ML20100G262
| ML20100G262 | |
| Person / Time | |
|---|---|
| Site: | North Anna  |
| Issue date: | 10/31/1983 |
| From: | Reid D VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.) |
| To: | |
| Shared Package | |
| ML20100G237 | List: |
| References | |
| TAC-57471, TAC-57472, VEP-NOS-8, NUDOCS 8504080139 | |
| Download: ML20100G262 (30) | |
Text
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VEP-NOS-8 Vepco A STUDY OF THE EFFECTS OF A REDUCED NUMBER OF THIMBLES ON THE RESULTS OF INCORE FLUX MAP ANALYSIS b
w lBR498 ansi 88ljge NUCLEAR OPERATIONS DEPARTMENT VIRGINIA ELECTRIC AND POWER COMPANY
VEP-NOS-8 A STUDY OF THE EFFECTS OF A REDUCED NUMBER OF THIMBLES ON THE RESULTS OF INCORE FLUX MAP ANALYSIS By D. L. Reid 3
Reviewed by: $ G. Miller, Staff Engineer Approved by:
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J D(. W. J. Loft'o, Director Nuclear Fuel Operation Nbrear Fuel Operation Nuclear Fuel Operation Subsection l
Nuclear Operations Department Virginia Electric and Power Co.
Richmond, Virginia October, 1983 l
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ABSTRACT The ptirpose of this study is to examine the effects of reducing the number of monitored thimbles on incore map analysis ~ results produced by the INCORE code. The present Technical Specifications for the Surry and North Anna power stations require a minimum'of thirty-eight monitored thimbles for a full core map. This study was performed to derive incremental con-servative factors which can be used to produce conservative results when applied to the power distribution parameters for incore maps which have less than the prer :ntly required minimum number of monitored thimbles and, thereby, allow such maps to be acceptable for incore analysis.
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J' TABLE OF CONTENTS Section
' Title Page t
Abstract
......... i List,of Tables........................
iii List of Figures................................... iv 1
Introduction.....................................
1 2
Description Of The INCORE Code Modifications.....
3 3
Description Of The Random Thimble Selection Process 5 4
Description Of Code Output
........ 6 5
Statistical Analysis Methodology and Incremental Conservative Factor Development
............... 8 6
Results......
.................................... 11 7
Conclusions
..................................... 21 8
References
........................................ 22 Appendix 1 Study Basis Flux Maps........................... 23 Appendix 2 Verification....................................
24 11
LIST OF TABLES Table Title Page 6-1 Maximum F-delta-H Results Summary....
13 6-2 Maximum Fq Results Summary.........
14 6-3 Minimum Fq*P Margin Results Summary..
15 6-4 Maximum Fxy Results Summary.......................... 16 6-5 Minimum Fxy Margin Results Summary................... 17 6-6 Incremental Conservative Factors for Reduced Data Cases
................................................ 18 6-7 Average Axial Offset Results Summary................. 19 6-8 Average Quadrant Power Tilt Results Summary......... 20 iii c
LIST OF FIGURES J
Figure Title Page 2-1 Core Map of Monitored Locations..................... 4 iv
SECTION 1 - INTRODUCTION The Technical Specifications for the Surry and North Anna Power Stations require that any valid full-core flux map be taken with a minimum of thir-ty-eight monitored thimbles.
In the event of a malfunction in the f1tix mapping system hardware, it might be desirable to take valid full-core flux maps with a lesser number of monitored thimbles. This study shows tl a behavior of the results of flux map analyses using less thimbles.
From those results, appropriate incremental conservative factors have been determined for important incore power distribution parameters based upon the number of monitored thimbles that provided data for the analysis.
These factors, when applied to the appropriate power distribution parame-ters, yield results that are equivalent to or conservative with respect to the results of a map utilizing the present minimum number of required thimbles.
In order to perform this study, the INCORE code was modified to reduce the program output and to provide an automatic random selection of thimbles.
The program output for this study consisted of a core map of the chosen thimbles, the average axial of fset, the maximum F-delta-H, the maximum Fq, the Fq*P minimum margin, the average quadrant power tilt, the Fxy at the core midplane for Surry maps, and the maximum Fxy and the minimum Fxy mar-gin for North Anna maps.
A total of eight flux maps from Surry and North Anna were used as the ref-erence data base for this study. For each of these flux maps, three major analysis cases were considered. The major analysis cases utilized data obtained from thirty-eight, thirty-two, and twenty-six monitored thimbles. For each of the major analysis cases, a minimum of one hundred 1
individual analyses were performed.
(The-tiux maps and the number of major analysis cases that were performed for each map are described in Appendix 1).
Following this, a statistical study was performed on the data that was generated. Each map analysis result was checked for unique-ness and only analyses with at least four thimbles per quadrant were used.
The applicability of this report is limited to incore flux map analysis results developed by the Vepco staff for the Surry and North Anna Power Stations.
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SECTION 2 - DESCRIPTION OF THE INCORE CODE MODIFICATIONS l
The current Vepco version of the INCORE code was modified in order to reduce the program output to a minimum and to allow the automatic selection of randomly chosen thimbles. The calculational basis of the code was not changed in any manner. Output statements were deleted from the program until the output consisted only of the values for the parame-ters of interest to this study.
The fifty possible monitored thimble locations in the core were repres-ented by a one-dimensional array of fifty columns, the location of each column in the array corresponding to a particular thimble location. The INCORE codo assigned a value to each of the fifty columns dependi_.g on whether the thimble location corresponding to that particular column was 4
monitored or not. A value of one was assigned if the location was amni-tored, and a value of zero if it was not. This provided an efficient ceth-od for checking on the uniqueness of a randomly selected map. A map of the possible monitored core locations is given as Figure 2-1.
Af ter the program output had been reduced to a minimum, the code was used to analyze the same flux map several times during one execution. This step was performed in order to verify that the modified code would cor-rectly analyze a sequence of flux maps.
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f FIGURE 2-1 CORE MAP OF MONITORED I4 CATIONS R
P N
M L
K J
H G
F E
D C
B A
50 1
19 2
14 34 2
30 3
27 40 23 4
37 42 20 32 9
44 5
7 46 15 6
49 1
4 26 8
7 25 31 17 35 12 39 8
47
'41 18 11 9
6 36 21 24 10 13 10 28 3
' 11 43 48
'45 38 12 22 16 la 5
33 14 29 15 9
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4 t......... _..
Q.. _ _ _
l SECTION 3 - DESCRIPTION OF THE RANDOM THIMBLE SELECTION PROCESS I
A single dimensional array of size fifty was inicalized before beginning the analysis of a map. This array contained the numeric identification of all,the valid thimbles for the map (see Figure 2-1). The first element of the array contained the identication number of the calibration thimble.
This was typically a "1" which stands for the J-7 core location which is the calibration thimble for the North Anna 1 and 2 and Surry 2 maps. For the Surry 1 maps, the first element of the array contained a "4" which is the identification number of the G-7 core location which is the cali-bration thimble for that unit. The remaining elements of the array con-tainod the identification of the other valid thimbles.
A shuffle of the data was accomplished by randomly choosing two numbers, m and n, between two and i inclusive, where l is the maximum number of valid thimbles (the number measured in the original case) and m is not equal to Elements m and n of the array were interchanged. After the shuffle had n.
been performed a random number of times (from 200 to - 300), the first j elements of the array contained the thimbles used for the map analysis.
For this study, j was twenty-six, thirty-two, or thirty-eight. Af ter the o
map was analyzed using this list of thimbles, the array was shuffled again in the same manner and the analysis continued.
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l SECTION 4 - DESCRIPTION OF CODE OUTPUT l
The output of the : modified INCORE code was stored in a data set for fur-ther use. The first line'of the data set is a title line which contains the station, unit, cycle, and map identification, the numbar of thimbles used, and the numerical representation of the valid thimbles. As seen in the examples below, the list of valid thimbles given on the title line is composed of ones and zeroes. A one represents a thimble that was moni-tored in the original map and a zero represents a thimble that was not.
This convention was also used in the numerical representation of the flux map case described below.
For a North Anna reduced thimble case, each flux map is described by three lines of information. The first line con-tains the numerical representation of the map of monitored locations and the number of thimbles per quadrant. The second line contains the assem-blywise power distr'ibution standard deviation, the average absolute per-cent difference to prediction, the average axial offset, the maximum F-delta-H, the maximum Fq, the minimum Fq*P margin and its nodal location, and the average quadrant power tilt. The third line contains the nodal location of the maximum Fxy, the maximum Fxy, and the minimum Fxy margin for the rodded and unrodded core regions respectively. Zero entries for the parameters on this line indicate that no rodded Fxy and minimum Fxy margin values existed. The following is an example of the output associ-ated with the first two reduced thimble cases from a North Anna map:
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N1-2-01 26 THIMBLES 11111111111111111111111111111111111111011111011111 i
l 11101101110111010110100110000110101001011000010100 4.5 6.5 5.5 9.5 3.97681 6.13923 47.67577 1.67375 3.27350 11.04805 10 1.07207 1
0 0.0 0.0 40 1.84261 2.19095 l
10101010010111011000111000100111011001010101011100 8.0 6.0 '
6.0 6.0 l
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4.10122 6.23767 48.53163 1.58809 2.99493 18.61774 10 1.08003 0
0.0 0.0 40 1.84034 2.31153 For a Surry case study, the first line of the data set is a title line and is identical with the North Anna case. Each reduced thimble flux map con-sists of two lines of information. The first line contains the numerical representation of the map of monitored locations and the number of thim-bles per quadrant. The second line contains the assemb laise power dis-tribution standard deviation, the average absolute pere nt difference to prediction, the average axial offset, the maximum F-de ita-H, the maximum Fq, the minimum Fq*P margin and its nodal location, Fxy at the core mid-plane, and the average quadrant power-tilt. The following is an example of the output associated with the first two reduced thimble cases from a Surry map:
S2-6-12 32 THIMBLES 11110111111111111111111111111001100111011111111110 11110111011111110111111101011001100001001000011110 6.0 8.5 6.0 11.5 0.75552 1.14992 -2.38548 1.33039 1.59392 21.03532 33 1.33541 1.00413 10110111110101101110001111111000100111001110111010 8.5 8.0 6.5 9.0 1.04885 1.30237 -2.30167 1.35062 1.63676 18.91289 34 1.36192 1.00458 7
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SECTION 5 - STATISTICAL ANALYSIS METHODOLOGY AND INCREMENTAL CONSERVATIVE FACTOR DEVELOPMENT The current Technical Specifications for Surry and North Anna require that full core flux maps be taken with at least thirty-eight thimbles.
In order to justify using less thimbles for a full core flux map for Techni-cal Specifications surveillance compliance, it is necessary to show that the results obtained using cata from less than' thirty-eight thimbles are equivalent to or conservative with respect to the results obtained using i
data from thirty-eight or more thimbles. 'In order to evaluate this, the results for the twenty-six thimble and thirty-two thimble - case studies were compared with the results of the thirty-eight thimble case studies.
The results for the thirty-eight thimble case studies were defined to be the bounding values for each parameter obtained in accordance with the current Technical Specifications.
For the parameters F-delta-H, Fq, and Fxy, it is'necessary that the results for the twenty-six and thirtyltwo thimble case studies be greater than the minimum result associated with the thirty-eight thimble case stu-l dies for these parameters. The mean minus three times the standard devi-ation of the case studies was used to estimate the-lower bound on the -
expected range of values for these parameters. The percent difference between the result of the thirty-eight thimble case and the reduced number of thimbles case was then calculated as shown below:
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(M-30)fI
% penalty n
1-
- 100 g
(M-30)38 where M is mean value for the parameter o is the standard deviation i is the flux map I.D.
j is the case study I.D.;
i.e., 26 or 32 thimbles For a few of the cases, the minimum value for a parameter was less than M-30.
For those cases, the minimum value was used to calculate the % pen-alty.
For the parameters minimum Fq*P margin and the minimum Fxy margin, it is necessary that the results for the twenty-six and thirty-two thimble case studies be less than the maximum result associated with the thirty-eight thimble case study. For these parameters, the maximum value for each case study was used as an estimate of the upper bound on the expected range of values for these parameters.
The difference between the result of the thirty-eight thimble case and the reduced number of thimbles case was then l
l calculated as shown below:
% penalty 1=MVf-MV38 1
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where MV is the maximum value of;the paramotor being considered i is the flux map I.D.
j is;the case study I.D.,
i.e., 26 or 32 thimbles.
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4 Finally, incremental conservative factors were derived for each parameter using the percent penalty values. For the parameters F-delta-H, Fq, and Fxy, this was done by first taking the nost conservative percent penalty value for each and rounding the values up to the next highest integer.
These values were then used to calculate the incremental conservative fac-tors as shown below:
ICF = 1 + *. penalty
/100
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1 where ICF is the incremental conservative factor i designates the parameter of interest; i.e.,
F-delta-H, Fq, or Fxy
- penalty is the maximum value for the percent penalty rounded up to-the next highest integer.
For the parameters minimum Fq*P margin and the minimum Fxy margin, the ICF values were developed by taking the highest percent penalty value for g
each and rounding them up to the next highest integer.
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SECTION 6 - RESULTS A summary of the results for all of the case studies for the maximum F-delta-H, the maximum Fq, the minimum Fq*P margin, the maximum Fxy, and the minimum Fxy margin is presented in Tables 6-1 through 6-5, respective-ly. The columns labeled " measured" are the values that were obtained from the analysis for the eight incore flux maps used as the basis for the stu-dy utilizing all of the available data. The mean, minimum and maximum values, and the standard deviation are the results associated with the analysis of each case studied. As can be seen from the information listed on these tables, the results associated with the twenty-six and thirty-two thimble case studies are kuite similar to the results associated with the thirty-eight thimble case study for each flux map. The percent penalty values on Tables 6-1 through 6-5 were calculated in accordance with the methods described in Section 5.
Based on these data, it is clear that the results are not always conservative relative to the results for the -
thirty-eight thimble case results. Therefore, it was necessary to use the percent penalty values to develop the incremental conservative factors as described in Section 5.
These factors are summarized on Table 6-6.
Addi-tionally, percent penalty values and incremental conservative factors 2
were derived based on a 95% probability and a 95% confidence level. The results presented here were consistent or conservative relative to the results.of that statistical treatment.
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Case study' data were also obtained for the average axial offset and the incore quadrant power tilt ratio. These results are presented in Tables 6-7 and 6-8, respectively. This information shows that the results for.-
the twenty-six and thirty-two thimble case studies are in good agreement with the results for the thirty-eight thimble case studies. It was not 11
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necessary to develop percent penalty values or incremental conservative factors for these parameters since the Surry and North Anna Technical Spe-1 cifications do not specify limiting values for them.
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TABLE 6-1 MAXIMUM F-delta-H RESULTS
SUMMARY
26 Thimbles Minimum Maximum Standard Mean -
percent Map Measured Mean Value Value Deviation 3
- sigma penalty N1-2-01 1.5735 1.62221 1.53953 1.72121 0.03346 1.52183
-1.37 N1-2-16 1.3488 1.37701 1.34825 1.40534 0.01456 1.33333 0.08 N1-3-23 1.3c27 1.39781 1.34008 1.45298 0.02185 1.33226
-0.10 N1-3-39 1.3777 1;38795 1.36187 1.45428 0.01580 1.34055 0.78 N2-1-54 1.2290 1.22508 1.21103 1.23528 0.00467 1.21107 0.53 SI-6-23 1.4469 1.45868 1.43732 1.50100 0.01166 1.42370 0.67 S1-6-28 1.3661 1.36931 1.35646 1.38234 0.00581 1.35188 0.75 S2-6-12 1.331.8 1.33969 1.32261 1.38043 0.00808 1.31545 0.37 32 Thimbles Minimum Maximum Standard Mean -
percent Map Measured Mean Value Value Deviation 3
- sigma penalty N1-2-01 1.5735 1.61657 1.53985 1.70314 0.03057 1.52486
-1.58 N1-2-16 1.3488 1.36999 1.34138 1.40216 0.01323 1.33030 0.31 N1-3-23 1.3827 1.38149 1.33667 1.41848 0.01513 1.33610
-0.39 N1-3-39 1.3777 1.38467 1.36260 1.43099 0.01094 1.35185
-0.05 N2-1-54 1;2290 1.22712 1.21340 1.23415 0.00372 1.21596 0.34 S1-6-23 1.4469 1.45322 1.44082 1.48312 0.00834 1.42820 0.36 S1-6-28 1.3661 1.36870 1.36201 1.38004 0.00418 1.35616 0.43 S2-6-12 1.3318 1.33470 1.32147 1.35308 0.00538 1.31856 0.13 38 Thimbles Minimum Maximum Standard Mean -
Map Measured Mean Value Value Deviation 3
- sigma N1-2-01 1.5735 1.60202 1.54820 1.71141 0.0336i 1.50119 N1-2-16 1.3488 1.36088 1.34447 1.33734 0.00881 1.33445 N1-3-23 1.3827 1.38064 1.33087 1.44135 0.01386 1.33906 N1-3-39 1.3777 1.38307 1.36158 1.41781 0.01064 1.35115 N2-1-54 1.2290 1.22814 1.21749 1.23162 0.00220 1.22154 SI-6-23 1.4469 1.45104 1.44264 1.47583 0.00590 1.43334 S1-6-28 1.3661 1.36667 1.36253 1.38100 0.00154 1.36205 S2-6-12 1.3318 1.33319 1.32588 1.35263 0.00430 1.32029 13
TABLE 6-2 MAXIMUM Fq RESULTS
SUMMARY
26 Thimbles F
Minimum Maximum Standard Mean -
percent Map ' Measured Mean Value Value Deviation 3
- sigma penalty N1-2-01 2.8565 3.04230 2.79113 3.42864 0.11047 2.71089
-2.85 N1-2-16 1.'7594 1.80294 1.72230 1.87444 0.04344 1.67262 1.72 N1-3-23 1.7232 1.73611 1.66985 1.81171 0.02891 1.64938 0.96 N1-3-39 1.6022 1.61274 1.58231 1.67700 0.01286 1.57416 0.23 N2-1-54 1.4657 1.45850 1.43517 1.47379 0.00951 1.42997 0.63 SI-6-23 1.7875 1.79824 1.75267 1.84917 0.01278 1.75990 0.94 S1-6-28 1.6194 1.61900 1.59914 1.63195 0.00526 1.60322 0.79 S2-6-12 1.5982 1.62124 1.57549 1.67029 0.01858' 1.56550 0.33 32 Thimbles Minimum Maximum Standard Mean -
percent.
Map Measured Mean Value Value Deviation 3
- sigma penalty I
N1-2-01 2.8565 2.99545 2.80678-3.29265 0.09875 2.69920
-2,41 i
N1-2-16 1.7594 1.78748 1.72347-1.87020 0.03351 1.68695 0.88 N1-3-2311.7232 1.71462 1.67153 '1.76953-0.02211 1.64829 1.03 N1-3-39 1.6022 1.60758 1.58786 1.64950 0.00842 1.58232
-0.28 N2-1-54 1.4657 1.46147 1.43642 1.47189 0.00850' 1.43597 0.22 SI-6-23 1.7875 -1.79329 1.77312 1.83104 0.00908.
1.76605 0.19 S1-6-28 1.6194 1.62055-1.61298 1.62692 0.00297 1.61164 0.02 S2-5-12 1.5982 1.60773 1.58451 1.65243 0.01449 1.56516 0.35 38 Thimbles-Minimum Maximum Standard Mean -
Map -Measured Mean Value Value Deviation 3
- sigma N1-2-01 2.8565 2.95265 2.79980 3.40912 0.10566 2.63567 N1-2-16 1.7594 1.76951 1.72155 1.81917 0.02255-1.70186 N1-3-23 1.7232 1.71899 1.66541 1.79722 0.01578-1.67165 N1-3-39 1.6022 1.60726 1.58201 1.63640 0.00981 1.57783 N2-1-54 1.4657 1.46418 1.43907 1.46887 0.00528' 1.44834 SI-6-23 1.7875 1.79111 1.78211 1.81491 0.00725' 1.76936 SI-6-28 1.6194 1.61974 1.61191 1.62447 0.00185 1.61419 S2-6-12 1.5982 1.60379 1.58643 1.65187 0.01106-1.57061 I'
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P TABLE 6-3 MINIMUM Fq*P MARGIN RESULTS
SUMMARY
26 Thimbles Minimum Maximum Standard percent Map Measured Mean Value Value Deviation penalty i
N1-2-01 22.7666 14.81517
-6.12567 24.76039 6.57356 0.41 l
N1-2-16 10.7506 8.54072 4.91333 12.63127 2.20379
-0.04 N1-3-23 11.3465 12.25722 8.53306 15.69538 1.43272
-0.22 l
N1-3-39 18.4665 15.78865 2.26301 20.83746 5.55923 0.50 l
N2-1-54 23.2444 19.74305 6.51814 24.90408 3.27899 0.19 SI-6-23 38.7310 38.72426 36.59909 40.11696 0.42286 0.75 SI-6-28 19.7723 19.76704 19.15126 20.26709 0.22090 0.12 S2-6-12 23.1964 21.58110 15.48689 24.28880 1.75123 0.53 32 Thimbles Minimum Maximum Standard percent Map.
Measured Mean Value Value Deviation penalty N1-2-01 22.7666 16.41630
-5.83231 24.52682-6.37929
- 0.18 N1-2-16 10.7506 9.32467 5.12854 12.57201.1.70001
-0.10 N1-3-23 11.3465 13.27566 10.66297
-15.61026 1.13628
-0.31 N1-3-39 18.4665 15.14946 4.73440 20.63139 6.18373 0.29 N2-1-54 23.2444 21.96542 15.33199 24.66966 2.22322
-0.05 SI-6-23 38.7310 38.84861 37.66089 39.52805 0.35334 0.16 SI-6-28 19.7723 19.71588 19.40027 20.09106 0.14705
-0.05 S2-6-12 23.1964 22.66879 15.54896 23.85562 0.92154 0.09 38 Thimbles Minimum Maximum Standard i
Map Measured Mean Value Value Deviation.
N1-2-01 22.7666 19.20266
-5.88434 24.34816 4.74481 N1-2-16 10.7506 10.23618 7.71726 12.66910 1.14383 N1-3-23 11.3465 13.17474 9.26499 15.91940 0.80875 N1-3-39 18.4665 15.81585 4.73955 20.34164 5.40113 N2-1-54 23.2444 22.91280 16.62109 24.71875 1.13715 SI-6-23 38.7310 38.69663-37.84724 39.36475 0.22224 S1-6-28 19.7723 19.75579 19.52148 20.14369 0.09167 S2-6-12 23.1964 22.92681 20.61821 23.76332 0.53242 NOTE: All margin values are in. percent.
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TABLE 6-4 MAXIMUM Fxy RESULTS
SUMMARY
26 Thimbles l
Minimum Maximum Standard Mean -
percent Map Measured Mean Value-Value Deviation 3
- sigma penalty N1-2-01 1.843 1.93856 1.81054 2.08973 0.05642 1.76930
-2.36 N1-2-16 1.580 1.62851 1.55655 1.69891 0.03093 1.53572 0.11 N1-3-23 1.517 1.54594 1.47834 1.62483 0.02592 1.46818
-0.56 N1-3-39 1.512 1.52803 1.49933 1.59592 0.01788 1.47439 0.61 N2-1-54 1.381 1.37521 1.35450 1.39568 0.00821 1.35058 0.76 32 Thimbles Minimum Maximum Standard Mean -
percent Map. Measured Mean Value Value Deviation 3
- sigma penalty N1-2-01 1.843 1.91358 1.80896 2.05616 0.05719 1.74201
-0.78 N1-2-16 1.580 1.61271 1.55126 1.68710 0.02694 1.53189 0.36 N1-3-23 1.517 1.53692 1.47385 1.5944p 0.02711 1.45559 0.30 N1-3-39 1.512 1.52147 '1.49939 1.59098 0.01268 1.48343 0.001 N2-1-54 1.381 1.37811 1.'35639 1.39158 0.00737 1.35600 0.36 38 Thimbles Minimum Maximum Standard Mean Map Measured Mean Value Value Deviation 3
- sigma N1-2-01 1.843 1.88770 1.81106 2.02557 0.05304 1.72858 N1-2-16 1.580 1.59369 1.55107 1.63848 0.01874 1.53747 N1-3-23 1.517 1.52073 1.46770 1.58241 0.02026 1.45995 N1-3-39 1.512 1.52068 1.49641 1.58397 0.01241 1.48345 N2-1-54 1.381 1.38066 1.36087 1.38693 0.00430 1.36776 I
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TABLE 6-5 MINIMUM Fxy MARGIN RESULTS
SUMMARY
26 Thimbles Minimum Maximum Standard percent Map Measured-Mean Value Value Deviation penalty N1-2 2.181
-2.90223
-10.92666 3.89314 2.99471 0.28 N1-2-16
-0.334
-3.41682
-7.88761 1.15274 1.96445
-0.35 N1-3-23 3.407 1.97300
-1.96618 5.85736 1.50555
-0.68 N1-3-39 4.062 3.10760
-0.60979 4.84392 0.92984
-0.19 N2-1-54 11.473 11.87570 10.56395 13.20271 0.52590 0.41
-32 Thimbles Minimum Maximum Standard percent Map Measured Mean Value Value Deviation penalty N1-2-01
-0.334
-1.57597
-9.14464 3.97707 3.03572 0.11 N1-2-16 2.181
-2.41320
-7.13724 1.48910 1.71100
-0.01 N1-3-23 3.407 2.87956 0.01026 6.14316 1.32728
-0.39 N1-3-39 4.06f 3.46057 1.07899 4.84029 0.72437
-0.19 N2-1-54 11.473 11.68959 10.82674 13.08195 0.47225 0.29 38 Thimbles Minimum Maximum Standard Map Measured Mean Value Value Deviation N1-2-01
-0.334
-0.20252
-7.52087 3.86545 2.81548 N1-2-16 2.181
-1.20535
-4.05027 1.50067 1.18987 N1-3-23 3.407 3.34062
-0.77007 6.53482 1.09807 N1-3-39 4.062
'3.48892
-0.52766 5.02913 0.78748 N2-1-54 11.473 11.52639 11.12447 12.79473 0.27558 Note: All margin values are in percent.
l 17 I
L TABLE 6-6 INCREMENTAL CONSERVATIVE FACTORS FOR REDUCED DATA CASES Maximum F-delta-H................................
1.01 Maximum Fq.......................................
1.02 Minimum Fq
- P Margin............................
1.0%*
Maximum Fxy......................................
1.01 (North Anna maps)
Minimum Fxy Margin...............................
-1.0%*
(North Anna maps) o
- To be applied as a negative bias e
k O
18
l TABLE 6-7 AVERAGE AXIAL OFFSET RESULTS
SUMMARY
26 Thimbles Minimum Maximum Standard Min - Max -
Map Measured Mean Value Value Deviation Meas Meas N1-2-01 47.963 48.19846 47.22165 49.34341 0.30008
-0.741 1.380 N1-2-16
-7.267
-7.12161 -7.75098
-6.41297 0.23380
-0.484 0.853 N1-3-23
-5.422
-5.29266 -5.71196
-4.89387 0.15316
-0.290 0.528 N1-3-39
-3.225
-3.22555 -3.68119
-2.69379 0.17599
-0.456 0.531 N2-1-54
-0.426
-0.41376 -0.76181
-0.04274 0.11974
-0.336 0.383 SI-6-23 0.106 0.09841 -0.33934 0.49328 0.14701
-0.233 0.387 S1-6-28
-3.092
-3.04186 -3.63013
-2.53483 0.20014
-0.538 0.557 S2-6-12
-2.366
-2.41162 -2.84242
-1.90126 0.16802
-0.476 0.465 32 Thimbles Minimum Maximum Standard Min - Max -
Map Measured Mean Value Value Deviation Meas Meas N1-2-01 47.963 48.03935 47.47414 48.69701 0.20865
-0.489 0.734 N1-2-16
-7.267
-7.15923 -7.67807
-6.52845 0.16680
.-0.411 0.739 N1-3-23
-5.422
-5.37599
-5.69516
-5.08666 0.11548
-0.273 0.335 N1-3-39
-3.225
-3.21560 -3.66716
-2.87522 0.12740
-0.442 0.350 N2-1-54
-0.426
-0.42594 -0.64994
-0.19916 0.08771
-0.224 0.227 S1-6-23 0.106 0.12808 -0.15938 0.40529 0.10705
-0.265 0.299 S1-6-28
-3.092
-3.09990 -3.43446
-2.78490 0.13868
-0.342 0.307 S2-6-12
-2.366
-2.41352 -2.70218
-2.u4496 0.10997
-0.336 0.321 38 Thimbles Minimum Maximum Standard' Min - Max -
Measured Mean Value Value Deviation Meas Meas N1-2-01 47.963 48.03550 47.60269 48.65215 0.14933
-0.360 0.689 N1-2-16
-7.267
-7.22055
-7.49768
-6.92163 0.09617
-0.231 0.345 N1-3-23
-5.422
-5.45077
-5'.66420
-5.20620
.0.08719
-0.242 0.216 N1-3-39
-3.225
-3.26271
-3.46228
-3.02999 0.08260
-0.237 0.195 N2-1-54
-0.426
-0.44666 -0.57007
-0.32754 0.04216
-0.144 0.098 SI-6-33 0.106 0.13118
-0.02694 0.36816 0.06795
-0.133 0.262 S1-6-18
-3.092
-3.09404 -3.29442
-2.86888 0.08020
-0.202 0.223 S2-6-12
-2.366
-2.35996 -2.55156
-2.14061 0.07855
-0.186 0.225 Note: All axial offset values are in percent.
O 19
TABLE 6-8 AVERAGE QUADRANT POWER TILT RESULTS
SUMMARY
26 Thimbles Minimum Maximum Standard Min -
Max -
Map Measured Mean Value Value Deviation Meas Meas N1-2-01 1.0808 1.08017 1.04302 1.11551 0.01183
-0.0379 0.0346 N1-2-16 1.0117 1.01115 1.00032 1.02293 0.00406
-0.0114 0.0112 N1-3-23 1.0067 1.01010 1.00293 1.02244 0.00385
-0.0038 0.0157 N1-3-39 1.0054 1.00725 1.00130 1.01891 0.00284
-0.0041 0.0135 N2-1-54 1.0018 1.00403 1.00056 1.01221 0.00205
-0.0012 0.0104 S1-6-23 1.0634 1.06261 1.05117 1.07108 0.00399
-0.0122 0.0077 S1-6-28 1.0045 1.00565 1.00059 1.01249 0.00230
-0.0039 0.0080 S2-6-12 1.0034 1.00657 1.00226 1.01675 0.00195
-0.0012 0.0133 32 Thimbles Minimum Maximum Standard Min -
Max -
Map Measured Mean Value Value Deviation Meas Meas N1-2-01 1.0808 1.08010 1.04564 1.11529 0.00968
-0.0353 0.0344 N1-2-16 1.0117 1.01155 1.00461 1.01848 0.00264 -0.0071 0.0068 N1-3-23 1.0067 1.00754 1.00200 1.01681 0.00253
-0.0047 0.0101 N1-3-39 1.0054 1.00733 1.00190 1.01674 0.00294 -0.0035 0.0113 N2-1-54 1.0018 1.00301 1.00021 1.00910 0.00135
-0.0016 0.0073 SI-6-23 1.0634 1.06261 1.05341 1.07078 0.00315
-0.0100 0.0074 S1-6-28 1.0045 1.00452 1.00140 1.00918 0.00170
-0.0031 0.0047 S2-6-12 1.0034 1.00554 1.00238 1.01035 0.00138
-0.0011 0.0069 38 Thimbles Minimum Maximum Standard Min -
Max -
Map Measured Mean Value Value Deviation Meas Meas N1-2-01 1.0808 1.07984 1.05556 1.09885 0.00637
-0.0253 0.0180 N1-2-16 1.0117 1.01135 1.00444 1.01937 0.00263
-0.0073 0.0077 N1-3-23 1.0067 1.00749 1.00250 1.01441 0.00197
-0.0042 0.0077 N1-3-39 1.0054 1.00573 1.00215 1.01212 0.00185
-0.0033 0.0067 N2-1-54 1.0018 1.00254 1.00050 1.00512 0.00092 -0.0013 0.0033 SI-6-23 1.0634 1.06277 1.05694 1.06709 0.00179
-0.0065 0.0037 SI-6-28 1.0045 1.00453 1.00179 1.00691 0.00096
-0.0027 0.0024 S2-6-12 1.0034 1.00435 1.00235 1.00777 0.00099
-0.0012 0.0043 9
20
SECTION 7 - CONCLUSIONS As indicated by the summary of the data presented in Section 6, reliable flux map analysis results for the maximum values for F-delta-H, Fq, and Fxy, the minimum margin results for Fq*P and Fxy, the axial offset, and the quadrant power tilt may be obtained from maps based on as few as twen-ty-six monitored thimbles, with the requirement that there be at least four monitored thimbles per quadrant. Additionally, incremental conserv-ative factors have been developed. These factors can be applied to the flux map analysis results associated with flux maps utilizing data from at least twenty-six thimbles but less than thirty-eight thimbles. By use of these factors the results will be equivalent to or conservative with respect to flux map analyses results obtained in acco~rdance with the requirements.of the current Technical Specifications for the Surry and North Anna power stations using thirty-eight thimbles. This conclusion is based on several factors. First, the study results were based on the analysis of flux map data that were taken from different reactor cores, over a wide range of power level, power distribution, core burnup, and control rod configurations. Second, the number of study cases that were run were sufficiently large-so that the results have statistical signif-icance.
Third, two different methodologies were used to establish the values for the incremental conservative factors, and the results were con-sistent.
Finally, it is believed that the ca.;
chat were considered in this study are sufficiently diverse such that the results of this study are applica-ble to future flux map analyses for the Surry and North Anna nuclear units.
21
SECTION 8 - REFERENCES 1.
W. D. Leggett, III and L. D. Eisenhart, "INCORE Code," WCAP-7149, December 1967.
2.
J. G. Miller, " Derivation of Uncertainty Factors for Reduced Thimble INCORE Map Analysis Using 95/95 Tolerance Limits,"
Vepco, October, 1983.
3.
T. C. Hartsfield, " Evaluation of Results From INCORE Number-of-Thimbles Study," Vepco memorandum, October 18, 1983.
m 22
1 APPENDIX 1 - STUDY BASIS FLUX MAPS A description of the eight incore flux maps that were chosen as the refer-
- ence data base for this study is presented below. These maps are repre-sentative of various operational conditions that have been experienced at the four Vepco nuclear units.
N. Anna Map==> N1-2-01 N1-2-16 N1-3-23 N1-3-39 N2-1-54 thermal power (MWt) 1 2733 2772 2725 2681 cycle burnup (MWD /MTU) 0 349 2232 8899 12607 control rod position D/218 D/208 D/221 D/219 D/218 maximum quadrant power 1.09 1.0138 1.011 1.007 1.003 tilt ratio thimbles available 48 46 46 46 41
- 38 thimble cases 800 257 302 400 376
- 32 thimble cases 591 296 221 287 699
- 26 thimble cases 547 330 265 293 518 Surry Map==> SI-6-23 SI-6-28 S2-6-12 thermal power (MWt) 1660 2441 2368 cycle burnup (MWD /NTU) 5410 6472 3690 control rod position D/197*
D/228 D/216 maximum quadrant power 1.0736 1.005 1.005 tilt ratio thimbles available 42 43 44
- 38 thimble cases 453 400 402
- 32 thimble cases 297 110 400
- 26 thimble cases 432 231 624
- Rod B-6 was fully inserted 23
APPENDIX 2 - VERIFICATION The modified version of the INCORE code was benchmarked against the pro-duction version of the INCORE code by executing all of the eight reference flux maps with both versions of the code. Additionally, at least one of the randomly selected flux maps from each of the eight reference maps was analyzed using the production version of the INCORE code. In all cases, 3
the results were consistant.
An independent review was also performed which consisted of a hand picked random sampling of cases considered in the study. These maps were analyzed using the production version of the INCORE code in order to verify that the results would fall within the max-imum and minimum bands of the parameters of interest. In all ccses, the results of the hand picked samples did fall within the maximum and minimum bands of the parameters.
24
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