.927 0.856 0.951 1.820 0.800 6.667 1.310 1.435 1.480 1.315 1.070 1.036 0.950 0.736 1.243 1.372 1.422 1.270 1.041 1.034 0.970 0.782 , .
-5.115 -4.390 -3.919 -3.422 -2.710 -0.193 2.105 6.250 :
1.454 1.480 1.469 1.345 1.179 1.071 0.975 0.692 1.394 1.422 1.419 1.308 1.160 1.075 1.003 0.758
-4.127 -3.919 -3.404 2.751 -1.612 0.373 2.872 9.538 4
1.211 1.315 1.345 1.193 0.967 0.906 0.846 1.160 1.270 I -4.211 -3.422 1.308
-2.751 1.165
-2.347 0.952
-1.551 0.918 1.325 0.900 6.383 1
I 0.610 0.610 0.000 1.070 1.041
-2.710 1.179 1.160
*4.612 0.967 0.952
-1.551 0.471 0.484 2.760 0.686 0.701 2.187 0.597 0.656 9.883 0.935 1.036 1.071 0.906 0.686 0.585 .
0.927 1.034 1.075 0.918 0.701 0.642 ,
-0.856 -0.193 0.373 1.325 2.187 9.744 0.934 0.950 0.975 0.846 0.597 0.951 0.970 1.003 0.900 0.656 I 1.820 2.105 2.872 6.383 9.883 ,
0.736 I 0.692 0,750 AAA A - REFERENCE 0.800 0.782 0.758 BBB B PDQ 6 X 6 ; 6.667 6.250 9.538 CCC C - % DIFFERENCE , I MAX DIFFERENCE = 9.883 MAX DIFF (RPD>0.9) = -5.115 RMS DIFFERENCE = 4.558 2-15
t i FIGURE 2-9 IAEA 2 D BENCHMARK PROBLEM PDQ TWO ZONE 5 X 5 NON UNIFORM MESH RESULTS 0.746 1.310 1.454 1.211 0.610 0.935 0.934 0.750 0.736 1.274 1.424 1.183 0.611 0.930 J.944 0.772
-1.344 -2.745 -2.085 -2.276 0.204 -0.529 1.038 2.981 1.310 1.435 1.480 1.315 1.070 1.036 0.950 0.736 1.274 1.403 1.453 1.293 1.056 1.036 0.963 0.754
-2.745 -2.227 -1.817 -1,686 -1.327 0.017 1.336 2.506 l
m' 1.454 1.480 1.469 1.345 1.179 1.071 0.975 0.692 1.424 1.453 1.448 1.329 1.172 1.076 0.991 0.722 l W i
-2.083 -1.815 -1.423 -1.161 -0.625 0.485 1.631 4.334 1.211 1.315 1.345 1.193 0.967 0.906 0.846 I, 1.183 1.293 1.329 1.180 0.959 0.913 0.873 -2.272 -1,681 -1.178 -1.105 -0.796 0.753 3.213 O.610 1.070 1.179 0.967 0.471 0.686 0.597 0.611 1.056 1.172 0.959 0.479 0.691 0.622 g 0.213 -1.318 -0.618 -0.791 1.652 0.693 4.269 3 0.935 1.036 1.071 0.906 0.686 0.585 0.930 1.036 1.076 0.913 0.691 0,609 l -0.515 0.030 0.497 0.763 0.699 4.117 0.934 0.950 0.975 0.846 0.597 -
0.944 0.963 0.991 0.873 0.623 1.056 1.353 1.647 3.226 4.279 l 0.750 0.736 0.692 AAA A - REFERENCE ! 0.773 0.755 0.722 BBB B - PDQ 5 X 5 3.001 2.526 4.353 CCC C - % DIFFERENCE 1' MAX DIFFERENCE = 4.353 MAX DIFF (RPD>0.9) = -2.745 RMS DIFFERENCE = 2.102 I 2-16 I'
I I 2.3 CROSS SECTION GENERATION I 2.3.1 FUEL CROSS SECTION GENERATION The primary source of the basic nuclear cross section data is the ENDT/B V library used in the EPRI CELL 2 code. The library contains cross
- I sections for 68 fast energy groups ranging from 0.414 eV to 10 MeV and 35 thermal energy groups ranging from 0.000253 eV to 1.855 eV. Additional details of the library are available in Reference 2.
The CELL 2 code is used to calculate composition dependent energy spectra and then collapse the fine-energy group cross sections to produce two group- >ss sections for each unit cell. CELL 2 calculates two group ! spectri- +ghted cross sections for each type of unit cell used to ; represerit the reactor core. A unit cell can be either a fuel rod, a control rod guide tube, or a burnable poison rod, the moderator associated s with each type of rod, and an extra region around the cell to account for the impact of other assembly materials. A supercell is defined as the combined flux weighted homogenization of all the regions comprising a unit > cell. For the two zone model, the fuel unit cell consists of a fuel rod, 7 the cladding, moderator, and an extra region to account for guide tubes (with or without BP rods) and moderator gaps between assemblies. The supercell option is used to represent the fuel assembly in the two zone model because only a homogenized assembly can be represented due to the coarse mesh structure used. The homogenization is performed in a manner that results in all the mesh blocks within each zone initially having the same material composition. All fuel cross sections (not burnable poison 2-17
l' i or control rods) used in the two zone model are based on the CELL 2 sur 1rcell data. A more detailed description of the theory and use of the CELL 2 code is available in References 1, 2, and 18. The neutron energy spectrum calculated by CELL 2 depends on the material concentrations in the unit cell. The material concentrati.ns change during the operation of the reactor as a result of: g
- 1) Depletion of the fuel nuclides I
- 2) Changes in the soluble boron
- 3) Changes in moderator temperature
- 4) Removal or addition of BP rods The neutron spectrum is also dependent on the temperature of the fuel due to Doppler broadening of the resonance absorption peaks. CELL 2 is used to calculate the ef fect of changes in both the material concentrations ;
and the fuel and moderator temperatures on the neutron spectrum and spectrum-weighted two group crees sections. To provide a base of fuel cross section data comprehensive enough I for development of a thorough HARNONY tableset, CELL 2 fuel cell cases are run over a wide variety of conditions. Conditions modeled include:
- 1) Depletion at nominal power, temperature, and soluble boron. !
- 2) Moderator temperatures ranging from 620'F to 100'F.
- 3) Fuel temperatures from HFP nominal to 100'F. lll
- 4) Xenon concentrations ranging f rom HFP nominal equilibrium to no xenon.
- 5) Soluble boron ranging up to 2000 ppa.
2-18 _q i
- . . -- . _ - _ . . ~
l I i I 6) Samarium concentrations ranging from 0 to two times equilibrium. i I 7) U888, Pu8 " , Pu868, and Pu868 concentrations at nominal and 10% above nominal for each burnup. I 8) With and without the water displacement ef fect of burnable poison rods.
- 9) With and without the neutron absorption of the BP rod Bl8 I 10) Appropriate combinations of some of the above.
I t A 4ter identification of significant cross section sensitivities the t Virginia Power EThIL code is used to format the cross sections into f t HARMONY tableset format. 2.3.2 BP CROSS SECTION GENERATION Because CELL 2 cannot represent both BP rods and fuel rods in their actual geometry simultaneously, a two stage approach is used. The unit I cell for the BP model consists of the BP absorber, clad, moderator, and two cxtra regions consisting of fuel and moderator homogenized. The fuel , and moderator homogenization is performed in such a way that the flux 4 spectrum in the fuel region nearest -the BP pin is reasonably representative of the fuel pin cell spectrum. The neutron absorption rate ' of the BP pin is calculated and properly volume averaged for use as input to the CELL 2 fuel pin cell model for determining the sensitivity of fuel cross sections to BP neutron absorption. The BP cell model is also used to provide BP microscopic absorption cross sections and' flux depression factors which are input to the HARMONY tableset as a function of fuel , isotopics, boron, moderator temperature or specific volume, and BP B10 number density. 2-19 I
? , In J 2.3.3 CROSS SECTION REPRESENTATION ! l Sets of HARMONY cross section tables based on these CELL 2 i calculations are prepared by the ETHIL code. These tables represent:
- 1) Microscopic fast and thermal energy group absorption, fission I>
and transport cross sections for each material or isotope.
- 2) Fast and thermal Nu and Kappa for each fissioning isotope.
- 3) The macroscopic removal cross section.
- 4) Multiple G-factor tables applied to (1) and (3) above to model e any important cross section dependences not accounted for in g the cross section tables. The G-factor tables also model number density dependences (such as soluble boron as a function g
of moderator density) and flux depression factors (for BP or control rods). The cross section representation strategy is to account for all significant cross section dependences on a microscopic cross section level. Ideally, this removes the need to identify and consciously account for ' history' effects which lead to different burnup dependent fuel isotopics. For example, one such history ef fect is soluble boron history. Depletion at higher boron concentrations leads to a higher production of ! plutonium isotopes at any given burnup relative to depletion at lower boron concentrations. Unless the impact of soluble boron on the cross sections of each affected isotope is included in the HARMONY tableset, the isotopic differences will not be accurately reproduced. For this rasson, there are no lumped macroscopic cross sections or macroscopic > cross section sensitivities in the two zone HARMONY tablesets except for the removal cross section and control rod cross sections. In addition, use is made of the CELL 2 detailed fission product edit to model explicitly : 2-20
. - . , - , . . - - . , - . - . -- ~ - - , _ . . . , - . - , , , _
w several fission product production chains not typically modeled. The nuclide chains of intere st are those leading to isotopes which have [ significant reactivity impact due to changing concentrations during periods of zero or low power or during full power operation following zero or low power operation. Xenon and samarium are two such nuclides which are commonly modeled. Thos e not typically modeled have been removed from the lumped fission product representation produced by CELL 2 so as not to doubly account for any fiss ion products. 1 Once all cross section dependences have been represented, the tables are assembled in a HARMONY tableset along with depletion chain and other data required for PDQ to oc rrectly interpret the tables. A series of PDQ runs are made duplicating the initial CELL 2 calculations using a 2-D fuel assembly model with reflective ' flux boundary conditions. The number density predictions and K' infinity values are compared to those produced by the CELL 2 supercell fuel model to verify that all important cross section dependences have bee n accurately modeled. Additional CELL 2 runs I- are mado to check the validity of the data under other conditions, such as during long periods at z ero power followed by full power operation and during depletion at non' nominal moderator temperatures. The goal is for the PDQ/ HARMONY systes to reasonably reproduce the CELL 2 predictions for any condition within the expected range of actual core operation or analysis. 2-21
2.3.4 NORMALIZATION TO KEN 0*V.a BENCHMARK CASES Prior experience with , reacto: core modeling has indicated that adjusting the predictions of PDQ (and by extension the crosc section generation code) to higher order Monte Carlo predictions often imptsves the agreement between prediction and measurement. The Monte Carlo program used by Virginia Power for this purpose is the KENO-V.a code run using the SCALE 3 driver package with the 218 group ENDF/B-IV cross section set. The two zone HARMONY tablesets contain adjustment factors to normalize BP worth, soluble boron worth, and overall reactivity predictions to target predictions. The taiget predictions are based on adjusted eigenvalues from KENO for a frest fuel assembly (using reflective boundary conditions) at a variety of conc itions. In the KENO model each fuel pin, guide tube and BP rod is explicitly modeled including clad and voids. A bias is assigned to the KENO eigenvalues on the basis of the results from several modeled critical experiments. The adjustment factors are determined in an iterative process aligning the PDQ eigenvalue for each case to the biased KENO eigenvalue. Appropriate consideration is given to the statistical uncertainty of the KENO predictions. The normalization process is applied separately to each fuel enrichment in the HARHONY tableset. 2.3.5 KENO V.a CONTROL ROD CROSS SECTIONS I I A KENO-V.a model is also used to generate control rod cross sections for the two zone PDQ model. The geometry used is a checkerboard assembly arrangement in which every oth6r assembly can contain a control rod. The 2-22 I.
i I ! i 27 group ENDF/B IV cross section library is used because it contains 5 I fission products needed to simulate burned fuel. An edit code is used to coovert K-infinity, 27 group absorption rates, fission rates, and l fluxes into 2 group macrescopic absorption, fission, and r moval cross f sections. Rodded and unrWed cases at a variety of burnups, boron concentrations, and moderator temperatures are run to produce a set of macroscopic cross section differences due to the addition of the control ! rod. The cross section tables are appropriately volume weighted and added
- to the HARMONY tableset as microscopic cross sections and G-factors associated with the fictitious "crod" isotope. A checkerboard two zone I6 PDQ model is used in an iterative process to determine the correct flux !
depression factor to be applied to the control rod cross sections in each energy group so that the overall reactivity effect produced agrees well with the KENO predictions. Comparisons of measured and predicted integral and differential control rod worths presented in Section 3 indicate e excellent overall agreement using this model. I 2.3.6 REFLECTOR AND BAFFLE CROSS SECTIONS ' r Determination of coarse mesh baf fle and reflector constants for the two zone geometry- is done by appropriately volume weighting and then adjusting the coarse mesh constants to better match the power distribution and flux ratios predicted by a very fine mesh PDQ model. For the X Y W' plane, a quarter core geometry is used. The fine mesh geometry consists of a uniform 44X44 blocks per assembly plus additional mesh for the baffle, reflector, and core barrel, Cross section data for the stainless steel region is obtained by editing the clad region of a CELL 2 stainless 2-23 I
l II f steel clad fuel cell. Water and boron mixture cross sections are generated using the CELL 2 non-fuel option. The coarse mesh cross sections are then calculated such that the optical thickness through each region -, is preserved as nearly as possible. So that two mesh blocks may be used in the baffle region to better account for flux gradients, the baffle cross section optical thickness weighting is performed over the first two > mesh beyond the fuel boundary. PDQ quarter core fine and coarse mesh runs , l are made so that the relative power distributions and the flux ratios near the baffle can be compared. Small adjustments to the baffle constants , are made until the agreement between the models for a variety of conditions is judged acceptable. The maximum RPD error obtained for all assemblies in the quarter core model is less than 1.57., The final set Ii of macroscopic cross sections are tabulated in the HARMONY tablesets for use in the PDQ quarter core two zone model. A similar procedure is used to determine the axial reflector I representation. CELL 2 non-fuel runs are used to determine cross sections for each of several regions represented above and below the active fuel -length in the very fine mesh axial PDQ f tel model. The best mesh size (using two mesh above and two mesh below the fuel) and cross sections for => use in the coarse mesh PDQ two zone model are then iteratively determined on the basis of power distribution a n.' fuel end mesh flux ratio comparisons to the fine mesh mod e l . The chosen cross sections are - tabulated in the HARMONY tableset as a function of moderator temperature or specific volume and soluble boron concentration. The reflector mesh sizss are added to the standard 3-D quarter core PDQ geometry description. , 2-24 8
~ -
r 2.3.7 FUEL TEMPERATURE DATA L Fuel temperature data is obtained using the EPRI ESCORE code. Fuel pin construction, power level, and burnup data are input to the code for determination of the best estimate volume averaged fuel pin temperature as a function of burnup and power level. The temperature data is produced separately for 15x15 and 17x17 fuel. I . One set of adjustments is applied to the ESCORE fuel temperatures. ESCORE is typically run using ten concentric ring temperature zones in the fuel pin. The 10 ring temperatures are volume weighted to produce a single average temperature. However, from a neutronic standpoint, a more desirable temperature is the effective single temperature which results in the same resonance absorption as the more detailed 10 ring temperature distribution. To determine a set of correction factors, an XSDRNPM" 10 ring fuel pin cell model is set up with a typical temperature distribution across the fuel. NITAWL" resonance weighting is performed for each of the 10 fuel temperatures. A ten ring model is also run using a uniform temperature distribution across the pin. The uniform temperature which produces the same pin cell K-effective is determined by interpolation of several different unifore temperature runs. The difference between the. volume weighted average temperature and the equivalent uniform temperature is the correction factor. Factors are determined as a function of power level for f resh fuel and applied to the ESCORE best estimate average temperatures to provide the ef fective temper ature tables for the PDQ two zone thermal hydraulic input data. 2-25
. ,,, ,,a m - imm----e em==mi
I 2.4 PDQ QUARTER CORE CYCLE CALCULATIONS 2.
4.1 INTRODUCTION
The PDQ computer code, as used in the PDQ two zone calculational model, is a two-dimensional, two group, diffusion depletion program which is used to calculate the neutron flux, power, and nuclide concentrations as a function of position and burnup. The PDQ computer code uses the appropriate and properly formatted cross sections along with the initial description of the reactor core (i.e., geometry and material compcsition description) to calculate the eutron flux distribution at spatial mesh points for two energy groups at the desired core power. The spatially
~
dependent neutron flux is then combinea with the appropriate nuclide concentrations and cross sections to obtain the spatially dependent power distribution. Once the initial spatially dependent flux and power aist.ributions are obtained, the depletion of the nuclide concentrations is calculated. The boundary conditions used in the quarter core solution of the two dimensiona. diffusion theory equation are:
- 1) Zero current for the boundaries located along the core axis
- 2) Zero neutron flux for the boundaries located at the reactor vessel wall and at the end of the axial reflectors.
2.4.2 DEPLETION CALCULATIONS Each mesh block it. PDQ - itains a single homogenous composition. The volume-weighted nuclide concentrations for each mesh block in the core are input to PDQ for beginning of life core conditions. In addition, nuclide depletion chains which describe the prod'.ct Ma and loss 2-26 I: , e
s
- 8. mechanisms for .burnup dependent . nuclides uce incorporated into the HARMONY. tableset. The appropriate nuclide depletion. equations are assigned in PDQ to each mesh block. These equations are used by PDQ to
=
deplete the nuclide concentrations in each mesh block based on:
- 1) The average fast and thermal energy group neutron fluxos calculated by PDQ for the mesh block
- 2) The s. wrum-weighted fast and thermal group cross sections ,
detet' - by PDQ from the cross section tableset assigned to the mesh block Nuclides described by these depletion equations in the two zone model are listed in Table 2-1. Detailed chains used as the source for the PDQ cha' ins are described in Reference 21. I I i I I R I I 2-27
. . _ _ . . . . - ~ _ _ . . _ . _ _. _ - __ _ _ _ . _ . _ _ . . . _ _ . _ _ . _ _ . _ - ~ _ _
I , TABLE'2-1 3 NUCLIDES INCLUDED IN Ti!E PDQ TWO-ZONE DEPLETION CIIAINS- g' g}
-l FUEL NUCLIDES:
U234, U235, g236, g238,
-Np 239 ,
Pu239, Pu240, Pu 2 'I, Pu242 _ Am 241 .
'i .
!- 1 l FISSION PRODUCTS: l . Ru l03 Rh103, Rh105 g135- f Xe135, y,135m Nd147, Nd148 5j rmI '7,-Pm148, p,148m, p,149 Sel '9 Eu130, Eu155
~
'at F (stable lumped fission product) ~I ,
a I g? I, 2-28 I-
2.4.3 THERMAL HYDRAULIC FEEDBACK PARAMETERS: I Thermal-hydraulic feedback ef fects are represented in the PDQ two zone model in ordt.r to more accurately calculate t'..e power and burnup distribution.. The input to PDQ required for thermal-hydraulic feedback consists of: L 1)- 61st iMet onthalpy and flow rate per unit area I 2) Nn*bm of fuel rods t unit area
- 3) System pressure *
- 4) Difference between average fuel temperature sad moderator temperature as a function of relative power desity I and burnup The strategy used in the feedback calculation consists of first making an initial estimate of the fuel and moderator temperature for each '
r coolant channel. Based on this initial estimate and the cross section tables for each fuel cell, 'the PDQ code calculates the two group cross sections for each mesh block. These cross ' sections are used: in a diffusion theory calculation of power density in each mesh block. .This l power density is then used in a calculation of. the fuel and moderator. L temperature for each block. ' In turn, the new fuel. and moderator 1
. temperatures . are used to calculate new two group cross ' . s ec.:; ions for
- j. another diffusion theory power distribution calculation. This process ll is continued until the power density for each fuel mesh in the Nth iteration differs- from the power density in the (N-1)th iteration by less l.
li than the convergence criterion. I If an equilibrium xenon calculation is desired, the xenon and iodine concentrations are determined in a similar fashion to the THF iterations. 2-29
) -
L
. . - . - _ _ - . . . -~ .. . ..-
c
.I 1
Pairs of THF and xenon iterations (each associated with a new cross . section- and power . distribution calculation) are performed until the
)
convergence criteria for both have been satisfled. Because the temperature distribution resulting from the latest THF iteration changes 1
' he _ power distribution it also changes the next xenon distribution calculation. The same is true for the ef fect of the xenon iteration on the next THF calculation. Due to this interdependence, relaxation parameters have been determined which ensure proper convergence with a reasonable number of iterations.
L I 1.< I IL I; . I' l I Is I; , 2-30 I
Y 2.5 PIN POWER RECONSTRUCTION 2.5.1 USE OF SINGLE ASSEMBLY MODELS FOR PIN-TO BLOCK POWER RATIOS I The RECON pin power reconstruction scheme is based on the following
~
premises: 3
- 1. The 3D PDQ two zone model accurately predicts assembly -
power distributions and overall power gradients across assemblies.
- 2. Pin power behavior can be accurately calculated for the quarter core model by applying results from single essembly calculations to the 3D mesh block powers.
Support for the first premise is found later in this report through comparison- to measured power distributions and based on the results of I the 2D IAEA reference problem when run with the 5x5 uneq'ual mesh geometry. 'I The second premise involves judging _ the . accuracy of a - number of simplifying assumptions made for practical reasons. The method used to determine pin power behavior is to use two 2D single assembly PDQ models I (one a discrete pin and the second a two zone 5x5) and ' calculate for each pin the pin power divided by the nearest two zone block power. The PCF code is used to process the single assembly results in this way. This in effect corrects not only for pin to pin variations unknown to the-two zone model but also for intra-assembly power distribution inaccuracies in the two zone caused by homogenizing the BP over blocks rather than representing them in discrete pin locations. Inherent in this approach is the need to produce a finite database of pin information. Therefore, l single assembly cases are modeled with reflective boundary conditions (an 2-31
I infinite lattice of the same fuel type with no cross assembly gradient), depleted'at nominal power and THF conditions (not with the actual assembly power history), and history ef fects which are approximated (such as BP history). However, the 30 PDQ model can calculate flux gradients, power gradients. THF ef fects on block power, and history ef fects on block power. Because the pin powers are determined - relative to block powers, errors are only incurred if the pin to block relationship is in error. One way a
'g to judge the magnitude of the errors is to compare the pin power distributions of the 2D discrete quarter core PDQ model. to the reconstructed pin powers from the 3D.
I However, differences in predicted assembly power - distributions _ between the discrete and two zone models, and the fact that the 3D pin powers are collapsed over the axial planes with actual 3D power distributions make the comparison difficult. In the 3D pin power axial collapse, each plane has its own burnup, pin to block, and relative power sharing characteristics. This should lead to differences between- a 2D approach (volume weighted burnup and peaking characteristics) and a 3D approach (power and volume weighted burnup and peaking characteristics). Comparison of the 3D and 2D pin powers therefore must allow for these physical effects. A direct comparison of peak pin to assembly average power ratios between the models shows differences of about 1% for interior , assemblies and up to about 3% for peripheral assemblies. By comparing . . the 2-D - results to a single 3-D model plane of approximately average I-assembly burnup and adjusting for power gradients across each assembly caused by differences in predicted power, the differences are reduced to only a few tenths of a percent in calculated peak pin powers. 2-32
s W-N Similarly, two group instrument thimble fluxes are reconstructed by y. t- multiplying ratios derived from single assembly PDQ. calculations by the PDQ' 3-D model fluxes in the blocks containing the instrument thimble. The validity of this approach can be demonstrated directly by comparing
- measured detector- reaction rates to those predicted with the reconstructed thimble fluxes. Comparison data is provided in section 3'.4. ,
1 2.5.2 CORRECTING FOR FLUX GRADIENTS ACROSS A BLOCK I For-the purpose of determining the effect of a flux gradient on pin powers', there are two factors to consider:
- 1. The impact of a fast flux gradient on power is not the same as the impact of a thermal flux gradient.
- 2. The spatial flux-to power relationship changes significantly if a large burnup gradient is present across the assembly.
The first problem is addressed in RECON'by multiplying the fast flux by an input flux multiplier and adding the result ' to thc. thermal flux. The resulting synthesized flux is called the relative flux. The input value of the multiplier used for RECON validation calculations was based on the typical ratio of fast to thermal fission cross sections (approximately 0.05). The second concern is taken care of by calculating. the block power to relative flux ratio across the assembly. This. ratio will give the impact on power of a given relative flux distribution. The pin power tilt produced across each block is consistent with the power gradient from block to block within the assembly. The validity of th'is 2-33 -
. _ ~
. . _ .~ _. . _ . . _ _ . _ __ _ ____ .___ _ _ _ __ _ _ _ _ _ . . _ _ _ _
e approach can be seen'in the smooth variation of reconstructed pin powers: , across block boundaries. a E' 51 Ill 1 4 I j
- I gL I
IL I 2-34 I 5.
- SECTION 3 - RESULTS
3.1 INTRODUCTION
The purpose of this section is to present a comparison of analytical predictions from the PDQ two zone model with measured data obtained from the Surry and North Anna units. These comparisons encompass both initial and reload cycles of operation in order to demonstrate both the accuracy and flexibility of the _ two zone model. Virginia Power intends to optionally use the two zone model for all core calculations currently performed with one zone or discrete PDQ models. To justify this, a large number of comparisons to a variety of measured data will be presented. 3.2 ANALYTICAL CALCULATIONS The types of calcula* .ns described in this section fall into two general groups: power distribution calculations and reactivity calcula-tions. Power distribution calculations include:
- 1. Fuel assembly average relative radial power distribution as a function of cycle depletion (RPD(X,Y)).
- 2. Fuel assembly average relative radial power distribution with control rods inserted at beginning of cycle.
- 3. Core average axial power distribution as a function of cycle depletion (P(Z)).
4 Peaking factors F AH(X,Y) and qF (X,Y,Z) as a function of cycle depletion. 3-1
Power distribution' calculations as a function of burnup are .I
; performed to assure that the assemblywise relative powers, maximum pin -
4
-powers and local heat fluxes are within acceptable limits for the entire cycle depletion. Other important uses .of the 3-D model for power distributions include -vessel fluence predictions, benchmarking for the .'
2-D two zone version, benchmarking for the 3-D FLAME model, providing a good single source model for input to the 1-D NOMAD model, evaluating the merits of shortened BP rods or axial blankets, and quantifying the 3-D effects by comparing to an otherwise identical 2-D model. Reactivity calculations include:
- l. Integral control rod bank worths
- 2. Differential control rod bank worths
- 3. Critical boron concentrations and differential boron worths
- 4. Isothermal temperatura coefficients
- 5. Estimated critical control rod positions (ECP) for startup Integral control rod bank worths are calculated by holding all-reactor parameters constant except for the rod bank (s) whose worth is to be determined. For early cycles, control rod worths were measured >
individually using the boron dilution method. More.recent cycles have used the dilution method to measure the highest worth bank '(the reference bank) and then use the- rod - swap method of inserting a test bank and withdrawing the reference bank at a constant boron. The worth of the test bank is determined by the worth of the withdrawn portion of the reference bank. For comparison to the measured data, PDQ calculations are run in
- the same manner as the test is conducted. For dilution cases, an all rods 3-2 E
out case and a reference bank in case at the same soluble boron
=. concentration provide the reactivity worth of: the reference bank. For rod swap comparisons, onq case is. run with the reference and test bank.
[ in their final critical configuration, and another case is run with only the reference bank at its partially inserted final configuration. This provides the test bank worth in the presence of the partially inserted reference bank. Differential control rod worths are calculated by inserting the control rod one axial node at a time. The' reactivity change for each node insertion is divided by the number of rod steps associated 5 with each node. Core criticality is maintained by adjusting the boron concentration as a function of burnup, power Icvel, etc. The boron concentration at which the reactor is just critical is called the critical boron concentration. This value is calculated by first using an estimated input boron concentration to determine the core K-ef fective and then correcting r. 4 _q this boron concentration to a value which corresponds to the critical condition. Sufficient detail in geometry and cross section data exists in the two zone model such that the predicted critical boron falls within an acceptable uncertainty band about the measured critical boron and it is not necessary to establish a " target" K-effective based 'on measured data. In most of the comparison cases, the input boron concentration corresponds to the measured critical boron concentration. ; The isothermal temperature coef ficient is defined as the change in ; core reactivity per degree change in the moderator, clad, and fuel temperature (i.e., the sum of the moderator and Doppler temperature 3-3
p k Il' coef ficients). The calculation.of the isothermal temperature coef ficient.
, values at the hot zero power (HZP) condition is : important because they can be compared to plant measurements taken during startup physics testing ]
and therefore, can provide a basis for evaluating the accuracy of isothermal temperature coefficient, moderator temperature coefficient, and Doppler coefficient design predictions. The isothermal temperature ' coefficient is derived by. dividing the change in core reactivity caused by a uniform temperature change by the change in temperature. Estimated critical rod positions are required prior to restarting i the unit after a period of time at zero power (such as after a trip or maintenance outage). All reactivity elements of'the model are tested in this prediction because boron worth, power defect, partially inserted control ' rod worth, axial - flux redistribution effects, transient - fuel isotope and fission product. worth (such as Xel35, Pal 49, Np239 decay -to )
\
Pu239, and others) are all involved. The- xenon concentration may be higher or lower than the HFP equilibrium value depending on the power history and down time. ECP calculations were run for several cycles based .j on-the actual history and critical startup conditions. 3.3 MEASUREMENT DATA ,
=
i Measurement data ~is obtained from the routine physics testing l conducted.during'the startup of each cycle of operation as well as from W routino core performance monitoring conducted during the depletion of . ' each cycle. The methods used for measuring core power distribution, burnups, ' control rod, bank worths and critical boron concentrations are 3-4
..__m_ . . . . ..
1 ) t J described in Reference 12. Figure 3-1 shows the core locations of all
] movable detector thimbles.
J Several types of comparisons can be made to determine the accuracy of the power distribution and peaking factor calculations of the PDQ 3-D two zone / RECON system. First, the predicted power in monitored assemblies is compared to the inferred measured power, which was determined using the INCORE code with 2-D PDQ discrete model input as described in Reference 12. Measured peaking factors were also obtained from PDQ discrete / INCORE results for monitored assemblies. For F aH comparisons, the peak pin power for each monitored assembly from INCORE is compared to the F 6H from RECON. For Fq (X,Y,Z), the peak local pin power at each axial plane for monitored assemblies is read frem INCORE results and is output for axial planes between spacer grids. Because the grids depress power locally, power production peaks between the grids. The two zone model does not explicitly represent the grids and tends to underpredict power most versus measurement between grids. The RECON code provides Fg(X ,Y ,Z) interpolated using a three point Lagrangian scheme to the same axial location as the INCORE data for each monitored assembly, resulting in five points of comparison for each 15x15 assembly and six for each 17x17 assembly. Table 3-1 gives the axial location of the 15x15 and 17x17 INCORE points used for Fg (X,Y,Z) comparisons along with the three nearest PDQ two zone planes for each. For safety analysis, only powers greater than the core average are of interest. Therefore, only those observations which had measured and predicted values greater than 1.0 are used. 3-5
-Note that the comparisons' described above (assembly average power and _ peaking . factors) use results from the PDQ discrete 2-D model based _
INCORE measurements. Because RECON can generate INCORE input, statistics - can also be' determined relative to INCORE measurements based on the PDQ two zone 3-D / RECON system. By calculating:the measured versus predicted statistics in both ways, both the PDQ 3-D / RECON peaking factors and INCORE input generation capability can be verified. The INCORE. input . capability can also be verified using the average (average of the absolute percent differences) percent difference between predicted and measured - thimble reaction rates. This quantity is edited by INCORE and is the most direct comparison of measurement and prediction. Control rod bank worth determination with the rod swap method is described -in Reference 22. Figure 3-2 shows the core location of all control' rod banks. Isothermal temperature coefficients are measured during the startup of~each cycle by monitoring with the reactivity computer the reactivity changes associated with a uniform heatup or cooldown rate. The test is performed at a-very low power to assure that. L fuel and moderator temperatures are consistent. Reactivity is determined - using the reactivity computer and is plotted against RCS temperature on an x y recorder. The temperatura coefficient is then determined from the slope of the plotted line. l I I 3-6 I
I' I TABLE'3 1 AXIAL GEOMETRY FOR POWER DISTRIBUTION COMPARISONS . NORTH ANNA UNITS: SURRY UNITS:
% Core % Core Height Description- Height Description 103.5 Grid 1 104.0 Grid 1 89.2 Grid 2 90.8 Grid 2 89.1 PDQ Plane 20 89.1 PDQ-Plane 20 . .\
84.4 PDQ Plane 19 84.4 PDQ Plane-19 81.7 INCORE Node 12 83.3 INCORE Node 11' 78.1 PDQ Plane .18 78.1 PDQ Plane 18 74.9 Grid 3 72.6 Grid 3 71.9 PDQ Plane 17 71.9 68.3 INCORE Node 20 PDQ Plane 17 i 65.6 PDQ Plane 16 :+ _ 65.6 PDQ Plane 16 63.3 INCORE Node'23-59.4 59.4 PDQ Plane 15 PDQ Plane 15 60.6 Grid 4 54.4 Grid'4 59.4 1 PDQ Plane 15 53.1 PDQ Plane 14 53.3 INCORE Node 29 46.9 PDQ Plane 13 53.1 PDQ Plane 14 45.0 INCORE Node 34. 1 5 46.9 PDQ Plane 13 40.6' PDQ Plane 12 l 46.4 Grid 5 36.2 Grid 5 ( 46.9 PDQ Plane 13 34.4 PDQ Plane 11 , 40.6, PDQ Plane 12 28.1 PDQ Plane 10 38.3 INCORE Node 38 26.7 INCORE~ Node 45-
- I_. .. 34.4 PDQ Plane 11 .21.9 -PDQ Plane 9 I i
32.1 Grid 6 ~18.0 Grid 6 34.4 PDQ Plane 11 15.6 PDQ Plane 8 i 28.1 PDQ Plane 10 13.3 INCORE Node 53. .i 25.0 INCORE Node 46 10.9 PDQ Plane 7
. I'i 21.9 PDQ Plane 9 7.8 PDQ Plano 6 i
17.8 Grid 7 1.3 Grid'7 21.9 PDQ Plane 9
- g. 15.6 PDQ Plane 8 t
_g~ 15.0 INCORE Node 52 l- 10.9 PDQ Plane 7 l 0.8 Grid 8 3-7
1 I I FIGURE 3-1 FULL CORE MONITORED ASSEMBLY LOCATIONS ! I i i I l I no 1 I - l l I l I 4 l l 1 1 I I : 1 I I I i i e I i l- 1 I I I I I i
-l i I I '
I no I l- I-1. 1 I no I no i I I I I I .I I I I no l I
'.*5E I I I I I I '
I l l l l l 1 I I l- ' 1 I I I I I no i I l'no 1 1. no I l l I I I I I I I I l l I
' I .
I I I I I I I I i i I. I I I ; 1 I no l I no I i no l- 1 I I no - I - no l l no I I i l l_ l I I I I i l 1 -1 1. I I I I i i i i 1 i l i i l- 1 E1 1 1 1 no I i no I I I I I I I I I I i no l I I l I l I l-I 1: g i I l 1 i 1 l i l l l-i l I 1 I i i l I no l 1 l l no l I no I l- I no " 1 11 no I I I I I i i I I I I i l .I l- 1 I I l- 1 I l. I no 1 -I no I I I I I L l I l- 1 i no I l i i 1 e l- l l no I no l 1 ! 1 I I I I I I I I I I l i I 'l 4 1 I I I I I I i I 1 -1 I i 1 I i L-l~ l I- 1 I no : 1. I I I no' i no l I I l l' no: 1 I I l l l l' l l l ~l l I l _ l' I .I I I I I I I I I I i 1 -1 I I no l I ;l I no I i l- 1. I no I l no 1-1 I I l- 'l l I I l i I I I l' - 1 I i 1 l l 1 -l 1 -l, I i l I I I i 1 e i I I no 1 I no I no 1 I l i I I I l I l i 1 I I I I I I 1 I I l I i i l i I no - l l -1 I no 1 -l 1. I l- I l no I no . I 1 E i ~gi l l I I I I l I l- - I l I l- -l l l 1 l- 1 i l i 1- .I I 1 l no l l no - l l~- 1 4 I I l l l l l I I l- 1 l l 1 1 l l- 1 i -- I no - 1 I I I'e I l- 1 i l I i l i I I I l I i I no 1 I I 'g. E-I I I I MD - Movable Detector e a l lC L .IL 3-8 I. E_
_--,,,.,,..,,w,, , FIGURE 3 2
. FULL CORE CONTROL ROD BANK POSITIONS m
A D A SA ~; A , e 2 C B B C SB SS A B D C D B .A SA' SB SB SA D C C D
'SA SB SB 3A 1 _ .
, A B D C D. B A 3 I SB -SB C 'B B C l
SA SA A D' A l
]
Function Number of Clusters 1 _ _ Control Bank D 8 Control Bank C 8 Control Bank B 8 Control Bank A 8 Shutdown Bank SB 8 Shutdown Bank SA 8 3., q
lr > o 3.4[RESULTS-l Table 3-2 lists currently approved nuclear reliability factors (NRF)' by which the indicated ' two zone model results - can be judged. More information about the basis for the existing factors may be found in 1 Reference 23. Statistical results of the two zone model power ; distribution predictions compared to the measurements obtained from the . j. L Surry and North Anna Power Stations are presented in Table 3-3. 5 Statistics for reactivity parameter comparisons are given in Tables 3-5 ' and 3-6. The basis for the Table 3-2 two zone model nuclear uncertainty factors (NUF).is discussed below. 1 3.4.1 POWER DISTRIBUTIONS I , Figures 3-3 through 3-104 show the predicted versus' measured core
~
average relative axial power as a function.of cure height -(P(Z)). Data for both HZP and HFP at various core burnups 'is presented. for each cycle. Measured values were taken from INCORE runs with inputs generated. with thef PDQ ' discrete model. Data for all cycles has been included - to demonstrate the ability of the two zone model to predict both the changing j HFP axial power shapes of fresh and reload cores as well as the strongly top peaked reload-core HZP distributions. ' Figures3-105 through 3-192 are comparisons of measured and predicted. radial. power distributions. Only relative powers in monitored
' core -locations (as listed in INCORE runs) are included in the measured data. Predictions. for each full core location are symmetrically unfolded 3-10 I
from the quarter core PDQ ' model . The compariscar include . HFP (e 90% w power) and HZP (< 6% power) msps as well ar five rodded hZP maps for h further verification of the geometry and control rod model performance. For the four rodded maps for which a corresponding unrodded map exists (NIC3, S2C4, SICS, and S2CS), RMS dif ferences - in power in the ARO and I rodded maps are very similar. The very low assembly powers in the rodded assemblies are also well predicted. The root mean square of the power distribution differences for rodded HZP maps (Figures 3-191, 3-193, 3 194, and 3-195) compares favorably to the root mean square of the differences in the corresponding unrodded maps (Figures 3-108, 3-144, 3-171, and 3-174, respectively). In the rodded' assemblies, differences between measured and predicted powers are typical
- I of all assemblies in the map, indicating no loss - of accuracy in power distribution due to control. rod insertion. Differences are generally smaller for the HFP maps. This is due in part to core power tilts which are larger at _ low power ar.d possibly to gamma flux contributing to the measured neutron flux in-some very low power cases.
Table 3-3 presents RPD, F AH and Fq statistics determined by comparison to PDQ discrete based INCORE measurements and to PDQ 3-D / RECON based INCORE measurements. Only monitored locations with measured and predicted values greater than the core average relative power of 1.0 were retained. Included in the table are the 95%/95% one sided upper tolerance limits (uncertainty factors) based on the six of HZP, part power and HFP maps indicated.
-l' 3-11
I The PDQ- 3-D / RECON based flux map database used is listed in Table-3-4 For a common subset of 2-D discrete and RECON based INCORE maps- . consisting of 7 utrodded HZP and 41 unrodded HFP flux maps, the RECON based maps show the smallest average of the instrument thimble reaction' rates. This indicates that the PDQ 3-D / RECON system provides somewhat better power distribution and/or thimble flux predictions than the 2-D discrete model. Use of the 3-D PDQ / RECON system for INCORE mapping data m also appears to be conservative in that it results in a slightly (about g 0.5%) more negative mean of the measured peaking factor dif ferences. Because the predictions for these two cases are the same, this means that the measured peaking factors are slightly larger than those measured with the PDQ 2-D discrete based INCORE. For this reason, the reliability am factors listed in Table 3-2 have been chosen from the RECON based lNCORE g data consisting of the full set of maps indicated in Table 3-4. The _ assembly FAH 95%/95% one sided uncertainty factor of 1.034 for North Anna cycles and 1.031 for Surry cycles comparea well with the existing nuclear - - reliability factor of 1.05 Only monitored assemblies with measured and predicted FAH > 1.0 w',re used. Assembly_ Fq (Z) comparisons from the same maps at selected ".xial locations between. spacer grids for Fg values > 1.0 yield uncertainty factors of 1.067 for North Anna and 1.072 for Surry. These factors compare well with the existing nuclear reliability factor
~
of 1.075. Because of the margin to the existing reliability factors and . because of the apparent conservatism in the peaking factors measured using the PDQ 3-D / ' RECON based predictions, no additional conservatism is considered. necessary to account for possible uncertainty caused by= the g g. pin power reconstruction technique. 3-12 E1 lH
I
; 3.4.2 REACTIVITY PARAMETERS-I
~
Figure.3-193 is a plot of the difference between the predicted zero [ power critical boron concentration and the measured critical boron-concentration for startups. Data includes both BOC startups and restarts
- I>- in mid-cycle following a trip or maintenance outage. There is a tendency
; to overpredict tho' critical boron at hot zero power by an average of about 7 ppm. The standard deviation is 20 ppm and all' but one of the predictions is within 40 ppm of the measured critical boron concentration. The administrative startup acceptance criterion is 50 ppm.
I Figure 3-194 shows the dif ference ' between measured and predicted r control rod bank worths plotted versus- the predicted rod worth. The data includes all BOC measurements (boron dilution and rod swap method). All l d!fferences are well w thin..the indicated startup criteria ( 15% or 100 pcm for banks worth 667 pcm or less). All but 5 of the 157 predicted-points fall within 10% of the measured' values. . Of the 5 predicted points which. show errors greater than 10%, three .are very low worth banks averaging less than one-third of the average bank. worth. The. remaining two have differences of 10.3% and 10.8%. ' The statistical uncertainty . factor for the 157 rod worths of 1,10 matches the current nuclear reliability factor. Interestingly, rod worths measured by boron dilution exhibited no significant blas, but worths measured by rod swap indicated I a 1.8% average overprediction by the two zone model. Figures 3 195 i through 3-22'+ present a representative set of differential and integral rod worth comparisons as a function of control rod bank insertion. As shown in the plots, the two zone axial mesh structure is fine enough to 3-13 i i
1 obtain. good worth versus' insertion shapes compared ' to those measured. Localized dips in the measured differential rod worth are caused by thel 'l l fpresence of friel rod spacer grids. Grids were not explicitly modeled:in j the two zone due to the coarseness of the axial mesh. - j Figure '3-225 shows the predicted differential boron worth at BOC. , plotted versus the corresponding measured value. 'All points fall well within the 10% startup. acceptance criterion. There is no significant ; ; bias. The existing nuclear reliability factor cannot be met by the data - as measured. However, comparison of dilution method control rod worth errors and differential boron worth errors reveals a strong linkage between = these two independent parameters.- The common link between measured rod, worths' and boron worths is the reactivity computer. Because : i , the - boron worth is calculated based on the change in boron needed to - 1,
~
offset the reactivity inserted by one or more control rod banks, if the reactivity computer introduces a bias on the measured control rod worth, the same bias will be evident in the boron worth. This theory has been
~
tested successfully by finding the coefficients of the best fit 'line described by the following equation: D5W ERROR (%) = A + B
- ROD WORTH ERROR (%)
The 95%/95% confidence interval for the slope (B) includes the range . 0.42'to 0.'80, Indicating a statistically valid correlation (if the slope range includes 0, no correlation is proven). To quantify the degree of i ,i error introduced to the rod worth and boron worth statistics by the g 5 reactivity computer, the following assumptions are made: 3-14 I C
- 1. Predicted control rod worth and boron worth dif ferences from true core valu es are independent of each other.
- 2. The reactivity c mputer o introduces a bias on _ the standard deviation of each set of differences by introducing a random
^ bias (cycle to cycle)'to the measured values. If the two ' sets of observed percent differences (one set for rod worths and one set for boron worths) are truly independent, the standard deviation of the set of data obtained by adding _ the rod worth and boron , worth dif ferences together will be the same as that for the set of data obtained by subtracting the differences. Because the boron worth dif ferences an'd rod w o rth differences are not independent, subtracting tends to cancel out the reactivity computer bias and adding tends' to double it. Table 3-5 gives the statistics obtained for the dilution method rod worths diffe ences, r the associated boron worth- dif ferences ,- the added dif ference data, and the subtracted difference data. For cycles where more than one rod bank was used to determine the boron worth, the boron worth dif ference has been associated with each individual bank worth
~
difference. The standard deviation of the subtracted data is the smallest (4.0%) and represents the combined root mean square of the individual true rod worth and boron worth standard deviations. The added dif ference data shows a standard devistion of 8.6% which suggests that the standard deviation bias introduce d through use of the reactivity computer is on
~
the - order of 27,. This is verified by calculating the root mean square of the rod worth real standard deviation (observed minus 2%) and the boron worth real standard deviation. The calculated value of 3.8% is close to-that calculated for the subtracted difference data. Adding two times the reactivity computer bias to this gives 7.8% which is reasonably close to the added dif ference data standard deviation of 8.6%. The presence of a l 3-15 l t
I reactivity' computer bias'also explains why the rod swap control-rod data-exhibits a lower standard deviation (4.2%) than the dilution method control rod data (4.8%) even though the dilution method rod banks are the highest worth banks (with lower inherent test uncertainty). A portion of the reactivity computer bias:is present in the rod swap data as well because it is used to obtain the reference bank worth against which the l other banks are measured. ! I i Based on this analysis, both the integral rod worth and- the dif ferential boron worth predictive uncertainties are overstated. If >l there were an error of 5% in the total boron worth at beginning of cycle ;
-(when the average boron concentration is about 1400 ppm), a critical boron error of 70 ppm would be expected unless offset or added to by some other j factor. In 30 cycles, the largest BOC ' HZP critical .oron dif ference is '
58 ppm '(4.4%) . Using a 2% estimate for the bias it the Table 3-5 rod worth and boron worth statistics, the integral control rod worth uncertainty can be reduced to 1.057 and an uncertainty factor of 1.05 for' boron worth error is reasonable based on the estimated standard deviation of 2.4%. , The boron worth sample is small (31 points) and is non-normal so the statistical uncertainty factor is not easily calculated if the reactivity computer bias is to be accounted for. However, the magnitude of the
~
standard deviation, the observed maximum critical boron difference, and l the 20 ppm (1.4%) standard deviation of the BOC HZP critical boron differences all support the 1.05 estimated uncertainty factor. Figures 3-227 through 3-254 show the predicted versus measured boron I letdown curves based on HFP all rods out (ARO) operation. Both measured 3-16 5_'
, : and predicted data have been modified to remove the ef fects of off-nominal operation (operation. at reduced power, reduced temperature, or 1 with [L control rods partially' inserted). Data for all cycles has been included to demonstrate the flexibility of the model to handle high and low leakage loadings, large -or small numbers of fresh or depleted burnable poison rods, and a wide range of- fuel enrichme7ts without re-normalization of the model to measured data. - Significant scatter in the measured data. makes qttantification of dif ferences difficult. Letdown curve slope, shape, and overall agreement indicate that the 50 ppa' reliability factor is appropriate for HFP predictions as well. Differences are typically limited to about 30 ppm which is consistent with the HZP startup data. 1 Figure 3-255 presents a comparison of predicted versus measured isothermal temperature coefficients for both rodded and unrodded
-configurations at BOC. All points are within the t '3 pcm/'F startup criteria. A bias of approximately - 0.8 pcm/*F in the predicted data can be =er, in the plot.
I I 1 l l l ' 3-17 I
I TABLE 3-2
SUMMARY
OF NUCLEAR RELIABILITY FACTORS g
;g PARAMETER VEP-FRD-45A PDQ TWO ZONE I! I NRF NUT
- i
, Individual Integral Bank x 1.10 x 1.06 Worth Cumulative Integral Bank x 1.10 x 1.06 Worth' '
Differential Bank Worth. 2 pcm/ step < 2 pcm/ step. , Worth . Critical Boron Concentration 50 ppm 50 ppm Differential Boron Worth x 1.05 x 1.05 Moderator Temperature 3 pcm/'F 3 pcm/'F. . Coefficient . F AH x 1.05 x 1.034 North' Anna' I x 1.031 Surry. - s Fq x 1.075 x-1.067 North Anna x 1.372 Surry I ..( }
- Nuclear uncertainty factor ---defined as the 95%/95% one sided -
upper tolerance limit. '1 I
. IL I-I 3-18 I:
I-
I TABLE 3-3 POWER DISTRIBUTION STATISTICS NORTH ANNA UNIT DIFFERENCE FROH MEASURED (%) NUMBER STANDARD TOTAL UNC. DESCRIPTION OF PTS. MEAN DEVIATION FACTOR MAX. MIN. t (1) HZP &-HFP I.- RPD > 1.0 540 0.49% 1.9 % 1.028 8.7 -12.3 . HZP & HFP F AH > 1.0 696 0.54% 2 .1 *. 1.031 9.4 =-12.1 I- Fq HZP & HFP
> 1.0 4205 -1,67% 2.8 % 1.062 9.2 -14.1 (2) HZP & HFP I' RPD > 1.0 550 0.11% 1.6 % 1.025 7.7- -8.8 HZP & HFP I F AH Fq
> 1.0 HZP & HFP
- > 1.0 701 4205 0.03%
-2.24%
1.8 % 2.6 % 1.029 1.065 7.8 8.1
-9.6
-14.1 (3) ALL RPD > 1.0 1175 0.23% 1.8 % 1.028 7.8 -8.8 ALL I F AH Pg ALL
> 1.0
> 1.0 1479 "S46
. 0.12% -
-2,16%
1.9 % 2.8 % 1.034 1.067 8.8 11.2
-9.6
-14.1
'(1) Based on 4 HZP and 17 HFP flux maps (PDQ 2-D discrete based INCORE)
(2) Based on 4 HZP and 17 HFP flux maps (PDQ 3-D / RECON based INCORE) (3) Based on 6 HZP, 2 part power, and 32 HFP flux maps (PDQ 3-D'/ RECON
' based INCORE)
;I;
.g It l 3-19 I I: .
TABLE:3-3 (Continued) SURRY UNIT DIFFERENCE FROM MEASURED (%) NUMBER STANDARD TOTAL UNJ. DESCRIPTION OF PTS. MEAN DEVIATION FACTOR MAX. MIN. (4) HZP & HFP RPD > 1.0 775 0.507 1.9 % 1.030 o.7 -11.1 HZP & HFP _ F AH > 1.0 1018 0 . 51*. 2.0 % 1.031 10.9 -10.9 HZP & HFP Fq > 1.0 5080 -2.09*. 3.1 % 1.070 13.6- -13.0 (5) HZP & HFP RPD > 1.0 773- 0.09% 1. 7 *. 1.^28 5.9 -10.8' HZP & HFP : F 6H > 1.0 1016 -0.02% 1.7 % 1.031 7.2 -10.7 HZP & HFP
=F q > 1.0 5044 -2.61% 2.8 % 1.070 12.6 -13.0 (6) ALL RPD >~1.0 1447 0.107. 1.77. 1.027 5.9' -10,8 :
ALL - F 6H > 1.0 1878 -0.02% 1.7 7. 1.031 7.2 -10.7 ALL-F-q > 1.0 9372 -2.577. 3.0 *. 1.072 12.6 -16.21 - (4) Based 'on 4 HZP and 25 HFP flux maps (PDQ 2-D discrete based'INCORE)
- (5) Based on 4'HZP and 25 HFP flux maps (PDQ 3-D / RECON based INCORE)
(6) Based on 8 HZP, 2 part power, and 44 HFP flux maps (PDQ 3-D / RECON based INCORE)- . I B; 3-20 I B
m, W. ~ TA8LE 3 4 - FLUX MAP DATABASE LISTING ~ 1 Cycle inp Power D Bank Burnup Measured PDQ l (%) (MWD /T) A.O.(%) A.O.(%) I NIC1 NIC1 01A 25A HZP 96 228 216 300 0 +0.6 8,5
-0.2 *
-9.8 NICI $2A 96 218 8405 3.0 -1.5 i N1C1 NIC2 NIC2 68A 07A 15A 100 30 99 220 165 228 14070 300 28
-1.9
+0.8
+0.1
-1.7
-2.7
-0.8
- NIC2 26A 100 222 3277 -1.5 -2.5 I N1C2 NIC3 44A 02A 100 HZP 210 220 8109 0
-4.1
+17.0
-3.0
+17.6 N1C3 14A 100 224 486 -7.9 -7.3
..l NIC3 33A 100 213 6883 .8 . . -2.2 B NIC3 84A 100 216 11434 -J.9 -1.7 N1C4 02A 29 180 13 +4.4 +6.4 i N104 N1C4 N104 07A 17A-25A 100 100 lob 221 216 226 5520 10170 305 -1.2
-3.1
-4.0
~ -0.5
-1.9
-2.9
- N1C5 .01A HZP 228 0 +26.0 +25.6
- I NIC5 NICS 15A 23A 100 100 224 224 6831 225 -6.2
-4.0
-5.6
-2.1 NIC5 3/ A 100 228 12983 -3.2 -1.8
- I NIC6 N1C6 N1C6 09A 17A 29A 100 100 100 219 228 228 6690 14340 374 -3.0
-4.0
-3.9
-2.5
-2.6 2.8 N2C2 02A HZP 228 0 +57.5 +59.3
- N2C2 20A 100 224 3225 -0.6 -2.2
- N2C2 27A 100 218 6750 -4.0 -3.0 *
+23.0 I N2C3 N2C3 01A 14A HZP 100 211 228 1566 0
-4.6
+21.4
-4.9
- N2C3 25A 100 217 7647 -4.0 -2.8 i N2C3 N2C4 N204 37A 01A 08A 100 HZP 100 221 211 228 13940 1060 0
-2.7
+31.6
-2.4
-2.3
+34.5
-2.3
-N2C4 22A 100 220 6610 -3.8 -2.4
- N2C4 28A 100 228 11267 -3.2 -2.0
- N2C5 08A 100 228 250 -1.7 -2.3 *
~N2C5 19A 100 228 6075 -4.2 -2.9
- N2C5 29A 100 228 13671 4.5 -2.8
- N2C6 04A 100 228 222 -2.6 -4.0 N2C6 13A 100 228 4930 -3.9 -2.6 N2C6 22A 100 228 13175 -5.2 -3.2
- SU53ET FOR DISCRETE 2 D PDQ INCORE COMPARISON 3 21
t TABLE 3 4 (Continued) I' I! Cycle Map Power D Bank Burnup Measured PDQ (%) (MWD /T) A.O.(%) A . O . ( P. ) S1C2 12A 98 222 1085 +1.6 -0.4
- I! i SIC 2 17A 99 223 4065 -1.8 2.4
- SIC 3 200 100 225 7175 -1.8 2.5 * '
S1C4 02A HZP 220 0 +24.0 +19.9 SIC 4 10A 100 215 930 -2.1 -4.3 SIC 4 17A 100 214 4444 -3.4 -2.0 , l SIC 4 23A 100 206 8400 4.2 -2.7 ; S1CS 01A HZP 218 0 +27.4 +24.8 l' SICS 11A 100 220 1300 -1.2 -3.4 SICS 23A 100 224 7411 -3.2 -2.2
- SICS 32A 100 216 11580 -3.5 -1.9 S1C6 01A HZP 201 0 +21.4 +19.6 S1C6 13A 100 217 973 -1.9 -2.2
- S1C6 $6A 100 228 7516 -2.5 -1.5
- SIC 6 70A 100 222 13207 -3.0 -1.9
- S1C7 02A HZP 221 0 +40.3 +40.0
- SIC 7 03A 51 180 6 -0.1 -2.8 SIC 7 08A 100 223 807 -0.2 -1.3
- SIC 7 14A 100 228 4329 -2.5 1.7
- S1C7 22A 100 226 7630 -2.9 -2.1
- SIC 8 08A 100 228 925 -4.0 -4.2
- SIC 8 37A 100 227 8081 3.3 -2.3
- SIC 9 06A 100 220 240- 0.4 -0.4
- E SIC 9 28A 100 222 7295 -2.5 -0.8
- 5 SIC 9 40A 100 217 14606 -4.0 -3.0
- SICA 06A 100 225 238 -0.2 -1.8 g SICA 22A 100 225 5254 -1.6 -1.8 g i
- SUBSET FOR DISCRETE 2-D PDQ INCORE COMPARISON I .
I. I I' l 3 22
+
N 4
, TABLE 3-4 (Continued)
Cycle Map Power D-Bank Burnup Measured PDQ (%) (MWD /T) A.O.(%) A.O.(%) S2C2 01A HZP 199 0 +20.3 +21.8 S2C2 07A 100 210 730 +2.5 +1.1 l- S2C3 08/. 100 219 137 +0.1 -0.3 S2C3 13C 100 222 3127 1.0 -1.6
- S2C4 01A HZP 228 0 +21.9 +21.6
- I S2C4 10A 100 223 1186 -2.9 -3.7 * .
S2C4 23A 100 201 8250 -4.5 -6.1 S2C4 34A 100 226 11934 0.8 +1.5
+35.9 +35.9 1 S2C5 S2C5 01A 17A HZP 100 216 217 1690 0
+1.0 +0.9 S2C5 23A 100 219 5619 0.5 1.5 S2C5 35A 100 226 11320 -4.1 -3.6 i S2C6 01A HZP 223 0 +24.8 +25.0
- S2C6 07A 100 228 1116 -2,2 -3.7
- S2C6 18A 100 228 7390 -3.0 -1.3
- I S2C6 S207 29A 02A 100 47 227 178 13900 10 2.7
+0.2
-1.4 *
-0.4 S2C7 13A 99 226 1647 -1.2 -1.2 * ;
S2C7 100 226 5781 2.4 l S2C7 19A 38A 100 223 13122 2.5
-1.4 *
-2.0
- S2C8 01A HZP 228 0 +29.5 +30.9
- S2C8 13A 100 211 2423 -2.7 1.2 I S2C8 23A 100 218 6525 -2.2 -1.1 S2C8 34A 100 221 12391 -2.7 -1.2 3 S2C9 09A 100 208 1072 +2.2 +0.6
- l S2C9 S2C9 17A 27A 100 100 223 224 6887 13553
-1.5
-3.7
-1.7 *
-2.5
- SUBSET FOR DISCRETE 2 D PDQ INCORE COMPARISON 1
1 3 23
I h i : TABLE 3 5 e REACTIVITY PARAMETER STATISTICS CRITICAL BORON CONCENTRATIONS DIFFERENCE FROM CRITICAL (ppe)
. NUMBER OF STANDARD TOTAL DESCRIPTION POINTS MEAN DtVIATION UNC FACTOR MAX. MIN.
HZP 54 6.3 20. ppm 47.4 ppm 57.9 -30.3 BORON WORTHS DIFFERENCE FROM MEASURED (%) NUMBER OF STANDARD TOTAL DESCRIPTION POINTS MEAN DEVIATION UNC. FACTOR MAX. MIN. HZP 30 -0.3 4.4 ---- 7.4 -6.1
- ADJUSTED 30 0.3 2.4 < 1.05 ---- ----
ISOTHERMAL TEMPERATURE COEFFICIENTS DIFFERENCE FROM MEASURED (pen /'F) l W NUMBER OF. STANDA!!D TOTAL DESCRIPTION POINTS MEAN DEVIATION UNC. FACTOR MAX. MIN. HZP 57 0.8 0.96 2.9 pen /F 2.6 -2.9 j- CONTROL ROD BANK WORTHS E l DIFFERENCE FROM MEASURED (%) 3 NUMBER OF STANDARD TOTAL 3 DESCRIPTION POINTS MEAN DEVIATION UNC. FACTOR MAX. MIN. g l BORON DILUTION 62 0.2% 4.8 % 1.099 10.7 -9.9 R0D SWAP 95 1.8% 4.2 % 1.099 11.5 -11.3 COMBINED 157 1.0% 4.5 % 1.095 11.5 -11.3
- ADJUSTED 157 1.0% 2 . 5 *. 1.057 ---- ----
- See Table 3-6 3-24 ;
I I TABLE 3-6 REACTIVITY COMPUTER INDUCED BIAS ERROR ESTIMATE DATA ANALYZED MEAN STANDARD DATA COMMENTS DEVIATION POINTS I BORON WORTH % -0.1% 4.6% 62 31 actual points ! DIFFERENCE repeated for cycles I (RAW DATA) which used multiple i bank dilutions. . I CONTROL ROD % DIFFERENCE (RAW DILUTION
-0.2% 4.8% 62 Early cycles used dilution method for more than one rod bank.
METHOD DATA) i l BORON WORTH % 0.3% 8.6% 62 Represents combined DIFFERENCE std. dev, impacts of I PLUS CONTROL ROD % DIFFERENCE rod worth error, boron worth error and double reactivity computer ' bias. BORON WORTH % 0.0% 4.0% 62 Represents combined DIFFERENCE std. dev, impacts of I MINUS CONTROL ROD % DIFFERENCE rod worth error and boron worth. error. Reactivity computer 7' bias cancelled out. I Estimated standard deviation bias due to use of the reactivity computer: 2% Estimated standard deviation of boron worth data excluding bias: 2.4% ; I 4 Esti.at.d standard deviation o, inta ,a1 control rod worth data excluding bias:
~
2.5% I
'-2' g
em uma em as aus num amm aim uma amm aus an en use amm aus ama men amm NORTH TWO ZONEANNA PDG3D RESU P(li) RNO INCORE DATRZ COMPARI UNIT =NIC1 BURNUP=0 FZ I.6 15 -
-er-I.4 I.3 I.2 ,
I.I-I .0 - w 0.9 - 3 0.8 0.7 - ,Y 0.6 . 0.5 04-0.3 0.2 - O .1 - 0.0 - - iiii i ri - ii-r- i iii 1 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 ifs 0 CORE HEIGHT IINCHES1 NETH00 we INCORE 6-a--a PD0 30
i ~ Z i NORTH ANNA P(LT) RND INCDRE DRTRCOM TNG ZONE PD030 RES UNIT =NICI BURNUP=881 I n FZ j l.4- ,..m , i.3- l 12 1.1 [
- 1.0 .
i ' i O .9 - '
- 0.8 2 1 m
* ~ g ,
(93 0.6 - j .
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^ P0030 l
an em aus an em aus uma en as me as aus aus em aus use sus sua em j SURRY P(Z) COMPARISON TNG ZONE POS3O.RESULTS RNO INCORE ORTH WIT =5lCS BURNUP=14606 FZ l .2 -
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I FIGURE 3-72
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M M M M M M M M M M M M M M M M M M M ' i SURRY P(Z COMPARISON TWOZONEPD030R)SULTSRNDINCORED UNIT =S2Cl BURNOP=12770 i i FZ l .2 - j I ! l 1.0- .,. -3 , 0.9 t i 0.8 m t I ! T 0.7
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.e-INCORE a a PD030 l '
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. CORE HEIGHI (INCHESI l l ! METHOD e e e INCORE a a a PD030 . k t I i
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=52C3 80R18DP=3127 SIN.IS AND 'III FZ i.2-I -I -
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I FIGURE 3-86 m
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=
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SURRY P(Z) COMPARISON TW0' ZONE PD030 R SULTS AND INCORE DHIR
' UNIT =S2C6-BURNUP=1I16 FZ l .3 W l .2 - .
N.
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-CORE HEIGHT (INCHESI' ' NE T1100 +-*-* INCORE-a a a PD030
COMPARISON SURRY TWO ONE PD03D P(Z)SULTS R
~ UNIT =S2C6 BURNUP=7390 AND INCORE .
DHT a
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. CORE HEIGHI (INCHES 1 F1E T H00 - 'c c- c-:1NCORE: o a a PD030 j i . . .. i l IM M M M M M.M M' " M --l M L M -' M .; M .M 1 M. M M .j
B ." 0 i 5 1 0 i 4 1 0 i 3 1 H - NTR i2 0 0 OO h 1 3 0 SE IR i1 0 0 P O 1 R C0 N0 e
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ua. COMPARISON
- SURRY TWO 70NE-PD030 P(Z)SULTS R
UNIT =S2C7 BURNUP=0 AND' INCORE DATH FZ l.6- ^ ^ ^ 1.5-
.l . 4 -
13-1.2 - 1.1 - 1.0 - 0.9 - 3 u 0.8 - N d 0'- w 0.6 - a N l 0.5 - I j 0.4 - 0 . 3 '- f 0.2 - 0 .1 - 0.0 - iiiiiii i i i i r- . - s i i i 0 10 20 30 40- 50 60 70 80- 90. 100 110 120 130 140 150-
~
CORE HEIGHT tINCHES)
' HETH00 e c'* INCORE.- 's a a.P0030
- m. . M m M M M M' M- M- m~ M M M M M-W W W W
I- m :p m W: mm Wg m im- g g m W M M M M M SURRY P(Z[ COMPARISON TWO TONE PD03D R Sul.18 RND INCORt DATR UNIT =S2C7-80RNUP=1647 FZ - l 1.2-
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Y~V~
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l FIGURE 3-94 8* 3
'a
~
p . g O'.8 ; ~g to w . g
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e
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l
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SURRY.P(Z) . COMPARISON TWO-ZDNE PD03D R SULTS AND INCORE DRTR
-UNIT =S2C9 BURNUP=1072 FZ
= 1.2 -
9,,_
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1.0-
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0.8 - 0.7-21 y o .8 -
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0 .1 - 0.0- - - - - - i i i
- i. - i i i s s i i i i 0 10 '20 30 40 50 60 70 80 90 100 110 120 130 140 150 i
CORE HEIGHT'tINCHES1 MElH00 e ele INCORE a-a--6 P0030 in M M M'M M Ml M .M IM' M M M M M M M ~M: M :-
-w - - w v- w w SURRY:P(Z) COMPARISON TWO ZONE P003D R SULTS RNO INCORE ORTH UNIT =S2C9 BURNUP=6887 FZ l .
II- AO: 0 0 g g e t q , , 1.0 - 0.9 - . 0.8 - . 0 . 7 '- 3 0.6 i - Y U w i '
- 0.5 - ..
S 0.4- . O.3 , i 0.2 l l
^
0.1 - 0.0- t--' - i - i - i - i ' s - i - i ' .i - T. - i 1'i - r - i ' - T-~ ~ r 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 CORE HEIGHT-IINCHES). cc ~INCORE t1E T H00 c c c PD030
FIGURE 3-102 B NIC1 3D PDG VS. MEABERED RPD COMPARISON HEP. D-828. O ledD 4 N MIC1-01A I 0.87
..,; 0.88
-0.9 0.94 0.99
-5.4 0.65 1.16 1.19 .45 0.67 1.13 1.19 .68
-3.9 0.3 0.4 0.3 0.96 1.19 1.10 0.98 1.18 1.13
-3.0 0.5 -8.6
.98 1.09 1.16 1.09 0.96 0.61
.89 1.09 1.18 1.10 0.97 0.63
.1 -0.8 -1.9 -1.0 -1.5 -8.1 1.10 1.11 1.14 1.17 1.17 I 0.00 5
-0.6 -1.3 .
1.16 1.13 1.13 1.13 1.05 1.18 1.15 1.14
-1.3 -1.7 -0.8 1.09 3.9 1.05 0.3 l
g 0.88 1.22 1.07 1.14 1.22 1.11 0.00 1.31 1.05 1.lf 1.17 1.09 0.8 2.7 -0.b 3.3 3.4 g 11.16 l1.16 1.13 1.13 1.13 1.13 2.66
.67
- 5 0.1 - 0.8 -0.7 .4 1.00 1.13 .. 1.11 0.94 0.M 1.07 1.14 0.95 1.4 4.3 .g,g 3,g 1.09 1.07 1.10 1.09 -
1.13 1.01 1.09 1.10
-3.5 S.9 1.1 -0.9 0.65 1.13 0.84 0.65 :
0.68 1.03 0.88 0.65
-0.8 4.0 0.7 -0.9 1.19 1.13 0.99 0.96 l
5 6.8 3.7 0.61 1.05 - 0.63 1.01
-1.5 3<t ..
0.66 0.68 R9 s MAE0.;tt MAE 81t .4.f
- 6.83 4 -*g<.9) e 6.33 N pgggg g K.EI MEASERED RIRB D * . -e .:
- a 3.80 - E.X Pitamrt DIFFERE3CE I
I 3-125 I!
FIGURE 3-103 N1C1 3D PD0 VS.- MEASWEB RPD COMPAft! SON NFP.-D-220. 14070 19fD4870 NIC1-66A A.'74 0.76
-2.8
- 10.88 l0.90
-3.6 0.70 1.06 1.13 0.70 l-1 0.71 1.06 1.13 0.73
-0.3 -0.1 -1.1 -3.0 1.10 1.10 1,09 1.11 1.10 1.18 1 1.08
-1.1 1.09 1.10
-0.3 -3.8 1.09 1.10 0.64 0.98 1.08 1.13 1.11 1.18 0.67 3.5 0.6
~
-1.3 -1.9 -3.3 -4.9 1 1.15 1.16 1.10 1.18 1.10 1.13
-0.3 -1.4 -3.6 1.06 1.10 1.10 1.18 1.00 1.II 1.11 1.12 1.13 0'.99
-7.7 -1.2 -1.6 1.2 1.1 0.74 1.13 .l.14 1.10 1.13 0.06 0.74 1.11 1.13 1.10 1.10 0.00 0.1- 1.0 1.3 -0.4 2.0 1 1.10 1.10 1.13
.61 1.08 1.10 1.13 .68 1.8 0.3 -0.3 1.6 1.07 1.15 1.09 0.84 1 1.05 B.8 1.13 3.0 -
1.11
-1.7 0.89
-1.3 1.09 1.14 1.15 1.09 1.09 1.11 1.16 1.10 1 0.70
-0.3 3.3 -0,4 -0.9 1.15 0.92 0.70 0.70 1.11 0.94 0.73 0.1 3.3 -3.0 -2.3 1 1.18 1.09 1.07 1.06 3.7 1.7 0.64 1.00
-1 0.64
-0.6 0.99 1.3 0.61-0.61 0.0
.g.
MAX DIF9einre . -7,7 MAR D3FF (RFD>0.9) = -7.7 N PREDICTED K.EX HEASSED EMS Duremman.a a 1.17 X.X PERG37 DIFFERENCE
~3-126
-+ i
FIGRE 3-104 g1 g. NIC2 3D PD0 VS. MEA 81 RED RPD COMPARISON
. NZP. D-224. 0 MWD /pffU NIC2-03A a -l 1
- 0.97 '
0.90 7.9 1.10 l'.03 l]l W 6.2 0.75 0.97 1.11 4.75 0.76 0.88 1.04 l0.70 Ii gj
-1,3 10.4 6.9 E.8 '
1.06 0.93 1.09 1.05 0.83 0.98 EI i 1.5 10.3 11.1 1.30 0.95 0.91 .95 1.07 0.74 5il 1.15 0.93 0.87 .45 0.97 0.73
-3.9 1.8> 5.3 12.0 0.9 5.8 1.14 .91 0.97 1.13 .44 0.87 . l 0.5- .8 10.8 l' 0.99 l0.84 .44 1.05 1.30 1.02 10 . 8 4 .81 0.95 1.34
-3.3 t2.2 .6 10.9 5.0 0.98 1.14 1.03 0.91 1. 14 1.08 1.02 1.21 1.11 0.88 1.06 0.00
-4.4 -5.3 -7.6 3.4 7.7 .
0.92 0.84 1.05 0.SS O.98 0.45 1.06 0.77
- -4.4 3.3 -0.4 3.4 0.99 1.44
-4.3 1.05 1.11 1.10 1.09
. 1.11 1.04 -3'
-5.4 1.1 4.0 0.95 1.02 1.14 0.95 1.03 1.99 1.13 0.94 E'
-7.S -4.3 0.6 0.8 0.75 1.04
'g'~
0.81 0.75 0.81 1.09 0.00 0.74
-8.7 -4.9 1.11 0.99
. -2.1
- g' B'
1.19 0.99 '
-4.6 -0.7 0.76 1.28 :
0.83 1.39
-0.9 -7.5 =
0.79 l 0.04 m.
-7.8 s
NAX DIFFE R NCE
' MAX O!PF (RFD>0.9) e 13
= 12 N g.xx PEEDI -
105 DIFFEM NCE = 4.39 X.X l PEEER DIFFERBmC:
.i
?l i
l 1 L 3-127 t l l
.FIERE 3-105 8
NIC3 3D PDG Vs. MEAIBERED RPD COWARISON RFP. D-338.: 300 88EVWTU NIC3-ISA 0.89 0.91
-3.5 I' 1.03 1.05
-3.9 I 0.74 0.75
-1.5 1.04 0.96 1.09 0.93 1.08 3.8 0.8 0.96 1.10 0.74 0.77
-4.0 1.05 0.93 1.07 1.1 3.1 3.3 8 1.14 0.98 0.98 0.98 1.06 0.73 1.14 0.96 .98 0.98 1.94 0.77
-0.7 1.7 .7 3.8 1.5 -4.4 1.17 1.01 1.03 5 -
1.17 0.3 0.99 1.9 1.00 1.8 0.97 0.99 0.99 1.07 I 0.90 0.91 0.96 0.5 1.11 1.13 1.10 1.11 0.97 1.6-0.96 3.4 1.01 1.08 4.5 1.18 1.18
-0.1 11.11 11.00 1
-1,3 0.99 11 . 0 8 0.00 l
-1.6 1.1 1.4 0 , ,
i B .98 98 0.99 1.14 0.97 1.15
.74
.3- l '. 3
.76
-0.7 3.3 0.97 1.14 -
1.18 1.08 0.96 5 0.3 1.15
-0.8 1.09 0.8 1.98
-3.3 0.98 1.09 1.17 0.98 0.98 1.10 1.17 0.97
-0.3 0.3 1.1 8 0.74 1.07
-0.3 0.83 0.74 0.75 1.88 0.0910.77
-1.5 1.8 . 1-3.1 1.09 0.96 I.. 1.09 0.94
-0.1 3.9 0.73 1.17 I 0.75
-3.8 0.74 1.19
-0.9 0.76
~3.8 8
I MAX Dit- M e A MAR 8 ra- a+ RMB D w n * *M .9) e= 4.47
= 4.47 3.08 N
K.EX X.R PREDICTED i=&-- - PERTII? DIFFEREBCE I I I ' I: 3-128 !
FIGURE 3-106 ! met so P00 vs. MEAsumED RPD COMPARISON I
- we. o-taa. 3277 mavwfu mica-26A 0.9) 0.94
-2.7 1.04 -
~
1.06
-2.3 0.77 10 . 9 7 1.09 10 . 7 7 0.77 10 . 9 4 1.09 10 . 7 9
-1.0 13 . 1 -0.3 -I-3.5 ;
1.05 0.96 1.09 ' 1.04 0.94 1.08 1.0 2.1 0.7 1.15 .97 - 0.96 .97 1.05 0.75 1.13 .96 0.94 .96 1.05 0.79 1.8 1.5 2.1 1.5 0.0 -4.4 1.15 0.99 1.00 1.15 0.98 1.00 ,
-0.3 1.1 0.1 .l
.97 0.97 0.97 1.07 -
1.19- !
.95 0.96 0.98 1.03 1.80 1.9 1.0 2.1 J.1 -0.3 {
0.92 1 1.11 !1.00 1 0.99 1.11 1.00i ' O.00 1 1.11 11 . 0 9 0.97 1.10 0.00 i
. t 0.0 1-0.6 1.5 1.3 .
j 0.97 .97 1.12 0.76 ;! 0.96 .95 1.13 0.78 0.7 .7 0.0 -3.3 _- ;
.97 :.13 -
1.09 1.94 -l
.97 1.11 1.09 1.06 t
.4 0.1 -0.1 -3.2
.97 1.08 1.15 0.97
.97 1.08 1.15 0.96 0.8 0.5 -0.3 0-9.
0.77 1.06 0.83 0.77 ' O.?? 1.04 0.90 0.78
-0.1 13 . 3 . -1.8 l 1.99 0.97 1.08 0.94 ,
0.7 3.3 ; 0.75 1.19 I 0.76 1.19
-1.6 : -0.1 0.76 '
O.77
-1.4 MAR D a .4.4 & PREDICTED MAX 0 3583 D
.9) e 3.30.
s 1.*P K.XX E.E MBA55EED B.. , PIEELTEft DIFTERENCE I' IJ g
'i 3-129 I
I
~. - . .- . . ~ . - - . . _ . . .
FIGURE 3-107 is. NIC2 3D PDG VI. COMPARISON NFP, D-210.-8109 NIC3-44A j
)
9 O.40
\
0.90
-2.0 ,
1.00 1.01
-1.0 O.77 0.97.1.00 0.77 1
- , 0.70 0.94 1.09 0.80
- -1.3 2.6 -0.3 -3.3 i- 1.05 0.94 1.09
' 1.05 0.97 1.09
- l
- 0.3 1.4 -0.5 1 W 1.11 0.99 0.99 1.09 0.98 .99 1.05 0.74
}0.90 .98 1.06 0.78 1.7 0.9 1.3 .7- -1.1 -4.6
-)
'I 1.15 1.03 1.03 i r.g 1.14 1.02 1.03 .!
-0.7 0.4 0.3 0.97
- I i
0.08 0.M i.i 1.10 1.11 1.01 1.00 0.4 1.01 0.99 i.6 1.04 1.06 i.6 1.14 1.14
- 0. -
1 l
- 0.00 1.11 1.03 1.10 .97 1.11 1.01
-0.7 -0.3 1.09 .00 1.1 0.8
!I-- 1.00 1.01 1.14 ' 0.98 1.00 1.15 .74 ? 1.1 1.1 .75
-0.3 1.9 i 0.96 1.14 1.99 0.M 1.13 1.00 . e' 0.0- 1.10 1.03 l 1.3 -4.4 -3.0 i 0.99 1.11 1.15 0.99 l 9.98 1.10 1.16 0.98 0.5 j .
1.1 -0.4 0.7 0.77 1.04 0.85 0.77 0.76 1.96 0.00 0.79 1.8 3.0 _f i
. -3.3 I.' l.09 0.96 1.04 0.94 O.8 3.7 1 0.74 1.14 0.75 I. -0.9 0.74 1.14
-0.3 0.74
-0.1 NAE D = -4 '. 4 l NAE D .9)
- 3.67 E"R" PREDICTED' o
lus B K.XX ISASIMS
= 1.44 X.X PERCENT DIFFERENCE l
I 4 ~ + I ..1 1.16 1.13 1.27 1.13 1.0$ 1.12 - 2.9 0.0 4.4 , 1.07 '. 1.27 .96 1.37 1.15 .41 i 1.12 1.32 .49 1. 1.13 .43 '*
-4.5 4.3 .0 3.31 9 2.5 3.7 1.14 1.15 0.94 .l, 1.10 1.04 0.91 m 3.1 6.4 3.4 1.88 1.18 1.13 1.17 1.19 ?
1.31 1.05 1.0$ 1.13 1.16 E.>
-2.3 6.3 5.8 3.5 2.0 g 0.76 1.09 :0.99 l- 1.13 1.09 1.23 0.00 0.00 l0.99 1.10 1.03 0.00 1
10.1 1.9 5.1 E
.94 1.11 0.99 0.40 gl
.94 1.09 0.98 0.41 -l 0.3 2.0 0.9 -1.9 ,
1.80 1.00 .. 15 1.00 1.88 1.01 1.37 1.06 ', 0.1 -0.5 -1.6 -4.4 l 1.37 1.01 1.16 1.27 l 1.39 1.08 1.18 1.29 - 7,
-1.7 -1.9 -3.0 -1.7 '
O.39 1.19 0.93 0.39 - 0.48 1.25 0.00 0.48
-6.S -5.0 . -5.8 1.10 1.33 1.14 1.38
~
-5.8 -4.9 0.42 1.81 0.47 1.30 .
-11 -7.1 O.41 0.45
-0.4 \
MAX R15 (RPD>0.9) a 10.3
= 5.02 or K.EX X.X IRASIMB :s.
PEMENT DIP N M M E
, .I I
gu
.l 3-131 l
{1
._.L__._L____-__ - - . , . . . - , . . . - -. - - - . , - - . . .
re- FIGIRE 3-109 $ i" NIC3 3D PD0 VS. M RPD COMPARISON NFP. D-313. 6843 M N1C3-33A' 0.M I 0.66 0.3
.8 .
. 9.9 1.9 )
lI o 0.44 1.13 0.97 ,44 l 0.44 1.11 0.96 .44 1 4 0.0- 1.5 1.8- 4.3 1.33 1.15 1.31 1.33 1.14 1 !I 1.05 1.88
-1.3 1.34 1.31 1.83 1.01 0.5-1.33
-0.4 1.34 1.31 1.34 1.31 0.43 0.45 0.3 3.4 1.0 -0.1 0.1- -5.7 F 1.36 1.30 1.83 1.25 1.30 1.04 4
1.0 0.8- -1.3 . 1.13 1.30 1.3f 1.34 , 1.14 1.13 1,33 1.03 1,34 1,g3
-1.1 .l 1M ,
10 . 8 0.1 1.3-0M q.93 1.11 1.20 0.00 0.94 1.11 0.94 0.99 1.19 0.95 0.99
-0.3 05 0.7 3.4 0.4
!- 1.03 1.30 1.13 i 1.93 l 1.19 1.13 0.33 0.4 0.9 0.33
- i. 0.5 1.4 1.18 5 1.15 R.S 1.13 1.10 1.31 1.31 0 49 0.93 "
- , 3.6 -e.3 -4.3 3 L .
1.34 1.1 1.37 1.34 ,-' 1.34 1. 1.34 1.33
- -0.4 3.0 0.9 1.0 8.44 1. 4 0.94 0.44 0.45 1. 0.00 0.44
,I
-3.9 8.6 . -3.7
.i O.97 1.18 0.95 1.16 i B.4 1.7 0.43 4
1.03 4 1-0.45 1.01
-4.5 1.0-0.34
, 'I 0.39
-1.s
=
{
=
, MAX MAE
= -5.7
.9) = 3.38 N
M E.EX
- 3.03 X.X PERCErr DIFFERENCE r
I, I LI q 3-132
. . -. 1 _
. . - _. . _ . _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ . _ _ . _ -_. _._ _ __.________._.~._-._ ____ _ ._
1 Tim 3-110 MIC3 3D PDG VS. 00pgatam i MFP, D-116. 11 ElCG-444 ' J 4 65 ~' h'.t g!
- 3 8!
s:l! 1.0 ; 10.4) 1.99 4 . 0.45 ! 4.45 1.094.4 95 0.4 ' O.0 0.6 h.5 -4.4
- 1. F, 1.15 1.19 I
. 1.E l 1.15 1.19 i
-1. '
O.8 -0.3 ;
- 1. 1.2 ; 1.94 1. L 1. , 3 0.44 i
- 1. 3 1. li l 1.43 it . 1.; 3 0.47' O. ll.4 0.4 5. 0.; ;
-4.0 l
.l $ 1.19 1.83 l !
t 1.; :7 1.14 1.05 '.~ .6.i l 9.5 .-l.3 ___ 1.09 1.19 t,64<
~
1.19 1.L4
- l. t 1.18 1.18 1.M 0.99
-0.7 1.1 ! 0.4 13 i 0.0 :
L 03 0.69 0.96 0.97 1.14 :.l.19 a 10.94 it<.'i
~
1.13 l
't .
-0 0.9 L.10 4.54 v.s *c 94 I
~'
!: 1:11 1:1!
?:!!
0.11 i.i 0.. ..9 1 1 1.19 1.15 1.19 0.87 ! ,' l.14 1. ' s 1 19' O.91 l R.1 B.P -0.3 -4.8 ! i
- 1. 1.14 1. 1.
- 1. 1. ' ) 1. 1. j
- 0. 5.0 0 1. ,
0 . 41 '
- 1. 0.94 0.45
^
0 . 4' 1. 0.00 -0.47
-8.0 1. . -3.6 l S. 1.18
- 9. 1.14 '
) B. 0.4 0.44 1.99 0.46 0.99 _3 . 9 1.1 ' r 1 0.39 0.44
-3.0 l l
- i. u g1.&50.9,.s 1.H
.. B.r zuur IL
,s .
3.X MDN < I. I.: I- ; It 3-133 l-
. _ . - . . - . - - - . - . - - . - - . . ~ . - . - . _ . . . - . - _ . - - - - - . - . . - . - - . . - - . _ . _ . _ - . _ - -
FIGURE 3-111 I, NIC4 30 PDG VS. M RPD COWAR180N 1827. D 330. O M N1C4-01A ,1 3 o
- 8. I '
f. 10.00 2.95 F4.7
- 6. 9 1.34 1.36 .9 LI 1 00
-3.3 1.34 1.30
-1.3 -1.4 .0 3.6'
- l. n 1.10
{j.l7 .I t lgH
- i. -i.l l
8.79 1. lll li*! II .g 1.13 0.99 i f'l 1:F lli.i li, li'l 6.I1
'4.I 1 39 4. 1.
?.1s 1. ,7 1. 4
_, 39 0. 8. I
- 1. 1. 9 1.39
- 1. 1. 1.10
- 1. 1.47 1. 1 1,23
*1. . 9. 1.6 3.
0.77 1.39
-1 0
't.36 1 34 1,29 1.15 0.00 1.39 0.00 I .
0.1 . 1.09 1.1
-0.95
- 1. 9 1.
1.30
- 11. 0 1.
1.84 1.1 B.4 -0. 0.g 0.M l i B. 1. 0.0 I 1.99 1. ; 4 1.19
- 1. l .; 3 0.89
- 0. 1. t 1.to 0.98 >
i 3.0 -3.4 1.13 1. 1.30 1.1;l I 1.11 1. 1 1.14 1. I ' . 1.9 3. 4.9 B.3 i I:lj 1: 3.l1 1:,'l 1:13 I -3. l. 1. 3. 1.00 1. i.04
-3.1 -1.4 I
- 0. i i.09 0.li i.0, i.0 ... .
0.4 i 0.44 '
-0.8 l
HAN M
= -,.S
.9, . . 91
= 3.59 NX.X DIFFFRENCE 4 ul '
l 1
- I '
3*134
e i t :, FIERE 3-112 ! N1C4 30 PDG VS. RPS COWARISCII j 9 NFP, D-33), 30 NIC4-074 g 31 4. i 3.7 0..i 0.95
-4.0 I'
0.34 0.34 1.33 1.34 1.13 1.84 0.34 0.38 hWt
-1.5 0.0 0.4 -4.8 1.48 1. 1.17 1.03 1. 4 1.14 l -
-1.7 9. -04
.l
- 8. 1. 14-- 1.06 1.14 1.01 0.34 8.
1.' S 1 97 1.14 0.00 0.37 1. 11 . i 8 1.7 1.; le 1.
-0.7 : .
-7.3 g, 6 3!
Li . ? 4 1. ; l4 1. a3 0.l ;
-0. '
- 1. l t3 1.; 2 1 85 1.34 1.
- 1. 4 1.ll4 1.
1.99 0.00 E 1 . ,' ' 4.8 9. 2.4 T g: i 4.81 1. l 4 11 . 3 4 1.; l1.34 1.14" 0.00 1. ; 3 't .33 1.; jL., 1.33 1.13 . 3.; ' W.9 1. , i B.4 1.3 i 1.9 1. 1. < L3 I
- i. 8
- 0. 9 .i .i.t i.ai i.a 811 0.
i:'t i.!. 1:I.
.i:if 1:3!
I;; 1.14 1.53 1.18 1.14 ! 1.14 8.M 1.14 1.13 '
-0.8 .
R.1 04 S.M 1.51 0.F9 0.N ' O.88 1.18 0.88 8.34 ( -S.4 3.3 1.34 1.08 18 . 4 -1 8 l1 5 i 1.5 1.97 t 1.4 0.8 0.44 0.34 1.98 1.99 l,! g
-3.s -e.: 1
,,t
- 0. ;
-l i
e 184E 884 5 s -7.3 T
.9) = -4 K .R 33 s 3.31 3.3 gryyggggg a
l 4 l I: I: , 3 13, g.
FIRRE 3-113 I
"'u mm ,nrnw,== - 1 l
8 !
- H
-i.i l 1
-1
.l i
.. . -g , l
,I .!! i.i. i.
- i. . : .
.. .i.i. i...
i.i i. i.i .l i i.i
.i... i 4
- - . - -i. -, .
g.3 i.i? i..g , _,g. . i. i..is .i.g
,i.i,,, ..i. .i I
.i ... n.
i.i i.
.i... i,v .i . .i
'l .
- I!
}!!I j:jl i:l!
[!}I li}I l!lI A:! 1:li I o.s .i:ll 1:.: i., ., .
'i! I
!!!I !!!I !:#
A:! i: I . i.l: 1:1
.! ::I
..I*.
1.i i .; i.i.? .i.ie
. i .: .?
i.i.7 ,I -i.i . i.m .i ... i I i.Tf i.i B.97 i.i. i.13 i.i .,
. 37 i,.3 l '"
':3 i:t*
n.. .g
- I ilillEE >!T:! IIllgp'_
I ;
- I i
'I : I 3-136
- - - - - - . ~ - . - - . .-. - -. - - - - - .....
FIGURE 3-114 a! l Nice 3e roe vs. NE. sues are coNPAR180N El MFF. D-286, 19170 stererty NIC4-8&A 10.71 10 . 7 1 ; l-0.8 0.80 g)I 1. 0.89 gl
-i.i 1
- l. .42 1.1011.05 #0.47 l
.41 0.00 11.05 10.0c { t
.7 10 . 4 1. I '
l.20 1.10 1.10 1.21 0.99 1.17 *
-1.1 . 0.1 0.97 1.17 1.03 1.17 1.30 .40 0.00 1.14 1.64 0.60 1.10 .4 a lt.5 -0.5
~
. 1.4 5.40 )
.30 1.13 1.10 1.30 1.13 1.19 0.0 -0.1 -0.$
l.it 1.15 1.15 s.34 1.08 1.09 1.15 1.18 1.12 1. 0,1 0.5 0.4 0.4 1.6 1.~ 0 0.71 1.06 1.101 1.13 1.04 0.061 0.00 0.00 1.10 0.00 1.98 re.00 i
. . 0.3 .
3.8 1. I gi 1.44 , 1.15 1.87 0.44 3l 1.94 l 1.14 1.27 0.44 .
-0.3 1 1.5 -0.2 1.3 l 1.17 1.87 .. l.17 0.44 '
1.14 1.25 1.18 0.91 04 1.4 l
-0.4 -4 9 1 1.17 1.10 1.30 1.17 1.14 1.M 1.39 1.17 i
-0.0 3.8 0.4 0.5 '
O.48 1. 4 .91 0.41 ' O.43 1. 4 .93 0.00
-4.4 8. 3.3 .
l.05 1.17 1.04 1.17 ,. 1.3 0.3 ; 0.40 1.03 i 0.41 0.00 '
-2.0 .
3 0.48 0 49 g MAX D ( >t.3) = 3.48
.0 -
K.EK 5 gge 3 e 1.75 X.X DIFFERENCE I I 3-137 I 8;
FHMtE 3-115 ; 4 , N1CS 30 PDG VS. RPD COIDARISON i NEP. D Rat. 0 NICS-41 ' r r ! 10.43 ; 10 . 4 1 + r 13 . 1 t 10.41 t i 0.65 '. I 4.53 0.90 1.44.l.37 1.21 1.3 6.1 4.?
-4.7
.33
.40 1
+
1.14 1. 1.31 , 1.14 1. 1.M i5 1.4 3. -3.3 l 1.99 1. l l1 1; L4 1.3'l 1.19 0 84 I 1.91 1.; 4 1.l 3 1.3 L 1.19
-1.1 0.00 t
,W l l 1. i > 0.; i
-0 . i i
-0.3 .
.. 19 1.01 1.31
! 1.; ;4 1.03 1.34 , 4 4.< > _ -1.4 -3 3 (E 1. ; l9 1.; $ 1.99 1.99 1. 0.98 ! Ig 1.18 0.04 1. 1.00 j 3.l l -3.6 . -1, 1.9 } 10.43 1.; L3 1. ; I.08 E 0.00 1.; le 1.; L3 I 1.38 .95 - L3 l 1.43 1.30 .94 '
- E 1.; 4 1.99 1.84
- 1. ; 4 0.37 l 1.11 1.30 0.44 -'
. 0.; L -3.3 -3.1 . i 1.18 1.85 1. 1 0.41 1.04 1.87 1. 0.90 ! { 4.8 -1.4 9. . 1.; 1. 9 1. l l1 iI 3
- 1. I
- 1. 7 1.; L1 1. 9 1.l l?
l' 3. 1. ; , S. 3. ; O.33 1. 0.34 0.33 il;W 5 9.98 1. ? 9.90 0.M '
- l. '
. -4.0 t
- 1. 7 1.18 '
- 1. 1.H *
- 1. 3.8 I 0.44
~~
0.98 O.8 g 0.9.7 i IIAE IIAE o -4 . 7 -
.9) = 6.11 N
K.NE } WWL = 1.90 X.X DIFFEREBCE ! e i
!E :
3-138 il .- _ _ _ _ . -- - _ - .
_ .- - - - - . . . . .. - - .. - - . - - - - . . -- . - . - - - . - - - - - - - - ~ - . - - . - - - - - FIGURE 3 116 NIC5 3D Pb4 VS. MEASWEB RPD C0fMRSSON MFP. D-334. 323 80ergrFU NICS-ISA i ' e
- 11 !
-0.0 0.M 0.M i
-l.1 l 4.37 1.36 1.34 0.37 0.37 1.33 1.33 {
c. 1.0 3.8 1.1 -1. j i 1.16 1. 1.37 1.17 1. 1.17 - i
-0.0 1. -0.3 1.0 1.; ;7 1.33 1. J.14 1.0 0 88 1.l l4 1.83 1. 1.14 0.33
-0 3 1. ' ) -0.4 9. 0.3 -1.0 l 1.84 1.04 1. I 1.23 1. M 1.
1.4 -1.1 -1. l .; le I*I I*I4 I*0I 1.; 3 1.1 *e 1.15 1.1 1.82 1.01 3.; -3.0 -3. 1.4 0.1 i 0.50 1.; !4 1.30 1.05 1.34 0.90 0.00 1.l 3 0.00 1. M 1.84 0.90 j
. 1. - l .
-0.4 0.4 0.7 1.M 1.13 1. O.
1.u 1.13 1. O. 0.4 -1.8 -3. 8. 1.11 1.34 1.37 0.M 1.10 1.25 1.47 0.M 0.9 -0.4 -0.3 -3.4 1.37 1.l q 1.M 1. 7 1.84 1. s 1.88 1. 0.0 1.5 1.t 8.
- 8. l. 4 0.M 0.37
- 8. 1. 1 0.09 0.37
- 9. 3. -1.0 -0.8 1.34 1.11 =
1.33 1.10 1.4 0.7 -' O.38 1.01 ; 0.33 1.00 l l
-3.7 1.5 i
' 0.31 !
- i. 0.32 1 l
-3.1 1
, l ag43 MAR !MCT 3.g) e
. 3 3.4 N 1 Ks3R l RIS = 1.55 2.2 DN )
.I I r I;
I' I? 3-l*9
-... ,, .. ..- ~...I,-._rm _,-.._.--r,....
. . . . , , . r . - - - , _ , , . . - - ~:,r.
flare 3-117 NICS 39 PD0 VS. "M RF9 CCBBWB8805 llPP. D-824, 6881884VIerg 31CS-83A 0.47 4.44
-3.1
#0.63 2.64 l-3.3 0.38 1.14 1.83 4.
lI 0 38
.8 1.13 1.81
.. i.
8.
-1.
1:18 i:1 1:11 ll 8:li
. i.,
I: i:11 1: 1:1,1 8.@ 8.f ll:Il I 0.. -... t. -8 1.33 1.10 1. 7 0.00 1.10 1.
-0.4 -0.
1.16 I 1.14 1.14 g,gn 1, 1.14 1.17 1.16 1. 0.9I 1.9 -8.3 -1.7 3, e.g 0.47 1. 1.33 g,gg - g, ,g,gg 0.00 1. 1.39 1.10 1. 0.88
- 8. 3.6 0.8 g. e.g
- I 1.85 1.14 1.25 D. 1 0.00 1 1.37 o, g 1! -i.? 8.
I i:" i.!'. 1:11 i. i:0
-1., 8,:3 I:B I
8. 8*
-0.8 1.
1. 1: 1.p i:11 1:H B.O . 0.86 J.38 0.00 0.89 I B.
-1. . -1.8
- 1. 1.11 0.88 98 1.10
. 0.8 0 53_ 0.93 0.34 0.98
-3.6 1.4
- 9. 1 3.3 1845 qq.c3 y . s -3.6 804E '.o s alm x .g) e 3.37 N
E.EX mis + .- m : . e 1.66 N.R DIFFERENCE 3-140
FIGuitE 3-118 WICS 3D PDG VS. COMPARISON MFP D-aas. 12983 alCS-84A
- s
-S.5 0.H '
O.67
-1.8 0.41 1.14 1.83 .4%
0.48 1.12 1.88 .48
-1.9 1.3 1.6 8.1 T.;le 1.1 S-- 1.19
- 1. ; le 1.19 1.88 0.; t 10.1 -1 8
- 6. 1. 1. I 1.19 1.;LS 0.36 0, 1.1 1. 1.19 1. 9 0.36
- 1. 13 -0. -0.1 0.8 -1.4
- 1. l.08 1.8h
- 1. I 1.19 1.33 1.0 -1.8 -1.H 1.14 1.11 1.11 1.31 0.94 1.13 1.14 1.13 1.89 0.94 13 -2.8 -3.1 1.6 -0.3 10 . 5 1 1. 1.33 1.6l 1.
0.49 1. 1.88 1.0T 1.83 6.901 33 9.90 4.3 1.1 3.8 -1.1 1.1 Ft.7 . l.8) 1.11 1.38 0.; 4 1.18 1.18 1.34 0.: 3 3.9 -0.9 -1.1 B.'l 1.14 1. ., 1.19 0.M 1.10 1. 1.19 0.69 50 1.4 -0.7 -4.6 1.19 1. 1 88 %,19 1.81 1. 1.35 1.19
-1.8 1. 4.4 -0 8 0.41 ~. -
- 1. 1 0.88 9.41 0.48 1. ? 0.89 0.48
-1.9 B. -1.5 -1.4
- 1. 1.14
- 1. I 1.13
- 1. 1.9 0.36 0.94 0.37 0.94
-3.7 tot Mi g NAE
- e
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e 8.99 t.EI .3 mes . :. 4 .in a 1.83 3.3 08FFEREB3 I I I I g
,.161
FIERE 3-119 NIC4 38 PDG VS. RP9 COWARISON NFP. D-319. 3 8 NIC6-994 i I ) 4.47 1 I 0.44 ) 3.3 i j
.69 '
.49'
.1 i$ 0.38 1.25 1. ; te 0.38 i
l3 0 84 0.3 1.33 1.; tt 3.4 i;.? 0.39
-3.3 i
( 1.17 I 9. 8. 1.18
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1.; 3 l4 1.13 1.;
- 1. ,
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- 1. 4 1.17 0.44 i 1.14 I -1. 1. 1.17 0.41 '
it. 1.8 1. 9.1 . -1.7 ;
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1.18 1.18 1.14 1.14
- 1.M 0.b?
.. 1.M 9 71
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l I. i. 1. 9. i.i. 1.19
-1.0 I 0.44 0.41
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8.33
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i NAI' e -4.3 @ NAE .9) e 3.34 K.EK
)
NtB = 1.44 X.E DIFFERENCE . I t i I l
?-142
{ 's i
FIGURE 3 120 nie. ur, a n-ast.m vs. 64 g nice-174 e muses ; g;I 0.46 ! l' . 0.46 ; O.7 l. l 0.67 { 8.47
-4.9 0.M 1.17 1.; L5 0.40 1.15 1, .l4; 0.41 9.Iv
- i. a.0 i .
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t 0.. 0 85 i. 1..i 1. i:4 0.o -..s
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- 1. 1 1.
n.,17 0.11 B. -i. 0.48
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i.i7 1. i.i. 1.13 i.i 1.1 3 i. 1.88 i. 1.03 a. 5' 3 , 1.14 -0.4 -0.4 1.4 -0.6 j 0.44 1. , 2 1.21 1. ; L1 1. 0.91 0.44 1.; 3 4.8 0.o 1.80 0.6 1.; 4 II.. ' 1. O. 0.91
-0.3 E. 1 1.11 1.18 .; 9 8. 3' 1.11 1.13 1.89 8. i 0.3 0.8 -9.5 9. '3, 1.la 1. 9 .. 1. 0.47 g; i 1.18- 1. 7 1. 0.49 3.3 1. -9. -8.6 1, '1 ,
1.l L1 1.34 1. !
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- 1. 7 1.34 1.51 31 0; I B.O -0.7 9.4 '
O.40 1.34 0.84 0 48 4 0.43 1.39 0.M 0.44 .
-4.4 1.8 -3 3 -1.0
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- 1. 0.7 :
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-1.0 -S.S
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.g) = -S.3 E.II e 1.44 E.8 DIFFEMBCE
. -1 I"
I' I 3-143
, FIGURE 3-121 , NIC4 3D PDS VS. MEASERED RPD C0lWAR180N NFP, D-338,14340 0A8417U N1C4-29A ; I > 0 51 0.31
, I 0.3 0.70 0.71
-1.1 i
.44 1.14 1.27 .44 '
l .44 1.13 1.27 .45 l
.9 1.3 0.0 -1.3 ,
1 1.30 1.17 1.18 6 , 1.21 1.16 1.10
-0.3 0.5 -0.0 0.44 1.17 1.09 1.17 1.80 44 0.48 ,1.14 1.47 1,17 1,33 0l46 g
it.6 I 1.3 i -4.1 -e.4 -i.3 -0.4
.33 1.17 1.30 l 1.31 1.18 ' 21 0.7 -0.4 -1.3 i 3.14 '.10 1.10 1.30 1.03 t 1.13 i 1.11 1.10 1.27 1.01 1.5 -1.1 -0.6 3.4 0.3 "
0.C' l . 1. 7 1.14 1.16 1.37 10.03 0.4% 1. 1.10 g,1 g,gg g,gg 3.s g - 0.3 -i.s -0.7 1,3 i., 1.09 1.10 1.39 8. 't 1.10 1.11 1.31 g, y
-1.1 -0.7 -1.3 1,1 1.19 1.39 1.13 o,yg i 5 1*17 0.9 1.88 1.0 1.18
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- 1.17 1.14 1.33 1.17 .
1.16 1.14 1.31 1.16
- I. 0.44 9.7 1.30 1.9 -0.1 1.0 0.87 0.44
- 0. 1.33 g,gg g,43 I -3. B.0 1.3?
1.34 3.0 1.19 1.14 0.0
-1.7 -e.4 0.44 1.03 0.44 1.01 I-. -0.3 1.1 g.37
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- 3.
a 3.46 N K.ER NE. = 1. I.X DIFFERENCE I I LI 3-144
FIRiltE 3-122 N8C2 3D PDG VS. Perm RPD COMPARISON MZP. D-888. O PREVWTU NRC3-01A 4.90 0.98 I
-3.1 g 1.04 1.05
.74 0.95 8.94
-0.9
.74 g
.75 0.91 5.91 .79 g
0.0 4.0 2.3 S.3 6 .94 1.19 ~1.22
.99 1.18 1.88
.1 6.6 0.1 1.03 0.97 1.17 0.97 0.95 0.71 0.99 0.91 1.10 0.93 0.94 0.90 4.4 6.8 6.4 4.8 0.3 .
1.14 0.94 0.97 1.99 0.48 0.91 6.0 6.1 S.7 0.96 0.95 0.95 1.19 1.15 0.89 0.88 0.88 1.14 1.33 7.8.. 7.1 7.4 2.7 -6.6 0.91 0.96 1.05 0.94 0.96 8.94 0.88 0.00 0.96 0.90 0.98 0.97 3.1 . 10.0 4.9 1.5 -3.8 l.18 8.95 .01 0.74 1.04 0.89 .98 0.81 8.98 0.7 1.01 6.4 .0 1.08
-8.4 g 0.93 1.98
.. 1.38 g 1.87 1.13 4.6 -1.1 -3.4 -7 8 0.97' 1.98 1.15 0.97 E 0.93 4.7 1.06
-0.8 1.31 0.00
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- g 0.75 -4.18 0.98 0.75 0.96 0.90 1.08 0.83 8 8.4 .
-6.4 -19 '
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,., -18 0.73 p, 0.00 .
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g B B I 3-145
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I
, FIGURE 3-123 NSC3 3D PD0 VS. RPD C0fEPARISON $
I NFP D-334 3333 0.91 NSC3-20A
]
1 l; I 0.93
-1.0 1.04 1.05 I
-1.3 I T 10.M S.M 0.79 i
.41 10.M W.94 0.43
- 3.1 12 . 3 11 . 5 -3.8
.Mi (
1.14 1.17 I i.07 1.04
.95
.5
.M
.M ii.it I.13 1.5 1.17
-0.3
.M 0.M 0.u l
j 3.0
.1.10 .M 0.M 0 77 1 1.3 Lt .9 .3 0.0
'I 1.11 1.11 6. 0.9 0.97 s.M
-3,7 i
I 1.4 1.3 0.9 f I 10 . 9 1
.M
.3
.97 1.02 0.98 0.97 i.e 0.M 0.M i.s 0.M t.13 1.11 i.s 1.15 1.14
-i.e !
0.98 1 .93 0.99 0.97 9.95
-0. 0 l .4 0.94 0.94 5.94 3.5 lL.3 3.9 10 . 9 ;
1.11 0.98 .03 0.
~
1.99 0.95 1.03 0, 3.0 3.6 1.3 i I 0.'97 0.97 9.4 1.03 1.03 0.4 1.17 1.18
-0.9 1.
- 1. ?
-3.3
-3.
}
0.M 1.08 1.11 0.M
.I 0.79 0.97 1.1 1.13 1.00 3.4 1.11 0.M 0.3 1.5 0.81 1.01 9.
1.1) 1.43 9. I -3.0 1.0 0.M 0.94 1.3 0.97 0.97 0.7
-3.4 -3.
4.74 1.15
-I 0.70
-S.4 1.18
-3.6 0.74 I 0.79
-4.1 I
v IG4X D ftAE 9
= -S.4 H.9) e 3.97 N Pg8 K.EK IuS 8
- 3.33 X.X ! DIFFEFARCE 1' I l
I h h I I
, 3. s.
l l FIGURE 3-124 NEC3 3D PDG V5. RPD COIIPAR180N
- IFP. D-110. 6751 NSC8-27A (
l t 0.90 > 0.90 l 0.1 1.08 1.02 li e '
-0.1
.40
.88 0.M 10.95 0.M q.95 0 00 0.83 $ll 5t
, 3.4 1.6 s.O -3.1 0.M 1.11 1.15 0.M 1.11 1.15 E ;!
0.3 0.4 -0.4 gi 1.10 0.M 1.11 0.90 0.M 0.75 1.07 0.97 1 99 0.M D.96 0.77 i 3.0 0.4 1.5 1.1 -0 8 -8.0 gi 1.10 0.M 0.M 1.10 0.97 0.97 *E *
-0.3 0.7 0.9
~. .M 1.90 1.90 1.10 1.15 ('
.M l.00 0.99 1.99 1.15
.4 0.4 1.4 1.2 -0.8 I
0.90 0.M 1.08 4.M 0.M l0.94 ; 0.90 0.M 0.90 0.90 0.M 0.03
- -0.3 3.4 3.5 l L.0 R.7 1.5 '
1.11 1.00 .07 0 78 " i 1.04 0.90 3.M 0.77 - 3.0 B.1 1.1 0.97 1.07
-1.L l
1.15 1.02 0.M 1.07 1.15 1,64
-0.4 0.3 -0.1 -1.9 l 0.M 1. 1.10 0.98 0.97 1. 1.10 0.M 0.81 1.0 1.10
- 1. 0.4 1.4 1.01 E.Sh E:
g o.43 1.99 l 1.43 0.4ll'
-3.1 0.4 -1.4 -3 g' O.95 0.97 3 0.M 0.M 1.4 1.0 ;
0.75 1.15 E 0.79 1.16 g* ,. -4.7 -1.3
- i. 0.75 0.74 m j
l
-3.3 g,
Il4E # ~4.7 . "" 194E >4.9) = 3.90 K. NE 4 = 1.71 E.X DEFRMME I. , I! > i I I 3-147 E_
-I
FIGURE 3-12) N8C3 MEP. 3D D-Ill. PDG VS. N.BASEM3 IBMffU MSC3-01AP'O COWAR180N
- 11
-1.1 '
4 1...
- 1. M
-1 3 l 1..$. 1. 3 1 86 J M.71 F3.
l..) 1.8 l t 8
.6
. 6..
1.
.l.34
.0 i.81 1.l7 l .
i.. . i.i 14!.g lg i. i.: i... i:P i. i.g. 1:lI 1:.1
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I i.i
.3i ...
15!g . !6.1 !!!i l I:n ::l! ::R, i:l! 1:a!
-3.. -i.: -i. ..
1.g i.i ...i i.= ... l 1 -4.i l!!i f:10 ?:i' ::t* I:n
-i..
- 11 i.i 1:.n i
,:n g
1 I:l
-i.j i:
1:gt 3.l'1:* .
- 1. 1.1 1.14 1.
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-5. -1 1
8' 1.I ll 1.18 .. "" 8'.
*S
- 1. ' 9 1.0 1.18 ..
g.
-3 4 I
I:5
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.00 1.11
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. 35
. 0.0 I .
I Ril mi R..,. u, mig ... :?.:.R
. l'E, l
- 3. s.
FIGURE 3-126 NSC3 3D PD0 VS. RPD COMPARISON MFP. D-312.1566 NSC3-14A g a 2:
..E 0.98 1.0'
-3.9
.68 1.01 1. 0.64
.67 0.99 1.31 31 0.69 1.0 1.7 -0.3 -80 1 10 1.94 1.89 1.19 1.07 1.30 0.0 1.3 -1.0
- 1. 1. l.08 1.0811.19 0.59
- 1. 8. 1.08 1. 8 .18 0.60
-1.4 .
08 8. .3 -1.7 1.17 1.01 0.99 1.14 1 98 11.98 3.6 -0.4 l-3.3 1.01 1.01 1.01 1.80 1 06 1.01 1.01 1.03 1.16 1.07 03 -0.4 -3.1 4.1 0.6 0.54 ,.
, i.17 1.01 1.3 8.47 0.85 1. i 1.10 1.01 1.l{e 0.88
-0.9 -0. : i -0.0 -0.1 3.3 B2 1.08 1.01 1.1 8.
1.05 1.01 1.1 9. 0.8 0.1 -0. 3. l.16 1.11 1.M 0. 1.16 1.10 ** 9.M 1. 1.3 1.4 . -3. 1.08 1.17 1.17 1.08 1.04 1.18 1.16 1.00
-3.3 1.4 0.8 18
- 0. 1.89 1.11 0.M
- 0. 1.17 1.18 0.67 es. B.S -1.1 0.4
- 1. l l1 1.16
- 1. ' .8 1.13 1.9 R.7 0.59 1.08 0.. i.6
-3.9 1.4 0.88 0.u .
-31I g
..am R.5 o n. .9, :. :i..? ? EE x.x n====
I I 3- s, I
,4
0 FIGURE 3-127 NSC3 3D PDS VS. RPD CO m4RISON I ItFP, D-217, 7647 1 MRC3-8&A 8.Il 0. I 0.4 0.99 O.95 I
-5.5 ;
.45 0.95 1.19 4.65 '
.41 0.00 1.98 ;0.M l .6 . ll.3 l-3 0-E l .; 3 .85 1.t i '
- 1. ; !) 0.64 1.3' '
'g 1. . i .
- 1. ll 1.94 1.1 15 1.99 1.05 1. 6. '
O.00 1.08 1.99 1.44 1. 6. I B." >
-0.4 10 -4. -8. !
.; $ 1.07 1.04 1.l t3 1.07 1.68 O.9 -0.8 -8.4 iI i 0.51 0.95 8.95 0.4 1.11 ii.21 1 07 1.97 03 1 07 1.97
-0.3 1.06 l.
1. 3. 0.93 0.M
-0.7 4.88 1.11 10.79 lI 1.11 0.00 1.
.-e.. 0.9 l1.24 0.3 .
_ .19 l'. 00 1.99 1.97 1. 6. 1
-1 99 1.!5 1 O. i I
.i i. .
- 8. ~~ i
~
1:1! 0:lt i i: :8: i.. 1.0 1.ll1
.lt. . 9 I 1.R8 1. 5 '
1.0 1. 8 1.39 1. J
, , -4. B.ll -0 4 9.
0.65 1. 1.04 0. 0.67 1. 1.44 0.45 00
-3.0 1., . -3.4 .
l.40 1.17
- 1. 44 1.14 1.t k 8.4 '
I !.:lt ..
- 8 0.1
- 11
.g
- l. - .. .
l I L
- I ill5131"!!!!! W iER,,,,,,,, :
lI l 3 150 I
FIGURE 3-128 FP. D 181 '13 33c3 A l
- n
-0.s 0.89 l-i3 0.65 10.95 1.07 .45 I 0.64 10.00 1.07 .69 W 1.0 l. 0.j ; g.)
1.84 1.1 4 1. 1.84 1.1 18 1. E 0.98
-0 8 1.; l 0. g 1 95 1.08 1.05 1. 4 0.57 0.00 1.0a 1.88 0.00 1. 0 0.88 l1.1 -0 8 . 3. -1.6 3
.l l0 1.; ;9 1.06 1.07 1.86 1.19 5 0.l '
-0.9 -3.6 0.96 1.07 1.07 1. 0.98 0.95 1.07 1.09 1. 0.99 0.1 -0 3 -1.3 g, -0.8 '
4.54 l.08 11.30 1.gi; 1.08 it.79 O.S$ 1.09 Lt.80 1.96 1.0t 0.80
*l.3 -0.7 s.O -0.1 1.4 -0.8 1.08 1.07 7 9.
- i. 8 i.. 118
- i. 8.
0.3 0.8 -0.9 0.
~
1:11 3.s i:b' i. i:lt
-i.4 :lt.
l i:ff i:8
-0.I 31 1:18 i:8
-0 3 0.1 1: ::tt l
- lt. i:l'. -,31 l
-i. i. .9 -. 8 i.. i.i8
- 9. 7 i.io i..
0..? 0... 8.98, 0.9
~1.7 0.6 0.38 0.39
-8.3 HAE IEEE o
(
.9) e -3.6
- 1.78 or K.EI -
I E.I 9,FFEEEBCE I I I i l 3-151 l I'
l FIENtt 3-129 t NBC4 3D PDS VS. 00134B330N i MEP, D-311. 9 NBC4-41A I i i I:ll I l 0.49 ' 0.70
-3.4 ,
0 51_ 1.31 1. ; 2 0.51 0.54 0.99 I.: '1 0.49 1 i
-5.0 . 5. i 3.7 i 1:l 1:t
!l 1 1.08
-..a 1.0 i 1.19
.i:!!
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- 1. 1.19 0.4 1.16 0.6) 1.31 1. 1.16 6. f
-7.1 .
-1.4 4. B.3 -0.
1.17 1.91 09 1.33 1.0 0.v7
-4.0 -0.37 B.0 -1 t
i I 0.51 1.31 0.00 1.; 4 1.33 0.96 0.98
-1.6 8.
9. 3. 1.03 1.57 1.19 6.7 1.11 1.04 l1.1 1.88 .03 0.99 1.; ;7 1.34 0.94 1.80 1.01 0.; -4.4 4.4 6.4 B.3 - ; i 1.19 8.M 1.15 8. 4 1.37 0.98 1.13 ' 8. ! -6.3 4.4 1.9 B. !S 1.17 1.14 ~1. 0.69 !W 1 1.13
- 1. 0 69
- - *l.
i.. i. .9 i I:ft il -3.. .i:ft
.. .i:li 1:11
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~
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- -9..
1: 0.P I:li I:ll i.e ... 45 i .m i.iv 1.19 1.13 7.1 3.9 1 0.43 1.11 0.43 1.g4
-0. .a l 0.40
'3 0.gf jg 8' 1143 194 5 e -9.4
.9) a 7.14 N. .
4 E.XX M e 4.33 3.3 pm
- I I /
I l 3-152 l !
1 FIGURE 3-130 NSC4 3D PDS VS. RPD COMPARISON NFP. D-880. 6410 . If8C4-88A 2:H l si.i 0.64 0.69
-1.6 0.84 0.53 1.10 .1.88 0.00 1.17 0.84 0.84 W
8.1 . 4.4 0.6 1.80 1.18 1.19 1.M 0.00 1.18
-1.1 . 8.1 1.94 1.07 1.18 1.07 1.80 0.46 0.00 1.08 1.19 0.00 1.18 0.47
. 8.1 1.86
-1.8 1.07
. 1.4 ~1.9 g 1.07 g 1.M 1.07 1.10 0.8 -0.7 -8.1 1.10 1.06 1.06 1. 7 1.08 E 1.09 1. M 1.04 1. 1.01 g 0.9 -1.9 -8.0 3. 0.8 0 58 1. 61.17 1.07 1. h.95 0.58' 1. 11 . 1 5 1.07 1. h.94 E 8.
-0.4 11 . 0 1.18 n.0 l.06 . 86
- 1. 0.4 0.41 g
1.19 1.06 1.89 0.41
-0.9 -0.8 -1.8 --
-0.8 1.15 1 86 .. 1.19 0 64 1.18 1.86 1.80 0.70 8.8 0.4 -1.8 -8.1 1.07 1.14 1. 1.07 1.09 1.13 1. 1.07
-1.8 8.4 -0. 0.1 0.F4 1. 7 0.91 8. .
0.'48 1. 4 0.98 10.
..e 8. -1.8 1.88 1.15
-9. l 1.19 1.14 5
8.4 1.0 0.46 1.08 E 0 47 0.99 g 8.1 8.8 0.41 0.48
-3.1 s.
Nag MAR ; $
.1 e 4,44 i H .9) e 4.44 N
gag h. . .Mo c..
. ou = 1.84 K.g3 X.E DTFPEREBCE I
I I 3 153
FIERE 3-131 Ittte 30 PDS VS. RPD 00 WAR 180N ! KFP, D-334. 1134 N3C4 3M i
- i l
iI
=
-3.0 0.69 0 49
-$.7 i
. 1.07 11.33 0.5 I
. 1.0411.30 m.$ ,
3.9 8.3 he. > 1.33 1.13 1.17 ' 1 81 1.13 1.18 il 0.3 1.6 -1.$ ,W 1.04 1.07 l 1.0 1.44 1.17 1.17
?,7 1.31
- 1. 1.13
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-1.9T 1.3 -0.3 e.ios
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t 'g 1.M 1.05 1.07
-1.
1.39 1.07 1.11 i
-0.3 -1.8 -3.7 ;
! 1.07 1 . 91 > 1.94 1. 'E l.07 1. ti l 1.09 1. I,99 0.3 0.93 Il -3.' 3.1 3. 7.3 -, 0.53 1.33 1 1.13 1,44 1.33 0.g3 n 0.S4 1.18 1.14 1.e4 ,g -1.7 -0 3 1.16 0.89
-e.4 -1.9 S.4 4.4 i5 i
1.19 8-1.'* 44
- 1. *.*3
- -1.3 -3.1 -3. 0.44 l.14 -3.3 1.37 1.17 0.69 1.14 1.47 1.16 j 1.8 0.ti 0.1 ___ -1.3. .-3.3 1
1.07 1.13 1. 1.07 ! 1.08 1.11 1.58 30 1.88
-0.3 3.1 -1.0 -4.A
! 0.M 1. - 5.91 0, 9.M 1. 0.93 8.
-3.4 1. ,
l-l <g 1. 1.1
-1.9 -3. .
- 1. I 1.1{3
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i...
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t
. 43 0.
I
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r
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< .9>.7.li -
a 3.38
- 7. i ta.r
.. y3 E.X DSFFEMBCE
!I I 3-154 i
. .. - ._~. - . . - . - _.-. .. ~ . . - . - - -
FIGURE 3-132 N2C5 3D PDG VS. NEASW B RPD COMPAR280N
- NFP, D-188, . 250 atSdf1T N3C5-48A i
I.44
- l*
.4
.65 ll 1.5 r S.40 1.17 1.83 .44 p.41 1.16 1.14 .42 F3.4 0.7 -0.9 4.8' 1.11 I l .M 1.30 1.14 1.19 1.21
-3.8 1 3.4 -0 8 1.05 1.14 1.84 1.16 1.10 0.37 1.99 1.15 1.33 1.15 1.13 0.34 t
-3.3 1.0 1.4 0.8 -1.4 -3.1 >
1.86 1. t 1. I 1.27 1. 1. '
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.4 1.34 .38 g
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+
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FIGURE 3-133
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l . .i .. in ..i a. i.i, i.i. i.i. i.i. i.i. i.i. I i.*
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- i. .i .P. .i .. ....
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FIERE 3-135 MS NiE' s 8:R i.i. 1:l' L
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- W -' DIFFEREBCE I
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FIGURE 3-136 Il ;
$108 38 PDG V5.
MPP. D-3RR. 11 0 SPD COMPARISON 81-3-18A Ii i l nl .M I, 0.ea 1.48 l. 0.99 W 3.8 0 55 1.00 1.84 4. ; 0.55 1.00 1.11 8.
! 0.1 0.4 -0 3 -0 l
0.97 1.10 1.00 0.97, 1. M 1.00
-0.4 1.9 -0.8 1.04 1.03 1.1 i.n
- i. i.e
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i .* 8 .97
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0.77 l 4 i:1l 1:l
-i..l 1:ll l'
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- 0. ., 3 1.24 1.05 1. 2.40 g.
- 9. 1 .; 14 1.t2 1.11 1. R.80
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- 9. 1.84
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3.
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g i rar n . ..
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g as 3.77 _2. 7 DIFFEMBCE - i-t 1
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8:8l
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3-160
FIGURE 3-138 . ( --
$108 3D PDS VS. RPD COMPSISON MPP, D-818, 250 31-3-898 0.77 B.
0.76 1.8 0.90 $ 0.98 3
-8.7 0.68 J.83 1.08 0.68 0 71
-3.5 0.83 1.00 0.70 E
_ -0.8 1.3 -8.3 g
.96 1.10 1.18
.97. 1.07 1.80 ..
1.0 3.6 - -1.8 g-1.09 1.88 0.99 1.88 0.96 0.48 :E 1*e8 1 81 1.00 1.88 0.00 0.63 9.9 0.7
-1.3 0.3 . -1,4
- P . 1.81 0.89 1.05 1.83 0.88 1.06
-1.5 1.3 -0.8
.83 1.ise 1.80 i 1.14 it.09
.84 1.10 1.19 '
1.18 11.06 1.3 85 1.3 8.1 g.0 0.77 1.03 1.11 0.89 1.03 1.11 0.79 1.08 1.09 0.89 1.08 0.00 18 0.6 . 1.9 U.S 0.8 .- O.98 1.80 , .83 0.g l 0.00 0.00 t.81 0.& i
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-3.u 1.10 1.83 1,1y o,gg .
1.13 1.80 1 80 0.91
-8.8 8.4 -3,3 -3.3 .
- 1. 1.11 1.81 1.88
. 1.M53 1.07 0.00 1.88 I -0.7 3.9 . 0.3 - E-0.68 1.15 1.00 0.68 E 0.69 0.00 0.99 0.70
' "#.7 .
1.1 -8.3
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> ' 9t 1.12 i' -1,1 0.68 1.08 0.68 1.07
-3.7 1.6 h' O.63 0.64
-8.5 1_00 5 HRE 8 3.91
.9) a 3,91 N
g,gg 94 a.3
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3
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I 3-161 I I-i.
FIIMtE 3-139 m i L j I , SIC 3 3D PDS VS. IIRASIEED EPD COMPAR280R NFP. D-825 7175 30svirrU 31-3-208 1 0.40 ' 0.83
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l .91 L
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0.94 1.10 1.14 i 0.00 1.04 1.14 i
. 1.1 1.3 i o 1.08 1.17 0.99 1.17 0.94 .45
- 1.99 1.14 1.01 l 1.15 0.99 .47
-0.3 3.4 -1.9 1.4 - -1.9 '*-
3.1 : !I L 1.30 0.90 1.04 ' 1.17 0.91 1.05 l- 3.0 -0.0 -i.5 -- 0.44 1.14 1.14 1.13 I.00 ' O.00 1.13 1.14 1.10 - 1.00 1.5 0.4 3.5- 0.6 ' i- . 0.80 1.05 1.10 0.90 1.05 1.10 0.01 1.04 :( 1.04 0.90 1.05 1.11 '
-3.3 0.5 1 ~. 9 0.3 0.3 -0.5 0.99 1.14 1~.18 0.64 1.01 0.00 1.15 0.44
-1.Ro i I
. 3.3- -3.7 1.10
~
1.10 1.18 .91 ! 1.11 0.00 1.14 .93
-1.3 4
1.4 . 3.3 1.17 1.10 1.80 1.17 l 1.16 I 1.07 0.00 1.14 4 1.3 3.1 . 0.4
- 9. 1.13 1.01 0.73
- 8. 1.10 1.03 0.70 '
-0. -
3.3 -1. 9 --5.0
.gl. .,
1.03 11.10 t + 1.03 't.11 0.7 .4. 5 :
' ~
O.45 1.09 I 0.70
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3 i IIAE D fl4E D .9) = 3.09 e -4.7' @ K.XX WW D = 3.10 3.X DIFFERENCE I- , a
,e 3-16k ,
s N - g--.. w g. + - - ,.w,y
. . .- ..- - . ~ . = _ -. . . - . - . . - . . ~ - . _ . . . . . - . - . . - - .. . . - - .- ,
J l FIGURE'3-140= S1C4 30 PDG VS. HEASIEED RP9 CollPARISON l NEP ,D-330,. 0 10gvstry 31-4-03A l
.00
.91 l 3.3 :
1 1.01 ) 1.04 :,
-3.5 '
O.70 1.3e10.99 0.70 0.71 1.11 0.97 0.73
-1.7 1.0 1.9 -4.4 i '
1.06 1.13 1.13 1.04 1.00 0.00 .l - 1.4 4.3 . 1.00 1.13 1.06 1.13 1.04 0.45 1.00 1.13 1.06 1.13 1.05 0.69 O4 0.4 0.0 -0.4 0.6 -5.5 . 1.04 .93 1.00 % 1.04 .9 1.09 0.,3
-0.3 k0.4 ~
1.23 1.00 1.00 1.04 1.13 I 0.00 1.09 1.10 1.04 0.00
- -0.7 -1.5 -0.6 . .c 0.07 0.99 1.01 0.93 0.99 1.15 g 0.04 0.90 1.01 0.94 0.99 1.12 L
1.3 1.4 -0.3 -3.0 05 3.2 , 7
!b 1.06 1.00 1 00 0.49 L 1.07 0.00 1,03 . :- 0.70 m.
-P.7 . -3.5 -1.7 1.00 - 1.00 1.13 1.00 t 1.08 0.00 1.it i,03 1.7 , 1,3 3,3 i 1.13 1.01 1.04 1.13 i: 1.10 1.00 0.00 0.00 3.3 0.5 '
0.70 1.04 1.00 0.70 I.04 O.?R 1.00 0.72
- .y -3.3 -0.1 0.0 -3.3 -l 0.99 1.07
, 0.97 1.06 (: 1.4- -1.0 0.66 1.13 '. . J.
. 0.60 1.13 L
-3.3 0.5 li O.69
, 0.70 li s -1.3 .. ll; t y i NAE = -5 . 5 '. I"R" PagBICIED flAR ( .9) e 4.34 K.EK ISASIMD W i (. = 2.10 X.X M DIF M i:
- ,~(
^1 ll b
- I l <
l 1 3-163
c
, -FIGURE 3-141 m
8104 3D PDG VS. HEASEEED RPD COMPARISCE MFP. D-815. 030 ledWirrU 51-4-10A 0.85 0.88
-3.4 ls t .97
.98
-1.0 0.70 1.17 0.96 0.70 0.71 1.17 0.98 0.73 1 -1.7 0.5 0.9 -4.0 1.03 1.18 1.10 1.04< 1.07 0.00 l, -0.8 4.8 .
l A 0.99 1.11 1.09 1.11 11.08 0.66 0.90 1.11 1.06 1.11 1l . 08 0.69
-0.1 -0.1 2.6 -0.8 II.8 -4.9 1.07 1.01 1.18 ..l .r 0.00 1.00 0.5-1.13 10 . 7 1.17 1.17 1.17 1.03 1.08 0.00 1.17 1.17 1.04 1.07 0.0 0.5 -1.3 0.9 1 0.85 0.97 1.06 1.01 ?.97 1.09 0.87 0.97 -
1.08 1.00 0.97 1.07
-3.4 0.3 1.1 1.0 0.4' B.5 1.09 1.17 1.08 0.68 1.98 0.00 1.07 0.69 0.3 . 0.8 -3.e 1.04 , 1.08 1.10 0.97 1.05 0.00 1.06 1.00 I *1.1 .
3.8 -3.6 3 1.06 1.07 1.11 1.10 1.06 0.60 0.00 0.8 0.8 . . 1 0.74
.0.73 1.03 1.04 0.98 0.70 0.98 0.73 F3.7 -1.0
-0.5 -3.6 0.96 1.04
- 1. 0.96 0.8 1.05
-0.4 0.66 1.08 0.69 1.07
-3.9 0.3 l 0.68 0.71
. -3.7 l HAE
. -4.9
.9) a 4.29 or K.EX REE = 2.11 X.X BIFFFrmer l'
I
- 3. m i
3 t i
.. I FIGURE 3-142 l 8104 30 PD0 VS. IRA 3133D RPD COMPARISON ilFP, D-206, 8400 engvgrru 31-4-334.
I.l 1 g. 0.70 mi , . 0.71 i' -0.8 l: 0.85 t 0.88 l' -0.9 0.44 1.04 0.87 qT C.69 1.66 8.87 0.71 i
-0.7 0.0 0.0 -3.0 >l l 8 1.05 1.09 1.10 -4 i 1.05. 1.e4 1.09 .1 h I 0.4 3.3 0.8 g!
- . 1.00 1.11 1.30 1.11 1.05 .43 1.00 1.09 1.19 1.10 1.04 31 l-
.45
(; 0.0 1.4 0.5 0.7 0.8 . 3.1 . 1.30 1.07 1.15 1, 0.00 1.06 1.15
. 1.0 0.3 1.06 1.19 1.19 1.04 0.97 .
1.06 1.17 1.18 1.10 0.00 '
.I 0.1 1.4 1.1 -1.3 .
0.70 0.88 1.33 1.07 0.84 0.90 t 0.73 0.88 1.31 1.04 0.84 0.90
-3.5 -0.7 0.3 0.8 -0.2 0.0 '
1.30 1.19 1. 3', O.59 ' 1.19 0.00 1.3.;, ' 0.41 , 0.5 - . 1.0 -3.3 q 1.07 1.34 1.10 0.88 0.00 0.90 1.08 1.4 0.90
-3.8
'I"1 gH '
1.11 1.33 1.30 1.11 1.09 0.00 0.00 1.09 .' 1.3 . . 1.3 => 0.64 l 1.08 0.93 6.68 i 0.49 1.09 0.93 0.70 4
-1.7 -0.5 0.1 -3.3 0.87 1.07 -
-]'
8.87 n.00 O.1 O.64 0.9; 9.46 0.A .
-3.3 -0.4 .1 0.59 --
h 0.60 i
, -1.7 '{
l
.)
l183 IIAE ( s -3.3
.9)-= 3.54 1
K.ER I M DN = 1.45 X.X DIFFEREM:E .1 1 i a 3-165 1
- k!
i-~ _ _ . . -. , . _ , _ . . _ . . . , . ,, . _ _ _ , , __. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _
- oc .;
4 FIGURE 3-143 d sicsuzP, 30 PDG D-ais, Vs. PE4EEED RFD COMPARISON e m a nrre si-s-eta 'i I
.82 l
.79
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1.01 0.0 41 1.24 1.08 n.42 I -
.00 l.14 1.17.
1.24 0.00 0.0 1. 1. 1.84 1. 0.00
+
l -0.9 1. ' -0. 1.06 1.14 1. % 1.14 1.17 0.90 1.10 1.31 0.48 2.1 1.14 1.17 0.44
-8.7 -4.0 0.1 -0.4 -3.3 P . 0.98 1.13 4 1.16 1.01 1.14 1.10 e i
~
-1.3 -3.4 -1.3 i 1.27 1.08 1.04 1.14 1.13 1.84 1.11 1.13 0.00 0.5 1.12
-2.4 -3.2 . 0.5
! 0.42 1. ' 0 1.17 1.18 0.78 1. M 0.00 1.10 1.14 5.1 3.9 1.13 0.00 1.13 ;
-0.4 3.5 I
1.15 1.04 % 87 0.44 t 1.18 0.04 . 04 0.00
-1.8 . 1.1 .
1.18 1.88 1.34 1.11 0.00 1.01 i -0.6 1.2 1.91
-1.4 0.4 ,
l 1.14 1.17 0.99 1.14 i i 1.14 1.17 0.00 1.14 1-
-3.7 0.1 . -0.1 I ,- 0.43 1.14 0.89 0.43 0.48 1.11 0.91 0.45 7 -1.8 5.0 -3.3 -4.3 1.88 1.10 lI
[ 1.04 4.1-1.04 5.0 1 L 0.43 1.13 0.45 1.06 e l -5.8 5.9 hi ' 0.44 !( O.44 nag e 5.93 l';' NAR (RFD0.9)
- 5.93 I"E" ..
K.ER ' M = 2.44 -! E DIFFERENCE I A I
- 3. a.
p 1
+
p ," . g.- i FIGURE 3-144' _g I,i L [ SICS 3D PDG VS. IRASERED RFD COMPARISON j- .MPP. D-280. 1300 IREV1ml SI-5-11A
.60 . I;1 '
.78 l- .4
{
.97
.97 l '
[ 4.1 - O.44 1.80 1.04 .46 E, 0.44 1.20 0.00 .47
- 0.0- -0.3 . 3.0 l, L 1.15 1.07 1.31 1.15. 1.45 1.83 ,
0.1 B.1 -0.9 " , 1.00 1.14 1.17 1.14 1.16 .44 O.98 1.15 1.17 1.15 1.14 .45 3.3 -0.7 0.0 -0.3 1.3 0.7 , 1.83 1.16 1.19 . o 1.04 1.17 1.23 - l -1.0 -0.9 -3.1 l_ 1.30 1.14 1.14 1.17 1.04 L; i.30 0.te i.is 0.te i.05 - 0.0 -1.4 . 2.6 0.40 1.44 1.17 1.14 1.94 'I.09 ; ., 0.84 1.03 0.00 1.14 0.00 1.08
- t 0.8 2.5 . -0.7 . 1.3 1.16 1.14 1.13 0.47 1.17 0.00 1'.'14 0.47 m l -0.4 . -1.8 0.4 '[
1.88 1.14 1.31 0.98 1.88 0.90 1.38 0.99 1
-0.3 . -0.3 -1.5 1 1.14 1.18 1.93 1.14 '
1.13 1.14 0.04 1.15 0.4- 1.1 . -0.6 - -
' 0.44 1.17 0.91 0.46 sf O.44 0.3 1.11 4.8 -
P.93 0.47
-1.9 4.9
'l c
1.04 1.08 i 1.01 1.07 :! 3.0 0.3 - 0.44 1.07 - 0.49 1.05
-10 '
E.1 0.47 0.47
, -0.4 .
NAE D NAE D ( .9) = 4.85
= -10 Nm E.IK
'I 5--
SIS ON = 2.24 X.X DIFFEENCE < b I
. I.
3-167 0
& 4 _ . . . . _ - , .- ,- , - . . . , . - . - m.- ,wr.
FIGURE 3-145 ! SICS 3D PDG VS. 1 :s.w w RPS CCWM18e NFP, D-884,.7411 gegVHTU 51-5-88A C.75
= 0.73 B.6 '
I 1.13 0.98 0.65 a O.95 }' O.1
.50
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~ .30.
-1.1 .
1.88 1.00 1.17 1.18 FO a
.1 1.5 -0.8 I ,
1.87 1.08 3.9 1.00 1.09 0.0 0.97 1.11 1.11
-0.4 1.09 '1.83 1.09 1.19 0.1 3.6 10 . 4 7 0.47
-1.5 1.15 1.13 0.90 1.16 1.15
-1.7 -0.6 -1.1 1.13 1.10 1.18 1.31, 1.06 1.14 0.00 1.30 1.17' 1.03
-0.6 . .i.g g,4 g,g.
85- 0.99 1.10 1.15 0.99 1.00 g:.7y 0 f:P ? ,i:P ::p
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- 1. 1.,. ., ,. .
1.18 0.00 9. 0.46 i
*1.1 . -0.4 0.9 1.15 1. I 1.17 0.95 1.16 I 1.18 0.96
- 9. 0 4*O *
=0 8 -0.9 1.09 1.10 0.98 1.09 1.09 1.99 0.00 1.09 -
0.1 1.1 0.8 I 1,31 0.93 0.50 0.p0
- 9. 1.17 0.95 0.50
-0.4 3.3 -1.8 0.0 0.98 I
,1.15 0.95 - 11 . 1 5 B.8 10.1 0.47 1.06 0.47 1.04
-1.1 3.3 5 0.46 0.4 0.0 ll j g.9> :!:n i.55
,7 n.
rge h 4 I4 3-16,8 .
4 FIGURE 3-146 5 51C5 3D PDG V5. HEAS1 RED RPD COMPARISON MFP. D-826.19758 8BNVN75 51-5-81A l' O.75 W 0.78 1.5
.95 E-
.95 B
.1 0.51 1.11 0.96 0.51 0.51 0.00 0.94 0.53 0.4 . 3.1 0.8 1.25 1.00 1.15 1.33, 0.00 0.00 r
1.06,_ R.0 1.07 1.08 g 1.07 1.25 .48 3 0.09
- 1.08 1.09 1.08 1.33 .49
. -0.9 -0.6 -0.3 B.6 1.3 0.96 1.13 1.10 0.90 1.13 1.11
-3.0 -0.1 -0.6 1.12 1.16 1.16 1.33 1.07 1.13 0.G0 1.17 1.30 1.05
-0.6 .
-0.5 3.3 1.4 0.74 .97 1.07 1.13 0.97 0.98 0.73 .96 1.07 1.18 0.96 0.98 1.4 1.3 0.5 0.3 i4 .g,g 1.08 i.16. 1.38 0.47 1.09 0.00 1 31 0.47
-4.8 . 0.3 0.8 1.17 1.33 1.15 0.95 1.17 P.90 1.16 0.93
~
4 ,, 0.7 . 0.4 0.0 -- 1.07 1.07 0.96 1.07
- 1. 0 ft 1.06 0.97 1.07
-4.2 1.3 -0.9 -0.1 l 0.51 1.33 0.94 0.51 5 0.S8 1.15 0.96 0.51
-0.8 6.3 1.9 0.0 0.96 1.17 l 0.94 1.17 g 3.5 0.3 0.48 1.87 0.49 1.04 3
-0.8 3.0 0.47 5 0.47
, -0.8 NAE Barr-NAR DIFF (
= 6.32 9.9) = a.32 N
E.gg i' R E B D Ig @!at m E 2 = 1.55 X.E . DIFFERENCE f i I 3-169 m,
- FIGURE 3-147 51C6 3D PDQ VS. MEABtBED RPD COMPARISON NZP. 3-20). 0 ISO /NTU $1-6-01 A m
.68
.69
-1.8 1 0.90 0.88 1.4 0.40 1.24 1.83 0.40 l 0.40 0.00 1.88 -
0.39
-0.8 . 2.8 3.4 1.18 1.87 1.86 1.09 0.00 0.00 -
2.8 . . 0.91 1.87 1.85 1.87 1.18 10.35 0.00 1.85 1.19 1.89 1.19~ .40
. 2.8 4.9 -1.8 -2.0 10 I 1.85 1.84
.08
.99 :-
1.80 1.17 - 0.5 .7 2.8 ly 1.85 1.31
.09
.00
.89
.89 1.36 1.88 1.01 1.03
-4.0 . 0.8 3.0- -1.9 0.69 1.88 1.17 1.03 1.88 1.05 0.69 1 88 1.11- Ih99 -
1.18 1.07 0.4 0.5 5.4- ll.6 1 1.86 0.89 .15 2.9 -1.9 0.44 1.86 - 0.90 1.18 0.48 0.0 . 3.1 -3.9 1.13 1.14 1 1.14 0.00 1.88 1.88 0.90 0.92
-1.0 . 1.8 -8.1 l.87 1.16 1.83 1.87 1.86 1.14 0.00 1.89 I 1.I' 2.1 . -1.8 0.40 1.84 0.86 .40 0.44 1.88 0.90 .00
-11 ~7.6 -3.7 .
1 <1.15 1.18 1.84 1.13 0.6 -1.1 0.35 1.00 1 0.00 1.93
-3.0
.. 0.40 0.39 1.8- ,
L = -11 N PEEDICTED MAR Sa.@ MAX D!f (RF0>0.9) smsus = -7.6 K.X1 MEASURED RMS DIFFEREBCE = 3.69 X.X PERfTiff DIP 7ERENCE 3-170
. ~ _ . _ _ . _ . _
- FIGURE- 3-148 j
'. *i 1
l 1 SICS 3D PDG VS. ItEA5tRED RFD COMPARIS0Bi 'I MFP, D-217. 973 IREVIffU 51-6-13A
.73 : 1
.70
.1 ~ ,
i
.49 'l
.(1 ~j 2.0 0.44 1.19 1.31 0.44 0.45 0.00 1.19 0.44 )
-3.0 . 3.0 -1.4 l 1.10 1.33 1.33 1 1.11. 0.94 0.00
-0.5 . . ;
0.93 1.33 1.33 1.33 1.10 .38 0.04 1.33 1.31 1.34 1.13 .40 .
. 0.8 1.4 -0.3 -1.3 4.9 J 1.33 1.07 1.33 -
c. 1.31 1.06 1.19 - 0.7 0.7 3.3 ' l.20 0.96 0.M 1.31 1.00 1.19 0.00 0.97 1.31 1.01 a 0.5 . -1.3 0.3 -1.0 ' O.73 1.33 't.17 1.07 1.33 1.07 .. 0.74 1.33 1.13 1.06 1.31 1.04 !!
-1.3 1.3- 4.4 1.3 1.6- 0.7 1.33 0.94 1.18 .43 1.33 0.00 1.17 .44 4 0.8 . 1.1' 1.1 1.10 1.14 1.33 0.90 -'
1.11 0.00 1.M 0.93 >
-0.9 . -0.1 -3.8 -
1.33 1.14 1.33 1.33 1.34 - 1.13 1.31 1.34 Y' -
, -0.4 3.7 0.3 -0.7 ,
0.43 1.31 0.49 0.43 O.44 1.31 0.91 0.45 }
-5.3 0.1 -3.1 -4.4
- 1.31 1.10 1- 1.19 1.11 1.8 -1.5 5 0.34 .60 s 0.00 .99
. .7 ,
0.43 I i 8.44 >' 4
" IIAE DIFFERENCE = -5.3 E"E" PEEB!tNED -'
IIAR DIFF (EPD>e.9) = 4.57 K.EX q NS DhN = 3.11 X.X DIFFERENCE i I I I 3-171 N
a .. _ .. . _ _ . . - - . lll
- ~
FIGURE 3-149 IM >
~ $1CS 3D PDG VS. HEASWED SPD COMPA3180s
-NFP,'D-338. 7518 lesysttir st-e-MA-i
.45 1
~
.63
.3
- .45
.45
{ .3-0.44 1.08 1.04 0.44 0.47 0.00 1.04 0.47 'l -1.5 . 1.9 -1.9 '5 , 1.14 1.14 1.15 0.00 1.14 - t 0.06 0.3 s
- $ 0.97 1.31 1.30 1.31 1.18 .40
'g 0.M 1.30 1.30 1.31 1.19 0.6 0.7 .41 ' , 0.7 -0.4 -0.9 3.0 E 1.39 1.09 1.30 1.39 1.09 g ' O.3 0.3 1.39 0.4 l 1.09 1.00 1.00 1.34 .95
- - 1.08 0.00 1.03 1.33 .M c 0.5- .
-1.9 1.1 1.1 i ;
0.65 1.04 1.37 1.99 1.08 10.93 0.M - 1.07 1.33 1.07 0.00
-1.7 0.7 4.1- 1.09 ~~
- 11. 7 ^ 0.7
!~ - 1.31 9 . 38
- 1. 0'~
1.34 0.41 i ! 1.01 '. 0.41 0.4 0.R
-1.3 9 -1.9
$ l 1.13 1.38 1.14 0.85 1.13
- I b
, -0.4 1.31 0.00 1.37 1.39 1.31 1.18
-4.3 0.87
-3.0 1.33 1.33 0.00 1.33
-1.0 0.3 . -1.1 s l 0.46 1.34 0.99 0.46 i
0.47 0.00 0.93 0.47 1 -3.1 .
-3.4 -3.3 1.M 1.13 a
'1 l i, 6.40 1.05 1.5-1.11 1.4 i 1 .- .95 ' 0.41 .M lE' -* 7 ' 'i l3- 0.41 , i i 0.43 i
" -3.4 ll .
t i NAESIFF NOR SN(RFDO.9)
- 4.10
= 4.18 N P W ICTED i K.EX
( W SM = 1.83 2.3 BIFFEREME !I .i , e '3 l 3-172 e
- t. ._____-______:: _ _ - _ _ _ _ - _ _ _ _ - _ - _ _ _ _ _ _ - - . ..
FIGURE 3-150 7 SIC 6 3D PDG VS. MEAS 1 RED RPO COMPARISDN - NFP. D-222. 13207 PRfD/N7U SI-6-70A -
.45 B..
.0 'j .- t 0.46 i 0.87
.49
-1.3 -
i s 1.06 1.03 .49 'a
.51 1.84 1.02 .00 ~
2.8 - 1.6 1.9 . 1.31 1.11 1.15 0.00 1.44 0.00
. 2.7 .
1.01 1.17 1.16 1.17 1.20 43 1 1.00 1.16' 1.14 0.00 1.21 44 1.0 0.9 1.8 . -0.1 2.3 .i 1.24 1.07 1.16 1.27 1.07 1.13 0.8 -0.3 2.0 1.04 0.94 0.98 1.23 98 . $o 1.44 0.00 1.01 0.00
.98
-0.3 3
-2.5 - .
4.4 0.47 1.94 1.28 1.07. 1.04 0.93 0.00 1.04 1.34 1.87 1.03 0.93
. 0.3 3.5- -es5 1.3 E. i i.i. 0..
-0.3 g, i.37 0.
liti ?" 4 1.14 i:15 1.37
!i* 1 1.15 0.84 !
l.17 1.38 1.15 0.00 1
-0.6 1.4 0.1 . j 1.17 1.84 1.27-1.17 1.17 1.M 0.00 1.17 <i
-0.4 3.5- . -0.1 0.49 I .23 i 10 . 9 2 0.49
~
0.84 1.11 l0.93 0.50
-2.4 1.6 51.0 -1.4 1.83 1.16 0.00 1.17
. -0.3 .
.94 0.43i L 0.44' .98 -
-1.5
~
.1 0.43 O.00 -
? MAX D N MAR DTFF (Rppe.9) = 3.47
= 4.00 N PRBICIED l K.EX MEASIMB '
RMB DIFFERENCE = 1.74 X.X PEMENT DIFFERENCE i la I 3-17 w- m- w w y- --v,- - - - - + , , ww--wae - - - . v. ,+-g-9., w- - t- g m we4 ia--
ec:-lt FIGURE 3-151 9
. - . N'
' 51C7 3D PDG VS MEASERIED RPD COMPARISON MEP. D-811. O SSvH79 81-7-93A 11.66
! 11 . 0 1
!5.0
'0.65 0.00 O.32 1.17 1.16 .33
'l 0.00 1.13 1.09 .33 l . 3.5 6.3 1.3
- Y --- 1.80 1.09 .97' 1.15 1.07 .94 4.4 1.6 .0 l 1.44 .97 0.89 5 0.97 1.23 0.35 1.18 .96 0.00 0.99 1.21 0 .?,4
-6.8 1.1 .
1.8 1.3 -e.3 1.18 1.88 I ,' 1.18
-0.1
.91
.90
.4 1.17 1.4 1.27 1.18 1.13 1.23 1.35 l 1.32 0.00 1.10 1.18 1.31
{ 1.83
-3.8 1.89 1.14
. .o.3
.90 0.9 3.0 1.39 1.17 i.29 0.00 0.00 .91 0.00 1.15
-ic ?
1.8 . 1.s
.91 1.18 1.80 0.98
.96 1.18 0.04 0.gg S.0 0.3 .
3.s i.15 1.30 1.00 0.7) I* 1.31
-4.6 0.97 1.84
-3.3 1.11 1.18 p.97 0.98 0.71 0.1 S.00 1;10 0.80 9.98
. 1.3 . 3.8
'Io 0.33 1.17 0.61 0.33 0.85 1.16 10.60 9.34
-6.8 1.4 g,3 3.1 lp 1.16 1.09 1.88 0.08 6.3 .
0.33 1.19 1 0.83 1.14 l -0.3 4.4 '-
.9
- lf 8
MAR MAR D
= -6.8 & PREDICTED 9.9) * -6.8 E.XX -
EMB D
- 3.33 X.X - ' - DIPPERENCE 3-174
. . . - . -~ ..-- . - - - . -.- - . - . . . . - . - . . - - - . . . - -.
s' r J E FIGURE 3-152 l Y
$1C7 30 PDG VS. HEASIRR?) RPD COMPARISON =J MPP, D-228. 807 IRS. WT1151-7-04A o,
,.0,
..Si
- I~
1.3 3 (0.49 O b.66.3 ' B-l 0.37 ' 1.17 1.14 .37 0.35 l1.14 1.12 .3 E1 5.1 1 12 . 5 3.1 2.4 gi ' [ 1.23 1.12 1.03 1.18. 1.10 1.01 y ) 1.05 4.3 1.01 0.95 1.4 0.5 1.01 1.23 0.34 g; 1.04 1.01 0.92 3, 1.02 1.22 0.39
-1.5 -0.4 2.4 -1.9 1.1 -1.8 '
1.30 0.94 1 88 1.30 0.96 1.30
-0.3 -1.2 -1.5 I
!. .c 1.18 1.17 1.17 1.21 1.20 1.30 0.00 1.21 1.22 1.19 y
-1.5 . -2.7 -0.7 1.1 1.05 1.19 1.16 .93 1.19 1.04 ;
I' 1.09 1.19 1.16 .95 1.17 1.04
-3.1 -0.4 0.0 2.1 1.4- -0.3 l0.94 1.17 1.31-
?
0.83 -
. 97 ' 1.19 1.32 l p-2.8 l 0.88 L :
.}}