ML18092B001
| ML18092B001 | |
| Person / Time | |
|---|---|
| Site: | Salem  |
| Issue date: | 01/10/1986 |
| From: | Blake R, Brown R, Kent R Public Service Enterprise Group |
| To: | |
| Shared Package | |
| ML18092B000 | List: |
| References | |
| NFU-0039, NFU-0039-R00, NFU-39, NFU-39-R, NFU31-1, NUDOCS 8601280221 | |
| Download: ML18092B001 (79) | |
Text
PS~G NFU-0039 Revision 0 July 31, 1985 The Energy People SALEM REACTOR PHYSICS METHODS VOLUME I MODEL QUALIFICATION I
NFU-0039 Revision 0 July 31, 1985 SALEM REACTOR PHYSICS METHODS VOLUME I MODEL QUALIFICATION Prepared by: Date:
R. T. Brown Senior Engineer Nuclear Department Prepared by: ~ R. S. Kent Date: 12/16/as-
~
- Senior Staff Engineer N ear aartrn k Reviewed by: Date: -/-1D-8f.o A. Blake clear Tee nology Engineer
. <~l;,ar 1~a~rtrn~n,~4 /
Approved by: L, . ././.... til""l..<.'- 0/( Date:
Copy No. _ _7_3___
1
NFU-0039 Revision 0 July 31, 1985 ABSTRACT This topical report describes the methodology used by Public Service Electric and Gas Company (PSE&G) to determine calcula-tional uncertainties and the resultant reliability factors associated with the PSE&G ARMP reactor physics model of the Salem pressurized water reactors
- NFU31/l 2 i
NFU-0039 Revision 0 July 31, 1985 TABLE OF CONTENTS PAGE
1.0 INTRODUCTION
1 2.0 OVERVIEW OF THE CALCULATIONAL MODEL 2 3.0 MODEL VERIFICATION AND RELIABILITY DETERMINATION 5 3.1 Rod Worth Benchmarking 7 3.2 Isothermal Temperature Coefficient Benchmarking 13
- 3.3 3.4 3.5 Doppler Coefficient Benchmarking Isotopics Reliability Factors for Delayed Neutron Parameters 16 20 25 3.6 Power Distribution Benchmarking 29 3.7 Verification of Transient Power Distribution Simulation Capability 59
4.0 REFERENCES
60 APPENDIX A Statistical Methods for the Determination and Application of Uncertainties *A-1 APPENDIX B Computer Code Summary Description B-1 ii NFU31/l 3
NFU-0039 Revision 0 July 31, 1985 LIST OF TABLES Table 3.0.1 Reliability Factors and Biases for PSE&G Model Applied to Salem 6 3 .1.1 Dilution Mode Rod Worth Comparisons 9 3 .1. 2 Rod Exchange Rod Worth Comparisons 10 3 .1. 3 Rod Worth Reliability Factors 12 3.2.1 Measured and Calculated Isothermal Temperature Coefficients 15
- 3. 3 .1 Comparison of Measured and Calculated Doppler Test Parameters 18 3.4.1 Comparison Between EPRI-CELL and SAXTON E~perimental Data 21 3.6.1 Reactor State Points 36 3.6.2 Reactor State Points 37
- 3. 6. 3 Reactor State Points 38 3.6.4 Mean Observed Differences Axial Model Bias 48 3.6.5 Axial Region Definitions 49 3.6.6 Confidence Limits for X(i,k,m) Distri-bution by Subgroup 52 3.6.7 Confidence Limits for X(i,m) Distribution by Subgroup 53 NFU31/l 4 iii
NFU-0039 Revision 0 July 31, 1985 LIST OF FIGURES Figure
- 2. 0. 1 Salem Physics Model 4
- 3. 3. 1 Comparison of Measured and Calculated Doppler Test Parameters 19 3.4.1 Comparison of EPRI - CELL to Yankee Pu239/Pu240 Isotopic Ratios 22
- 3. 4. 2 Comparisons of EPRI - CELL to Yankee 23
--3 Pu240/Pu241 Isotopic Ratios Comparisons of EPRI - CELL to Yankee Pu241/Pu242 Isotopic Ratios 24
. 3.6.1 Salem Unit 1 and Salem Unit 2 Moveable Incore Detector Locations 34 3.6.2 Axial Locations of Grids and Detectors 35 3.6.3 Measured and Calculated Integrated Detector Responses Salem 1 Cycle 4 MAP 1411 39 3.6.4. Measured and Calculated Detector Responses Salem 1 Cycle 4 MAP 1411 40 3.6.5 Measured and Calculated Detector Responses Salem 1 Cycle 4 MAP 1411 41 3.6.6 Measured and Calculated Integrated Detector Responses Salem 1 Cycle 5 MAP 1522 42 3.6.7 Measured and Calculated Detector Responses Salem 1 Cycle 5 MAP 1522 43
- NFU31/l 5 iv
NFU-0039 Revision 0 July 31, 1985 LIST OF FIGURES (continued)
Figure 3.6.8 Measured and Calculated Detector Responses Salem 1 Cycle 5 MAP 1522 44 3.6.9 M~asured and Calculated Integrated Detector Responses Salem 2 Cycle 1 MAP 2133 45 3.6.10 Measured and Calculated Detector Responses Salem 2 Cycle 1 MAP 2133 46 3.6.11 Measured and Calculated Detector Responses Salem 2 Cycle 1 MAP 2133 47 3.6.12 Distribution of Errors X(i,k,m) 50 3.6.13 Distribution of Errors for Integral X(i,m) 51
- 3. 6 .14 Confidence Levels for ~(i,k,m) versus Reactor Power % 54 3.6.15 Confidence Levels for X(i,k,m) versus Cycle Exposure 55 3.6.16 Confidence Levels for X(i,k,m) versus Axial Height 56 3.6.17 Confidence Levels for X(i,m) versus Reactor Power 57 3.6.18 Confidence Levels for X(i,m) versus Cycle Exposure 58 NFU31/l 6 v
- NFU-0039 Revision 0 July 31, 1985
1.0 INTRODUCTION
This report describes the Salem reactor physics model and addresses the qualification and quantification of reliability factors for application of the model to operations and reload safety evaluations of the Salem Nuclear Reactors.
A summary description of the computer codes used to model the Salem reactors is given in Section 2.
The qualification of the model is described in Section 3.
Whenever possible, directly observable parameters (such as rod worths, and incore detector fission rates) are utilized for this qualitication. The data used in this evaluation span seven (7) reactor operating cycles. The reactor cycles
- included are Cycles 1 through 5 for Salem Unit 1, and Cycles 1 and 2 for Unit 2.
After the measured data to be used in the benchmark process are defined, the model calculations are performed and are compared to measurements. These comparisons are presented in this report as part of the quantification of the PSE&G model calculational uncertainties and reliability factors. A statistical approach is used to derive the uncertainties and reliability factors. These uncertainties and reliability factors are consistent with the model application procedur~s and methodology.
The uncertainties and reliability factors are evaluated by direct comparison.to experimental data.
In order to provide a continuing verification of the conservatism of the reliability factors determined herein, ongoing comparisons are made each cycle using statistical methods consistent with those described in this report *
- NFU31/l 7 1
NFU-0039
- Revision 0 Ju 1 y 31 , 19 8 5 2.0 OVERVIEW OF THE CALCULATIONAL MODEL The model used to analyze the Salem Units was constructed using the Advanced Recycle Methodology Program (ARMP) system developed under EPRI sponsorship by UAI. (Reference 1)
A flow diagram for this model is shown in Figure 2.0.1.
The spectral code, EPRI-CELL (ARMP, Part II, Chapter 5),
produces initial nuclide concentrations, depletion and fission product chain data, and tables of microscopic and macroscopic cross sections varying with burn-up for input to the XY diffusion - depletion code, PDQ7/HARMONY (Reference 2 and 3). Lumped absorber data for PDQ7/HARMONY are generated by a capture fraction matching procedure between PDQ7 and either EPRI-CELL (ARMP, Part I, Chapter 6, Section 4) for burnable poisons or CPM (ARMP, Part I, Chapter 6, Section 3) for control rods. PDQ7/HARMONY is run both in the full core (XY) geometry representation and the fuel type (color set) representation. The full core representation is used for nodal code normalization, local peaking factor generation, and for the establishment of assembly loading patterns.
In the fuel type (color set) mode, PDQ7/HARMONY supplies input data for PSE&G's nodal code, TRINODE, a derivative of the EPRI-NODE-P program (ARMP, Part II, Chapter 14). The TRINODE program contains improvements over the EPRI-NODE-P program which include input/output changes, execution options, and file management. However, the primary calculational sequence and physics methodology have been preserved from the EPRI-NODE-P program.
It is recognized that the methods used for the construction and application of the Salem model are as much a part of the model definition as are the codes. It is essential, therefore, that the methods used to calculate core safety marqins be consistent with those used in the model benchmarking and qualifications process. This is particularly true in the calculation of core power distribution and local peaking factors in which the results are heavily dependent on the methods used to normalize the nodal model.
8 2
NFU-0039 Revision 0 *
,luly 31, 1985 2.0 OVERVIEW OF THE CALCULATIONAL MODEL (continued)
The TRINODE model is normalized to the PDQ model. A consistent methodology is used for this normalization throughout the benchmark calculations and will be used in future safety related calculations.
In addition to the main sequence computer codes, a number of auxiliary computer codes are employed to provide a user tailored code package. These auxiliary computer.codes are not basic to the physics methodology, but are vital for automation and transformation of the large volume of calculated and measured parameters required for core analysis. The auxiliary computer codes are summarize600 PCM RF ROD = lS% 0 MEAS(600 PCM RF ROD = lOOPCM 0 TOTALS RF ROD = 10% 0
. Temperature Coefficient Moderator (MTC) RFMTC = 2.1 PCM/°F 0
=
Isothermal (ITC) RF ITC 2.1 PCM/°F 0 Doppler RFDC = 10% 0 Doppler Defect RFDD = 10% 0
. Delayed Neutron Parameters 13 e ff RFB = 4% 0
,Q,
- RFL = 4% 0
. Power Distribution FQ P> .so RFFQ = 0.10 **
P< .so RFFQ = 0.16 -(0.12*P) **
F L1 H P> .30 RFF H = 0.08 0 P< .30 RFF H = 0.09 -(P/30) 0
- See Table 3.6.4 NFU31/l 12 6
NFU-0039 Revision 0 July 31, 1985 3.1 Rod Worth Benchmarking The* purpose of this section is to benchmark the PSE&G Salem model to rod worth measurements. This is accomplished by first presenting and qualifying the available measurements and second by computing model reliability factors.
Rod worth measurements have been performed at Salem using two techniques; the boron dilution method and the rod exchange technique. (Reference 9)
Boron dilution rod worth measurements were performed on Unit 1 Cycles 1 through 5 and Unit 2 Cycles 1 and
- 2. The results of these measurements are summarized on Table 3.1.1 along with PSE&G model predictions.
Rod exchange measurements were performed on Unit 1 Cycles 1, 3, 4, ~nd 5, and Unit 2 Cycle 2. These results, along with model calculations are tabulated on Tables 3.1.2 (a) and {b).
For purposes of model benchmarking, some rod worth measurements are disqualified on the basis of known measurement errors. Measurements disqualified are-the boron dilutions for Unit 1 Cycles 1 and 2, and Unit 2 Cycle 1. Additionally, rod exchange measurements for Unit 1 Cycle 1 are disqualified. The basis for this disqualification is measurement errors discovered in dilution measurements made prior to Cycle 3. These errors are due to the effects of spatial flux redistribution caused by rod motion during the dilution (Reference 9). Test procedure changes were implemented prior to Cycle 3 measurements to reduce these effects. Since rod exchange measurements use the reference bank dilution measurement to interpret exchange worths, rod exchange measurements for Unit 1 Cycle 1 are disqualified on the same basis.
Support for the disqualification of dilution measurement made prior to Cycle 3 is available using comparisons to calculated worths. The average difference between measured and calculated rod worths for dilution measurements performed prior to Cycle 3 and those using the improved test procedure are 11%
and 1% respectively. This difference is significant at the 99.9% confidence level, and is attributed to the known measurement errors.
NFU31/l 13 7
NFU-0039 Revision 0 July 31, 1985 Rod worth reliability factors were obtained by bounding the results of the comparisons between measured and calculated rod worths. These factors are tabulated on Table 3.1.3.
Comparisons were taken from 7 dilution measurements and 24 exchange measurements spanning 4 reactor cycles, and represent all measurements through Cycle 5 of Unit 1 and Cycle 2 of Unit 2, except those disqualified above.
Using a bounding value for the reliability factor is justi-fied due to its conservatism relative to normal statis-tics. Calculation of reliability factors representing 95/95 confidence levels using normal statistics yields a 91 PCM reliability factor adder for rods worth less than 600 PCM, and 12% reliability factor for rods worth more than 600 PCM. The exception is the reliability factor for rod worth totals, which is computed to be 16%. However, this large value is due to the small sample size of only 5 values. Since the error for rod worth totals can be no larger than the largest error for the individual rod banks, the reliabilty factor for rod worth totals should be bounded by the maximum observed error for individual banks with worth greater than 600 PCM; 10%. Thus, the factors tabulated on Table 3.1.3 conservatively bound the observed data, and will be used as model rod worth reliability factors.
NFU31/l 14 8
NFU-0039 Revision 0 Ju 1 y 3 1 , 1 9 8 5 TABLE 3. 1. 1 DILUTION MODE ROD WORTH COMPARISONS DATE UNIT/ BANK MEAS CALC DIFFERENCE*
% /';.
12/76 1/1*** D 1107 1030 7.5 c 1183 1005 17.7 B 766 724 5.8 A 1241 1114 11. 4 SD 745 681 9.4 SC 1181 1060 11. 4 TOTAL 6223 5614 10.8 12/79 1/2*** D 1041 924. 12.7 c 938 846 10.9 B 534 599 -65 A 1163 973 19.5 TOTAL 3676 3342 10.0 8/80 2/1*** D 1391 1241 12. 1 c 1185 1026 15. 5 B 1359 1262 7.7 A 501 385 116 SD 750 712 5.3 SC 1052 961 9. 5 TOTAL 6238 5587 11. 7 12/80 . 1/3 D 834 797 4. 6 c 960 900 6.7 B 565 600 -35 A 1023 1058 -3.3 TOTAL 3382 3355 0.8 4/82 1/4 D 862 860 0.2 2/83 1/5 D 926 939 -1. 4 7/83 2/2 D 878 835 5. 1
=
=
( ( M-C) /C)
- 100 for measurements >600 PCM.
(M-C) for measurements (600 PCM
- Data disqualified as discussed in text.
NFU31/l 15 9
NFU-0039 Revision 0 July 31, 1985 TABLE 3 .1. 2 ROD EXCHANGE ROD WORTH COMPARISONS DATE UNIT/ BANK MEAS CALC DIFFERENCE CYCLE PCM PCM. M>600 M< 600 12/76 1/1*** *D 1107 1030 ( 7. 5 )
c 825 741 11. 3 B 522 467 - 55 A 924 858 7.7 SD 469 403 - 66 SC 351 305 - 46 TOTAL 4198 3804 10.3 12/80 1/3 *D 834 797 ( 4. 6 )
c 696 674 3.3 B 395 450 - -55 A 816 789 3.4 TOTAL 2741 2710 -1.1 4/82 1/4 *D 862 860 ( 0
- 2) c 596 588 - 8 B 370 407 - -37 A 818 789 3.7 SD 265 316 - -51 SC 285 281 - 4 SB 614 649 -5.4 SA 750 733 2.3 TOTAL 4560 4623 -1. 4 2/83 1/5 *D 926 939 (-1.4) c 613 617 -0.6 8 331 361 - -30 A 784 814 -3.7 SD 269 292 - -23 SC 317 291 - 26 SB 769 793 -3.0 SA 735 779 -5.6 TOTAL 4744 4886 -2.9 NFU31/l 16 10 (continued)
NFU-0039 Revision 0 July 31, 1985 TABLE 3. 1. 2 ROD EXCHANGE ROD WORTH COMPARIOSNS (continued)
DATE UNIT/ BANK MEAS CALC DIFFERENCE*
% /:,
7/83 2/2 *D 878 835 ( 5. 1) c 770 731 5.3 B 660 603 9. 5 A 252 233 19 SD 299 287 12 SC 292 275 17 SB 787 757 4.0 SA 562 491 71 TOTAL 4500 4212 6.8
- Measurement performed by dilution
- % = ((M-C)/C)
- Data disqualified as discussed in text
- 11 NFU31/l 17
NFU-0039 Revision 0 July 31, 19 TABLE 3. l . 3 RODWORTH RELIABILITY FACTORS Individual Rod Worth a) Rod worth <600 pcm RF ROD = 100 pcm b) Rod worth >600 pcm RF ROD = 15%
Total Rod worth RF ROD = 10%
NFU31/l 18 12
NFU-0039 Revision 0 July 31, 1985 3.2 Isothermal Temperature Coefficient Benchmarking The objective of this section is to benchmark the PSE&G model to measured isothermal temperature coefficients (ITC). Based on comparisons between measured and calculated coefficients, a reliability factor for both the isothermal and the moderator temperature coefficient (MTC) is inferred.
A total of 19 ITC measurements are tabulated on Table 3.2.1. These measurements span 7 reactor cycles and range from unrodded conditions to all control banks inserted.
The PSE&G model calculations for ITC are presented on Table 3.2.1 along with the corresponding measurement.
Statistical tests were performed on the comparisons to evaluate normality and pooleability. Normality was demonstrated using the W-test (Reference 8), while pooleability was assured using the Bartlett test (Reference 4). The computed standard deviation of the comparisons between measured and cal.culated ITC' s is 0.85 PCM/F.
The observed standard deviation of 0.85 PCM/F ( oossvl is assumed to be made up of three independent components; measurement uncertainty, model calculational uncertainty on moderator temperature coefficient, and, model calculational uncertainty on Doppler temperature coefficient. This relationship is expressed as:
a 2 + a 2 + a2 a 2 = (0.85)2 MEAS MTC DC OBSV Since each component is greater than or equal to zero,each component is bounded by the observed error, Therefore, a conservative estimate of the model uncertainty ( a ) for both the isothermal and moderator temperature coefficients is 0.85 PCM/F. This is summarized as:
= 0.85
= 0.85 19 13
NFU-0039 Revis ion 0 July 31, 1985 PSE&G model reliability factors for both ITC and MTC are computed as the product of the standard deviation and the one-sided critical factor (K c) for a 95/95 confidence level using nineteen (19) samples. This product yields reliability factors for ITC and MTC of 2 .1 PCM/F.
RFITC = 0.85
- 2.42 = 2.1 PCM/F
-RFMTC = 0.85
- 2.42 = 2.1 PCM/F NFU31/l 20 14
- NFU-0039 Rev is ion 0 July 31, 1985 TABLE 3. 2. 1 MEASURED AND CALCULATED ISOTHERMAL TEMPERATURE COEFFICIENTS ROD POSITION ITC PCM/°F UNIT CYCLE BANK (STEPS) BORON MEAS CALC DIFF 1 1 D 197 1369 -3.51 -3.59 0.08 c 201 1264 -4.11 -4.34 0.23 B 175 1151 -6.17 -6.45 0.28 A 175 1085 -7.85 -9.06 1. 21 SD 175 965 -11.25 -11.90 0.65 1 2 D 219 1137 -6.06 -4.45 -1. 61 c 214 1025 -5.79 -5.45 -0.34 1 3 D 219 1258 -3.33 -3.26 -0. 07 c 206 1157 -4.85 -4.10 -0.75 1 4 D 202 1309 -3.61 -5.29 1. 68 1 5 D 214 1499 -1. 52 -2.60 1. 0 8 2 1 D 205 1334 -0.65 -0.59 -0.06 D 188 1329 -0.84 -0.70 -0.14 D 102 1285 -2.68 -1. 89 -0.79 c 184 1197 -4. 34 . -4.85 -0.51 B 203 1083 -10.53 -9.09 -1. 44 A 198 955 -10.50 -9.83 -0. 67 SD 192 910 -13.48 -13.22 -0.26 2 .2 D 218 1362 -4.16 -4.55 0.39 Mean o.oo Standard Deviation 0. 8 5 15
NFU-0039 Revision 0 July 31, 1985 3.3 Doppler Coefficient Benchmarking The objective of this section is to make comparisons between measured and calculated Doppler coefficients and establish model reliability factors for Doppler reactivity calculations.
Doppler reactivity coefficient measurements have been performed at the Salem units using two measurement techniques. Both test procedures require the compensation of a reactivity imbalance induced by a reactor power change. The first test procedure balances reactivity using control rods and measures the reactivity changes using a reactimeter. This technique was used in Cycle 1 of both Salem Units. The second measurement procedure maintains reactivity balance with changes in moderator temperature. The ratio of power change to moderator temperature change is then converted to reactivity using an isothermal temperature coefficient. This technique has been used for Cycles 2 through 5 on Unit 1, and Cycle 2 for Unit 2.
The measurements using rod banks for reactivity control are not used for purposes of model benchmarking. The basis for this disqualification is the large uncertainties associated with reactimeter interpretation for at-power measurements.
The results of all Doppler coefficient measurements performed using the moderator temperature control procedure have been tabulated on Table 3.3.1. This measurement technique requires calculated isothermal temperature coefficients to infer the Doppler coefficient tempe~ature. Since it is the ratio of the changes of these two quantities that is actually measured, this ratio is tabulated along with the inferred Doppler coefficient on Table 3.3.1. The precision associated with each measured ratio has been determined based on the standard deviation of multiple measurements.
NFU 31/1 22 16
NFU-0039 Revision 0 July 31, 19 Calculations of the ratio of power to moderator temperature changes have been made using the PSE&G model. Comparisons of the measured.and calculated ratio are shown on Table 3.3.1 and also Figure 3.3.1 in which the vertical bars represent the measurement precision.
Figure 3.3.1 demonstrates that the measured and calculated ratios typically agree to witbin the measurement precision, and therefore confirms model capability to calculate these ratios. The scatter in the data shown in Figure 3.3.1 is due primarily to the poor measurement precision.
It is apparent from Figure 3.3.1 that the measurement precision is of the same order of magnitude as the observed differences between measurement and calculation. Thus, the model calculational uncertainty is assumed to be small. For purposes of assigning a model reliability factor for Doppler coefficient (RFDC.)
a conservative value of 10% is assumed. The same reliability factor will be assigned to the model for Doppler only power defect (RFDD). Thus:
RFDC = 10%
RFDD = 10%
NFU31/l 23 17
zt"Ij c:
w f-.1 f-.1 N
Ul TABLE 3.3.1 COMPARISCN OF MEASURED AND CALCULATED OOPPLER TEST PARAMETERS UNIT/ PWR NUMBER a D ( l'i p ) MEAS ( l'i P)
CYCLE % OF MEAS PCM/% (l'i T )MEAS PRECISICN ITTICALC MEAS-CALC 1/2 39 6 -13 .67 -0.95 0.04 -0.86 -0.09 93 6 -13.15 -1.39 0.09 -1.41 0.02 f-.1 1/3 44 6 -13 .31 -0.77 0.02 -0.83 0.06 00 94 6 -10.91 -1.40 0.17 -1.28 -0.12 1/4 43 4 -10.11 -0.90 0.23 -0.84 -0.06 99 4 -11.49 -1.28 0.09 -1.31 0.03 1/5 46 4 -11.45 -0.66 0.04 -0.70 0.04 97 4 -12.01 -0.99 0.11 -1.10 0.11 2/2 98 2 -11.33 -1.34 0.35 -1.33 -0.01 c..,
C CD
~ zt"Ij f-.1 <: c:
I<: f-'* I
[I] 0 w f-'* c:i f-.10 w
.. ::J l..O f-.10 l..O 00 Ul
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.3.l COMPARISON OF MEASURED AND CALCULATED DOPPLER TEST PARAMETERS
- l. 7
- l. 6
- l. 5
- l. 4
- l. 3
~
0 o\O
- l. 2 E-i
<l
~ 1.1
<l
'O Q)
~ l. 0
~
- I rn cO l
Q)
- E! 0. 9 Zero erroi (m=l)
- 0. 8 0.7 0.6 0.5 .......~--1L....-~...a..~~..a...~--i1--~....a;.~~.......~---~~--"-~~--~--
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Calculated ~P/ ~T, %/°F 19
NF'U-00 39 Revision 0 July 31, 1985 3.4 Isotopics Isotopic compositions calculated by EPRI-CELL have been compared with spent fuel isotopic data obtained from Yankee Rowe fuel rods irradiated beyond 35 GwD/MTU. The reactor representation used for the EPRI-CELL benchmarking in the calculations is described in the ARMP documentation (Part 1, Chapter 1, Sec~ion 4.0).
Experimental and analytic isotopic ratios for plutonium from the Yankee Rowe spent fuel are plotted versus accumulated fissions in Figures 3.4.1-3.4.3. The dots are experimental results and the line the EPRI-CELL results.
The agreement between calculated and experimental isotopic ratios is good. The calculated ratios Pu-239/Pu-240 and Pu-240/Pu-241 are within the scatter of the experimental results and the ratio Pu-241/Pu-242 is slightly over-predicted.
Calculated and measured isotopic compositions for MU2 fuel (6.6w/o) irradiated in the Saxton Core II (pellet, rod MY, zone 6) are compared in Table 3.4.1. The agreement is good for the most important uranium and plutonium isotopes as well as for americium and curium. The measured burnup ranged from 7 to 22 GWD/MTU. The reactor representation for the EPRI-CELL benchmarking is described in the ARMP do~umentation (Part 1, Chapter 3, Section 4.)
NFU 31/l 26 20
NFU-0039 Revision 0 July 31, 1985 TABLE 3.4.1 COMPARISON BETWEEN EPRI-CELL AND SAXTON EXPERIMENTAL DATA NUCLIDE EXPERIMENT EXPERIMENTAL UNCERTAINTY
~ PRI-CELL Exp.
J *100%
ATOM %
U-234 .00465 28.7 - 3.7 U-235 .574 .9 + 1. 7 U-236 .0355 5.6 - 7.6 U-238 99.386 0 0 Pu-238 .109 2.2 -32.1 Pu-239 73.77 0 + 0.6 Pu-240 19.25 .2 - 3.5 Pu-241 6.29 .3 + 4.6 Pu-242 .579 .9 -11.7 ATOM RATIOS 4
Np-237/ 1.14 x io- 15 -26.9 U-238 Pu-239/ .04383. .7 + 2.0 U238 3
Pu-238/ 1. 75 x lo- .4 -17.6 Pu-239 Am-241/ .0123 15 + 2.4 Pu-239 + 0.4 4 10 Cm-242/ 1.05 x lo-Pu-239 Cm-244/ 1.09- 4 20 - 3.2 Pu-239 21 NFU31/l 27
NFG -0039 Revision 0 July 31, 1985 FIGURE 3.4.l COMPARISON OF EPRI-CELL TO YANKEE Pu2J9/Pu240 ISOTOPIC RA~IOS 10.0 .,
' I 9.0 a.o 7.0
~ :
\\
5.0 ~
~
~
- 4. 0
~
~ *'
- 3. 0
- o. J o.o 5.0 10.0 15.0 20.0 25.0 30.0
-1 5 Accumulated Fissions (barn-cm) x 10 22
NFG-0039 Revision 0 July 31, 1985 FIGURE 3.4.2 COMPARISON OF EPRI-CELL TO YANKEE Pu240/Pu241 ISOTOPIC RATIOS a.a I
7.a
\ I I,
i
.*\
6.a
\
0 1-1 e--
~ 5.a r-1
~
N ii.
0
~
N ii. 4~a
.\:: * .
\:
3.0 a.a 5.a 10.a 15.a 2a.a 25.a
-1 Accumulated Fissions (barn-cm) x 10 5 23
' . NFG-0039 Revision 0 July 31, 1985 FIGURE 3.4.3 COMPARISON OF EPRI-CELL TO YANKEE Pu241/Pu242 ISOTOPIC RATIOS
- 10. 0 . ...
- 9. 0
.\
B. 0
'"\
Ul 0
H
~
N
"'2' N
- 7. 0
~.
\
I\
p..
r-l
"'2' N
p.. 6. 0
- s. 0
\ :
""**~
- 4. 0
- o. 0 0.0 s.o 10.0 15.0 20.0 25.0 30.0 Accumulated Fissions (barn-~)-l x 10 5
24
NFU-0039 Rev is ion 0 July 31, 1985 3.5 Reliability Factors for Delayed Neutron Parameters This section deals with determining reliability factors for the effective delayed neutron fraction and the effective neutron lifetime which are values which can be calculated but whose measurement is not practical. In these cases, an argument is made for the general magnitude of the reliability factor without making direct comparisons between measured and predicted values.
The importance of the reliability of the calculated values of the delayed neutron parameters is primarily associated with the core Beff* The uncertainties in the calculation of Beff are composed of several components, the most important of which are listed below:
- a. Experimental values of S, and A, by nuclide;
- b. Calculation of the spatial nuclide inventory;
- c. Calculation of core average S as a flux weighted average over the spatial nuclide inventory;
- d. Calculation of Beff from the core averaqe as Beff = I*S, where I = importance factor.
The experimental determination of the S's and A's are assumed to be accurate to within 1%. The most important nuclide concentrations with respect to core Sare u 238 , u 235 , and Pu 23 ~. Tables 3.4.1 and 3.4.2 indicate that the difference in the calculation of these concentrations is about 1.7% for ECELL.
Therefore, components (a) and (b) above are combined as
- 2. 7 %*
25
- 31/1 31
NFU-0039 Revision 0 July 31, 1985 The uncertainty in the calculation of a core average S depends on the relative flux weighting of the individual assemblies in the core. For demonstration purposes, consider a three region core, each with a different average burnup and average S. This is typical of advanced PWR cycles in that about a third of the core has seen two previous cycles, a third only one previous cycle and a third is the feed fuel.
Typical reg ion al S 's are given below:
Region 1 (third cycle fuel) s (1) = 0.005 Region 2 (second cycle fuel) s (2) = 0.006 Region 3 (feed fuel) s (3) = 0.007 The effect of errors in the calculated flux distribution can be evaluated in terms of the effect on the core average s. As a base case, flux weighting factors (FWF) are all set to 1.0. In this case, the core average S = 0.006. Using a maximum error in the calculation of the core average is obtained by increasing the weight of the Region 1 fuel and decreasing the weight of the Region 3 fuel.
revised S is calculated as follows:
(l)xl.07 = .00535 (2)xl.O = .0060 The (3)x0.93 = .00651 S = .00595, which yield a -0.8% error for component (C) above.
NFU3 l/l 32 26
NFU-0039 Revision 0 July 31, 1985 The last uncertainty component, (d), concerns the reduction of core average B to obtain Beff by using the importance factor. Since this reduction is typically about 3% to 4%, an error of 10% in this component would lead to an error in Beff of less then 0.5%.
The sum of the errors for these four factors for ECELL are as follows:
2.7%(a+b) + 0.8%(c) + 0.5%(d) = 4.0%
So the reliability factor for delayed neutron parameters {RFB)is set at 4%.
An argument similar to the delayed neutron parameter argument is applied to the determination of the effective neutron lifetime ( £*) uncertainty. The uncertainty components which go into the calculation of £* are as follows:
(a) Experimental values of microscopic cross sections; (b) Calculation of the spatial nuclide inventory; and (c) Calculation of the core average effective neutron lifetime, i*, as a flux weighted average over the spatial nuclide inventory which includes the effects of leakages.
Uncertainties for components (a) and (b) are assumed to be the same as described for the calculation of B eff, that is, a combination of 1% uncertainty in the experimental determination of nuclear cross sections and 1. 7% uncertainty in the det*ermination of
- NFU 31/1 33 27
NFU-0039 Revision 0
- July 31, 19 the spatial nuclide inventory of ECELL. The core average neutron lifetime depends on flux weighting of local absorption lifetimes £*. If a conservative estimate of the error in regional power sharing (7%)
is used in determining the impact on the core average lifetime ( £*), the error in lifetime is on the order of 1.0%. Combining all of these uncertainties linearly results in a total uncertainty of 3.7%. Therefore, a 4% reliability factor (RFL) will be applied to the neutron lifetime calculation when applied to safety related calculations.
NFU3l/l 34 28
NFU-0039 Revision 0 July 31, 1985 3.6 Power Distribution Benchmarking It is the purpose of this section to quantify the PSE&G Salem model power distribution calculations. This is accomplished by first presenting the measurement data base, followed by a description of the calculational methodology. Second, comparisons are made betwe~ the measured and calculated quantities, and lastly, model reliability factors for power distribution calculations are computed.
- The primary source of power distribution measurements for Salem Units 1 and 2 is the incore detector system.
This system consists of moveable incore fission chambers which respond to neutron flux. These neutron detectors traverse through instrument guide thimbles which are located at 58 positions throughout the core as shown in Figure 3.6.1. Measurement signals from these detectors are taken at 61 axial positions up the fuel assembly as illustrated in Figure 3.6.2, and are corrected by the on-site process computer to account for detector sensitivity, drift, and background. The corrected signals are then used to compute measured" power distributions using analytical data to convert the detector signals to interpreted powers in both instrumented and uninstrumented assemblies.
A total of forty-nine (49) flux maps were chosen for the purpose of benchmarking the PSE&G Salem model.
These flux maps span six reactor-cycles and represent typical steady state operation conditions. These include maps taken at powers ranging from near zero to 100 percent, and cycle exposures of zero to end of cycle, including some coastdown state points. A description of reactor conditions for each flux map chosen is given in Tables 3.6.1 through 3.6.3.
The approach taken to .benchmark and qualify the PSE&G Salem models for power distributions was to compare calculated and measured detector signals. The basis for this is twofold. First, the detector signals
- NFU31/l 35 29
NFU-0039 Revision 0 July 31, 1 9 .
represent raw measurements and do not include interpretation, unlike "measured" power distributions.
Second, the ability of the model to compute the detector signal requires the same processes as required to compute pin powers. Both calcuations require the prediction of the localized fission rate, one in a pin pellet, the other in a fission chamber. The accuracy of the two calculations is essentially the same. The only difference is that there is a small self-shielding or flux depression in the pin which is not in the detector. The impact of this difference on the power distribution reliability factor is assumed to be negligible.
The simulated detector signals are calculated in a manner which is consistent with the calculation of local power peaking factors for the purpose of safety evaluation. The first step is to compute the power distribution under consideration. The resolution used is one node per fuel assembly, with 12 axial levels .
- The simulated detector signals are obtained by using the nodal power at each axial level to predict a siynal power density for that assembly at that level. This power is then converted to a relative reaction rate.
The conversion factors are calculated for each asembly location as a function of assembly exposure using a two-dimensional, full core PDQ7, fine mesh model. The 12 axial values in each assembly location are then synthesized using a truncated fourier sine series.
Grid flux depressions are then superimposed on the synthesized function using an empirical function designed to match the characteristics of flux depressions measured with in-core fission detectors.
The effect of the grid flux depressions is to raise the flux level in the axial region between grids while depressing the flux in the grid region. Consistency between the above calculations of instrument signals and the calculation of local peaking factors is assured by:
NFU31/l 36 30
NFU-0039 Revision 0 July 31, 1985 A. Using a common full core PDQ7 model, B. Using a common nodal model, and C. Using a common procedure to account for axial flux gradients and grid effects.
Typical comparisons of measured and calculated detector signals are shown in Figures 3.6.3 through 3.6.11. The figures are in sets of three and are representative of various core exposures including coastdown conditions.
For each statepoint the first figure of the set presents the differences between the measured and predicted signal integrals for all instrumented locations. The instrumented core locations are indicated with circles in each of the figures. The second and third figures of each set present axial comparisons in two specific instrumented core locations. The measurements are shown as a solid continuous line over 61 axial levels. The predicted reaction rates are represented as open circles. The two core locations were chosen as typical of regions on the interior of the core and on the core periphery.
In all comparisons, both the predicted and measured reaction rates have been normalized to a core average value of unity for each map.
For purposes of quantifying comparisons, it is convenient to define the variable ORR (I,K,M) which represents the difference between measured and calculated detector signals or reaction rates at location I,K, and map M. Thus, DRR(I,K,M) = RRM(I,K,M) - RRC(I,K,M) where I = Radial Detector Location K = Axial Detector Location M = Map Index RRM = Measured Detector Reaction Rate RRC = Calculated Detector Reaction Rate NFU31/l 37 31
NFU-0039 Revision 0
- July 31, 19 An average difference between measured and calculated reaction rates can be computed for each axial level as:
l l DRR(I,K,M)
ORR( K) = I M
~~~~~~~~~~~~-
l l 1 I M where the summation over I is performed for each available radial location, and M represents all flux map data except zero power maps. The mean observed differences thus computed are the axial model bias and are listed in Table 3.6.4. Since it is easier to describe the model uncertainties in terms of aeviations relative to the observed bias, a second variable can be defined as X(I,K,M) = ( RRM ( I , K, M) - RRC ( I , K , M) ) - DRR ( K )
Where X(I,K,M) = The difference between measured and calculated reaction rates adjusted for the observed bias.
All model power distribution behavior can now be characterized by quantifying the difference population X(I,K,M) or the integral of X(I,K,M); X(I,M). This latter quantity is the biased c ifference between the measured and calculated detector signal integrals.
To better evaluate the behavior of the distributions of X(I,K,M) and X(I,M), the difference population was divided into selected subgroups. The subgroups were chosen to parameterize the difference behavior as a function of axial height, reactor power level, and cycle exposure. These subgroups were defined in a manner to exclude the axial points at grid locations and the upper and lower six axial points.
The axial regions are defined on Table 3.6.5.
The difference population was evaluated for normality using the chi-squared test. This test demonstrates NFU 31/1 38 32
- NFU-0039 Revision 0 July 31, 1985 that most of the subgroups cannot be considered normal. Typical comparisons of the difference population and a normal distribution is illustrated in Figures 3.6.12 and 3.6.13.
As indicated in Tables 3.6.6 and 3.6.7 and Figures 3.6.12 through 3.6.17, 95/95 confidence limits assuming normal statistics and 95/95 confidence limits based on non-parametric statistics are in good aqreement. In some cases the non-parametric limit is somewhat lower than the normal limit which simply indicates that the actual (not *normal) distribution is slightly more peaked with fewer samples in the upper (higher M-C values) tail of the distribution than is predicted by the normal distribution.
To be conservative, 95/95 confidence limits were evaluated using both normal and non-parametric statistics as described in Appendix A. Confidence limits (95/95) were computed for each subgroup. These results are summarized on Tables 3.6.6 and 3.6.7 and Figures 3.6.14 to 3.6.18. Inspection of the figures show that the confidence limits are a function of axial height, reactor power level, and cycle exposure.
Generally, the confidence limits decrease with increased power and exposure. The approach taken to compute PSE&G model reliability factors, was to bound the computed confidence limits. Thus, the model reliability factors are:
RFFQ = 0.10 p >
- 50 0.16 - (0.12*P) p <
- 50 RFF fl.H = 0.08 P> *30 0.09 - (P/30) P<
- 30 In order to assess the impact of possible dependence among data samples on reliability factors for local peaking factors, the effects of reducing the sample sizes by two thirds ( 2/3) were evaluated. It was found that the reliability factors are relatively insensitive to this reduction in sample size resulting in an increase reliability factors of approximately .002 units for X(I,K,M) and .004 for X(I,M). As can be seen in Figures 3.6.14 through 3.6.18, the PSE&G reliability factors remain bounding and are therefore not impacted significantly by possible dependence among data samples.
33
NFU-0039 Revision 0
- July 31, 1985 FIGURE 3.6.l SALEM UNIT 1 AND SALEM UNIT 2 MOVABLE INCORE DETECTOR LOCATIONS R p N M L K J H G F E D c B A 28 15 l 4 3 51 2 10 30 39 52 3 5 36 43 11 38 31 24 5 17 54 14 6 8 6 44 32 16 47 7 23 58 29 46 48 50 49 34 8 57 22 9 56 9 4 1 12 10 33 40 26 11 -
21 13 12 41 55 7 13 45 35 20 25 18 27 42 37 53 2 I
34
- FIGURE 3.6.2 NFU-0039 AXIAL LOCATIONS OF GRIDS AND DETECTORS Revision 0 July 31, 1~85 T
21il.5'U'I
. 21il.561il 21il.551il AXIAL GRID 21il.551il AXIAL DETECTOR LOCATIONS SIGNAL LOCATIONS 21il.551il 21!1.550 ALL ME~SUREMENTS ARE IN INCHES 24.43111 1...-----t 1.243 '-------IJ"J BOTTOM OF FUEL ROD 35
NFU-0039 Revision 0 .
July 31, l TABLE 3.6.l REACTOR STATE POINTS SALEM l CYCLE 2 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSITION
( MWD/MTU) ( %) (STEPS) 174 0 o.o 228 188 2160 100.0 228 190 3097 100.0 228 194 4382 100.0 228 196 6250 100.0 225 198 7275 82.0 206 1201 7945 67.0 218 SALEM l CYCLE 3 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSITION
( MWD/MTU) ( %) (STEPS) 1300 0 0 212 1313 500 100 228 1315 1040 100 222 1324 3165 99.5 221'3 1330 4100 97.0 220 1333 5670 ~7.0 228 1338 7060 96.8 228 1342 8800 75.0 202 NFU 31/1 41 36
- NFU-0039 Revision 0 July 31, 1985 TABLE 3.6.2
- REACTOR STATE POINTS SALEM 1 CYCLE 4 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSITION
( MWD/MTU) ( %) (STEPS) 1400 0 o.o 211 1408 180 84.0 228 1411 560 100.0 228 1412 1580 100.0 225 1413 2589 98.6 228 1414 3715 100.0 215 1416 3836 100.0 228 1417 4998 100.0 228 SALEM 1 CYCLE 5 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSITION
( MWD /MTU) ( %) (STEPS) 1500 0 o.o 216 1503 25 47.3 228 1507 140 99.3 228 1509 1391 100.0 228 1512 2531 99.9 226 1517 4662 99.5 228 1520 5444 100.0 218 1522 7185 99.9 228 1524 8923 100.0 228
- NFU 31/l 42 37
NFU-0039 Revision 0
- July 31, 19 TABLE 3.6.3 REACTOR STATE POINTS SALEM 2 CYCLE 1 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSITION
( MWD/MTU) ( %) (STEPS) 2004 0 o.o 206 2102 2435 100.0 222 2115 4677 96.7 228 2120 7386 99.8 228 2122 9196 100.0 224 2127 11755 82.2 219 2129 13357 82.0 220 2131 14192 82.8 228 2133 15403 82.5 219 SALEM 2 CYCLE 2 MAP NO. CYCLE EXPOSURE POWER LEVEL D BANK POSIT ION
( MwD/MTU) ( %) (STEPS) 2201 0 o.o 220 2203 21 48.6 180 2205 47 72.1 214 2209 292 98.4 228 2210 564 99.0 228 2213 1120 99.0 228 2214 2106 99.1 228 2217 3195 99.2 228 NFU 31/1 43 38
NFU-0039 Revision O July 31, 1985 FIGURE 3.6.3 Measured and Calculated Integrated Detector Responses SALEM 1 CYCLE 4 MAP 1411 Absolute Differences Power = 100.0%
Exposure 560 MWD/MTU R p N M L K J H G F E D c B A I/ '\ Abs. Diff =
(Meas.-Calc)*lOO 1 I\. 4.1.)
/
-0.1
' 2
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v """
-2.3 v-0.5""" I/
0.6 3.3 3
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v ' v ' 14 2.9 -0 .1 I'. ,I I\. ,I v3.5' 15 I\.. _,)
39
NFU-00 39 Revision 0
- July 31, l<j85 FIGURE 3.6.4 MEASURED AND CALCULATED DETECTOR RESPONSES SALEM 1 CYCLE 4 MAP1411 2.5 .
Legend MEASURED 2 ******.. 1l-Ml.E = LI> ........ .......-.........................
~ .----
0 PREDICTED h
I r UJ
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z 0
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0 o..___....,.._...,__...,._________...,__.....,__....____...,.__.....,__..-__
0 5 10 15 20 25 30 35 40 45 50 55 60 AXIAL POINTS 40
.. L
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.6.5 MEASURED AND CALCULATED DETECTOR RESPONSES SALEM 1 CYCLE 4 MAP1411 2.5~----~---------------------------------------
Legend
~ = 560 l.A&ll'\Aln I mna.ym1.., MEASURED 2 ........
n-t.e.£ =N3 0 PREDICTED LiJ Vl z
0
~
~ 1.5 ........ ........ *******-***************** .......... *******-******** .................. *******-******** ....... .
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- o o.......--.P-.~--_,. ___,,___...___,.___..,___...__....__...... ~~--;.---t 0 5 10 15 20 25 30 35 40 45 50 55 60 65 AXIAL POINTS 4l
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.6.6 Measured and Calculated Integrated Detector Responses SALEM 1 CYCLE 5 MAP 1522 Absolute Differences Power = 99. 7%
Exposure = 7185 MWD/MTU R p N M L K J H G F E D c B A v v Abs. Di ff =
0.3
.J
-0.0 I\.
,)
(Meas.-Calc)*lOO 1 v '
0.8 '
/
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0.9
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r 'I ' ./
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42
NFU-0039 Revision O July 31, 1985 FIGURE 3.6.7 MEASURED AND CALCULATED DETECTOR RESPONSES SALEM 1 CYCLE 5 MAP1522 2.5-------------------------------------------------
POwtR= 99.73 Legend EXPOSlR: = 718.5 MWD;iffiJ MEASURED 2 . . . . . .. . 11-IMl.E =LtJ ********~********
.... .. ********~***************------
0 PREDICTED w ... ...
(/)
z .... .....
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o e o I f o I I
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o 5 10 15 20 25 30 35 40 45 50 55 60 65 AXIAL POINTS 43
I I I
FIGURE 3.6.8 NFU-003~
Revision O July 31, 1985 I
I MEASURED AND CALCULATED DETECTOR RESPONSES
,I SALEM 1 CYCLE 5 MAP1522 2.5------------------------
- I
- I POWER= 99.73 Legend 8<POSlH: = 7185 MWD/MTU MEASURED 2 . *..*... l1-M3l...E =N13 ********-:******** :.. ........ .;........ *******------
0 PREDICTED w
CJ') ..... ....
z .. ..
0 ..... .....
a.. . ..
~ ............................................ ********-********* ..... ........... .................... .
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o I o o o I o o o o
-.;.-..._*--~---*----;.----*
0 5 10 15 20 25 30 35 40 45 50 55 60 AXIAL POINTS 44
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.6.9 Measured and Calculated Integrated Detector Responses SALEM 2 CYCLE 1 MAP 2133 Absolute Differences Power 82.5%
Exposure = 15403 MWD/MTU R p N M L K J H G F E D c B A v Abs. Di ff =
/
(Meas.-Calc)*lOO 1 1\.0. 3.) '- 1.1.)
v v I\..
0.5
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15 45
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.6.10 MEASURED AND CALCULATED DETECTOR RESPONSES i* SALEM 2 CYCLE 1 MAP2133 iI I
2.5...--~~-~-~---~--------~---io--
II I ..
I I
2 ....... .1=.::m~L. . . . . . .-.. . . . . . . . . . . Le=-~= 0 I.
I
\
w
(/)
z 0
a.. .......... *******-******** ....... .
(/)
w .. ...
1.5 ................ .********-************************** .. *******-*****************
0:::
0:::
0 . ...
t3 w
1--
w c
w I'.
~
II
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0:::
0.5 ................ ~ ********~******** ................* *******-******* ********* .......... *******-********:********
- o 0 .......- -...........,__......,__...,___.,___._,....,.__....,__......._.,...__i--.....,__
0 5 10 15 20 25 30 35 40 45 50 55 60 AXIAL POINTS 46
NFU-0039 Revision 0 July 31, 1985 FIGURE 3.6.11 MEASURED AND CALCULATED DETECTOR RESPONSES SALEM 2 CYCLE 1 MAP2133 2.5-------~-~-~-~~---i-o-~-~---~--.
POWER= 82.53 Legend
~ =5403 MWD,IMTIJ MEASURED 2 ******** nM3l.E = N13 ........*........ ******* ........ ********------ 0 PREDICTED LaJ V>
z 0
a..
V> 1.5 ................*....... ********* ................ ******* ................ ********-:********-********:********
LaJ
~
a::: .... ....
a::: ...
0 ....
t5 ..... ....
LaJ .... ...
I- . ...
LaJ 0 ... .
LaJ
~
.....J LaJ a:::
- o o_..,__......,.....,.____...,__.;-_____,,_____,___......,.......,._____..,.
- 0 5 10 15 20 25 30 AXIAL POINTS 35 40 45 50 55 60 65 47
NFU-0039 Revision O July 31, 1 TABLE 3.6.4 MEAN OBSERVED DIFFERENCES AXIAL MOD EL BIAS AXIAL LEVEL MEAN D IFF AXIAL LEVEL MEAN DIFF I X(I) I X (I)
(TOP) 61 .119 31 -.012 60 -.024 30 -.014 59 -.023 29 -.016 58 .005 28 -.062 57 .018 27 -.039 56
- 015 26 -.015 55 .018 25 .007 54 -.031 24 .010 53 -.020 23 .009 52 -.021 22 . 010 51 -.009 21 .031 50 .003 20 -.041 49 -.001 11;1 -.033 48 -.005 18 -.018 47 .011 17 -.009 46 -.016 16 -.003 45 -.040 15 -.001 44 -.024 14 -.001 43 - .OBl 13 .012 42 -.017 12 .029 41 -.023 11 -.024 40 -.033 10 .015 39 -.033 9 .035 38 -.004 8 .052 37 -.069 7 .066 36 -.036 6 .068 35 -.009 5 .064 34 -.001 4 .056 33 .005 3 .038 32 .007 2 .024 1 .016 NFU 31/l 53 48
NFU-00 39 Revision 0 July 31, 1985 TABLE 3.6.5 AXIAL REGION DEFINITIONS REGION AXIAL POINTS 1 7 - 10 2 14 - 18 3 22 - 27 4 31 - 35 5 39 - 44 6 48 - 52 NFU 31/1 54 ' 49
FIGURE 3.6.12
- DISTRIBUTION OF ERRORS X(i,k,m) 0.5 NON PARAMETRIC STATISTICS 95/95 CONFIDENCE LIMIT OBSERVED 0.4 DISTRIBUTION
/~ I NORMAL STATISTICS I I 95/95 CONFIDENCE LIMIT u
I z
w 0.3 PSEG RF FQ U1 :::>
00 w
et:
\
LL w
~ 0.2
\
_J w
et:
\
I 0.1 NORMAL DISTRIBUTION
\ c.-i :::0 c: ro
...... < c:
z "IJ I\ '< I-'* I Wl-'*0 en o I 1' ...... 0 w
.. ::l IL) 1-'0
\D CL
-.3 -2 -1 0 1 2 3 4.
STANDARD ERROR UNITS (Z)
~--*~~~~~~~~~----------------------------------------------~--
FIGURE 3 -I DISTRIBUTION OF ERRORS FOR INTEGRAL X(i,m) "!'
NON PARAMETRIC STATISTICS 95/95 CONFIDENCE LIMIT
NFU-0039
~*
Revision July 31, TABLE 3.6.6 CONFIDENCE LIMITS FOR X( I ,K,M) DISTRIBJTION BY SUBGRaJPS REACTOR CYCLE AXIAL !\UMBER ST. DEV 95/95 CONFIDENCE LIMITS POWER (%) EXPOSJRE (G/T) REX;ICNS SAMPLES NORMAL NON - PARAMETERIC 0 ALL 1-6 10075 .075 .125 .139 50< p <70 ALL 1-6 8059 .045 .076 .063 100 ALL 1-6 49573 .036 .059 .063 100 E<2.5 1-6 22966 .041 .067 .072 100 2.5<E<6 1-6 19105 .031 .051 .052 100 6(E 1-6 7502 .028 .047 .040 100 ALL 1 6396 .036 .061 .069 100 ALL 2 7991 .033 .055 .065 100 ALL 3 9587 .034 .057 .069 100 ALL 4 7995 .035 .059 .067 100 ALL 5 9595 .037 .062 .079 100 ALL 6 8009 .039 .066 .073 NFU 31/1 57 52
NFU-0039 Revision 0
- July 31, 1985 TABLE 3.6.7 CONFIDENCE LIMITS FOR X(I,M) DISTRIBUTION BY SUBGRaJP REACTOR CYCLE NUMBER ST. DEV 95/95 CONFIDENCE LIMITS POWER (%) EXPOSURE (G/T) SAMPLES NORMAL NON - PARAMETER!:
0 ALL 322 .045 .081 .075 SO< p <70 ALL 258 .034 .062 .056 100 ALL 1593 .028 .048
- 055 100 E<2.5 739 .033 .057 .066 100 2.5<E<6 614 .CJ24 .042 .042 100 6(E 240 .021 .038 .045 NFU31/l 59
- 53 NfU 31/1 58
--*-----*-T FIGURE 3.6.14 CONFIDENCE LIMITS FOR X(i,k,m) VS REACTOR POWER % II 0.20 I
0.18 0.16 0.14
~ .......
Ul ~ . 0.12
~
- J ~ .......
~ ~"~----
PSEG RrrQ w
()
z 0.10 NORMAL STATISTICS
- w 0
G:
5
()
0.08 95/95 CONrlDENCE LEVEL '--::::-- ::---_
0.06
!_....... NON-PA;;.METRI~
.... --- -=------..::::_
STATISTICS- - -
95/95 CONFIDENCE LEVEL
~ :;oz 0.04 C: CD 'Tl t-' <: c
'< ..,.. I en o w ..... o t-' 0 w 0.02 ~ ::l \D 0.00 25 50 75 REACTOR POWER %
0.14
- FIGURE 3 CONFIDENCE LIMITS FOR X(i,k,m) VS CYCLE EXPOSURE
- 0.12 PSEG RFFQ 0.10--+----------------------------------
(/)
I-U1 U1
~ NON-PARAMETRIC STATISTICS
~ 0.08 95/95 CONFIDENCE LEVEL -=-
w
(.)
zw 0
u.._ 0.06 l '
z NORMAL STATISTICS 0
(.)
L________ l ---95/95 CONFIDENCE LEVEL---. ---
1 0.04 c... :;cl z C: CD '-r;
..... < c
'< f-'* I Ul 0 Wf-'*0 0.02 ..... 0 w
~ :J l.D 0.00 -+--------~-
0 2 4 6 8 10 12 CYCLE EXPOSURE (GWD/MTU)
FIGURE 3.6.16 CONFIDENCE LIMITS FOR X(i,k,m) VS AXIAL HEIGHT 0.14 0.12 PSEG RFFQ 0.10-+----------------------------------
~
V1 ~
~ 0.08 7 ..... .....
O'\
NON-PARAMETRIC STATISTICS w 95/95 CONFIDENCE LEVEL - '
u zw 0
u... 0.06
/
z 0
u
~ --N-O~AL STAT-IS-Tl-CS- - +
95/95 CONFIDENCE LEVEL_j 0.04
'-I :;o z C: CD ~
I-' <: c
'< I-'* I I-'
Ul 0 Wl-'*0 0 w .
I I
0.02 ' ::i l.O 1-'0 l.O OJ lJl 0.00 I I I I I I I I 1 2 3 4 8 9 *10 11
FIGURE CONFIDENCE LIMITS FOR X(i,m) VS REACTOR POWER %
0.12 0.10 PSEG RF FAH 0.08
~ ----- NORMAL STATISTICS
- E
~ CON~
\_- --- --=-= =---=-----
Ul
-...] ~ - - - - - ----- 95/95 w
()
z 0.06 w
0 NON-PARAMETRIC STATISTICS .- - - - - - -:::::......::: - - - -
Li... 95/95 CONFIDENCE LEVEL -----
z 0
()
0.04
'-l :;d z c:: co '"IJ 1--' <: c
'< I-'* I 0.02 en c Wl-'*0 1--' 0 w
.. :i l.O 0.00-'--~~~~~~~~~~~~~~~~~~~~~~~~~-r--~~~~~~~---,
0 25 5() 75 100 PERCENT REACTOR POWER%
*-------~~-------,-,---------------~~~=====~,------,
FIGURE 3.6.18 CONFIDENCE LIMITS FOR X(i,m) VS CYCLE EXPOSURE 0.12 0.10 PSEG Rr rAH 0.08
~
lJ1 ::::E 00 -
_J w - - - -
u 0.06 z
w 0
G:
z I NON-PARAMETRIC STATISTICS 95/95 CONrlDENCE LEVEL 1
0 u
0.04 I
NORMAL STATISTICS "
95/95 CONrlDENCE LEVEL_/
c...i :;c z c:: (1) 'Tl f-'<:C
'< ,_.. I 0.02 (fJ 0 Wt-'*0 t-' 0 w
~ ::l l.D
.I t-' 0 l.D cc 0.00 f-----~2-----~4------6rl l------.8------1~0------.12~
CYCLE EXPOSURE (G T
NFU-0039 Revision 0 July 31, 1985 3.7 Verifiication of Transient Power Distribution Simulation Capability (To be completed later) 61 59
- NFU-0039 Revision 0 July 31, 1985 4.0 References
- 1. Advanced Recycle Methodology Program (ARMP)
System Documentation CCM-3 Research Project 118-1, September 1977.
- 2. Pfeifer, C. J., "PDQ-7 Reference Manual II",
WAPD-TM-947(L), Westinghouse Electric Corporation, February 1971.
- 3. Breen, R. J., O. J. Marlowe, and C. J. Pfeifer, "HARMONY: System for Nuclear Reactor Depletion Computation," WPAD-TM-478, Westinghouse Electric Corporation, January 1965.
- 4. Walpole, R. E., Myers, R. H., "Probability and Statistics for Engineers and Scientists, MacMillan Publishing Company, New York, 1978.
- 5. Owen, D. B., "Factors for One-Sided Tolerance Limits and for Variables Sampling Plans", SCR-607, Sandia Corporation, March 1963. (Available from office of Technical Services, Department of Commerce, Washington D.C.)
- 6. USNRC Regulatory Guide 1.126, "An Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification.", March 1978.
- 7. Somer~ille, P. N., "Tables for Obtaining Non-Parametric Tolerance Limits", Annals of Mathematical Statistics 29, 59.9 ( 1958).
- 8. Assessment of the Assumption of Normality (Employing Indiviaual Observed Values), ANSI Nl5.15-1974.
- 9. Safety Evaluation of the PSE&G Rod Exchange Methodology, NFU-004, Revision 2, August 22, 1984.
60 NFU 31/l 61
NFU-0039 Revision 0 July 31, 1985 APPENDIX A STATISTICAL METHODS FOR THE DETERMINATION AND APPLICATION OF UNCERTAINTIES NFU 31/1 62 A
NFU-0039 Revision o*
July 31, 1 APPENDIX A STATISTICAL METHODS FOR THE DETERMINATION AND APPLICATION OF UNCERTAINTIES The purpose of using statistical methods is to compute the value X such that there is a 95% probability at the 95% con~idence level that XR will be conservative with respect to X (true value) when applying the calculational met~ods to safety related reactor analyses.
The first step is to determine whether or not a distribution is normal. If it is, the methods describea in Section A.l are used. If the distribution cannot be treated as normal, but the distributions are known, then the methods described fn Section A.2 are used.
NFU31/l 63 Al
NFU-0039 Revision 0 July 31, 1985 A. l Application of Normal Distribution Statistics Treatment of Measurement and Calculational Uncertain ties Comparison of measured and calculated reactor parameters include the effects of both the measurement and calculational uncertainties. Methods used in this report to isolate the calculational uncertainties are described below in terms of the followirig definitions:
XT = true reactor parameter XM = measured reactor parameter XC = calculated reactor parameter eM = XM XT = measurement error ec = XC XT = calculation error eMC = XM - XC = observed differences
µi = ei =mean error (i = M, C, or MC)
If eM ana ec are independent, then the following relationships exist. (Note that these relationships apply for non-normal distributions as well) .
NFU-0039 Revision 0
- July 31, 1985 2 2 2 0
MC = 0 c + 0 M
(A-1)
µ = µ µ (A-2)
MC M C These equations can be solved for CJC andµc. Once a~ and µC are calculated from hitor1cal data tney can be used to apply conservatism to future calculations of reactor parameters, XR' as follows:
XR = Xe - Mc +/- Kc (Jc The factor Kc is defined as described in Table A.l to proviae a 95% probability at the 95%
confidence level that XR is conservative with respect to the true value, XT.
Alternatively, as done in most instances thi~
report, it can be noted that since each term in equation (A-1) is greater than or equal to zero each term is bounded by the variance in the observed differences. Thus the calculational uncertainty can be conservatively estimated as the uncertainty in the observed differences between measured and calculated values:
2 2 CJ =CJ MC (A-3) or c ac - 0 (A-4)
MC In the later alternative, once CJMC and µMC are calculated from historical data they can be used to apply conervatism to future calculations of reactor parameters, XR as follows:
(A-5) where RF = KC CJMC The quantity µMC is used as a bias on the calculated parameter and K is as defined above. The term RF is cal~ed the reliability factor as described below.
A3 NFU3 l/l 65 I
NFU-0039 Revision 0 July 31, 1985 Reliability Factors It is the objective to define reliability factors which are to be used to increase or decrease calculated results to the point where there is a 95%
probability at the 95% confidence level that they are conservative with respect to actual parameters.
For any given application, we are only concerned with_one side of the component; that is, if the calculated value is too large or too small. We may therefore use one-sided tolerance limits based on normal distributions to find a Kc which will give a 95% probability at the 95% confidence level to the reliability factor defined by RF = Kc* Oc
- Numerical values of Kc for various sample sizes used to calculated oc are provided on Table A.l (Reference 5).
NFU31/l 66 A4
NFU-0039 J.
Revision c July 31, 1 TABLE A.l SINGLE-SIDED TOLERANCE FACTURS N Kc 2 26.26 3 7.66 4 5.14 5 4.20 6 3.71 7 3.40 8 3.19 9 3.03 10 2.91 11 2.82 12 2.74 15 2.57 20 2.40 25 2.29 30 2.22 40 2.13 60 2.02 100 1. 93 200 1. 84 500 1. 76 co
- 1. 645 N = Number of samples used to calculate a.c NFU 31/l 67 AS
NFU-0039 Revision 0 July 31, 1985 A.2 Application of Non-Normal Distribution Statistics This section documents the procedure used to determine the value XR such that there is a 95%
confidence level that XR will be conservative relative to the actual value (X ) when the .
distribution of X is not assumed to be a normal distribution. The approach taken is consistent with non-parametric methods given in reference 6 and 7.
In general, the procedure requires the ordering of N samples taken from a continuous but unknown distribution function. The statistic "m" is determined such that, at the 95% confidence level, 95% of the population lies between the rth smallest and the sth largest value in the ordered N samples, where m = r + s. The statistic m can be determined from Table A.2 (Reference 7). Since, for any given application we are usually only concerned with one side of the component, one-sided tolerance limits are required. Therefore, for upper one-sided tolerance limits, r is set to zero, and m = s.
This procedure has been implemented to obtain reliability factors using the following steps.
First, the mean error µMC = eMc was determined, where eMc = XM - Xe. (See Section A.l for definitions). Next, the population of N errors eM - µ was computed, and the resulting dis~ribu~lon ordered. Using Table A.2, the mth value of the error distribution defines error eR,which, at the 95% confidence level, 95%
of the error distribution will be less than eR*
NFU31/l 68 A6
NFU-0039
- Revision 0 July 31, 1 "
Once e and µMC are calculated from histor~cal data they can be used to apply conservatism to future calculations of the rector parameter, XR, as follows:
XR = XC + µ MC +/-_ RF (A-6) where RF = eR.
The term RF is the reliability factor which provides the desired 95% probability at the 95% confidence level for the computed parameter x.
NFU 31/l 69 A7
NFU-0039
- Revis ion 0 July 31, 1985 TABLE A.2 Values of m fo~ 95% Confidence and 95%
Probability Tolerance Limits Number of Observations (n) m 50 55 60 1 65 1 70 1 75 1 80 1 85 1 90 1 95 2 100 2 110 2 120 2 130 3 140 3 150 3 170 4 200 5 300 9 400 13 500 17 600 21 700 26 800 30 900 35 1000 39 For n> 1000 Increase m by 4 for each additional 100 observations NFU31/l 70 AS
NFU -00 39
- Revision 0 July 31, 1985 APPENDIX B COMPUTER CODE
SUMMARY
DESCRIPTION NFU31/l 71 B
NFU-0039 Revision 0 July 31, 1 APPEND IX 8 COMPUTER CODE
SUMMARY
DESCRIPTION COMPUTER CODE DESCRIPTION CPM CPM is a multigroup two-dimensional collision probability code for depletion and branch calculations for a single assembly.
Reference 1 EPRI-CELL EPRI-CELL computes the space, energy and burnup dependence of the neutron spectrum within cylindrical cells of light water reactor fuel rods. It is used to generate cross sections for PDQ on a ECDATA file.
Reference 1 INTEGRAL INTEGRAL edits PDQ files to obtain pin and assembly powers. Pin to box ratios are then input to TRINODE.
NU PUNCHER NUPUNCHER prepares HARMONY cross section tables from cross section data on an ECDATA file.
Reference 1 PDQ7/ PDQ7/HARMONY is a nuclear reactor HARMONY analysis program which solves the neutron diffusion equatioris and performs depletion calculations.
Reference 2,3 NFU 31/1 72 Bl
NFU-0039 Revision 0 July 31, 1985 COMPUTER CODE DESCRIPTION SHUFFLE SHUFFLE is the same as EPRI-SHUFFLE and will read a PDQ7 concentration file and write a new updated concentration file. It is used to simulate assembly movement between cycles.
Reference 1 SIGMA SIGMA calculates the predicted detector reaction rates using nodal power distribution and PD07 detector reaction rate to assembly power factors. The predicted detector reaction rates are then compared to measured detector reaction rates.
TRI NODE TRINODE is a modified version of the EPRI-NODE-P computer code program.
Modifications are summarized as follows:
a) Automated file management b) User friendly input c) Rod search for constant axial offset control d) Separate BP reactivity insertion equations e) Flexible edit options TAU TAU is a computer code used to compute statistics from residual reaction rates generated by SIGMA *
- NFU 31/l 73 B2