Text

Rev 2 to NFU-0039, Salem Reactor Physics Methods
	ML18096A119
Person / Time
Site:	Salem
Issue date:	05/28/1991
From:	Kent R, Rosenfeld E, Schwartz G; Public Service Enterprise Group
To:	;
Shared Package
ML18096A117	List: ML18096A116; ML18096A119;
References
	NFU-0039, NFU-39, NUDOCS 9107110131
	Download: ML18096A119 (119)
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I The Energy People NFU-0039 Revision 2 May 28, 1991 SALEM REACTOR PHYSICS METHODS II I

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NFU-0039 Revision 2

. May 28, 1991 I

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I SALEM REACTOR PHYSICS METHODS I

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5'" lzgA I Prepared by:

Date:

I G::i.rtz, P.E.

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Senior Staff Engineer Reviewed by: /&/4-Date: s-/zr1ft1 R. S. Kent I

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Nuclear Fuels Engineer f/l1#-

I Approved by:

Date:.s/z7/7/

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. E. S. Roseni:id I

Manager - Nuclear Fuel I

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I ABSTRACT NFU-0039 Revision 2 May 28, 1991 This docu~ent is a Jopi~al Report describing the Public Service £lectric and Gas Company {PSE&G) physics methods for application to the Salem units.

This report describes the calculational model and the model verification and determination of calculational uncertainties. A separate document addresses the application of these methods to the reload safety evaluations for the Salem units.

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REVISIONS Reyjsjon 2 The following sections of Revision l have been deleted:

a) Section 3.7 b) Section 4.0 through 4.6 c) Section 5.0 through 5.14 d) Appendix C e) Appendix D f) Appendix E NFU-0039 Revision 2 May 28, 1991 The Reference section has been moved from Section 6 to Section 5.0 in this revision.

The following sections have been added to Revision 1:

a) Section 4 - entire section is new

. Other changes in Revision l to create Revision 2 of this topical report are indicated by double solid bars in the right hand margin of the appropriate pages. The text from Revision l has been retyped.

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I NFU-0039 Revision 2 May 28, 1991 Table of Contents 1 INTRODUCTION 2 OVERVIEW OF THE CALCULATIONAL MODEL..*..........*.....*..............

3 MODEL VERIFICATION AND RELIABILITY DETERMINATION....................

3.1 Rod Worth Benchmarking....*.*...*.*. : *.***..*.***....*....*......

3.2 Isothermal Temperature Coefficient Benchmarking ******.*.*.......*

3.3 Doppler Coefficient Benchmarking **.....**.*...**.*...............

3.4 Isotopics **********o****************************************.e****

3.5 Reliability Factors for Delayed Neutron Parameters...............

3.6 Power Distribution Benchmarking..................................

4 EXTENDED BURNUP MODEL VERIFICATION...................................

4.1 Rod Worth Benchmarking...........................................

4.2 Isothermal Temperature Coefficient Benchmarking..................

4.3 Doppler Coefficient Benchmarking............................... ~.

4.4 Isotopics........................................................

4.5 Reliability factors for Delayed Neutron Parameters...............

4.6 Power Distribution Benchmarking..................................

5 REFERENCES APPENDIX A Statistical Methods for Determ;nation and Application of 1 - 1 2 - 1 3 - 1 3 - 3 3 - 9 3 - 12 3 - 16 3 - 21 3 - 24 4 - 1 4

3 4 - 7 4 - 9 4 - 11 4 - 16 4 - 17 5 - 1 Uncertainties *********************************************** A - f A.I Applic~tion of Normal Distribution Statistics.................... A - 3 A.2 Application of Non-Normal Distribution Statistics................ A - 8 APPENDIX B Computer Code Summary

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NFU-0039 Revision 2 May 28, I991 Table of Figures 2.0.1 Salem Physics Model.............................................

2.0.2 Salem Physics Extended Burnup Model *..........**.......*........

3.3.l Comparison of Meas and Cale Doppler Test Parameters *.*..........

3.6.l Salem Unit land Salem Unit 2 Movable Incore Detector....*.....

3.6.2 Axial Locations of Grids and Detectors *..****.**.......**.*.....

3.6.3 Salem l Cycle 4 Map 1411 Integrals.****.*****.................*.

3.6.4 Salem 1 Cycle 4 Map 1411 TMmble LIO....*.......................

3.6.5 Salem l Cycle 4 Map 1411 Thimble Nl3............................

3.6.6 Salem 1 Cycle 5 Map 1522 Integral...*...........................

3.6.°7 Salem I Cycle 5 Map I522 Thimble LIO............................

3.6.8 Salem I Cycle 5 Map I522 Thimble NI3................... ~........

3.6.9 Salem 2 Cycle I Map 2I33 Integrated.............................

3.6.IO Salem 2 Cycle I Map 2I33 Thimble LIO............................

3.6.II Salem 2 Cycle I Map 2133 Thimble NI3............................

3.6.I2 Distribution of Errors X(i,k,m) *................................

3.6.I3 Distribution of Errors For Integral X(i,m)......................

3.6.I4 Confidence Limits For X(I,K,M) vs Reactor Power%...............

3.6.IS Confidence Limits For X(l,K,M) vs Cycle Exposure...............

3.6.I6 Confidence Limits For X(I,K,M) vs Axial Height..................

3.6.I6 Confidence Limits For X(l,M) vs Reactor Power%.................

3.6.18 Confidence Limits For X(l,M} vs Cycle Exposure....... ~..........

4.4.1 Yankee Isotopic Ratio Pu-239/Pu-240.............................

4.4.2 Yankee Isotopic Ratio Pu-240/Pu-241.............................

4.4.3 Yankee Isotopic Ratio Pu-241/Pu-242..**.....*...................

4.6.1 Integrated Detector Responses for S1C7, Map 170S................

4.6.2 Detector Responses for SlC7, Map 170S, Thimble-LIO 4.6.3 Detector Responses for SIC7, Map 170S, Thimble NI3 4.6.4 Integrated Detector Responses for SICS, Map lSlI 4.6.5 Detector Responses for SICS, Map lSll, Thimble LIO 4.6.6 Detector Responses for SICS, Map lSil, Thimble NI3 4.6.7 Integrated Detector Responses for SIC9, Map I916 4.6.8 Detector Responses for SlC9, Map 1916, Thimble LIO v

2 ~ 3 2 - 4 3 - I5 3 - 30 3 - 3I 3 - 35 3 - 36 3 - 37 3 - 3S 3 - 39 3 - 40 3 - 41 3 - 42 3 - 43 3 - 46 3 - 47 3 - 50 3 - 51 3 - 52 3 - 53 3 - 54 4 - 12 4 - 13 4 - 14 4 - 20 4 - 2I 4 - 22 4 - 23 4 - 24 4 - 25 4 - 26 4 - 27

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I Table of Figures Continued 4~6.9 Detector Responses for SlC9, Map 1916, Thimble Nl3

NFU-0039 Revision 2 May 2S, 1991 4 - 2S 4.6.10 Integrated Detector Responses for SICS, Map lSil C

........... 4 - 29 4.6.II Detector Responses for SICS, Map ISll C, Thimble LIO............ 4 - 30 4.6.I2 Detector Responses for SICS, Map ISII. C, Thimble NI3............ 4 - 3I 4.4.13 Confidence Limits for X(I,K,M} vs Reactor Power *..............*. 4 - 35 4.4.14 Confidence Limits for X(I,K,M} vs Axial Height.................. 4 - 36 4.4.. 15 Confidence Limits for X(I,K,M) vs Reactor Power...... ~ *......... 4 - 37 vi

NFU-0039 Revision 2 May 28, 1991 Table of Tables 3.0.1 Reliability Factors and Biases For PSE&G Salem Model............. 3 - 2 3.1.1 Dilution Mode Rod Worth Comparisons ***..***...**.*............... 3 - 5 3.1.2 Rod Exchange Rod Worth Comparisons **.*.*.**...**.*............... 3 - 6 3.1.2 Rod Exchange Rod Worth Comparisons

- ~**************************** 3 - 7 3.1.3 Rod Worth Reliability Factors.*.....*********......*.*........... 3 - 8 3.2.1 Measured and Calculated Isothermal Temperature Coeff **..*......*.

'3.3.1 Comparison of Meas and Cale Doppler Test Parameters **..*.........

3.4.1 Comparison Between EPRl-CELL and Saxton Experimental Data.......*

3.6.1 Reactor State Points Salem 1 Cycle 2.............................

3.6.2 Reactor State Points Salem 1 Cycle 4.............................

3.6.3 Reactor State Points Salem 2 Cycle 1.......................... ~..

3.6.4 Mean Observed Differences Axial Model Bias.......................

3.6.5 Axial Region Definitions.........................................

3.6.6 Confidence Limits For X(I,K,M} Distr By Subgroups................

3.6.7 Confidence Limits For X(l,M} Distribution By Subgroups...........

4.0.1 Reliability Factors and Biases for PSE&G Extended Burn...........

4.1.1 Dilution Mode Rod Worth Comparisons for Extended Burn............

4.1.2 Rod Exchange Rod Worth Comparisons for Extended Burnup...........

4.2.1 Measured and Calculated Isothermal Temperature Coeff.............

4.4.1 Comparison Between CPM and Saxton Experimental Data........... -...

4.6.1 Reactor State Points for Extended Burnup Benchmarking............

4.6.2 Mean Observed Differences of Axial Model Bias for Extended.......

4.6.3 Confidence Limits For X(l,K,M} Distr By Subgroup.................

4.6.4 Confidence Limits For X(l,M} Distribution By Subgroup............

A.I Single-Sided Tolerance Factors..****.*.***... ~.....*.............

A.2 Values of m for.95/95 Probalility Tolerance Limits...............

vii 3 - 11 3 - 14 3 - 17 3 - 32 3 - 33 3 - 34 3 - 44 3 - 45 3 - 48 3 - 49 4 - 2 4 - 4 4 - 5 4 - 8 4 - 15 4 - 19 4 - 32 4 - 33 4

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1 INTRODUCTION NFU-0039 Revision 2 Hay 28, 1991 Sections 2 and 3 of this report describe the Salem reactor physics model and address the qualification and quantification of reliability factors for application of the model to operations and reload safety evaluations of the Salem Nuclear Reactors.

A su11111ary 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 qualification. 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.

Section 4 of this report describes the extension of the methods for the calculation of the Salem extended burnup cycles with multiple burnable poisons.

The benchmarking data for the "extended burnup model" is presented_

in Section 4.

After the measured data to be used in the benchmark process are defined, the n~dal calculations are performed and are compar~d 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 evaluate the uncertainties and reliability factors. These uncertainties and reliability factors are consistent with the model application procedures 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.

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NFU-0039 Revision 2 May 28, 1991 The ne~ cycles of the Salem units have extended cycle burnups compared to those benchmarked in Section 3 of this report. Cycles currentJy being designed will have multiple burnable poisons) standard BPRs (burnable poison rods) and IFBAs (integral fuel burnable absorbers).

For these reasons, the model described and benchmarked in Revision 1 of this report was enhanced and is described in Section 2 as the "extended burnup model". Section 4 presents the benchmarking of the "extended burnup model" for Salem 1 Cycles 7, 8, and 9 and Salem 2 Cycles 5 and 6. Selected comparisons are also presented for the original model and the "extended burnup model" for Salem 1 Cycle 8. All future PSE&G physics analysis will utilize the "extended burnup model".

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2 OVERVIEW OF THE CALCULATIONAL MODEL NFU-0039 Revision 2 May 28, 1991 Two calculational models have been used to analyze the Salem units. The first model was constructed using the Advanced Recycle Methodology Program (ARMP) system developed under EPRI sponsorship by UAI (Reference 1). The second model is the same except the CPM code replaced EPRl-CELL, and the linking codes were changed correspondingly.

The PDQ and TRINODE codes are con111on to both models.

For continuity, both models have been run in parallel for the three most recent cycles of each Salem unit. All future cycles will utilize the second model.

A flow diagram for the first model is shown in Figure 2.0.1. The spectral code, EPRl-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 XV diffusion - depletion code PDQ7/HARMONV (Reference 2 and 3).

Lumped absorber data for PDQ7/HARMONV 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/HARMONV is run both in full core (XV) geometry representation and the fuel type (color set) representation.

The full core representation is used for the nodal code normalizati6n, local peaking factor generation, and for the establishment of assembly loading patterns.

In the fuel type (color set) mode, PDQ7/HARMONV supplies input data for PSE&G's nodal code, TRINODE, a derivative of the EPRl-NODE-P program (ARMP, Part II, Chapter 14). The TRINODE program contains_ improvements overt.he 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.

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NFU-0039 Revision 2 May 28,_ 1991 A flow diagram for the second model is shown in Figure 2.0.2. Note that functionally the EPRI-CELL/PDQ color set path has been replaced by CPM.

The PSCPM code is the EPRI-CPM code described above, but modified by EPRI for input processing to become EPRI-CPM2 (Reference 11), and then modified by PSE&G to become PSCPM.

The PSE&G modifications were for the treatment of the IFBA fuel design and for linking to PDQ and TRINODE.

PSCPM performs eighth assembly calculations and provides cross sections to PDQ via the PLINK linking code and provides input to TRINODE via the BLINK linking code.

The TRINODE code was_ modified to accept table input instead of curve fit input, and the reactivity dependence for burnable poisons was accounted for ex-plicitly in the tables. The full core PDQ to TRINODE normalization is the same as in the first model.

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 margins be consistent with those used in the model benchmarking and qualifications process. This ii 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.

The TRINODE model is normalized to the PDQ model. A consistent methodology is used for this normalization throughout the benchmark calculation~ 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 ~alculated and measured parameters required for core analysis. The auxiliary computer codes are summarized in Appendix B.

All comparisons to measurement data presented in this topical report "are based on TRINODE calculations.

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EPRl-CELL

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NUPUNCHER*

Figure 2.0.1 Salem Physics Model CPM EPRl-CELL NFU-0039 Revision 2 May 28, 1991 Lumped Absorber Procedure PDQ/HARMONY Fuel Type (Color set)

Full Core H

EPRl-FIT Normalization Reaction Rates Pin to Box SUPER LINK.

TRINODE. -

I SIGMA I Plant Measurement~ I

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BLINK NFU-0039 Revision 2 May 28, 1991 ~

Figure 2.0.2 Salem Physics Extended Burnup Model I

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PSCPM TRI NODE I

Plant Measurements l Page 2 - 4 PLINK PDQ/HARMONY Full Core Normalization Reaction Rotes Pin to Box SIGMA

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3 MODEL VERIFICATION AND RELIABILITY DETERMINATION NFU-0039 Revision 2

May 28, 1991 The PSE&G model is benchmarked against Salem Unit 1 measurements made during Cycles 1 through 5, and Salem Unit 2 measurements made in Cycles 1 and 2.

This benchmark serves as the basis to quantify the reliability factors to be used in safety related calculations.

The term reliabilitv factor (RF) is used to describe the allowances (either absolute or relative) to be used in safety related calculations to assure conservatism.

The term uncertainty factor is used to describe the actual model precision and is defined as the standard deviation (u). The reliability factor is always larger than the uncertainty factor.

The term ~

is used to describe the statistical difference between an observed or measured distribution and the calculated values:

Table 3.0.1 summarizes the model reliability factors and biases computed as a result of the model benchmark.

The remainder of Section 3 is a detailed account of the derivation of these factors.

The statistical methods employed are described in Appendix A to this report.

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Table 3.0.1 Reliability Factors and Biases for PSE&G Model Applied to Salem Parameter Reliability Factor Rod Worth Meas.~ 600 pcm RFROD.. 15%

Meas < 600 pcm RFROD

100 pcm Total Inserted Worth RFROD = 10%

Temperature Coefficient Moderator (HTC)

RFMTC = 2.1 pcm/°F Isothermal (ITC}

RFITC = 2.1 pcm/*F Doppler,

RFDC = 10%

Doppler Defect RFDD = 103 Delayed Neutron Parameters

/Jeff RFB = 4%

t*

RFL = 4%

Power Distribution Fo p ~.50 RFFQ = 0.10 p <.50 RFFQ = 0.16-(0.12xP)

AFo/Fo RFTZ = 8%

FtiH p ~.30 RFFDH = 0.08 p <.30 RFFDH = 0.09-(P/30)

- See Table 3.6.4 Page 3 - 2 Bias 0

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I 3.1 Rod Worth Benchmarking NFU-0039 Revision 2 May 28, 1991 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, and 5, and Unit 2 Cycle 2. These results, along with model calculations are tabulated on Table 3.1.2.

For purposes of model benchmarking, some rod worth measurements are disqualified on the basis of known measurement errors.

Measurem~nts disqualified are the boron dilutions for Unit 1 Cycles 1 and 2, and Unit 2 Cycle 1. Additionally, rod e~change 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 Page 3 - 3

NFU-0039 Revision 2 May 28, 1991 procedure are 11% and 1% respectively. This difference is significant at the 99.9% confidence level and is attributed to the known measurement errors.

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 reliablilty factor is justified due to its conservatism relative to normal statistics. 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 reliablity 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.

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Table 3.1.1 Dilution Mod~ Rod Worth Comparisons NFU-0039 Revision 2 May 28, 1991 Difference **

Unit/

Meas Cale M ~ 600 Date Cycle Bank (pcm}

(pcm}

(%}

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 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 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 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 3 = ((M-C}/C} x 100 for measurements ~ 600 pcm A = (M-C} for measurements < 600 pcm

- - Data disqualified as discussed in text Page 3 - 5 M < 600 (A}

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Date 12/76 12/80 4/82 Table 3.1.2 Rod Exchange Rod Worth Comparisons NFU-0039 Revision 2 May 28, 1991 Difference **

Unit/

Meas Cale M ~*600 M < 600 Cycle Bank (pcm)*

(pcm)

(%)

1/1***

D*

1107 1030 (7.5) c 825 741 11.3 B

522 467 A

924 858 7.7 SD 469 403 SC 351 305 Total 4198 3804 10.3 1/3 D*

834 797 (4.6) c 696 674 3.3 B

395 450 A

816 789 3.4

Total 2741 2710

-1.1 1/4 D*

. 862 860 (0.2) c 596 588 B

370 407 A

818 789 3.7 SD 265 316 SC 285 281 SB 614 649

-5.4 SA 750 733 2.3 Total 4560 4623

-1.4 Measurement performed by dilution method

% = ((M-C)/C) x 100 for measurements ~ 600 pcm

. A = (M-C) for measurements < 600 pcm (A) 55 66 46

-55 8

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Date 2/83 7/83 Table 3.1.2 (continued)

Rod Exchange Rod Worth Comparisons NFU-0039 Revision 2 May 28, 1991 Difference **

Unit/

Meas Cale M ~ 600 M < 600 Cycle Bank (pcm)

(pcm)

(%)

1/5 D*

926 939

(-1.4) c 613 617

-0.6 B

331 361 A

784 814

-3.7 SD 269 292 SC 317 291 SB 769 793

-3.0 SA 735 779

-5.6 Total 4744 4886

-2.9 2/2 D*

878 835 (5.1) c 770 731 5.3 B

660 603 9.5 A

252 233 SD 299 287 SC 292 275 SB 787 757 4.0 SA 562 491 Total 4500 4212 6.8 Measurement performed by dilution method

% = ((M-C)/C) x 100 for measurements ~ 600 pcm A = (M-C) for measurements < 600 pcm (A)

-30

-23 26 19 12 17 71

- - Data disqualified as discussed in text.

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Table 3.1.3 Rod Worth Reliability Factors Individual Rod Worth Rod Worth < ~00 pcm Rf ROD

= 100 pcm Rod Worth ~ 600 pcm Rf ROD

.. 15 %

Total Rod Worth Rf ROD = 10 %

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3.2 Isothermal Temperature Coeffjcjent Benchmarking NFU-0039 Revision 2 May 28, 1991 The objective of this section is to benchmark the PSE&G model to measured isothermal temperature coefficients (ITC).

Based on comparisons ~etween measured and calculated coefficients, a reliability factor for both the isothermal and the moderator temperature coefficient (MIC) 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 betw~en measured and calculated ITCs is 0.85 pcm/°F.

The observed standard deviation of 0.85 pcm/°F (a085v) 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 ~xpressed as:

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 sun111arized as:

O'MTC = 0.85 O'nc = 0.85 Page 3 - 9

NFU-0039 Revision 2

May 28, 1991 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 (Kc) 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 x 2.42

2.1 pcm/*F RFMTC

0.85 x 2.42

2.1 pcm/*F Page 3 - 10 I

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Unit Cycle 1

1 1

2 1

3 1

4 1

5 2

1 2

2 Table 3.2.1 Measured and Calculated Isothermal Temperature Coefficients ITC pcm/9F Rod Position Bank (steps)

Boron Meas.

Cale.

D 197 1369

-3.51

-3.59 c

201 1264

-4.11

-4.34 B

175 1151

-6.17

-6.45 A

175 1085

-7.85

-9.06 SD 175 965

-11. 25

-11. 90 D

219 1137

-6.06

-4.45 c

214 1025

-5.79

-5.45 D

219 1258

-3.33

-3.26 c

206 1157

-4.85

-4.10 D

202 1309

-3.61

-5.29 D

214 1499

-1.52

-2.60 D

205 1334

-0.65

-0.59 D

188 1329

-0.84

-0.70 D

102 1285

-2.68

-1.89 c

184 1197

-4.34

-4.85 B

203 1083

-10.53

-9.09 A

198 955

-10.50

-9.83 SD 192 910

-13.48

-13.22 D

218 1362

-4.16

-4.55 Mean Standard Deviation Page 3 - 11 NFU-0039 Revision 2 May 28, 1991 Di ff.

0.08 0.23 0.28

. 1.21 0.65

-1.61

-0.34

-0.07

-0.75 1.68 1.08

-0.06

-0.14

-0.79

-0.51

-1.44

-0.67

-0.26 0.39 0.00 0.85

3.3 Dopoler Coefficient Benchmarking.

NFU-0039 Revision 2 May 28, 1991 The objective of this section is to. make comparisons between measured and calculated Doppler coefficients and to 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 bas been used for Cycles 2 through~ on Unit 1, ~nd 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 temperature.

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 bas been determined based on the standard deviation of multiple measurements.

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I NFU-0039 Revision 2 May 28, 1991 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 within 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 ~he 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%

Page 3 - 13

Table 3.3.l Comparison of Measured and Calculated Doppler Test Parameters Unit/ Power

of Oo AP/AT Measured Cycle Samples pcm/%

Measured Precision 1/2 39 6

-13.67

-0.95 0.04 93 6

-13.15

-1.39 0.09 1/3 44 6

-13.31

-0.77 0.02 94 6

-10.91

-1.40 0.17 1/4 43 4

-10.11

-0.90 0.23 99 4

-11. 49

-1.28 0.09 1/5 46 4

-11.45

-0.66 0.04 97 4

-12.01

-0.99 0.11 2/2 98 2

-11.33

-1.34 0.35 Page 3 - 14 AP/AT Cale

-0.86

-1.41

-0.83

-1.28

-0.84

-1.31

-0.70

-1.10

-1.33 NFU-0039 Revision 2 May 28, 1991 Meas minus Cale

-0.09 0.02 0.06

-0.12

-0.06 0.03 0.04 0.11

-0.01

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0 Q) 2 1.7 1.6 1.5 1.4 1.3 1.2 1. 1 1.0 0.9 0.8 0.7 0.6 0.5 0.5 0.6 Figure 3.3.1 Comparison of Measured and Calculated Doppler Test Parameters (AP/AT, I Power/*F)

Zero Error (m= 1) 0.7 0.8 0.9 1.0 1. 1 1.2.

Calculated Page 3 - 15 1.3 NFU-0039 Revision 2 May 28, 1991 1.4 1.5

3.4 Isotopjcs NFU-0039 Revision 2 May 28, 1991 Isotopic compositions calculated by EPRl-CELL have been compared with spent fuel isotopic data obtained from Yankee Rowe fuel rods irradiated beyo_nd 35 GWD/MTU.

The reactor repres~ntation used for the EPRl-CELL benchmarking in the calculations is described in the ARMP documentation (Part 1, Chapter 1, Sect~o~ 4.0).

Experimental and analytical 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 M02 fuel (6.6 w/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 documentation (Part 1, Chapter 3, Section 4.)

Page 3 - 16

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I Nuclide U-234 U-235 U-236 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Nuciide Np-237/U-238 Pu-239/U238 Pu-238/Pu-239 Am-241/Pu-239 Cm-242/Pu-239 Cm-244/Pu-239 Table 3.4.1 NFU-0039 Revision 2 May 28, 1991 Comparison Between EPRl-CELL and Saxton Experimental Data Atom %

Experimental Experiment Uncertainty %

(EPRI CELL/Exp)xlOO 0.00465 28.7

-3.7 0.574 0.9

1. 7 0.0355 5.6

-7.6 99.386 0.0 0.0 0.109 2.2

-32.1

73. 77 0.0 0.6 19.25 0.2

-3.5 6.29 0.3 4.6 0.579 0.9

-11. 7 Atom Ratios Experimental Experiment Uncertainty %

(EPRI CELL/Exp)xlOO l.14*10-4 15.0

-26.9 4.383*10-2 0.7 2.0

1. 75*10-3 0.4

-17.6

l. 23*10-2 15.0 2.4 l.05*10-4.

10.0 0.4 l.09*10-4 20.0

-3.2 Page 3 - 17

10.0 9.0 a.a 7.0 s.o 4.0

3. 0

o. J o.o s.o

.. ' \\

Figure 3.4.1 Comparison of EPRl-CELL to Yankee Pu-239/Pu-240 Isotropic Ratios

\\

~

i

. *'. \\\\

~

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10.0 15.0 20.0 Accumulated Fissions (barn-cm)-l x 105 Page 3 - 18 NFU-0039 Revision 2 Hay 28, 1991

~ ~

25.0 30.C

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c.

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I Figure 3.4.2 Comparison of EPRI-CELL to Yankee.

Pu-240/Pu-241 Isotropic Ratios

\\ \\

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\\*.*.,

"<.:; ~

.. i=--.......

5.0 10.0 15.0 20.0 Accumulated Fissions (barn-cml-l x 105 Page 3 - 19 25.0 NFU-0039 Revision 2 May 28, 1991 30.0

10.0 9.0

a. 0

~

E-4

~ 7. 0 N

~

N

~

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~ 6.

Clo 0

s. 0

4. 0

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o.o s.o Figure 3.4.3.

. Comparison of EPRI-CELL to Yankee Pu-241/Pu-242 Isotropic Ratios

. \\

.. \\

-.. I\\

NFU-0039 Revision 2 May 28, 1991

~

10.0 15.0 20.0

-1 5

Accumulated Fissions (ba%Tl-cm) x 10 Page 3 - 20 i'-,

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25.0 30.0

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I 3.5 Reljability Factors for Delayed Neutron parameters NFU-0039 Revision 2 May 28, 1991 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 who~e 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 Peff*

The uncertainties in the calculation of Peff are composed of several components; the most important of which are listed below.

a. Experimental values of p, and)., by nuclide;

b. Calculation of the spatial nuclide inventory;

c. Calculation of core average p as a flux weighted average over the spatial nuclide inventory;

d. Calculation of Peff from the core average as Peff = I x p, where I = importance factor.

The experimental determination of the Ps and ).s are assumed to be accurate to within 1%.

The most important nuclide concentrations with respect to core p are U-238, U-235, and Pu-239. Tables 3.4.1 and 3.4~2 indicate that the difference in the calculation of these conce~trations is about 1.7%

for ECELL.

Therefore, components (a) and (b) above are-combined as 2.7%.

The uncertainty in the calculation of a core average p 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 p. 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.

Typi~al regional ps are given.below:

Page 3 - 21

Region 1 (third cycle fuel) p (1) s 0.005 Region 2 (second cycle fuel) p (2)

0.006 Region 3 (feed fuel) p (3) = 0.007 NFU-0039 Revision 2 May 28, 1991 The effect of errors in the calculated. flux distribution can be -evaluated in terms of the effect on the core average p.

As a base case, flux weighting factors (FWF) are all set to 1.0.

In this case, the core average p = 0.006. Using a maximum error in the regional flux weighting of 7%, the worst error in the calculation of the core average P is obtained by increasing the weight of the Region 1 fuel and decreasing the weight of the Region 3 fuel. The revised pis calculated as follows:

(1) x 1.07 =.00535

{2) x 1.00 =.00600

{3) x 0.93 =.00651.

p =.00595, which yield a -0.8% error for component {C) above.

The last uncertainty component, {d), concerns the reduction of core average p to obtain Peff by using the importance factor. Since this reduction is typically about 3% to 4%, an error of 103 in this component would lead to an error in Peff of less than 0.5%.

Th~ sum of the errors for these four factors is as follows:

2.7%(a+b) + 0.8%{c) + 0.5%{d} = 4.0%

Therefore, 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 ce*) uncertainty.

The uncertainty components which go into the calculation of e* are as follows:

Page 3 - 22

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(a) Experimental values of microscopic cross sections; (b) Calculation of the spatial nuclide inventory; and NFU-0039 Revision 2 May 28, 1991 (c) Calculation of the core average effectve neutron lifetime, e*,

as a flux weighted average over the spatial nuclide inventory which includes the effects o~ leakages.

Uncertainties for components (a) and (b) are assumed to be the same as described for the calculation of ~eff, that is, a combination of 13 uncerainty in the experimental determination of nuclear cross sections and 1.73 uncertainty in the determination of the spatial nuclide invertory of ECELL.

The core average neutron lifetime depends on flux weighting ~f local absorption lifetimes e*.

If a conservative estimate of the error in regional power sharing (7%) is used in determining the impact of the core average lifetime (t*), the error in lifetime is on the order of 1.03.

Combining all of these uncertainties linearly results in a total.

uncertainty of 3.73. Therefore, a 43 reliability factor (RFL) will be applied to the*neutron lifetime calculation when applied to safety related calculations.

Page 3 - 23

3.6 Power Djstrjbutjon Benchmarking NFU-0039 Revision 2 May 28, 1991 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 d~scription of the calculat.ional methodolgy.

Second, comparisons are made between 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, d~ift, 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 conditi~ns 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 model for power distributions was to compare calculated and measured detector signals. The basis for this is twofold.

First, the detector signals represent raw measurements and do not include interpretation, unlike "measured" power distributions. Second, the ability of the model to Page 3 - 24

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I NFU-0039 Revision 2 May 28, 1991 compute the detector signal requires the same processes as required to compute pin powers.

Both calculations 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 signal 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 assembly 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 1oca1 peaking factors. is assured by:

Page 3 - 25

a. Using a co11111on full core PDQ7 model,

b. Using a co11111on nodal model, and NFU-0039 Revision 2 May 28, 1991

c. Using a co11111on 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 tore locations are highlighted 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 Page 3 - 26

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I NFU-0039 Revision 2 May 28, 1991 An average difference between measured and calculated reaction rates can be computed for each axial level as:

LL DRR(l,K,M)

I M

DRR(K) = ---=~,,...---

LL 1 I

M where the su11111ation over I is performed for each available radial location, and H 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 deviations relative to the observed bias, a second variable can be defined as X(I,K,M) = (RRM(I,K,M)-RRC(l,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,H,) or the intergral of X{l,K~M); X{I,M).

This latter quantity is the biased difference between the measured and ca.lcul ated 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.

Page 3 - 27

NFU-0039 Revision 2 May 28, 1991 The difference population was evaluated for normality using the chi-squared test. This test demonstrates that most of the subgroups cannot be consi_dered normal. Typical comparisons of the difference pop.ulation and a normal distribution are 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 agreement. 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. l 2xP)

P <

50 RFFDH = 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 Page 3 - 28

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NFU-0039 ReviSion 2 May 28, 1991 size resulting in an increase in 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 therefore are not impa~ted significantly by possible dependence among data samples.

Page 3 - 29

1 2

3 4

5 6

7 8

9 10 11 12 13 14 15 R

P N

M 4

5 36 17 54 44 23 58 57 33 45 18 Figure 3.6.1 Salem Unit 1 and Salem Unit 2 Movable Incore Detector Locations L

K J

H G

F E

28 15 3

51 10 30 43 11 38 31 14 6

32 16 29 46 48 22 9

4 1

40 26 21 41 55 35 20 27 42 53 2

Page 3 - 30 D

c 39 24 47 50 49 12 7

37 NFU-0039 Revision 2 May 28, 1991 B

A 52 8

34 56 13 25

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Figure 3.6.2 NFU-0039 Revision 2 May 28, 1991 Axial Locations of Grids and Detectors 61 60 59 58 57 56 55 54 53 52 51 50 20.550 49

't 48 47 46 45 44 43 42 20.550 41 t

40 39 38 37 36 35 34 20.550 33

+

32

31.

30 29 28 27 26 25 20.550 24 t

23 22 21 20 19 18 17 20.550 16 15 14 13 12 11 10 9

8 7

6 5

4 3

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.c u c Axial Detector Signal Locations All Measurements Are In Inches Bottom of Fuel Rod

Table 3.6.1 Reactor State Points Salem l Cycle 2 Cycle Exposure Power Level Map No.

(MWD/MTU)

(I) 174 0

0.0 188 2160 100.0 190 3097 100.0 194 4382 100.0 196 6250 100.0 198 7275 82.0 1201 7945 67.0 Salem 1 Cycle 3 Cycle Exposure Power Level Map No.

(MWD/MTU)

(%)

1300 0

0.0 1313 500 100.0 1315 1040 100.0 1324 3165 99.5 1330 4100 97.0 1333 5670 97.0 1338 7060 96.8 1342 8800 75.0 Page 3 - 32 NFU-0039 Revision 2

May 28, 1991 D Bank Position (steps) 228 228 228 228 225 206 218 D Bank Position (steps) 212 228 222 228 220 228 228 202

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Map No.

1400 1408 1411 1412 1413 1414 1416 1417 Map No.

1500 1503 1507 1509 1512 1517 1520 1522 1524 Table 3.6.2 Reactor State Points Salem 1 Cycle 4 Cycle Exposure Power Level (MWD/MTU)

(i) 0 0.0 180 84.0 560 100.0 1580 100.0 2589 98.6 3715 100.0 3836 100.0 4998 100.0 Salem 1 Cycle 5 Cycle Exposure Power Level (MWD/MTU)

(%)

0 0.0 25 47.3 140 99.3 1391 100.0 2531 99.9 4662 99.5 5444 100.0 7185 99.9 8923 100.0 Page 3 - 33 NFU-0039 Revision 2 Hay 28, 1991 D Bank Position (steps) 211 228 228 225 228 215 228 228 D Bank Position (steps) 216 228 228 228 226 228 218 228 228

Table 3.6.3 Reactor State Points Salem 2 Cycle 1 Cycle Exposure

Power Level Map No.

(MWD/MTU)

(S) 2004 0

0.0 2102 2435 100.0 2115 4677 96.7 2120 7386 99.8 2122 9196 100.0 2127 11755 82.2 2129 13357 82.0 2131 14192 82.8 2133 15403 82.5 Salem 2 Cycle 2 Cycle Exposure Power Level Map No.

(HWD/MTU)

(%)

2201 0

0.0 2203 21 48.6 2205 47 72.1 2209 292

.98.4 2210 564 99.0 2213 1120 99.0 2214 2106 99.1 2217 3195 99.2 Page 3 - 34

.1 NFU-0039 Revision 2 ~~

May 2~, 1991.-

D Bank Pos ;ti on 1

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(steps) 206 222 228 228 224 219 220 228 219 D Bank Position (steps) 220 180 214 228 228 228 228 228 I

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10 11 12 13 14 15 R

p 6.4 4.6 3.2 3.3 4.4 Figure 3.6.3 NFU-0039 Revision 2 May 28, 1991 Measured and Calculated Integrated Detector Responses Salem 1 Cycle 4 Map 1411 Absolute Differences Power

100%

Exposure

560 MWD/MTU N

M L

K J

H G

F E

D c

B A

L 4.1 5.9 2.8

-0.1

-2.3

-0.5

-0.6 3.3 1.5

-2.1

-1. 5

-2.7

-1.8 1.2

-0.l

-2.9

-1.1

1. 7

-1. 2

-1.8

-1. 7

-1.3

-2.3

-2.1

-2.7

-1.3

-1.8 -2.7 -0.5

-4.2

-4.0 2.6

-1.4

-3.3

-2.1 D

-2.3

-2.6 2.9

-2.7

-1.3 0.4

-1.2

-3.8 1.3 2.9 0.4

-2.6

-0.1 3.5 1.1 Absolute 'Difference = (Meas.- Cale.) x 100 Page 3 - 35

Figure 3.6.4 Measured and Calculated Detector Responses Salem I Cycle 4 - Map 1411 100% Power, 560 MWD/MTU Thimble ~IO NFU-0039..1 Revision 2 May 28, 1991 ~

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I 2.5.--~~~~~~~~.--~~~-.--~~~~.--~~~~~---.-~~,.........,

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(/) 6 2.0 0..

(/)

Q) 0:::::

I..... 1.5 0

-+-'

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-+-'

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-+-'

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1.0 0.5 Predicted Measured 0

0.0 '-'--J'-'--L--'-'-....L.....L..-'-'-'--'-L--'-'-..L....L.._,_._.__.__,'-'--L_._,_....L.....L...J..-.L-'--'--J-L-J.....J.....L....J.....L..'--'--J'-'--L--L..L.....L.....L....J.....L...l......L-'--'-L--L..l.......L.....l.....L....L...J 0

5 1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 3 - 36 I

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(f) c 0

o__

(f)

Q) 0::::

L 0

--+--' u Q)

--+--'

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--+--'

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2.5 2.0 1.5 -

1.0 0.5 Figure 3.6.5 Measured and Calculated Detector Responses Salem 1 Cycle 4 - Map 1411 j'

I 100% Power, 560 MWD/MTU-

-Thimble t03 Predicted Measured 0

NFU-0039 Revision 2

-May 28, 1991 0.0 '--'-----'__._._---'--'----'--'-..__._'-----'---'---'--'-----'---'--'--'-'--'-----'__._._-'-'----'---'--'--'--'__.__...-'-'----'--'--'------'-------'---'---'--'-----'----'----'-----'--'--'-'--'-----'__.__...........__,_---'--'--'----'--'

0 5

1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 3 - 37

1 2

3 4

5 6

7 8

9 10 11 12 13 14 15 R

p

1. 7 1.2 1.3 1.1 Figure 3.6.6 NFU-0039 Revision 2

. Hay 28, 1991 Measured and Calculated Integrated Detector Responses Salem 1 Cycle 5 Hap 1522 Absolute Differences Power* 9~.7%

Exposure

7185 HWD/HTU N

M L

K J

H G

F E

D c

B A

0.3

-0.0 0.8 0.9

-1. 7

-1.8

-0.6 0.1 0.6 0.9 1.6 0.1

-0.0 0.9 2.2

-0.4 0.6

-1.5

-0.3

-1. 7

-0.1

1. 7

-3.0 0.7

-0.5 1.2 1.5

-1.5 0.8

-2.3 0.9 0.5 0.7

-0.9

-1.9 0.6

-2.3 0.1 0.7

-1.5

-1.9

-0.3 0.8 Absolute Difference * (Meas.- Cale.) x 100 Page 3 - 38

.1..

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1 I

II J

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I Figure 3.6.7 Measured and Calculated Detector Responses Salem 1 Cycle 5 - Map 1522 99.7% Power, 7185 MWD/MTU Thimble LIO NFU~0039 Revision 2 May 28, 1991 2.5.--'-~~~~~~~~~~~~~~~~~~~.....--~~~~~~~

Q)

(f) § 2.0 0...

(f)

Q) 0::::

\\....._ 1.5 0

-+-'

u Q)

-+-'

Q) 0 Q)

-+-'

0 Q) 0::::

1.0 0.5 Predicted Measured 0

0.0 '-'-'-'--'--'-'-......................_"'--'--'--'--'-'-_.__._"'"-'-L...L...l.--'-'-_._._.._.._._.__.__._.._.__.._.........._"'--'--'--'--'-'-_.__.._..J.....L_~'-'--'--'-'-_._._..l......L....,

5 1 0 15 20 25 30 35 40 45 50 55 60 Axial Points 0

Page 3 - 39

G)

(f)

Figure 3.6.8 Measured and Calculated Detector Responses Salem 1 Cycle 5 - Map 1522 99.7% Power, 7185 MWD/MTU TMmble N13 NFU-0039 Revision 2

. May 28, 1991 2.5.------~----~------..--------~i:================:----~--------~----~----~,-.

§ 2.0 I.

I Pred~cled Measured I

0...

(f)

G) 0::::

1.._

0

-+-'

u

. G)

-+-'

G) 0 G)

-+-'

0 G) 0::::

1.5 1.0 0.5 0

0.0._.__..__.__._,__,_--'-'--'-'--'"-'-'--'--'-~-'--'-.J._J,_..__.__._,__,_--'-'-.J._J,_L-'-'--'--L~--'-'-.J._J,_J.-'-'--'--L~-'--'-.J._J,_LJ.._l-'-l.--L..J.....J._J._J 0

5 10 15 20 25 30 35 40 Axial Points Page 3 - 40 45 50 55 60

.1 I

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1.

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1 I

2 I

3 4

5 6

7 I

8 I

9 10 I

11 12 I

13 I

14 15 I

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I R

p

-1. 5 Figure 3.6.9 NFU-0039 Revision 2

. Hay 28, 1991 Measured and Calculated Integrated Detector Responses Salem 2 Cycle 1 Map 2133 Absolute Differences Power

82.5%

Exposure

15403 MWD/HTU N

H L

K J

H G

F E

D c

B 0.3

-1.1 0.5 0.1

-5.5

-1.3 0.8 1.4 2.2 1.8 0.6

-1.4 1.9

-0.8 0.7

-0.0 3.3

-1.5 2.2

-3.0

-1.5

-3.1 0.8 0.1 -2.2 1.5 2.4 0.7

-0.7

-1.3 3.2

-1.1 2.1 1.2 H-2.3 3.3

-0.1

-0.5

-4.8

1. 7 0.1

-1.9 42.4 0.2 Absolute Difference = (Meas.- Cale.) x 100 Page 3 - 41

!......_ 1.5 0

-+--' u (1)

-+--'

(1) 0 (1)

-+--'

0 (1) er:

1.0 0.5 Figure 3.6.10 Measured and Calculated Detector Responses Salem 2 Cycle 1 - Map 2133 82.5% Power, 15403 MWD/MTU Thimble LIO Predicted Measured 0

NFU-0039 Revision 2

. May 28, 1991 0.0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0 5

1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 3 - 42

,1..

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1.

I I

1*

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I 2.5

(])

(/) c 2.0 0

0...

(/)

(])

er:::

L 1.5 0

+-'

u

([)

+-'

(])

0

(])

+-'

0 1.0 0.5

(])

0 er:::

Figure 3.6.11 Measured and Calculated Detector Responses Salem 2 Cycle 1 - Map 2133 82.5% Power, 15403 MWD/MTU Thimble N13 Predicted Measured 0

NFU-0039 Revision 2 May 28, 1991 0.0 L...L..J--1-L...J.-J-..L....L..J....L.._L....L...J--1-L...J.-l-..L...1-.J....L.._L...L...L...J.-l--'-1-L....L...JL...L...L-J-l.....L....i....L....J_J...J...JL...L...L--l....J....L...l-.J....L.._J...J...JL..J....L--l....J.....L....i...J....J....J 0

5 1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 3 - 43

Axial Level I

Top 61 60 59 58 57 56 55

54.

53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32*

Table 3.6.4 Mean Observed Differences Axial Model Bias Mean Diff Axial Level X( I)

I

.119 31

-.024 30

-.023 29

.005 28

.018 27

.015 26

.018 25

-.031 24

-.020 23

-.021 22

-.009 21

.003 20

-.001 19

-.005 18

.011 17

-.016 16

-.040 15

-.024 14

-.019 13

-.017 12

-.023 11

-.033 10

-.033 9

-.004 8

-.069 7

-.036 6

-.009 5

-.001 4

.005 3

.007 2

1 Page 3 - 44 Mean Diff X( I)

-.012

-.014

-.016

-.062

-.039

-.015

.007

.010

.009

.010

.031

-.041

-.033

-.018

-.009

-.003

-.001

.012

.029

-.024

.015

.035

.052

.066

.068

.064

.056

.038

.024

.016 NFU-0039 Revision 2 May 28, 1991 I..

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I

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I I

I 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 Page 3 - 45 NFU-0039 Revision 2 May 28, 1991

>-u z w

=>

0 w Q:'.:

u..

,w

'~

w Q:'.:

0.5 0.-4 O.l 0.2 0.1 NORMAL DISTRIBUTION

-l NFU-0039 Revision 2 Hay 28; -1991 Figure 3.6.12 Distribution of Errors X(I,K,H)

OBSERVED DISTRIBUTION

-2 I

I

\\

-1 0

1 STANDARD ERROR UNITS (Z)

Page 3 - 46

\\

NON PARAMETRIC STATISTICS 95/95 CONFlDEHCE LIMIT I NORMAL STATISTICS 95/95 CONFlDENCE LIMIT

I PSEG Rr rQ 2

l

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I

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>-u z w

J

,a w

a:::

i.....

w

~

_J w

a:::

I I

I

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I I

Figure 3.6.13 NFU-0039 Revision 2 May 28, 1991

Distribution of Errors for Integral X(I,M) 0.5 0.4 o.:s 0.2 OBSERVED DISTRIBUTION 0.1 NORI.CAL DISTRIBUTION I

I I

\\

NON PARAl.IETRIC STATISTICS 95/95 CONFlDENCE Ul.llT NORI.CAL STATISTICS 95/95 CONFIDENCE Ul.llT I

PSEG., '""

o.o-+-~~....=:::;..:::::=-,L_~.,----~~~.,----~*~~.---~~~.---~L-L-.,-~~--=z~~~--,

-1

0 I

2 3

-4

-:s

-2 STANDARD ERROR UNITS (Z)

Page 3 - 47

Reactor Power 0

50~P~70 100 100 100 100 100 100 100 100 100 100 Table 3.6.6 NFU-0039 Revision 2 May 28,.1991 Confidence Limits for X(I,K,M) Distribution by Subgroup 95/95 Confidence Limits Cycle Axial Number Std Non-Exposure Regions Samples Dev Normal Parametric all 1 - 6 10_075 0.075 0.125 0.139 all 1 - 6 8059 0.045 0.076 0.063 all 1 - 6 49573 0.036 0.059 0.063 E<2.5 1 - 6 22966 0.041 0.067 0.072 2.5~E<6 1 - 6 19105 0.031 0.051 0.052 6~E 1 - 6 7502 0.028 0.047 0.040 all 1

6396 0.036 0.061 0.069 all 2

7991 0.033 0.055 0.065 all 3

9587 0.034 0.057 0.069 all 4

7995 0.035 0.059 0.067 all 5

9595 0.037 0.062 0.079 all 6

8009 0.039 0.066 0.073 Page 3 - 48 I

.1..

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Reactor Power 0

50sPs70 100 100 100 100 Table 3.6.7 Confidence Limits for X(l,M) by Subgroup Cycle Number Std Exposure Samples Dev all 322 0.045 all

.258 0.034 all 1593 0.028 E<2.5 739 0.033 2.5sE<6 614 0.024 6sE 240 0.021 Page 3 - 49 Distribution NFU-0039 Revision 2 May 28, 1991 95/95 Confidence Limits Non-Normal Parametric 0.081 0.075 0.062 0.056 0.048 0.055 0.057 0.066 0.042 0.042 0.038 0.045

en 0.18 0.16 0.14

-~ 0.12

_J Q)

~ 0.10 Q)

-0

~ 0.08 0

u 0.06 0.04 0.02 Figure 3.6.14 Confidence Limits for X(I,K,M) vs Reactor Power%

Non-Parametric PSEG RFFQ I NFU-0039 Revision 2 May 28, 1991 0.00 L--~~--'-~~---'-~~~-'--~~---',-~~----'~~~--'-~~---'-~~~

0 25 50 75 100 Reactor Power %

Page 3 - 50

, I I

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I Figure 3.6.15 Confidence Limits for X(I,M) vs Cycle Exposure Cf)

E 0.12 -

..::J 0.08._

<!)

(..}

Non-Po~ometric C

I t

o. 06 :---------L==~===~===~===~-=i PSEG RFFQ I NFU-0039 Revision 2 May 28, 1991 0

~------------------------------

I 0.04- -

L----------------------------------------------------

0.02.....

0.00 I

I I

I 0

2 4-6 8

10 12 Cycle Exposure (GWD/~TU)

Page 3 - 51

en

-+-'

E

0. 12,_

..J 0.08 -

Q) u c Q)

~ 0.06 -

4-c 0

0 0.04 -

0.02 -

Figure 3.6.16 Confidence Limits for X(I,K,M) vs Axial Height Non-Parametric PSEG RFFQ I

~-

NFU-0039

' ~

Revision 2 May 28, 1991..

I.

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0.00 ~_._~1~,___.__1_._~1~,__~1__,____,1.___.__~1__.~,__1_.__~1__.~_.__1_._~l~,__~1__,_,__,

I I

1*

0 2

3 4

5 6

7 8

9 Axial Height (Feet)

Page 3 - 52 10 11 12 I

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0.10 2 0.08 E

_J Q)

~ 0.06 Q)

-0

.;: :: c 0 () 0.04 0.02 0.00 Figure 3.6.17 Confidence Limits for X(I,M) vs Reactor Power%

Non-Parametric

PSEG RF FL:.H I NFU-0039

Revision 2 May 28, 1991

~----~~~~~~~::::~~~~::::-::::~~~~~~~~~~~

____________ :=.-::-.=:::.::::*_-::~'-"'--:.:::::::------~---~----

0 25 50 75 100 Reactor Power %

Page 3 - 53

~---------------------------

NFU-0039, I Revision 2

May 28, 1991..

Figure 3.6.18 Confidence Limits for X(l,M) vs Cycle Exposure 0.12.-----------------------------------,

Non-Parqmetric PSEG RF F.a.H I

- 0.10 -

2 0.08 t--------------------------------1 E

_J

<!)

u 0.06._

..= c

~

1*

()

i r----------------------------------------------------

0 0. 04._

~-------<L 0.02._

I I

I 0.00.___ _ _.__ _ _,__ _ ___., __

L__

...1_._~

0 2

4 6

8 1 0 12 Cycle Exposure (G/T)

Page 3 - 54 I

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I 4 EXTENDED BURNUP MODEL VERIFICATION NFU-0039 Revision 2 May 28, 1991.

The CPM based model is benchmarked against Salem Unit 1 measurements made during Cycles 7 through 9, and Salem Unit 2 measurements made during Cycles 5 and 6.

Salem 1 Cycle 8 benchmarking for the CELL based model, original benchmarking described in Section 3, is described in this section to provide continuity and the transistion to the CPM model.

The same approach to benchmarking and the same statistical techniques are used in this section as was used in Section 3.

T*ab le 4. 0.1 summarizes the model reliability factors and bi as es computed as a result of the extended burnup model benchmark.

The remainder of Section 4 is the supporting descriptions and data.

Page 4 - I

Table 4.0.l Reliability Factors and Biases for PSE&G Extended Burnup Model Applied to Salem Parameter Reliability Factor Rod Worth Meas ~ 600 pcm RFROD = 15%

Meas < 600 pcm RFROD = 100 pcm Totals RFROD = 10%

Temperature Coefficient Moderator (MTC}

RFMTC = 2.1 pcm/°F I sotherma 1 (ITC}

RFITC = 2.1 pcm/°F Doppler RFDC = 10%

Doppler Defect RFDD = 10%

Delayed Neutron Parameters Pe ff RFB = 4%

t*

RFL = 4%

Power Distribution Fo p ~.50 RFFQ = 0.10 p <.50 RFFQ = 0.16-(0.12xP}

FtiH p ~.30 RFFDH = 0.08 p <.30 RFFDH = 0.09-(P/30)

Page 4 - 2 Bias 0

0 0

+l.31

+l.31 10%

10%

0 0

NFU-0039 Revision 2 May 28, 1991 I

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4.1 Rod Worth Benchmarking NFU-0039 Revision 2 May 28, 1991 As described in Section 3.1, rod wbrth measurements can be via the boron dilution method or the rod exchange technique.

For the cycles of interest, only the reference bank was measured via dilution with all remaining banks measured via rod exchange. Table 4.1.1 shows the dilution measurements and predictions, Table 4.1.2 shows the rod exchange results.

For continuity, the CELL based model results are shown at the bottom of each table for Salem 1 cycle 8.

The results for the extended burnup model show that all predicted rod worths are well within the reliability factors for rod worths previously presented (see Table 3.1.3, page 3.1-6). The extended burnup model results show differences of +71 to -40 pcm compared to the rod worth reliability factor of 100 pcm for banks whose worth is less than 600 pcm.

For banks worth greater than 600 pcm the model results of +11.0 to -2.9%

compared to the reliability factor of 15%.

The total predicted rod worth results are+/- 4% compared to the total rod worth reliability factor of 10%.

The data in Table 4.1.2 shows the model predictions for Salem 1 cycle 8 for both models.

Based on this comparison and the reliability factor comparisons above, it is concluded that the model reliability factors established in Table 3.1.3 are applicable to the extended burnup model.

Page 4 - 3

Date 11/88 6/90 5/86

2/88 6/89 Date 2/88 Unit/

Cycle 2/5 2/6 1/7 1/8 1/9 Unit/

Cycle 1/8 Table 4.1.l NFU-0039 Revision 2 May 28, 1991 Dilution Mode Rod Worth Comparisons Extended Burnup Model Difference **

Meas Cale M ~ 600 M < 600 Bank (pcm)

(pcm)

(%)

(A)

D 956 961

-0.5.

SB 882 899

-1.9 D

1045 1051

-0.6 SB 949 960

-1.1 D

1036 1055

-1.8 CELL Model Difference **

Meas Cale M ~ 600 M < 600 Bank (pcm)

(pcm)

(%)

(A}

SB 949 971

-2.3

% = ((M-C)/C) x 100 for measurement~ ~ 600 pcm A = (M-C} for measurements < 600 pcm Page 4 - 4

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Date 11/88 6/90 5/86 Table 4.1. 2 Rod Exchange Rod Worth Comparisons Extended Burnup Model NFU-0039 Revision 2 May 28, 1991 Difference **

Unit/

Meas

Cale M ~ 600 M < 600 Cycle Bank (pcm)

(pcm)

(%)

2/5 D

956 961

-0.5 c

874 813 7.5 B

' 780 758 2.9 A

406 390 SD 398 380 SC 401 389 SB 896 871 2.9 SA 220 196 Total 4931 4758 3.6 2/6 D

907 876 3.5 c

846 822 2.9 B

713 714

-0.1 A

312 334 SD 433 440 SC 430 437 SB 882 899

-1.9 SA 273 267 Total 4796 4789 0.1 1/7 D

1045 1051

-0.6 c

555 505 B

469 463 A

901 859 4.9 SD 358 324 SC 352 382 SB 1005 980 2.6 SA 916 825 11.0 Total 5601 5389 3.9

% = ((M-C)/C) x 100 for measurements ~ 600 pcm

~ = (M-C) for measurements < 600 pcm Page 4 - 5 (A) 16 18 12 24

-22

-7

-7 6

50 6

34

-30

D~te 2/88 6/89 2/88 NFU-0039 '. I Revision 2 May 28, 1991 ~

Table 4.1.2 (cont.)

Rod Exchange Rod Worth Comparisons Extended Burnup Model Difference ** *

I I

I I

I, Unit/

Meas Cale M ~ 600 M < 600 Cycle Bank (pcm)

(pcm)

(%)

1/8 D

962 980

-1.8 c

479 469 B

355 371 A

891 887 0.5 SD 383 374 SC 270 296 SB 949 960

-1. l SA 851 806 5.6 Total 5140 5143

-0.l 1/9 D

1036 1055

-1.8 c

540 500 B

452 427 A

808 832

-2.9 D

451 419 SC 354 354 SB 890 857 3.9 SA 713 667 6.9 Total 5244 51ll 2.6 CELL Model 1/8 D

962 966

-0.4 c

479 516 B

355 395 A

891 902

-1. 2 SD 383 417 SC 270 273 SB 949 971

-2.3 SA

. 851 865

-1.6

. Total 5140 5305

-3.1

% = ((M-C)/C) x 100 for measurements ~ 600 pcm A = (M-C) for measurements < 600 pcm Page 4 - 6.

(A) 10

-16 9

-26 40 25 32 0

71

-37

-40

-34

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4.2 Isothermal Temperature Coefficient Benchmarking NFU-0039 Revision 2 May 28, 1991 A total of 5 ITC measurements are tabulated on Table 4.2.1 for the extended burnup model comparisons.

These results show that the extended model predicts a more negative temperature coefficient than measurement, the mean difference is +1.31 pcm/°F. This requires that a bias be used with the extended burnup model.

The standard deviation of the five measurements is smaller than that reported in Section 3.2, 0.50 versus 0.85 pcm/°F.

Based on these results it is concluded that the reliability factor of 2.1 pcm/°F with a bias of +1.31 pcm/°F should be applied for the extended burnup model applications.

Page 4 - 7

Table 4.2.1 NFU-0039.

Revision 2 ~

May 28, 1991 ~*

I Measured and Calculated Isothermal Temperature Coefficients

I

.1 Rod Unit Cycle Bank 2

5 D

2 6

D 1

7 D

1 8

D 1

9 D

Rod Unit Cycle Bank 1

8 D

Extended Burnup Model ITC pcm/°F Position (steps)

Boron Meas.

Cale.

202 1493

-7.85

-9.09 216 1669

-5.86

-7.00 202 1532

-6.01

-7. 71 204 1513

-7.90

-8.50 203 1766

-4.46

-6.31 Mean Standard Deviation CELL Model ITC pcm/°F Position (steps)

Boron Meas.

Cale.

204 1513

-7.90

-4.55 Page 4 - 8 Diff.

1.24 1.14 I. 70 0.60 1.85 1.31 0.50 Diff.

-3.35 I

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I 4.3 Doppler Coefficient Benchmarking NFU-0039 Revision 2 May 28, 1991 Section 3.3 established Doppler coefficient and Doppler defect reliability factors based on Doppler tests performed during the early cycles of Salem unit 1 and 2.

These tests have not been performed for the cycles considered in the benchmark of the extended burnup model.

The results reported in reference 12 show that Doppler coefficients calculated by EPRI-CPM2 can be up to 203 larger than those calculated by EPRI-CELL.

Based on the lack of direct data for the cycles of interest and the results reported in reference 12, a different approach was used to derive the reliability factors for the extended burnup model.

The investigations of reference 12 showed the differences between EPRI-CELL and EPRI-CPM2 was attributable to the U-238 resonance calculations and the observed decrease in the difference with exposure to be attributable to the Pu-240 contribution which was calculated the same by both codes.

Further investigations into the calculation of the U-238 resonance integral were made in reference 12 utilizing the Hellstrand measurements.

These results showed that the change in the resonance integral from 900°K to 300°K was calculated closest to measurement by EPRI-CELL and EPRI-CELL2/ENDF/B-V with the CELL being lower and the CELL2 being slightly larger than measurement.

Results reported in reference 13 compared the Doppler coefficient as calculated by the Continuous Monte Carlo code, MCNP-3A, to be very close to those calculated by EPRI~CELL2/ENDF/B-V. From these investigations, it is concluded that; 1) the "true" value of Doppler most probably lies between EPRI-CELL and EPRI-CELL2/ENDF/B-V, 2) CPM2 most probably over predicts the Doppler coefficient and defect compared to EPRI-CELL and measurements, and thus 3) a bias/reliability factor different than the traditional 03 bias/10%

reliability factor, is warranted for the CPM2 model.

Page 4 - 9

NFU-0039 Revision 2 May 28, 1991 For the Salem cores, a typical BOC core average exposure is = 14 GWD/MTU and the cycle length is= 17.5 GWD/MTU or an average EOC exposure of= 32 GWD/MTU.

Using this and the data from reference 12, the following table is constructed:

3.9 U-235 w/o Fuel Pin Doppler Worth Exposure EPRI-CELL CELL2/ENDF/B-V CPM2 CPM2 x.8 14

.0091

.0102

.Olll

.0089 32

.0112

.0127

.0134

.0107 The CPM2 values, which are bounding on the high side as calculated by the code, when multiplied by.80 are bounding on the low side. This combined with the conclusions drawn above, technically justify Doppler reliability factors for the extended burnup model of 0% / -20%.

The 0% / -20% can be restated as a 10% bias with an uncertainty of +/- 10%.

Thus:

Bias = 10%

RFDC = 10%

RFDD = 10%

Page 4 - 10 I..

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4.4 I~otopjcs NFU-0039 Revision 2 May -2a, 1991 Isotopic compositions calculated by CPM have been compared with spent fuel isotopic data obtained from Yankee and Saxton.

The reactor representation in the calculation is analogous to that used for the EPRI-CELL benchmarking described in Section 3.4. The documentation and reference list for these benchmarks is described in the ARMP documentation*

(Reference 1).

Isotopic ratios for plutonium in Yankee are compared in Figures 4.4.1-4.4.3. The abscissa is a fission-product number density assuming a yield of unity and volume averaged over the pin cell. The corresponding burnup in MWD/KgU is also shown.

The dots are experimental results and the line the CPM results.

The agreement between calculated and experimental isotopic ratios is good and comparison of Figures 4.4.1-4.4.3 with 3.4.1-3.4.3 show similar results for EPRI-CELL and CPM.

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 overpredicted.

Calculated and measured isotopic compositions for Saxton are compared in Table 4.4.1 as was presented for EPRl-CELL in Table J.4.1. The ag~eement is good for the most important uranium and plutonium jsotopes as well as for the americium and curium.

The concentrations of Np-237, Pu-238 and Pu-242 are underestimated.

Page 4 - 11

0 -"'

0

~

N a.. -

en M

N a...

NFU-0039.. I*

9.0 8.0 6.0 5.0 Figure 4.4.1 Yankee Isotopic Ratio Pu-239/Pu-240 Comparison Between EPRl-CPM and Experiment

* \\..

Revision 2 May 28, 1991 3.0---t-----t-----;-----+-----+-----1 5.0 10.0 15.0 20.0 F. P. vol. wgt. number density >< 105 25.0 3.0 0

10 20 30 MWd/kgU Page 4 - 12 I,.

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8.0 7.0 6.0 0

5.0

'*o 3.0 2.0

~

0.0 0

-~

Figure 4.4.2 Yankee Isotopic Ratio Pu-240/Pu-241 Comparison Between EPRI-CPM and Experiment NFU-0039 Revision 2 May 28, 1991

-~

~

5.0 10.0 15.0 20.0 25.0 30.0 F. P. vol. wgt number density ">< 105 10 20 30MWd/kgU Page 4 - 13

10.0 9.0

... 8.0 0

--7.0 C'O....

... 6.0

-5.0 4.0

(

0.0 0

Figure 4.4.3

. Yankee Isotopic Ratio Pu-241/Pu-242 Comparison Between EPRl-CPM and Experiment

~

\\

\\

I\\

- ~

a '

.,I NFU-0039 Revi*sion 2..

May 28, 1991 I

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5.0 10.0 15.0 20.0 25.0 30.0 I.

I F. P. vol. wgt. number density )( 105 10 20 Page 4 - 14 30 MWd/kgU **

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Table 4.4.l Isotopic Composition in Saxton NFU-0039 Revision 2 May 28, 1991 Comparison Between CPM and Experimental Data Atom.%

Experi mental Nuclide Experiment Uncertainty %

(CPM-Exp)/ExpxlOO U-234 0.00465 28.7 15.9 U-235 0.574 0.9

-0.3 U-236 0.0355 5.6 2.8 U-238 99-.386 0.0 0.0 Pu-238 0.109 2.2

-11.4 Pu-239 73.77 0.0

-0.3 Pu-240 6.29 0.3 0.4 Pu-242 0.579 0.9

-16.0 Atom Ratios Experimental Nuclide Experiment Uncerta_i nty %

(CPM-Exp)/ExpxlOO Np-237/U-238

'1.14*10-4 15.0

-26.4 Pu-239/U-238

4. 383*10-2 0.7 0.2 Pu-238/Pu-239

1. 75*10-3 0.4

-9.8 Am-241/Pu-239 I. 23*10-2 15.0

-10.6 Cm-242/Pu-239 I. 05*10-4 10.0 0.0 Cm-2.44/Pu-239 I. 09*10-4 20.0 0.0 Page 4 - 15

NFU-0039..1 Revision 2 May 28, 1991"'

4.5 Reljabjljty factors for Delayed Neutron Parameters The discussion presented in Section 3.5 is applicable to the extended*

burnup model and therefore, a 4% reliability factor will be applied to the I

I delayed neutron (RFB) and effective neutron lifetime (RFL) parameters.

~

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I 4.6 p~wer Distribution Benc.hmarkjng NFU-0039 Revision 2 May 28, 1991 A_ total of 25 flux maps were chosen for the purpose of benchmarking the extended burnup model. A description of reactor conditions for each flux map chosen is given in Table 4.6.1. for each cycle three full power maps, BOC - MOC - EOC, and several reduced power maps were chosen for benchmarking.

. Typical comparisons of measured and ca 1. cul ated detector s i gna 1 s are shown in Figures 4.6.1 through 4.6.9. The figures are in sets of three, as was presented in Section 3.6, and are representative of the various core exposures.

For each statepoint, the first figure of the set presents the difference between the measu*red and predicted s i gna 1 i ntegra 1 s for a 11 instrumented lo~ations. The second and third figures of each set present axial comparisons in two specific instrumented locations.

Figures 4.6.10 through 4.6.12 shriw the CELL based model results for the Salem 1 Cycle 8 statepoint.

The statistical analysis for the extended burnup model was performed in a conservative manner compared to the CELL model results presented in Section 3.6. *For the extended burnup model, the entire difference between measured and predicted reaction rates was taken as a model error arid no axial bias was used.

Thus, Table 4.6.2 lists no axial bias for the extended burnup model.

The statistics for the extended burnup model are shown in Tables 4.6.3 and 4.6.4 for various subgroups of the population as was done in Section 3.6.

A comparison of Tables 4.6.3/4.6.4 with 3.6.6/3.6.7 illustrates the similarities in overall power distribution capability of the two models.

Figures 4.6.13 through 4.6.15 show a comparison of the confidence limits as reported in Section 3.6 with the confidence limits calculated for the Page 4 - 17

0 NFU-0039..1 Revision 2 May 28, 1991...

extended burnup model (labeled as PSCPM).

All extended burnup model confidence limits fall below the reliability factor lines (RFFQ and RFFDH).

Thus, all reliability factors are the same for both models.

The extended burnup model reliability factors are:

RFFQ

= 0.10 p :!!:.50

= 0.16 - (0.12xP) p <.50 RFFDH

= 0.08 p ~.30

= 0.09 - (P/30) p <.30 Page 4 - 18 I

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I Map No.

2501 2504 2508 2514 2601 2602 2603 2604 2605 1701 1703 1708 1714 1719 1720 1801 1802 1805 1811 1816 "

1901 1902 1905 1910 1916 Table 4.6.l Reactor State Points NFU-0039 Revision 2 May 28, 1991 for the Extended Burnup Model Benchmarking Salem 2 Cycle 5 Cycle Exposure Power Level D Bank Posit fon (MWD/MTU)

(%)

(steps) 9 26.1 182 338 100.0 228 3316 99.7 228 9210 90.l 211 Salem 2 Cycle 6 5

20.l 173 13 43.6 186 127 98.4 228 1043 99.3 228 2069 99.8 228 Sal em 1. Cycle 7 0

23.4 169 245 99.7 227 4749 100.0 227 10210 70.3 187 15237 99.5 228 15963 80.7 228 Salem 1 Cycle 8 3

20.0 181 13 43.9 197 2364 100.0 228 6597 99.7 228 12381 99.8 228 Salem 1 "cycle 9 4

19.7 163 24 46.0 182 1048 100.1 228 5869 100.1 228 11356 98.7 224 Page 4 - 19

1 2

3 4

5 6

7 8

9 10 11 12 13 14 15 R

p

-1. 2

-1.3

-0.4 0.1

-0.6

. 1-c NFU-0039

Revision 2 May 28, 1991..

Figure 4.6.1 Measured and Calculated Integrated Detector Responses SALEM 1 Cycle 7 Map 1708 Absolute Differences Power =.100%

Exposure = 4749 MWD/MTU N

M L

K J

H G

F E

D c

-2.0

-1.6

-1.4

-0.9

-3.7

-4.2

-0.9 1.2 0.5

-0.1

-2.6 1.3 1.2

-1.0 0.6 0.8 2.5 1.9

-2.5 2.7 1.5 1.1 0.0 II 2.3 2.2 II 2.3 3.0 0.4

1. 7

-0.9 1.0

-1.6

-1.5

-0.6 0.4 2.0

-0.3

-0.6

-0.2 Page 4 - 20 B

A

-0.6

1. 7

-1.5 I

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I* **

I Q)

(/) § 2.0 0..

(f)

Q) 0:::

I-1.5 0

-+---'

u Q)

-+---'

Q) 0 Q) 1.0

-+--'

0 0.5 Q) 0:::

Figure 4.6.2 Measured and Calculated Detector Responses SALEM l Cycle 7 Map 1708 100% Power, 4749 MWD/MTU Thi mb 1 e. Ll 0 Predicted Measured 0

NFU-0039 Revision 2 May 28, 1991 0.0 LJ__J_J._L-.L-J'---'--J'---'--JL.l-J--'---L--'---L--'--L...L..L-'-'-.i.-L-'-'-J_J_JL.l-JL.l-J-1-l--'---L--'---L--'--L--'--L...L..L-'-'-.L.L...L.l......L....1-.L..J-'-'-'-'-L-.L..I 15 20 25 30 35 40 45 50 55 60 Axial Points 0

5 1 0 Page 4 - 21

<D (f) c 2.0 0

Q_

(f)

Q) 0::::

L 1.5 0

-+-'

u

<D

-+-'

<D 0

<D >

-+-'

0

<D 0::::

1.0 0.5 Figure 4.6.3 Measured and Calculated Detector Responses SALEM 1 Cycle 7 Map 1708 100% Power, 4749 MWD/MTU Thimble. N13 Predicted Measured 0

NFU-0039, Revision 2 May 28, 1991

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0.0 ~~~~~~~~~~~~.........._~~~~~~.........._~~~.........._

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0 5

1 0 15 20

. 25 30 35 40 45 50 55 60 Axial Points Page 4 - 22 I

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-1.8 5

6 I

7 8 0.2 I

9 0.8

1 10 11 -0.7 I

12 13 I

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I Figure 4.6.4 NFU-0039 Revision 2 May 28, 1991 Measured and Calculated Integrated Detector Responses SALEM l Cycle 8 Map 1811 Absolute Differences Power = 99.7%

Exposure = 6597 MWD/MTU N

M L

K J

H G

F E

D c

B A

-2.5

-2.2

-3.2

-3.8 0.1 0.3

-0.9 0.6

-3.0 4.2 0.3

-0.8 2.9 8.1

-0.6 3.1 2.8

-2.2

-2.9 4.6 6.0 6.7

-0.5 -1.1 -0.7 2.4 6.6

-1.6 2.0 2.7

-2.3 2.4

-3.3 0.7

-0.8

-2.9

-4.8

-1. 2

-2.l

-3.6

-3.l

-1.6 Page 4 - 23

NFU-0039.1 Revision 2, May 28, 1991..

Q) if)

§ 2.0 Q_

if)

Q) 0::::

Figure 4.6.5 Measured and Calculated Detector Responses SALEM 1 Cycle 8 Map 1811 99.7% Power, 6597 MWD/MTU Thimble. LIO Predicted Measured 0

o.o~~~~~~~~~~~~~~~~~~~~~~~

0 5

10 15 20 25 30 35 40 45 50 55 60 Axial Points Page 4 - 24 I

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1 2

3 4

5 6

7 8

9 10 11 12 13 14 15 R

p

-2.3

-2.5

-1.8 0.7

-0.5 l

NFU-0039. I Revision 2 May 28, 1991~

Figure 4.6.7 Measured and Calculated Integrated Detector Responses SALEM 1 Cycle 9 Map 1916 Absolute Differences Power= 98.7%

Exposure = 11356 MWD/MTU N

M L

K J

H G

F E

D c

-0.3

-3.2

-3.9 Jl

-4.3

-0.1 0.6

-0.6

-2.3

-1. 2

-1.6

-2.3 0.2

-0.5 2.8 2.6 2.4

-2.1 5.6 6.3 1.0 -1.1 5.5

1. 7

-0.2 5.5 0.1 1.5 4.3 0.4 JI

-0.5 2.5 0.9 0.0

-0.2

-2.1 0.6

-0.l

-1.4

-1.0

-1.1

-2.3 Page 4 - 26 B

A

-1.1

-1. 7

-1.4

-0.0 I -,

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Q)

(f) c 0

()_

(f)

Q) 0:::

~

0

+-'

u Q)

+-'

Q) 0 Q)

+-'

2.5 2.0 1.5 1.0 0 0.5 Q) 0:::

Figure 4.6.8 Measured and Calculated Detector Responses SALEM 1 Cycle 9 Map 19i6 98.7% Power, 11356 MWD/MTU Thimble. LIO Predicted Measured

0.

NFU-0039 Revision 2 May 28, 1991 0.0 L...J.._J--'--L--'--1......J......L....J.._J._L..J.....J.--'--1.........__._...__._J_J_J--'--L--'--'--'--'-.L.J.._J--'--L--'--1......J......L.....L....J..._L...J.._J--'--L....c.J.....J......L....J-.L.._J_J_J'--'--L--'-L..........._..l..-.J....J 0

5 1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 4 - 27

I Figure 4.6.9 Measured and Calculated Detector Responses SALEM 1 Cycle 9 Map 1916 98.7% Power, 11356 MWD/MTU Thimble N13

.1 NFU-0039 Revision 2..

May 28, 1991 1-1 2.5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I I

Q) if) § 2.0 Q_

if)

Q) er:

L 1.5 0

-+-'

u Q)

-+-'

Q) 0 1.0 Q)

+-'

0 0.5 Q) er:

Predicted Measured 0

-TT'T-TTTTTTrl

, r r r 1 l r-r-r I r--,

0.0 "-'--'--'-'-'-'--'-'-~~~~~-'-'---'---'--~~~~~~-'-'-~~~~--'-'-'-'--'-'---'---'--~~~

0 5

1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 4 - 28 I

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2 3

4 5

6 7

8 9

10 11 12 13 14 15 R

p 1.6 4.3 2.2 3.1 Figure 4.6.10 NFU-0039 Revision 2 May 28, 1991 Measured and Calculated Integrated Detector Responses SALEM 1 Cycle 8 Map 1811 Absolute Differences Power = 99.7%

Exposure = 6597 MWD/MTU EPRI-CELL Based Model N

M L

K J

H G

F E

D c

B A

1. 7

-0.1

-1.0

-2.7

-1.4 1.3 1.9 1.8

-4.6 0.3

-1.8

-0.6 2.0 3.3 1.4 0.7

-2.3

-2.4

-2.1 1.0 0.7 2.0

-2.1 0.2 1. 7 I

II

-2.5 2.5

-1.4

-2.3 D

-4.4

-1.0

-4.7

-1.6 0.1

-0.6

-4.7 2.1

-0.4

-0.5 1.0 1.3 3.5 Page 4 - 29

Q)

(fJ 6 2.0 Q_

(fJ Q) 0::::

L 1.5 0

-+-'

u Q)

-+-'

Q) 0 Q)

-+-'

0 Q) 0::::

1.0 0.5 Figure 4.6.11 Measured and Calculated Detector Responses SALEM 1 Cycle 8 Map 1811 99.7% Power, 6597 MWD/MTU Thimble LIO EPRI-CELL Based Model Predicted* Measured 0

NFU-0039 Revision 2 May 28, 1991 0.0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0 5

1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 4 - 30

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Figure 4.6.12 Measured and Calculated Detector Responses SALEM 1 Cycle 8 Map 1811 99.7% Power, 6597 MWD/MTU Thimble. N13 EPRl-CELL Based Model NFU-0039 Revision 2 May 28, 1991 2.5 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

. Q)

. (/)

§ 2.0 Q_

(/)

Q) 0:::::

L 1.5 0

-+--' u Q)

-+--'

Q)

.o Q)

-+--'

1.0 0 0.5 Q) 0:::::

Predicted 0

Measured 0.0 ~__.__................ _._.__,_._~__.__..~_,_._._._.__.__.._._,_~._._.__.__................ _._._~..___.__.__.__.._._,__._.__,_._._._.__.__................ _._._~

0 5

1 0 15 20 25 30 35 40 45 50 55 60 Axial Points Page 4 - 31

Axial Level Table 4.6.2 Mean Observed Differences Axial Model Bias Extended Burnup _Model Mean Diff Axial Level Mean Diff No Axial Model Bias For Extended Burnup Model Page 4 - 32 I

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Reactor Power P<30 40~P~80 P>90 P>90 P>90 P>90 P>90 P>90 P>90 P>90 P>90 P>90 Table 4.6.3 Confidence Limits for X(I,K,M) Distribution by Subgroup for the Extended Burnup Model NFU-0039 Revision 2 May 28, 1991 95/95 Confidence Limits Cycle Axial Number Std Non-Exposure Regions Samples Dev Normal Parametric all 1 - 6 7668 0.067 0.110 0.128 a 11 1 - 6 7681 0.045 0.074 0.088 all 1 - 6 23126 0.039 0.065 0.074 E<2.5 1 - 6 10664 0.040 0.065 0.061 2.5~E<6 1 - 6 4681 0.036 0.059 0.077 6~E 1 - 6 7781 0.041 0.068 0.082 all 1

2984 0.040 0.066 0.086 all 2

3730 0.048 0.079 0.080 all 3

4476 0.035 0.058 0.067 all 4

3730 0.034 0.056 0.062 all 5

4476 0.037 0.061 0.061 all 6

3730 0.042 0.070 0.077

. Page 4 - 33

Reactor Power P<30 40~P~80 P>90 P>90 P>90 P>90 Table 4.6.4 I

NFU-0039 Revision 2 ~II May 28, 1991...

Confidence limits for X(l,M) Distribution I

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by Subgroup for the Extended Burnup Model 95/95 Confidence Limits Cycle Number Std Non-Exposure Samples Dev Normal Parametric al 1 251 0.033 0.062 0.075 all 247 0.025 0.045 0.070 all 745 0.022 0.037 0.047 E<2.5 343 0.022 0.040 0.031 2.5~E<6 151 0.020 0.038 0.065 6~E 251 0.025 0.046 0.063 Page 4 - 34 I

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I

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--1-------

I I

I

(/)

+-'

0.18 0.16 0.14

-~ 0.12

_J Q)

~- o:-ro-Q)

"D

~ 0.08 0 u 0.06 0.04 0.02 Figure 4.6.13 Confidence Limits For X{I,K,M) vs Reactor Power Normal Non-Parametric PSEG RFFQ PSCPM-Non Parametric PSCPM-Normol NFU-0039 Revision 2 May 28, 1991 o.ooL-~~---'--~~~-'--~~---.J'---~~---'--'-~~--'---~~--L~~~-'--~~____J 0

25 50 75 100 Reactor Power %

Page 4 - 35

(/)

+--'

E

_J Q) u c Q)

-0

~

c

o u

NFU-0039 Revision 2

I May 28, 1991..

Figure 4.6.14 Confidence Limits For X(I,K,M) vs Axial Height 0.14.-----------------------------------,

0. 12 I-0.10 0.08 -

0.06

~

0.04 ~

0.02 I-Normal

Non-Parametric PSEG RFFQ PSCPM -

Non Parametric PSCPM -

Normal I

,,,,,,,,---------------~

~-------

~------________,,,'

________________...A--------..:-----:----

I I

I 0.00 '----'------'---'-----'--'---'---'-----'--'----'-----'---'-----'--'---'---'------'--'----'-----'---'-----'--'----

0

2 3

4..

5 6

7 8

9 10 11 12 Ax i a I Height (Feet)

Page 4 - 36 I

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I 0.10 2 0.08

.E QJ

~ 0.06 QJ.

-0 c

0 u 0.04 0.02 0.00 0

Figure 4.6.15 Confidence Limits _For X(I,M) vs Reactor Power Normal Non-Parametric PSEG RF FL>H PSCPM -

Non Parametric PSCPM -

Normal 25 It.

50 Reactor Power %

Page 4 - 37 75 NFU-0039 Revision 2 May 28, 1991 100

I..

NFU-0039 Revision 2 May 28, 1991

~

5 REFERENCES I *

1. Advanced Recycle Methodology Program (ARMP) System Documentation CCM-3 I

I I

I,.

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., 0. J. Marlowe and C. J. Pfeifer, "HARMONY: System for Nuclear Reactor Depletion Computation", WAPD-TM-478, Westinghouse Electrjc Corporation, January 1965.

4.

Walpole, R. E., R. H. Meyers, "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.

6.

USNRC Regulatory Guide 1.126, "An Acceptable Model and Related Statistical Methods for the Analysis of Fuel Densification", March 1978.

7.

Somerville, P. N., "Tables for Obtaining NonParametric Tolerance Limits",

Annals of Mathematical Statistics 29, 599 (1958}.

8. Assessment of the Assumption of Normality (Employing Individual Observed Values}, ANSI Nl5.15-1974.

9.

Safety Evaluation of the PSE&G Rod Exchange Methodology, NFU-004; Revision 2, August 22, 1984.

10. Deleted, Not Applicable to Revision 2

11. ARMP-02 Documentation P~rt. II, Chapter 6 - CPM-2 Computer Code, Volumes 1-3, EPRI NP-4574-CCM, April 1987.

Page 5 - 1 II I

. NFU-0039 Revision 2 May 28, 1991

12. Evaluation of Discrepancies in Assembly Cross-Section Generator Codes, EPRI NP-6147, Volumes 1 & 2, July 1989; Volume 3, February 1990.

13. ENDF/B-V Doppler Evaluations, Eighth Semi-Annual Meeting of RPSUG, Richmond VA, November 17-18, 1988.

Page 5 - 2 I

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I APPENDIX A Statistical Methods for the Deter*ination and Application of Uncertainties Page A - 1

. NFU-0039 Revision 2 May 28, 1991

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NFU-0039 Revision 2

May 28, 1991 ~

APPENDIX A Statistical Methods for the Deter*ination and Application of Uncertainties The purpose of using statistical methods i_s to compute the value XR such that there is a 95% probability at the 95% confidence level that XR will be conservative with respect to Xr (true value) when applying the calculation methods to safety related reactor analyses.

The first step is to determine whether or not a distribution is normal.

If it is, the methods described in Section A.I are used.

If the distribution cannot be treated as normal, but the distributions are known, then the methods described in Section A.2 are used.

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A.l Appljcatjon of Normal Pistrjbutjon Statjstjcs Treatment of Measurement and Calculational Uncertaintjes NFU-0039 Revision 2 May 28, 1991 Comparison of measured and calculated !eactor 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 following definitions:

X T = true reactor parameter X M = measured reactor parameter Xe = calculated reactor parameter.

eM ::: X M X T = measurement. error ee =Xe -

XT= calculation error eMc = X M X c = observed differences

µi ei = mean error (i = M, C, or MC)

I ai (N~ 1 :E(ei-µi) 2 )2= standard deviation If eM and ec are independent, then the following relationships exist.

(Note that these relationships apply for non-normal distributions as well).

a~e a~ + a~

(A-1)

Page A - 3

NFU-0039 Revision 2 May 28, 1991 (A-2)

These equations can be solved for ac and Pc*

Once ac and Pc are calculated from historical data they can be used to apply conservatism to future

. calculations of reactor parameters, XR, as follows:

The factor Kc is defined as described in Table A.I to provide a 95%

probability at the 95% confidence level that XR is conservative with respect to the true value, Xr~

Alternatively, as done in most instances in this 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:.

or 02 c 0 C =

C1 MC (A-3)

(A-4)

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I In the later alternative, once aHc and IJMc are calculated from historical data they can be used to apply conervatism to future calculations of

~

reactor parameters, XR as follows:

x R = x c +

µMC :I: RF where Page A - 4 (A-5)

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NFU-0039 Revision 2 May 28, 1991 The quantity IJ.Mc is used as a bias on the calculated parameter and Kc is as defined above.

The term RF is called the reliability factor as described below.

Reljabjljty Factors It is the objective to define reliability factors which are to be used to increase of 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 distribution~

to find a Kc which will give a 95% probability at the 95% confidence level to the reliability factor defined by Numerical values of Kc for various sample sizes used to calculated Uc are provided on Table A.I {Reference 5).

Page A - 5

Table A.I Single-Sided Tolerance Factors N

Kc 2

26.26 3

7.66 4

5.14 5

4.20 6

3.17 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 I. 76 CID 1.645 N = Number of samples used to calculate ac Page A - 6 NFU-0039 Revision 2 May 28, 1991 I..

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I A.2 Appljcatjon of Non-Normal pjstrjbutjon Statjstjcs NFU-0039 Revision 2 May 28, 1991 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 (Xr) 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 toleranie 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 J.&Hc = eHc was determined, where eHc = XH - Xe.

(See Section A.l for definitions). Next, the population of N errors eHc - J.&Hc was computed, and the resulting distribution ordered.

Using Table A.2, the mth value of the error distribution defines error eR, for which, at the 95% confid~nce level, 95% of the error distribution will be less than eR.

Once eR and J.&Hc are calculated from historical data they can be used to apply conservatism to future calculatjons of the reactor parameter, XR, as follows:

x R x c +

µMC +/- RF (A-6) where Page A - 7

NFU-0039 Revhion 2 May 28, 1991 The term RF is the relability factor which provides the desired 95%

probability at the 95% confidence level for the computed par*ameter X.

Page A - 8 I..

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I Table A.2 Values of m for 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 NFU-0039 Revision 2 May 28, 1991 For n > 1000: Increase m by 4 for each additional 100 observations Page A - 9

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I APPENDIX B Computer Code Summary Description Page B - 1 NFU-0039 Revision 2 May 28, 1991

Computer Code CPM EPRI-CELL INTEGRAL NU PUNCHER Computer Code Su11111ary Description Description NFU-0039 Revision 2 May 28, 1991 CPM is a multigroup two-dimensional collision probability code for depletion and branch calculations for a single assembly. (Ref. 1)

EPRI-CELL computes the space, energy and burnup dependence of the neutron spectrum within cylindrical cells of light water reactor fuel rods.

It is u~ed to generate cross sections for PDQ on a ECDATA file.

(Ref. 1)

INTEGRAL edits PDQ files to obtain pin and assembly powers.

Pin to box ratios are then imput to TRINODE.

NUPUNCHER prepares HARMONY cross section tables from cross section data on an ECADATA file. (Ref. 1)

PDQ7/

PDQ7/HARMONY is a nuclear reactor analysis program HARMONY SHUFFLE SIGMA which solves the neutron diffusion equations and performs depletion calculations. (Ref. 2, 3)

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. (Ref. 1)

SIGMA calculates the predicted detector reaction rates using nodal power distribution and PDQ7 detector reaction rate to assembly power factors.

The predicted detector reaction rates are then compared to measured detector reaction rates.

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Computer Code TRI NODE Computer Code Sunlilary Description Continued Description NFU-0039 Revision 2 May 28, 1991 TRINODE is a modified version of the EPRl-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 f) Neutronic data tables instead of curve fits TAU TAU is a computer code used to compute statistics from residual reaction rates generated by SIGMA.

PSCPM PSE&G modified CPM code for depletion and branch calculations for single assembly.

CPM modified for intergral fuel burnable poison rods, IFBAs, and PLtNK BLINK linking to the linking codes listed belo~.

PLINK prepares PDQ/HARNONY cross section tables from PSCPM punch file.

BLINK prepares TRINODE neutronic input tables from PSCPM punch files.

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ML18096A119

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