ML20096C358

Qualification of Reactor Physics Methods for Application to Monticello

ML20096C358
Person / Time
Site:	Monticello
Issue date:	10/16/1995
From:	Bonneau C, Dean D, Matis L NORTHERN STATES POWER CO.
To:
Shared Package
ML20096C357	List: ML20096C354 ML20096C358
References
NSPNAD-8609-A, NSPNAD-8609-A-R03, NSPNAD-8609-A-R3, NUDOCS 9601170268
Download: ML20096C358 (93)

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S UNITED STATES g

Ig NUCLEAR REGULATORY COMMISSION 2

8 WASHINGTON D.C. 205S0001

%[ Ol.o September 11, 1995

)

Mr. Roger 0. Anderson, Director Licensing and Management Issues Northern States Power Company 414 Nicollet Hall l

Minneapolis, Minnesota 55401

SUBJECT:

MONTICELLO NUCLEAR GENERATING PLANT - REVIEW 0F TOPIC NSPNAD-8609, REVISION 2, " QUALIFICATION OF REACTOR PHYSICS METHODS FOR APPLICATION TO MONTICELLO" (TAC NO. M90277)

Dear Mr. Anderson:

By letter dated August 23, 1994, the staff review and approval, a Revision 2 of the Topical Report NSPNA

" Qualification of Reactor Physics Methods for Application to Monticello."

This submittal

'ccribes the new qualification of new methods based on CASMO-

~

3/ SIMULATE-3, for application to operations and reload safety evaluations for the Monticello plant.

The staff has reviewed the submittal and concluded that the application of CASM0-3/ SIMULATE-3 is acceptable for use in the Monticello boiling-water reactor reload analyses. Details of our review are provided in the enclosed safety evaluation.

This action closes TAC No. M90277.

questions concerning this action please call me at (301) 415-1392.If you have any Sincerely, g

f Tae Kim, Project Manager Project Directorate III-I p

Division of Reactor Projects - III/IV Office of Nuclear Reactor Regulation Docket No. 50-263

Enclosure:

Safety Evaluation cc w/ encl: See next page

)

l

)

O Mr. Roger 0. Anderson, Director Northern States Power Company Monticello Nuclear Generating Plant

)

cc:

8 J. E. Silberg, Esquire Adonis A. Neblett Shaw, Pittman, Potts and Trowbridge Assistant Attorney General 2300 N Street, N. W.

Office of the Attorney General Washington DC 20037 445 Minnesota Street Suite 900 U.S. Nuclear Regulatory Commission Resident Inspector's Office St. Paul, Minnesota 55101-2127 8

2807 W. County Road 75 Monticello, Minnesota 55362 Plant Manager Monticello Nuclear Generating Plant ATTH: Site Licensing Northern States Power Company 2807 West County Road 75 Monticello, Minnesota 55362-9637 Robert Nelson, President Minnesota Environmental Control Citizens Association (MECCA) g.

1051 South McKnight Road St. Paul, Minnesota 55119 Commissioner Minnesota Pollution Control Agency 520 Lafayette Road St. Paul, Minnesota 55119 g

Regional Administrator, Region III U.S. Nuclear Regulatory Commission 801 Warrenville Road Lisle, Illinois 60532-4351 Commissioner of Health Minnesota Department of Health 717 Delaware Street, S. E.

Minneapolis, Minnesota 55440 Darla Groshens, Auditor / Treasurer Wright County Government Center 10 NW Second Street 8

Buffalo, Minnesota 55313 Kris Sanda, Commissioner Department of Public Service 121 Seventh Place East Suite 200 St. Paul, Minnesota 55101-2145 2

.,y im e

go oco

' [

1 UNITED STATES n

E f

NUCLEAR REGULATORY COMMISSION k'ff(o8 WASHINGTON, D.C. 2055HC01

• ..,+

SAFETY EVALUATION BY THE OFFICE OF NUCLEAR REACTOR REGULA RELATING TO REVISION 2 0F TOPICAL REPORT NSPNAD-8609 "00ALIFICATION OF REACTOR PHYSICS METH00S FOR APPLICATION f.QE NORTHERN STATES POWER COMPANY MONTICELLO NUCLEAR GENERATING PLANT DOCKET NO. 50-263 1.0 JNTRODUCTION By letter dated August 23,1994 (Ref.1), the Northern States Power Company (N$P) submitted Revision 2 of the Topical Report NSPNAD-8609, " Qualification of Reactor Physics Methods for Application to Monticello," (Ref. 2) for NRC review.

for the Monticello Nuclear Generating Plant.NSPNAD-8609, Rev. 1-A describes capability of NSP to implement and apply new methods, based on CASM0-This revision design activities for the Monticello unit.3/ SIMULATE-3 methodology, to boiling Both the CASM0-3 and SIMULATE-3 computer program packages have been reviewed and accepted for referencing regarding the Yankee Atomic Electric Company (YAEC) Topica (Ref. 5 and YAEC-1659 (Ref. 6.

Specific limitations imposed on the use of these ms)dels at that time were):

1) that CASMO-3 is to be used for the core parameter ranges and configurations that were verified; i.e., new fuel designs will require additional validation, and

2) that SIMULATE-3 is to be used for steady-state physics analyses only with the approved versions of the CASH 0-3 and TABLES-3 codes.

NSP intends to use the CASM0-3/ SIMULATE-3 programs in licensing applications, including BWR reload physics design, calculations for startup predictions, generation of physics input for reload safety evaluation (RSE) analyses, core physics data books and setpoint updates for both the reactor protection and monitoring systems.

2.0

SUMMARY

OF THE TOPICAL REPORT Topical Report NSPNAD-8609, Revision 2, describes the NSP qualification of new reactor physics methods BWR and addresses the rea(ctor model description, qualification andCASM0-ENCLOSURE

)

O

, quantification of reliability factors and applications to operations and reload safety evaluations of Monticello.

The qualification benchmarking S:

compares the CASMO-3/ SIMULATE-3 model results with measurements obtained from benchmarking data covering operating cycles 11 through 15 of the Monticello unit. The plant analyses were performed over a wide range of conditions from cold (ambient) temperature to hot full power operation. The good agreement between the measured and calculated values presented in the topical report is used to validate the NSP application of _these computer programs for analysis of the Monticello BWR unit.

9!

NSP intends to use these methods for steady-state BWR core physics reload design and licensing applications, including fuel bundle and loading pattern analysis; for the generation of core physics control rod worth and startup predictions, reactivity coefficients for transient and safety analyses input; and for the potential support of the process computer core monitoring system.

2.1 Overview Section 1 of the topical report provides introductory and background J

information and an overview of the scope of the report. The philosophy for determining the calculational uncertainties (and bias) and reliability factors is presented in Appendix A of the topical.

2.2 Methodoloav 3

Section 2 of the topical report describes the NSP-specific CASMO-3/ SIMULATE-3 computer program package methodology, provides references for each of the individual components, and gives a flowchart for the model application.

CASM0-3 is the Studsvik Energiteknik lattice physics code (Ref. 7) used by NSP in determining the neutronics input to SIMULATE-3 for BWR core performance analyses.

CASMO-3 uses a binary-format cross section library based on the standard ENDF/B-IV cross-section set with some ENDF/B-V fission spectrum updates.

SIMULATE-3 was also acquired from Studsvik of America (Ref. 8). The code is based on a modified coarse mesh (nodal) diffusion theory calculational g:

technique, with coupled thermal hydraulic and Doppler feedback. The code includes the following modeling capabilities:

solution of the two group neutron diffusion equation, fuel assembly homogenization, baffle / reflector modeling, cross-section depletion and pin power reconstruction.

In order to ensure the flux continuity at nodal interfaces and perform an accurate determination of the pin-wise power distribution, SIMULATE-3 uses assembly 4

discontinuity factors that are pre-calculated by CASM0-3. These factors are related to the ratio of the nodal surface flux in the actual heterogeneous geometry to the cell averaged flux in an equivalent homogeneous model and are determined for each energy group as a function of exposure, moderator density and control-rod-state.

The two-group model solves the neutron diffusion equation in three dimensions, and the assembly homogenization employs the flux discontinuity correction factors from CASM0-3 to combine the global (nodal) flux shape and the assembly 4

l

- heterogeneous flux distribution.

The flux discontinuity concept is also applied to the baffle / reflector region in both radial and axial directions to

)

eliminate the need for user-supplied albedoes, normalization, or other adjustment at the core / reflector interface.

The SIMULATE-3 fuel depletion model uses tabular and functionalized without tracking the individual nuclide concentrations. macroscopic and/

)

effects are calculated by CASM0-3 and then processed by the TABLES-3 codeDep (Ref. 9) for generation of the cross-section library used by S.IMULATE-3.

SIMULATE-3 can be used to calculate the three-dimensional pin-by-pin power distribution in a manner that accounts for individual pin burnup and spectral effects. SIMULATE-3 also calculates control rod worth and moderator, Doppler and xenon feedback effects.

)

ESCORE is an Electric Power Research Institute (EPRI) developed computer code (Ref.10) for predicting best-estimate, steady-state fuel rod performance parameters for light-water reactor (LWR) fuel rods. This program has been previously reviewed and approved (Ref.11) for use in calculating fuel rod temperatures for input to reload and safety analyses as a function of burnup and power history.

)

2.3 Benchmarkino and Model Verification Section 3 of the topical report discusses benchmarking of the NSP models to the five operating cycles which provided measured plant data from a range of plant startup and normal operation conditions.

)

2.4 Model Acolications for Reactor Operatina Suonort Section 4 of the topical report discusses the application of the NSP models to both predictive and plant monitoring modes.

2.5 Model Acolications to Safety Evaluation Analyses

)

Section 5 of the topical report describes the methods used to apply the reliability factors and biases to calculational physics results for safety applications.

3.0 TECHNICAL EVALUATION

3 Backaround The previously approved YAEC topical report (YAEC-1363) for CASM0-3 applications included a detailed description of the neutronics modeling methodology together with the YAEC validation of the code system.

The basic nuclear cross-section data, unit cell calculation, two-dimensional transport theory and diffusion theory calculations, and the determination of flux discontinuity factors for use in SIMULATE-3 were described.

J' D

~

9

. The original CASHO-3 validation was carried out by the code developer -

Studsvik Energiteknik. This benchmarking included the calculation of a set of S

pin-cell critical experiments, with varying pin radius and pitch, and fuel enrichments.

The YAEC validation was based on comparisons with measured critical experiments, measured fuel isotopics, and measured pin-wise La-140 distributions. These comparisons were intended to exercise and validate the i

depletion calculation, the spatial transport calculation and the nuclear data library.

The fuel depletion calculation was validated by comparisons with the Yankee Core-1 and Zion measured uranium and plutonium isotopics which are industry-standard benchmark sources.

These comparisons were performed for a range of pin-cell spectra and indicated good agreement for the fuel isotopics versus burnup. As further validation, a set of uniform critical measurements were also calculated.

CASMO-3 reproduced 74 criticals to within I percent delta-k/k.

The comparisons were analyzed as a function of rod pitch, fuel enrichment, H 0/U-ratio, soluble boron, buckling and moderator temperature, g

and no significant dependence of the calculation / measurement differences was observed.

In addition to the measurement benchmarks, the YAEC CASH 0-3 calculation of the Brookhaven National Laboratory (BNL) Fuel Assembly Standard Problem was compared to the BNL reference solution. Comparisons of reactivity defects, control rod worth, boron worth, fuel isotopics, and pin-wise power distributions were made. The agreement was found to be very good, with the 8

observed differences within the stated uncertainty of the BNL reference solution.

The previously approved YAEC topical report (YAEC-1659) for SIMULATE-3 applications focused upon three major areas.

The first was application to operating pressurized water reactors (PWRs) and included comparisons of SIMULATE-3 generated parameters to measured data, as well as to the BNL pWR g

Core Standard Problem. The second application was to operating BWRs and included comparisons to measured data. The third area focused on the pin-by-pin power distribution capabilities of SIMULATE-3.

This application compared multi-assembly SIMULATE-3 pin-by-pin power. distributions to higher order transport theory solutions.

In addition, pin-by-pin power distributions were compared between SIMULATE-3 and previously accepted PDQ-07 methods of pin power distribution calculations.

g The statistics from the cold (85'F to 209'F) zero-power comparisons quantify the model accuracy for predicting reactivity for beginning-of-cycle (80C),

xenon-free and in-cycle restart conditions.

Thirty-three measurements from the five operating cycles are included. Sixty-eight at-power statepoints with TIP [ traversing incore probe] traces are used for reactivity comparison and Si power distribution reliability factors.

The statistical analysis described in Appendix A was performed on the measured versus the SIMULATE-3 calculated reactivities and TIP reaction rates.

The sample distributions were tested for normality using standard methods.

The normality test is used since the standard 95 percent probability at the 95 percent confidence level [95/95] tolerance limit method assumes that the

'g' population has a normal distribution.

If the distributions are not normal, Ol

' but are known, a special treatment (Appendix A) allows equivalent 95/95 statistics to be generated.

conservatively bounded.

Parameters not covered by the above are Control rod worths The SIMULATE-3 prediction of control rod worths was compared by NSP with the BOC zero-power startup measurements for the five operating cycles.

standard deviation and the normality of the difference distribution A

SIMULATE-3 capability to predict the shutdown margin with the worst stuck rod The was qualified by comparison to local critical measurements as well as in-sequence rod withdrawal criticals.

Assembly power distribution distributions were verified at NSP by comparison with direc measurements. A total of 68 incore detector TIP) statepoints were taken at close to Hot-Full-Power (HFP) conditions from(Cycles 11 through 15.

detector, assembly location, and radial level to determine the m The standard deviation for the observed differences. The 95/95 tolerance limits I

for assembly peaking factors were calculated from multiplying the standard deviations by the k-value corresponding to the sample size for all statepoint conditions.

4.0

SUMMARY

AND CONCLUSIONS Northern States Power Company (NSP has performed extensive benchmarking us comparisons / SIMULATE-3 methodology).

the CASMO-3 This effort consisted of detailed of calculated key physics parameters with the measurements obtained from five operating cycles of the Monticello BWR plant.

results were used to determine the set of 95/95 (probability / confidence)

These tolerance limits for application to the calculation of the stated BWR physics parameters.

This effort also demonstrated the ability of NSP to use the CASMO-3/ SIMULATE-3 computer program package for application to the Monticello BWR unit.

Based on the analyses and results presented in the topical report, the staff concludes that the CASM0-3/ SIMULATE-3 methodology as validated by NSP can be applied to steady-state BWR reactor physics calculations for reload applications as discussed in the above technical evaluation.

)

this methodolo The accuracy of applications, gy has been demonstrated to be sufficient for use in licensing and transient analysis inputs, startup and control rod worth predic core monitoring system support.

As in the earlier approvals, application of the approved package is limited to the range of fuel configurations and core design parameters verified and referenced by this topical report; introduction of significantly different

)

fuel designs may require further validation by the licensee.

Principal Contributor:

E. Kendrick Date:

September 11, 1995

)

a;

. )

~

i

5.0 REFERENCES

Si

1. Letter from R. O. Anderson (NSP) to Document Control Desk (USNRC),

regarding " Revision 2 of Topical Report NSP-8609, ' Qualification of Reactor Physics Methods for Application to Monticello'," dated August 23, 1994.

2. NSPNAD-8609, Rev 2, " Qualification of Reactor Physics Methods fo~ r Application to Monticello," Northern States Power Company, August 1994.

g

3. Letter from A. C. Thadani (USNRC) to G. Papanic, Jr. (YAEC), regarding

" Acceptance for Referencing of Topical Report YAEC-1363, 'CASMO-3G Validation'," March 21, 1990.

4. Letter from A. C. Thadani (USNRC) to G. Papanic, Jr. (YAEC), regarding

" Acceptance for Referencing of Topical Report YAEC-1659, ' SIMULATE-3, g.

Validation and Verification'," February 20, 1990.

5. YAEC-1363, "CASMO-3G Validation," Yankee Atomic Electric Company, April 1988.

i

6. YAEC-1659, " SIMULATE-3, Validation and Verification," Yankee Atomic l

Electric Company, September 1988.

e

7. M. Edenius, A. Ahlin, B. H. Forssen, "CASM0-3, A Fuel Assembly Burnup Program, User's Manual, Version 4.4," STUDSVIK/NFA-89/3, Studsvik Energiteknik AB, Sweden, November 1989. [ Proprietary - Not publicly available]

8. K. S. Smith, J. A. Umbarger, D. M. Ver Planck, " SIMULATE-3, Advanced Three-S' Dimensional Two-Group Reactor Analysis Code, User's Manual, Version 3.0,"

STUDSVIK/SOA-89/03, Studsvik of America, Inc., November 1989. [ Proprietary

- Not publicly available]

9. K. S. Smith, J. A. Umbarger, D. M. Ver Planck, " TABLES-3, Library Preparation Code for SIMULATE-3, User's Manual, Version 3.0," STUDSVIK/SOA-89/05, Studsvik of America, Inc., November 1989. [ Proprietary - Not publicly available]

10.

"ESCORE - The EPRI Steady-State Core Reload Evaluator Code:

l General Description," EPRI-NP-5100, February 1987.

11.

Letter from A. C. Thadani (USNRC) to C. R. Lehmann (Pennsylvania Power 8

and Light Co.), regarding " Acceptance for Referencing of Licensing Topical Report EPRI-NP-5100, 'ESCORE - The EPRI Steady-State Core Reload Evaluator Code: General Description'," May 23, 1990.

l

.. i e

c

.,9 UNITED STATES NUCLEAR REGULATORY COMMISSION f

j wAsmNGTON. D. C. 20555 W

• ...*p I

ENCLOSURE 2.'

SAFETY EVALUATION BY THE OFFICE OF NUCLEAR REACTOR REGULATION RELATING TO NORTHERN STATES POWER COMPANY TOPICAL REPORT MSPNAD-8609

" QUALIFICATION OF REACTOR PHYSICS METHODS FOR APPLICATION TO MONTICELLO" NORTHERNSTATESPOWERCOMPANJ MONTICELLO NUCLEAR GENERATING PLANT: !

DOCKET NO. 50-263

1.0 INTRODUCTION

By letter dated October 2,1986 (Ref.1), the Northern States Power Company (NSP) submitted for review NSPNAD-8609, "Oualification of Reactor Physics Methods for Application to Monticello." The report describes the reactor model 'and qualification, cuantificatidn of reliability factors, and

' applications to operations and reload safety evaluations for the Monticello Nuclear Plant (Monticello). The infomation in this report was supplemented -

by infomation submitted with Reference 8 in response to questions from the NRC staff and consultants. The review by the staff of this report and supplemental infomation was perfomed with the' assistance of consultants from Brookhaven National Laboratory (BNL).

NSP intends to perfom the reload and transient calculations required for the.

operation of Monticello and, in support of this effort, has developed its own reactor physics methodology. The NSP steady state neutronic and themal-hydraulic methodology is based on two widely used codes: CASMO-II (Ref. 2) for the generation of lattice physics parameters and NDF (Ref. 3) for three-dimensional neutronic/themal-hydraulic simulation. NDH is a derivative of the FLARE-based EPRi-NODE-B program (Refs. 4 & 5). Normalization parameters and adjustment factors used in the three-dimensional calculation are derived frcm PDQ7/ HARMONY (Refs. 6 & 7). Model verification and reliability factor

~ ', :. :

• O determination are presented in,the report along with a discussion of the i

statistical methods used in the determination and application of uncertaint. es.

Applications of the NSP steady state calculational redel to reactor operatien and safety analysis are also outlined.

9 2.0 REPORT

SUMMARY

The CASMO-II and NDH codes are the principal MSP calculational tools for performing reload analyses and for determining input to transient The HSP application of these codes, the model verification, and calculations.

detennination of reliability factors, are briefly described in the following report summary.

2.1 CASMO-II O

CASM'0-II is used to derive the lattice physics constants which are needed for CASMO-II is a multigroup two-input to the three-dimensional code NDH.

dimensional transport theory code which calculates fuel assembly parameters such as reactivities, pin powers, reaction rates and nuclide concentrations at S

The code provides the standard assembly-averaged two-group' every.bursup step.

This code js also used in the generation of macroscopic cross section sets.

constants needed "in PD0/ HARMONY for deriving normalization parareters for N and generic'adustment factors for local peaking factor generation.

9 2.2 NDH A modified

~

This code is an expanded version of the FLARE-based EPRI-NODE-B.

The key input parameters in NDH f

one-group theory model is used in this code.

2 O !

These are the neutron multiplication. K-infinity and the migration area, M.

f parameters are derived from detailed energy and space-dependent calculations) for each fuel assembly type and are entered in the nodal calculation as a

~

function of coo'lant voids and exposure, including the effects of control, The fuel assemblies are coupled coolant temperature, Doppler and xenon.

O together in NDH using a transport kernel which is a function of the migration

3 area and the nodal mesh spacing. The transport kernel plays an important role in the nodal calculations since it, along with the local multiplication and leakage factors, is used by the code in the calculation of the three-dimensional power distribution. The code calculates the transport kernel in sach node in the horizontal and vertical directions using input constants which are selected such that the results of the basic model calculations are normalized to a more accurate caleviati.on such as PD0 or to measured data.

The inlet flow distribution is calculated by EPRI-THERM-B (Ref. 5) in the void iteration loop.

This code calculates the thermal hydraulic parameters of the core including flow distribution, subcooling, void and quality distributions based on total core power, recirculation flow, power distribution, and feedwater flow and temperature. Since the coolant flow distribution thrcugh the core is influenced by the void content and the power level, an iterative calculation is required to determine the power and flow distribution.

L.

The flow distribution is obtained by equalizine the pressure drop across each channel. This-calculation starts with an initial guess for the coolant velocity in each chiinnel ind the pumphead requirements,'and proceeds iteratively until coolant velocity converges' within a specified tolerance.

~

The process is repeated for each channel. When a distribution is obtained for all of the chanoels, all individual channel flows are sumed and compared to

~

the total core flow. The calculation is complete when the sumed flow is within a specified tolerance of the total core flow.

2.3 Model Verificat. ion and Reliability Factor Detemination The CASM0/NDH model has been benchmarked against Monticello measured data obtained during Cycles 7 through 10. Core reactivity, radial and axial power distributions evaluated at various statepoints spanning four operating cycles, and comparisons with measured data are presented.

Results of gama scan comparisons for selected assemblies at the end of two cycles are also provided. The derivation of reliahility factors and biases for the basic l

O I

~

j

^

4 O

safety parameters such as minimum critical power ratic, linear heat generatien rate, void and Doppler coefficients and delayed neutron parameters has been based on the above benchmarking. The model reliability factor for calculating power distributions is based on comparisons of measured and predicted traversingincereprobe(TIP) signals. The latter are corrected by.the process computer to account for detector' sensitivity, drift and background effects. Reliability factors have been detemined for local pin powers as well as for total bundle powers and are applied to the calculation of the linear heat generation rate (LHGR), the average planar linear heat generation.

,j rate (APLHGR) and the critical power ratio (CPR).

3.0 EVALUATION 9

3.1 Modeling Nuclear constants for the three-dimensional code NDH are derived from CASMO-II. These constants include infinite neutron multiplication, migration areas 'and' fission rates. The calculation of the Doppler reactivity effect in 9

each node is based on a square root of fuel temperature dependence with appropriate power and moderator density corrections. These representations are known from past reviews "to be suitable' for the analyses intended to be carried out with NDH. Exposure and void-dependent input reactivities allow the evaluattorr of nodal exposure effects. Nodal exposure is updated with each e

The nodal exposure step using the nodal power at the start of the step.

calculation accounts for control rod history effects. This exposure and local reactivity modeling in NDH is sufficiently detailed for core follow and reload-analyses and is acceptable.

O.

~

The NDH model has been nomalized to the Monticello Cycles 7 through 10 measurement data. Albedos and mixing factors used in simulating nomal operating conditions are based on Cycles 5 and 6 data. For cold shutdown conditions the albedos and mixing factors are d'etemined from Cycles 7 through O

10 measurements. These determinations are acceptable.

O S4 w

e

I.

o t

5 s

)

The review concludes that the NSP CASM0/NDH modeling, adepted from well known and/or previously reviewed methodology components, provides an acceptable.

calculation package for use in Monticello three dimensional steady state core analyses.

)

3.2 Qualification of Nethodoloey The steady state BWR methods summarized in NSPNAD-8609 have been verified and qualified with measured data obtained during four cycles of operation of the

)

Ponticello plant. The qualification process covered both cold zero power and het operating conditions.

In addition.the performance of the code was verified against gamma scan measurements made on selected discharged fuel assemblies at the end of Cycle 8 (EOC-B) and at EOC-9.

)

Cold Reactivity The NDH cold model has been verified with cold critical measured data from

[j Cycles 7 through 10, at core average exposures ranging from about 10 to about' 16 GWd/MTU and moderator' temperatures in the range from 97 to 172'. F.

Of the

)

22 cold critical measurements performed 14 were of the in-sequence type while eight were of the few-rod type.

~

The NSP results show that the cold NDH nodel is capable of calculating cold

)

, reactivities within 0.5% with a standard. deviation of about 0.2%.

Hot Reactivity A total of 56 statepoints spanning the operation of Cycles 7 throuch 10 of

)

Monticello were calculated using the NDH code. The resultant hot critical k-effective was in the range from 0.988 to 0.966. Most of the statapoints represented hot full power operation. Some coastdown operating data was also included in the analysis. The mean hot eigenvalue (k-effective) was 0.992 with a standard deviation of about 0.2%.

)

o D

o 6

e' It is seen from the NSP results that NDH underpredicts the core reactivity by less than 1% with a standard deviation of about 0.2%.

Power Distribution Uncertainties and Reliability Factors Comparison of measured TIP distributions with NDH-simulated TIP read'ings provides a measure of the ability of the NDH code.to match observed power shapes.

In the qualification of the NSP CASM0/HDH model, TIP sets representing 44 statepoints spanning four cycles and spread over a core average exposure range of 0.1 to 7.6 GWd/MTU were calculated and compared with corresponding

~

e measured data. However, in the evaluation of the uncertainties associated with the calculation of power distributions, selected TIP readings have been eliminated from the statistical analysis. The deletion of this data is based on the observation that this data results in the largest calculation / measurement differences. With the deletion of these NDH/TIP comparisons, the NDH power

1. l distribution calculational uncertainty is 4.75. NSP provides an alternate analysis in Reference B in response to questions in which the NDH calculational uncertainty is determined to be 4.3%. 'In this second analysis it is assumed (following a discussion presented in Reference 9) that the TIP measurement g;

a uncertainty is one-half the measured TIP asymetry.

Since it has not b'een demandtrated that the TIP measurement uncertainty is one-half the TIP measurement asymetry, and since sufficient justification for the j

8' deletion of the largest calculation / measurement TIP comparisons has not been provided, the, quoted 4.3% calculational uncertainty and resulting power distribution reliability factor are considered to be unacceptable.

It is therefore required, until such time as the elimination of some of the TIP readings is acceptably justified and approved, that all TIP comparisons be included in the determination of the NDH power distribution calculation uncertainties and resulting APLHGR, LHGR and MCPR reliability factors. This will increase the CPR, APLHGR and LHGR reliability factors from 8.1,11.1% and 11.1 to 9.5,12.3 and 12.3%, respectively.

l 0

l l

.,I 1

7 Accuracy of the Methodology and Uncertainties The validity of the CASM0/NDH model was tested by comparing results of calculations with measured data from a broad range of operating states. These states provide a suitable data base for determining NDH uncertainties in predicting basic core parameters. Based on the calculation-to-measurement comparisons for these states, it is concluded that the NSP predictions of cold reactivity are accurate to within 0.5% with a standard deviation of about 0.2%

and the het reactivity predictions are accurate to within about 1% with a standard deviation of about 0.2%. As discussed above, the approach used in determining the uncertainties associated with the calculation of power distributions has been found to be inadequate. However, NSP has agreed that the uncertaintier and reliability factors assigned to APLHGP, LHGR. and MCPR bdll, for the present, be' based on the entire data base including the eliminated TIP data. The only direct use of the reliability factors in reload safety analysis calculations is for the fuel bundle misloading and control rod withdra,wal events, which are done with " steady state" methods. These analyses will use the increased values.

=

Applications The report briefly discusses the approaches to be taken in using the

' reliability factors in application of the~ CASP0/NDH methodology to reactor operations, including prediction and monitoring of relevant parameters, and to safety analyses. However, it was not the intent of the report to describe such procedures or methods in detail, and the review thus simply notes,that-the approach is reasonable, and in the case of startup reactivity predictions, the results are satisfactory. A formal review in this area, presumably related to safety analyses or monitoring (if NSP elects to support the installed GE monitoring system), would have to be in connection with a full submittal of the relevant methodology or its qual.ification.

e O

O p.

e..

se

• • e op

I

?.y *.:

9 g.

s 9

\\

l 5.

Advanced Recycle Methodology Program (ARiiP) System Documentation, EPRI CCM-3 Research Project 118-1 September 1977.

6.

W. R. Cadwell, "PDQ-7 Reference Manual," WAPD-D4-678, Westinghcu:;c Electric Corporation, January 1967.

e s

7.

R. Breen, O. Marlowe, and C. Pfeifer, " Harmony: System for Nuclear Reactor Depletion Computation," VAPD-TM-478 Westinghouse Electric Corporation, January 1985.

e 8.

Letter from D. Musolf, NSP, to Director of Nuclear Reactor Regulation, USNRC, " Additional Infonnation to Support the Submittal of NSPNAD-860F andHSPNAD-8609," September 29, 1987.

O 9.

EPRI Feport NP-1278, "On-Line Nuclear Power Distribution Measurement,"

l

~

Appendix A.

6 9

9 e

O

'l i

.e I

o J

.O MONTICELLO NUCLEAR GENERATING PLANT J

QUALIFICATION OF REACTOR PHYSICS METHODS

.O FOR APPLICATION TO MONTICELLO O

NSPNAD-8609-A Revision 3 i

October 1995

O Principal Contributors 2

Anthony Bockelman, NSP Clifford Bonneau, NSP

^

David Dean, NSP lO Keith Dehnbostel, NSP 1

Thomas Iseman, NSP William Lax, NSP Ryan Maas, NSP 4

Michael Miller, NSP Peter Pankratz, NSP Richard Rohrer, NSP Ralph Rye, NSP Richard Streng, NSP

O Scott Vanevenhoven, NSP 1

l lO MA(j/d v w Date/O/s/

Prepared by David W.

Dean, Principal Engineer

/

Reviewed by

1. 8 J ^r-M Date /8 A!#7

. O C11 or A: g,onneau, Pro 7ssManager 7

(

[O /b I

Approved by Date Louis P.

Matis, Director Fuel Resources

//

'O NS PNAD-8609-A Rev. 3 Page 1 of 76

O O'

ABSTRACT This document is a Topical Report describing the Northern States Power Company O

(NSP) qualification of reactor physics methods for application to the Monticello Nuclear Plant.

This document addresses the reactor model description, qualification and quantification of reliability f actors and applications to operations and reload safety evaluations of the Monticello plant.

O LEGAL NOTICE i

This report was prepared by or on behalf of Northern States Power Company (NSP).

It is intended for use by NSP personnel only. Use of any information, apparatus, method, or process disclosed or contained in this report by non-authorized g

personnel shall be considered unauthorized use, unless said personnel have received prior written permission from NSP to use the contents of this report.

With respect to unauthorized use, neither NSP, nor any person acting on behalf of NSP:

a.Makes any warranty or representation, express or implied, with respect to the j

accuracy, completeness, usefulness, or use of any information, apparatus, method j

or process disclosed or contained in this report, or that the use of any such gl information, apparatus, method, or process may not infringe privately owned j

rights; or i

b. Assumes any liabilities with respect to the use of, or for damages resulting from the use of, any information, apparatus, method, or process disclosed in the report.

O O

,Q O

NSPN AD-8609-A Rev. 3 Page 2 of 76

D TABLE OF CONTENTS PAGE B

1.0 INTRODUCTION

6 2.0 GENERAL CHARACTERISTICS OF THE NSP CALCULATIONAL MODEL 6

3.0 MODEL VERIFICATION AND RELIABILITY FACTOR DETERMINATION.

9 3.1 Control Rod Worth 11 3.2 Temperature Coefficient 18 3

3.3 Void Coefficient 18 3.4 Dopoler Coefficient 20 3.5 Isotooics 20 3.6 Power Distribution Reliability Factor Determination.

20 3.6.1 Local Power Distribution 20 3.6.2 Intearated Power Distribution.

24 3.6.3 Gamma Scan comparisons 25 3.6.4 Standard Power Distribution Comparison 25

]

3.6.4.1 Axial Power Distribution Comoarisons 25 3.6.4.2 Radial Power Distribution Comparisons.

26 3.6.4.3 Nodal Power Distributions Comparisons 26

)

3.7 Delaved Neutron Parameters 26 3.8 Effective Neutron Lifetime 27 4.0 MODEL APPLICATIONS TO REACTOR OPERATIONS 55 4.1 Predictive Aeolications 55

{}

4.1.1 Cold criticals 55 4.1.2 Hot Full Power Criticals 55 4.2 Monitorina Aeolications 56 4.2.1 Process Computer 56 4.2.2 Isotopic Inventory 56 5.0 MODEL APPLICATIONS TO SAFETY EVALUATION CALCULATIONS 60 5.1 Linear Heat Generation Rate (LHGR and APLHGR) 60 5.2 Critical Power Ratio (CPR) 60 g

5.3 Control Rod Worth 60 5.4 Void Reactivity 61 5.5 Fuel Temperature (Doooler) Coefficient 61 5.6 Delaved Neutrons 61 5.7 Prompt Neutron Lifetime.

61

6.0 REFERENCES

62

)

APPENDIX A Statistical Methods for the Determination and Application of Uncertainties 66 A.1 Aeolication of Normal Distribution Statistics 67 A.2 Application of Non-Normal Distribution Statistics.

70 APPENDIX B Computer Code Summary Description 76 O

e O

NSPN AD-8609. A Rev. 3 Page 3 of 76

.. _. _..... _ _ _ _ - ~ _

O LIST OF TABLES TABLE TITLE PAGE O.

3.0.1 Reliability Factors for Monticello.

10 3.1.1 Measured to Calculated Rod Worth comparison 12 3.3.1 EOC Coastdown Statepoints 19 3.6.1 Full Power Statapoints.

28 3.6.2 Axial Power Distribution Comparison 30 3.6.3 Radial Power Distribution Comparisons 31 3.6.4 Power Distribution Standard Deviations in 20 Axial Planes 32 4.1.1 Few Rod and In-sequence Cold Criticals.

57 O

A.1 Single-Sided Tolerance Factors.

69 O

i t

9 4

0!

O O

el O

NSPNAD-8609.A Rev. 3 Page 4 of 76

.. ~ - -. -.. _ ~

- -. -. -.... - -......... - - - -. ~.. -. - - -. -....

T i

t) i LIST OF FIGURES t

IO FIGURE DESCRIPTION pag 1 2.0.1 Flow Chart: CASMO-3/ SIMULATE-3 Model.

8 3.1.1 Control Notch Worth Inventory Versus Exposure Cycle 11 13 3.1.2 Control Notch Worth Inventory versus Exposure cycle 12 14 3.1.3 Control Notch Worth Inventory Versus Exposure Cycle 13 15 3.1.4 Control Notch Worth Inventory Versus Exposure Cycle 14 16 3.1.5 Control Notch Worth Inventory Versus Exposure Cycle 15 17

()

3.6.1 Measured and calculated Detector Responses BOC Cycle 11.

33 3.6.2 Measured and Calculated Detector Responses MOC Cycle 11.

34 3.6.3 Measured and calculated Detector Responses EOC Cycle 11.

35 3.6.4 Haasured and Calculated Detector Responses BOC Cycle 12.

36 3.6.5 Measured and Calculated Detector Responses MOC Cycle-12.

37 3.6.6 Measured and Calculated Detector Responses EOC Cycle 12.

38 3.6.7 Measured and Calculated Detector Responses BOC Cycle 13.

39 3.6.8 Measured and calculated Detector Responses MOC Cycle 13.

40

' ()

3.6.9 Measured and Calculated Detector Responses EOC Cycle 13.

41 3.6.10 Measured and Calculated Detector Responses BOC Cycle 14 42 3.6.11 Measured and Calculated Detector Responses MOC Cycle 14.

43 3.6.12 Measured and Calculated Detector Responses EOC Cycle 14.

44 3.6.13 Measured and calculated Detector Responses BOC Cycle 15.

45 3.6.14 Measured and calculated Detector Responses MOC Cycle'15.

46 3.6.15 Measured and Calculated Detector Responses EOC Cycle 15.

47 3.6.16 Observed Differences Density Function Comparison.

48 3.6.17 Cumulative Distribution Function (CDF) Comparison 49

()

3.6.18 CDF in the Region of the 95th Percentile Model Comparison 50 3.6.19 Observed Differences Density Function Integrated Reaction Rates Comparison.

51 3.6.20 Cumulative Distribution Function (CDF) Integrated Reaction-Rates Comparison.

52 3.6.21 CDF in the Region of the 95th Percentile For Integrated Reaction Rates.

53 C).

Standard Deviation vs Measured Instrument Response.

54 3.6.22 4.1.1 Cold Criticals versus Core Average Exposure 58 4.1.2 Hot criticals 59

- C)

C)

O O

NSPN AD-8609-A Rev. 3 Page 5 of 76

()

1.0 INTRODUCTION

This report addresses the reactor model description, qualification and quantification of reliability factors, applications to operations and GD reload safety evaluations of the Monticello Nuclear Plant (Mnt).

This model, based on the Studsvik CMS system of codes, can be used as a substitute for the CASMO/NDH methods previously approved for use (Reference 2).

Adoption of the methods described here does not preclude the use the earlier CASMO/NDH methods as needed.

A summary description of the computer codes is given in Section 2.

This report stresses the aspects of implementation of the NSP model; the q) individual code descriptions are referenced in Appendix B.

Whenever possible, directly observable parameters (such as reactor critical k,and measured incore detector fission rates) are utilized.

The Mnt data used in this evaluation span cycles 11 through 15.

In order to be completely objective in the choice of data to be used for the comparitons, all Mnt cycles 11 through 15 measurements were reviewed and qualified prior to initiating the comparison calculations.

gp After the measured data to be used in the benchmark process had been defined, the model calculations were performed and comparisons are presented in this report as part of the quantification of the NSP model calculational uncertainties and reliability factors. A statistical approach was used to derive the uncertainties.

These uncertainties are consistent with the model application procedures and methodology.

The uncertainties are evaluated by direct comparison to experimental data.

In order to provide a continuing verification of the conservatism of the reliability factors determined by Mnt cycles 11 through 15 data, ongoing comparisons are made each cycle using the statistical methods described in this report. A discussion of the reliability factors is provided in Section 3.

gg The methods for use of the model and the reliability factors are described relative to reactor operation and reload safety evaluation in Sections 4 and 5.

2.0 GENERAL CHARACTERISTICS OF THE NSP CALCULATIONAL MODEL II The Monticello (Mnt) calculational model based on the Studsvik system of codes, is very similar to the calculational model previously approved for use by Yankee Atomic Electric Company for use with Vermont Yankee (see References 4, 5,

and 6), and is similar in many respects to the model previously approved for use with Mnt (see Reference 2).

A flow diagram of the Monticello model is shown in Figure 2.0.1.

The code acronyms used in these figures are defined in Appendix B.

In general, the CASMO-3" program is used to generate the lattice II physics parameters for input to SIMULATE-3n.2 MICBURN-3 is used to model gadolinia containing fuel pins and provides homogenized Gd cross sections for input to CASMO-3.

CASMO-3 produces fission product nuclide concentrations, depletion and product chain data, pin power distributions, microscopic and macroscopic cross sections, and other nuclear data input to TABLES-3'8 TABLES-3 constructs tables of these nuclear data as functions of local state variables (e.g. water density, fuel temperature etc.) for input to SIMULATE-3.

. gp SIMULATE-3 is a three-dimensional, two-group steady state reactor j

neutronic and thermal hydraulic simulator.

This simulator is used to generate eigenvalues, power distributions, and incore instrument predictions for use in reload safety evaluations, plant support, reload j

NSPN AD-8609 A Rev. 3 Page 6 of 76

.m 1

design, fuel management, and benchmark comparisons.

ESCORE s, Sit,is is an EPRI computer code for steady state fuel performance i

)

analysis.

The Monticello methodology uses ESCORE for fuel temperature l

predictions to be used as input to MICBURN-3, CASMO-3, and SIMULATE-3 l

for modeling fuel temperature related effects on the nuclear data (i.e.

l Doppler coefficient and power defect).

The S3 POST" program summarizes SIMUI. ATE-3 results including the measured and predicted incore reaction rates.

SPM, an NSP developed code, then combines all the statepoints to calculate overall uncertainties.

)

l The computer code descriptions are summarized in Appendix B.

).

l l

l I

I i

)-

l I

j l'

f l

J l

I i

~

I l

l 1

i J

NSPNAD-8609 A Rev. 3 Page 7 of 76 j

l-l

O Figure 2.0.1 Flow Chart: CASMO-3/ SIMULATE-3 Model e

e ESCORE

> MICBURN-3 y

> CASMO-3 v.

e TABLES-3 y

e

> SIMULATE-3 4-Plant Measured Data y

e S3 POST V

e SPM e

• l NSPN AD-8609-A Rev. 3 Page 8 of 76

-.. ~. -.... -. -.

- ~.

~.

. ~.. _ -. -

C) 4 3.0 MODEL VERIFICATION AND RELIABILITY FACTOR DETERMINATION The NSP models have been benchmarked against Mnt measurements made

()

during cycles ll:through 15 for the CASMO-3/ SIMULATE-3 model to quantify g,

the reliability factors to be used in safety related calculations.

The resultant reliability factors and biases are summarized in Table 3.0.1.

The remainder of this section is a detailed account of the derivation of 4

3 these factors.

The term reliability factor (RF) is used to describe the allowances to be used in safety related calculations to assure conservatism. The

' C) uncertainty factor (lo) is used to describe the actual model accuracy.

The reliability factor is always larger than the uncertainty factor.

The term king is used to describe the statistical difference between an observed or measured distribution and the calculated value.

Appendix A describes the statistical methods used in the evaluation of the uncertainties in the following sections.

j

()

During each cycle, measured and calculated parameters will be compared in order to verify and update the reliability factors determined in this section.

Results of the verification and an update for each parameter will be documented in the reload safety evaluation for the reload in which the updated values will be used. The updates to the reliability factors will be in accordance with the methods outlined in this section

)

and in Appendix A.

i O

O O

' C)

() '

C)

NSPNAD-8609-A Rey,3 Page 9 of 76

O TABLE 3.0.1 Reliability Factors for Monticello O

Parameter Reliability Reliability Bias Factor Factor (expressed as (expressed an applied)

%)

APLHGR RFm * *124 12.4 0

0 LHGR RFm =.124 12.4 0

MCPR RF,pp =.095 9.5 0

Rod Worth RF,ons =.10 10.0 0

Void Coefficient RFyoins =.10 10.0 0

0 Doppler coefficient RFro, =.10 10.0 0

Delayed Neutron Parameters A

RF =.04 4.0 0

4 D

RF, =.04 4.0 0

l Ol O

O

'O l

O NSPN AD-8609-A Rev. 3 Page 10 of 76

_ ~

1*

3.1 Control Rod Worth control rod worth in a BWR cannot be directly measured.

Control rod t

)

worth can be inferred from various reactor critical conditions.

The approach taken is to benchmark the NSP model to these critical conditions. The data base includes 9 few rod criticals and 24 sequence criticals taken at temperatures ranging from 85 'F to 209

'F.

This data represents the actual critical statepoints in cycles 11 through 15.

All measured statepoints at temperatures below the boiling point of 212 'F i

have been included. The results of the comparisons are shown in Table 3.1.1.

The standard deviation of the calculated k,y at the critical positions 1

l 1s.0027.

This difference includes the measurement uncertainty as well as the calculational uncertainty. The typical amount of reactivity i

being held down by rods is on the order of 10% Ak.

Using this value we l

can calculate an uncertainty in rod worth by dividing the standard deviation by this worth, i.e.

.27% ak / 10% ak = 2.7%.

For conservatism the rod worth reliability f actor (RF ) is defined as 10%.

)

Figures 3.1.1 through 3.1.5 present graphs of control rod notch inventory versus cycle exposure for hot critical conditions for cycles l

11 through 15.

The best estimate is the predicted control rod notch i

inventory using CASMO-3/ SIMULATE-3 with the tl%AK reactivity anomaly l

shown. Measured rod notch inventory is indicated as a det for each l

statepoint. All measured values are within the tl%AK bounds.

This l

indicates the well behaved prediction of the model and supports the use

)

of the conservative rod worth reliability factor used above.

i i

f b

l

)

J NSPN AD-8609 A Rev. 3 Page 11 of 76

- - ~.

O Table 3.1.1 Measured to calculated Rod Worth comparison cycle Notches Core Ave.

Temperature k,,

O Withdrawn Exposure

(*F)

(GWD/MTU) 11 60 12.802-85 0.9921 64 12.802 106.

0.9936 i

644 12.802 105 0.9948 394 12.802 113 0.9936 12 152 13.666 129.

0.9964 1416 13.666 128 0.9928

)

728 13.666 128 0.9938 j

734 16.922 141 0.9903 1498 19.926 206 0.9896 d

13 66 15.025 91 0.9905 106 15.025 91 0.9904 g,

978 15.025 91 0.9897 d

j 678 15.025 91 0.9908 2040 23.878 200 0.9876 1518 24.789 164 0.9851 14 108 16.683 109 0.9907 1076 16.683 111 0.9913 734 16.683 118 0.9936 108 21.252 122 0.9924 O

864 21.252 123 0.9919 738 22.494 152 0.9895 892 23.330 209 0.9905 1502 25.193 154 0.9923 1542 25.193 142 0.9920 i

15 118 16.217 108 0.9933 114 16.217 108 0.9963 (p,

984 16.217 113 0.9939 774 16.217 107 0.9963 2560 16.310 200 0.9979' 1516 16.310 147 0.9962 1632 17.833 181 0.9939 r

762 20.368 137 0.9922 702 22.419 129 0.9928 O

Mean k,g = 0.9923 o =.0027

?

OI I

I

.Q e

NSPN AD-8609-A Rev. 3 Page 12 of 76

...l

g g- _ _ - -- _ - _ g-_

Figure 3.1.1 Control Notch Worth inventory Versus Exposure Cycle 1-1 1000 i

i i

i i

i i

900 t

f-t a

i f.

y 800

'i 4

3 i

v s

?

700

+

9 i

V I

g 600 - i

-l t

?

e j

w M

l

-C

.\\

l'

-- i -

i i

500 m

o 3

i as l

J:

I o

e e

i t

i

• 400 i

+ - - -

g t

b 300

\\. -\\lq I

I Legend N.N i

e t

r

-1% Ak 200 t

s I

\\

---

Best Estimate I

100

['

7 I,

+1% Ak I

• Statepoints l

l I

0

'1 i

l 0

1 2

3 4

5 6

7 8

9 10 11 Exposure (GWD/MTU) i b

h Figure 3.1.2 Control Notch Worth Inventory Versus Exposure.

Cycle 12 1000 i

{

4 i.

I 900

}

+

800 i

z l

y 700 I

i

>e I

u

?

600 u

4 a

i y

y 9

t t

i I

Et3 e

L E

l i

500 j

m j

i a

e g

i i

o of I

o 400 -

., - i 4

i 7

z

/

~

4-,

5 i

s i

e t

2 300 -

• • /

l

-/\\/

.i Legend l

200 -

t

-1% Ak e

e I.

---

Best Estimate 100

/-

t

+1% Ak I

'\\

i j

w-

• Statepoints O

\\'

O 1

2 3

4 5

6 7

8 9

10 11 Exposure (GWD/MTU)

L 1

~

L e

O O

O'

'O O

O.

O O

O O_

O O~~

Figure 3.1.3 -

l Control Notch Worth Inventory Versus Exposure Cycle 13 j

1000 i

i.

i i

i i

900

}

t 800 z

4 z

i y,

700 t

j b

i S.

m e

I.

• 'N 600

/

?

g t

4 w

~c e

Soo

/e N..r.

e r

m e

l i

5

-m f

?---

400

/

.[.

4 i

s.

o i

u z

g.,

R l

'v f

i 3!

300

\\

Legend

-1% Ak i,

i s

200 x*

---

Best Estimate 3

\\

t 100 2.

l

+1% Ak l

k I

e statopoints l

O 0

1 2

3 4

5 6

7 8

9 10 11 Exposure (GWD/MTU) l

i Figure 3.1.4 Control Notch Worth Inventory Versus Exposure-Cycle 14 1000 9

9 i

i l

900 I.

t t

-i 5

i t

l 800 i

l 5

3 700 I

i

=

j S

A m

600

+

[

F u

M j

C i, *.\\

+

a--

500

- +

\\

i m

e t

e

.c g i i

\\.

4 tr o

400 9

i 5

y l

o a

z s

2 1

i I

a*

300

._N Legend i

I j

-- 1 % Ak 200 j

+

/

---

Best Estimate 100

'k

+1% Ak r

i-

'g.

• Statepoints 0

0 1

2 3

4 5

6 7

8 9

10 11 Exposure (GWD/MTU) j i

I

~

- '. e' o

e e

e o

e o

e' e.

o-o o

o o-o o

o.

o

,o Figure 3.1.5 Control Notch Worth Inventory Versus Exposure Cycle 15 1000 i

i i

i l

l 1'

1 900

+

i i

800 i

i i

3 3

3 700 i

4.

1 i

i i

5 m

i i

i y

600 e

... ^ -

C i

/,-

g i

i 500 6

• t-i N !-

--i f

./.

l

'3.,

i ics

'i N-ls c

d 400 - -D/

I j

l

.x;/

i i

s 1

z e.

i s

e o

i

_/'

s t

a F

./ -

300 4

Legend t

-1% Ak i

N t

200 i

---

-Best Estimate

[

I

\\

100

\\,

-N,:

+1% Ak i

\\.

'N.,*

I e Statepoints

\\

O O

1 2

3 4

5 6

7 8

9 10 11 Exposure (GWD/MTU) i

[

.__._____ - - -.--- - - - - ~ ~

()

3.2 Temperature coefficient _

The range of values of moderator temperature coefficients enco current BWR lattices does not include any that are significant from the untered in safety point of view.

The small magnitude of this coefficient, II to that associated with steam voids and combined with the lon relative time-constant associated with transfer of heat g

coolant, change insignificant during rapid transients.makes the reactivity contribution o For the reasons stated above, limits on the value of the temperature coefficient, current core design criteria do not impose design changes on the coefficient usually are not calculatedand effects of minor II 3.3 Void Coefficient The void ccefficient in a BWR cannot be directly measured, Doppler coefficient,are always present the effects of other parameters such as contro i.e.,

there xenon etc.

o s, void coefficient can be inferred, however,The magnitude of the uncertainty in the versus measured critical statepoints where the effect of the othfrom comparisons of predic db parameters is minimized.

Table 3.3.1 gives calculated values for the er measured critical statepoints from EOC coastdown for cycles 11 throu h 15.

The standard deviation of the calculated k,,'s is t g

the coastdown cases.

.0020 Ak for the average void fraction (35%)The total core reactivity held down by voids for An average tak/%av can be calculated from Table 3.3 1 whichat full power is on the ord the error in the predicted and measured value.

represents Multiplying by the average percent void gives the error in t

% Ak/% av =.0083.

% ak =.0083

• 35% = 0.29%.

d>

erms of ak.

Therefore the uncertainty in void can be calculated by dividing by the total void worth at 35% which gives 0 29%

/ 5% = 5.8% un from exposure, certainty.

xenon and Doppler.This uncertainty includes components of error 10% in void coefficient Therefore, a reliability factor of related calculation.

is deemed appropriately conservative for safety O

\\

NSPNAD-8609-A Rev. 3 Page 18 of 76 O

O Table 3.3.1 EOC Coastdown Statopoints O

Cycle Cycle Power Void k,,

Exposure

(%)

(%)

i (GWD/MTU) 11 5.624 100 34.5 1.0009 6.352 99 36.9 1.0017 6.756 92 34.3 1.0016 7.256 84 31.0 1.0015 l

-Q 7.764 74 27.6 1.0014 l

8.159 66 24.7 1.0016 l

12 5.478 100 37.8 1.0002 6.830 96 33.2 1.0004 7.148 91 32.7 0.9999 13 7.373 100' 36.7-0.9975 8.229 87 31.4 0.9970 0,

8.724 78 28.3 0.9968 9.103 71 25.7 0.9969 9.729 59 21.4 0.9969 10.165 51 18.4 0.9968 14 7.454 100 35.8 0.9992 8.237 93 33.7 0.9990 8.882 83 29.8 0.9988

'O 15 9.332 100 32.1 0.9982 10.301 91 29.8 0.9972 11.197 73 25.0 0.9960 Mean K,a =.9990 a =.0020 O

O

,O j

O O

NSPN AD-8609-A Rev. 3 Page 19 of 76

C) 3.4 Doooler Coefficient Measurements can be made in a power reactor which are directed at determining the Doppler coefficient at various power levels.

In a BWR GD the uncertainty associated with such measurements (e.g. rod repositioning, void feedback) are such that results are not reliable for direct validation of the calculational model.

Consequently, an indirect approach is taken.

The primary variable in the calculation of Doppler effects using the CASMO-3/ SIMULATE-3 model is the fuel temperature. A change in fuel temperature associated with a power change results in a reactivity GD change due to the change in the resonance absorption.

The algorithm in SIMULATE-3 that determines the model change in reactivity due to the fuel temperature change uses data calculated by CASMO-3.

The approach is to determine the accuracy of CASMO-3 in calculating the change in the resonance integral (RI) due to a known fuel temperature increase, then use engineering judgement to bound this uncertainty to assure conservatism.

gp Comparisons of CASMO-3 calculations to critical experiments (references 4, 23, 24, 25, 26, 27, 28, and 33) have determined that the uncertainty of CASMO-3 is well within the measurement uncertainty.

In view of this, a 10% reliability factor placed on the Doppler coefficient is judged adequate to assure a conservative value.

3.5 Isotonics gg The benchmarking of CASMO-3 to Yankee Rowe and Zion data is thoroughly discussed in references 4 and 36, 3.6 Power Distribution Reliability Factor Determination The purpose of this section is to discuss the methods used to determine the power distribution reliability factors. Reliability factors have gg been determined for the local fuel pin power in a node and for the total fuel bundle power. These factors can then be applied to the calculation of the linear heat generation rate (LHGR), the average planar linear heat generation rate (APLHGR) and the critical power ratio (CPR) respectively.

The statistics presented in Sections 3.6.1 and 3.6.2 follow those presented in the Prairie Island Topical, see reference 1.

gg 3.6.1 Local Power Distribution The model reliability factor for calculating power distributions is based on comparisons of measured and predicted traversing incore probe (TIP) flux detector signals for normal operating core conditions.

The signals from the detectors are corrected by the on-site process computer to account for such things as detector sensitivity, drift, and background.

It is these corrected signals, or reaction rates, which have been compared to simulated reaction rates calculated with the NSP models in order to derive model reliability factors.

The reliability factor, RF, is defined as a single value of aTPF/TPF, such that TPF, (I,J,K) times 1 + aTPF/TPF has a 95%

gg probability at a 95% confidence level of being conservative with respect to TPF. (I,J,K).

The subscripts c and m denote calculated and measured values.

TPF (I,J,K) is the total pin peaking factor for all I,J,K locations in the core. This value cannot be measured directly. What is measured by the detector system is the S

NSPN AD-8609-A Rev. 3 Page 20 of 76

.A) reaction rate in the instrument thimble. This measured reaction rate is a local value.

RR, = $It (measured).

l()

These measurements are collapsed down to 24 axial nodal values in each thimble consistent with the nodalization of SIMULATE-3.

The CASMO-3/ SIMULATE-3 model has been used to calculate the reaction rates in the instrument thimbles:

RR, = $2r(calculated). The observed difference distribution (ODD) has then been calculated by simply taking the relative difference of these two values:

ODD = ( RR, - RR,) / RR,

!C) for all measured locations in the core.

It is important to note that the ODD is not the difference between nodal powers but rather is the difference between local fission rate values.

It is assumed that the ODD is equal to ATPF/TPF,.

This is a valid assumption since the calculated and measured reaction rates are local fission rate values as is the TPF, the

()

only difference is the location.

The observed difference distribution determined above includes the uncertainties in the calculational model as well as the uncertainties in the measurement instrumentation. The calculational model uncertainty includes uncertainty in the calculation of the nodal power and in the conversion factors from nodal power to the pin power which is taken to be the same as the

()

total uncertainty in the calculated reaction rates.

Therefore, the total uncertainty in the local pin power can be written as follows:

1 RFrw " Crnss where otw33 is determined from the ODD determined above.

()

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 evaluations; see Section 5.1.

The first step is to compute the power distribution under consideration.

j The resolution used is 24 axial levels per fuel assembly.

The predicted detector signals are obtained directly from SIMULATE-3 calculated two group fluxes and fission cross sections

()

in the instrument locations.

A total of 68 core statepoints, or TIP traces, were chosen for the purpose of comparing measured and simulated in-core reaction rates for the CASMO-3/ SIMULATE-3 model. These statepoints span operating cycles 11 through 15 of Monticello.

The specific core conditions for each of the statepoints are given in Table 3.6.1.

()

Typical examples of the comparisons of measured and predicted reaction rates are provided in Figures 3.6.1 through 3.6.15.

The data is presented in sets of three figures, one set for each cycle, three TIP trace maps per cycle (BOC, MOC, EOC).

Each figure in each set presents the differences between the measured and predicted axial reaction rates for all instrumented locations in the core and the core average axial reaction rates (lower right hand corner).

()

The measurements are represented as squares at the 24 axial levels. The predicted reaction rates are shown as lines.

The distribution of observed differences between measured and calculated instrument signals for all 68 core statepoints was determined. For each trace, 2 of the 24 axial values were excluded O

NSPN AD-8609-A Rev. 3 Page 21 of 76

.. ___=.

() ~

from consideration.

These excluded values correspond to the top and bottom nodes.

These locations are areas of steep flux gradients, and small errors in instrument position result in large differences in measured to calculated values.

Since the reaction GD rates in these areas are always smaller (i.e., the high power point will never occur in the top or bottom nodes) these values were excluded from the determination of the observed differences density function. The reliability factors developed here include the measurement uncertainty as well as the calculational uncertainty.

However, known problems with the TIP measurement system such as TIP tube mislocation and channel bowing make the measurement uncertainty very large relative to the calculational GD uncertainty.

A 95%/95% confidence level was determined from the observed difference density function determined above.

The method of normalizing the calculated and measured reaction rates was used to adjust the average of all 24 detectors at the remaining 22 axial locations to 1.0.

This normalization technique was used to put the measured and predicted values on a common basis which-is consistent with the definition of the local peaking gp factors. The measurement uncertainty in core thermal power is accounted for in the transient and LOCA analysis.

All data was retained in the data base. The total number of nodal observations used was 35,904.

The total number of observations eliminated was 3,264.

All subsequent statistical' analysis has been performed using the gg methods described in Appendix A.2.

To ensure a conservative reliability factor at all power levels, the sample was divided into subsamples as a function of power (see Figure 3.6.22).

A standard deviation was calculated for each subsample using the methods described in Appendix A.2.

Figure 3.6.22 shows a distinct power dependence for the absolute difference. Therefore, to assure conservatism in the application, the reliability factor will be applied as a relative rather than an absolute value.

gg The distribution of observed differences is shown in Figure 3.6.16.

The following statistics therefore represent the total data base as described above using relative differences.

The first step using this me.thod is to determine the mean relative difference of the measured to calculated values ( me) and the standard deviation (ame):

O n}]ej pmc = "*

= 0. 002 n

O n

}[ (ej-pme) 2 cmc =

= 0. 071 where:

e; = ith observed difference n = total number of observations The second step is to transform the e3 to standard measure using NSPNAD-8609-A Rev. 3 Page 22 of 76

_J the following formulas

$)

2

=

3 omc and the resulting variates Z were then sorted into ascending order (see Figure 3.6.17).

A value of Z was chosen as an estimate of the 95th percentile of the distribution, i = 34,109.

This

,J gives the 95th percentile of 2 to be Zwo, = Qu = 1. 689 which implies that 95% of the errors are likely to be less than 1.689 standard deviations from the mean.

It remains then to calculate a 95% confidence interval on Qu using the following formula si VarQ,, = o* s = WI A ~f) g n in where:

q=

the quantile (.95)

[)

n=

number of independent observations in sample fi=

ordinate of the density function of the distribution function at the abscissa q Due to the dependence of the observed differences with axial j

height, the total number of observations was reduced by a factor of 5 to determine the total number of independent observations.

The factor of 5 was chosen to conservative bound based on the

[]

Prairie Island topical, Reference 1, value of 3.0 which is applicable to 48 axial data points rather than 24.

It is necessary to obtain an estimate of f (.95), and this was i

done by applying a linear regression analysis on a short interval of the cumulative distribution function (CDF) of Z in the region of the 95th percentile (see Figure 3.6.18).

The estimated slope of the CDF (estimated from the straight line in Figure 3.6.18) is

[]

an estimate of the ordinate density function.

The slope is calculated as 0.143.

This gives:

0.95(1-0.95)

= 0.00032 varp,3

'35904' O.143 2 o

5 o

and opss " /VdIOss = 0. 018 The estimate of the upper limit on Q is 95 c3 V

K, ons = 1. 64 5 0. 018 = 0. 029 thus:

0 NSPN AD-8609-A Rev. 3 Page 23 of 76

() l 0,5 s 1.689+0.029 GD '

The upper limit is then 1.689 +.029 = 1.718 which gives the following as the 95% confidence level that the calculated reaction rate (RR,) will be conservative with respect to the measured reaction rate (RR ).

RR, RR, ( 1 + me + (Qu + Kc on)ome)

=

c RR, ( 1 +.12 4 )

II RE,

=

Therefore orn.n =.124 with the bias absorbed into the reliability factor. Note that this value includes measurement error which adds conservatism to the calculation.

3.6.2 Intecrated Power Distribution The model reliability factors for calculating power distributions are based on comparisons of integrated measured and predicted TIP trace signals obtained from normal operating core conditions.

The reliability factor (RF) is defined as a single value of ARPF/RPF, such that RPF(I,J) calculated times 1 + ARPF/RPF, has a 95% probability at a 95% confidence level of being conservative with respect to the measured RPF(I,J).

The subscripts e and m GI will be used to denote calculated and measured values.

RPF(I,J) is the integrated peaking factor determined for all I,J locations in the core.

This value cannot be measured directly. What is measured by the detector system is the reaction rate in the instrument thimble. This measured reaction rate is a local value.

IRR, = $Er (measured).

These values are determined at each thimble b/ integrating the central 22 measured axial locations.

The three-dimensional model CASMO-3/ SIMULATE-3 has been used to GD calculate the reaction rate in the instrument thimbles.

IRR, = $Er (calculated).

The observed difference distribution (ODD) has then been calculated by simply taking the relative difference of these two values ODD = (IRR, - IRR,)/IRR, for all measured locations in the core.

GD The observed difference distribution determined above includes the uncertainties in the calculational model, the uncertainties in the measurement instrumentation, and the uncertainties in conversion factors from nodal power to instrument value.

The calculational model uncertainty includes uncertainty in the calculation of the nodal powers as well as uncertainties in the local pin powers.

Therefore the uncertainty in the local integrated pin power can be GD written as follows:

RF,ur = our.e where ong.n is determined from the ODD.

The distribution of observed differences between measured and calculated integrated instrument signals for all 68 statepoints was determined for the CASMO-3/ SIMULATE-3 model and is shown in

'O Figure 3.6.19.

The total number of integrated observations used was 1,632.

All subsequent statistical analysis has been performed using the methods described in Appendix A.2 on the entire sample.

O NS PN AD-8609-A Rev. 3 Page 24 of 76

()

The cumulative distribution function and the CDF in the region of the 95th percentile are given in Figures 3.6.20 and 3.6.21 respectively. The significant parameters calculated for this

()

distribution are as follows:

0.001 pmc

=

0.043 ome

=

1.728 Q,3

=

0.035 o

=

ps 0.058 K,a,3

=

n IRR.,5 IRR, ( 1 + 0. 07 9 )

=

O 0.079 o,p.,5

=

n where:

IRR, = Integrated reaction rate measured IRR, = Integrated reaction rate calculated For conservatism the reliability factor will remain at the value determined for CASMO-2/NDH (reference 2) as

()

RFnpg = 0.095 > o

= 0.079 ner.95 No dependence of the observed difference with position was found.

Therefore, n was not reduced.

3.6.3 camma Sean Comparisons

()

Gamma scan measurements are not available from Mnt cycles 11 through 15.

The reliability factors for the CASMO-2/NDH methods (Reference 2) were determined from TIP comparisons which bounded the gamma scan comparisons. The greater measurement uncertainties associated with neutron TIPS results in larger measured to calculated variance as compared to gamma scan.

Therefore, use of neutron TIP statistics, including the measurement uncertainty, will result in a conservative estimate of the power distribution

()

uncertainty.

Other benchmarks of the CASMO-3/ SIMULATE-3 power distribution predictions are available for gamma scan (references 4, and 35),

critical experiments (references 4, 28, 32, 33, 34, 38, and 51),

fine mesh PDQ (diffusion theory) (references 5, 37, 41, 42, 44, I

and 46), CASMO-3 color sets (references 5, 34, 41, 46, and 48),

gamma TIPS (references 5, 6, 40, and 45), and neutron TIPS r)

(references 5, 37, 38, 39, 41, 45, 47, 49, and 50).

These comparisons include both BWR and PWR type cores and geometries.

3.6.4 Standard Power Distribution Comparison The following is a presentation of the power distribution using the industry standard format.

Published power distribution data

()

is usually presented in tables of axial, radial and nodal comparisons and is usually compared at the la level.

Note that the entire data base is used.

3.6.4.1 Axial Power Distribution Comparisons Table 3.6.2 presents axial peak-to-average comparisons for selected statepoints from cycles 11 through 15.

()

The following results are taken from the entire data base presented in sections 3.6.1, 3.6.2.

Simulator to measured TIP traces rr NSPN AD-8609-A Rev. 3 Page 25 of 76

()

Unrodded Rodded n = 912 n = 720 y = 0.009 y = 0.010 a = 0.048 o = 0.052 II This data shows excellent agreement with other published data.

3.6.4.2 Radial Power Distribution Comparisons Table 3.6.3 presents radial peak-to-average comparisc7s from selected statepoints from cycles 11 SD through 15.

The following results were taken from the entire data base presented in Section 3.6.1, 3.6.2 and 3.6 3.

Simulator to measured TIP traces y = 0.001 o = 0.043 (b <

This data shows excellent agreement to other published data.

3.6.4.3 Nodal Power Distributions Comparisons Table 3.6.4 presents the nodal standard deviations for q) the 20 axial planes from the entire data base presented in Sections 3.6.1, 3.6.2.

Simulator to measured TIP traces

= 0.002 o = 0.071 This data shows excellent agreement to other published data.

3.7 Delaved Neutron Parameters This section deals with determining reliability factors for values which gg _

can be calculated but not measured.

In these cases, an argument may be 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 8.

4 The uncertainties in the calculation of 8,are composed of several components, the most important of which are listed belows gg a)

Experimental values of B, and A, by nuclide; b)

Calculation of the spatial nuclide inventory; c)

Calculation of core average B,as an adjoint-flux weighted average over the spatial nuclide inventory.

The experimental determination of the B's and Af s are assumed to be accurate to within 1%.

The most important nuclide concentrations with respect to core B are U"8, Uns and Pu '.

References 4 and 36 indicate g

D that the uncertainty in the calculation of these parameters is about 0.3% for CASMO-3. Therefore, components a) and b) above are combined as 1.3% for CASMO-3.

The uncertainty in the calculation of a core average B depends on the e

NSPNAD-8609-A Rev. 3 Page 26 of 76

GI relative adjoint-flux weighting of the individual assemblies in the core.

For demonstration purposes, consider a four region core, each with a different average burnup and average B.

This is typical of

,__)

advanced BWR cycles in that about a fourth of the core has seen three previous cycles, a fourth two previous cycles, a fourth one previous cycle and a fourth is the feed fuel.

Typical regional B's are given below l

Region 1 (fourth cycle fuel)

B = 0.00543 Region 2 (third cycle fuel)

B = 0.00581 7

Region 3 (second cycle fuel)

B = 0.00633

~

Region 4 (feed fuel)

B = 0.00745 i

The effect of errors in the calculated flux distribution can be evaluated in terms of the effect on the core average B,.

As a base case, weighting factors are all set to 1.0.

In this case, the core average B,= 0.00626.

Using a maximum error in the regional flux weighting of 7.0%, the worst orror in the calculation of the core

)

average B, is obtained by increasing the weight of the Region 1 fuel and decreasing the weight of the Region 4 fuel.

It should be noted that the average relative weighting factor is unity. The revised B is calculated as follows:

B(1) x 1.07 =.00581 B(2) x 1.00 =.00581 B(3) x 1.00 =.00633

')

B(4) x 0.93 =.00693 B=

.00622, which yields a -0.6% error for component c) above.

The sum of the errors for these four factors for CASMO is as follows:

1.3%(a+b) + 0.5%(c) = 1.8%

-1 For conservatism the reliability factor for delayed neutron parameters is set at 4%.

3.8 Effective Neutron Lifetime An argument similar to the delayed neutron parameter argument is applied to the determination of the effective neutron lifetime (/4 uncertainty.

The uncertainty components which go into the calculation of /Lare as

~,

follows:

s a)

Experimental values of microscopic cross sections; b)

Calculation of the spatial nuclide inventory; and c)

Calculation of the core average effective neutron life-time as an adjoint-flux weighted average over the spatial nuclide inventory.

Uncertainties for components a) and b) are assumed to be the same as cs described for the calculation of B,, that is, 1% uncertainty in the

'd experimental determination of nuclear cross section and.3% uncertainty in the determination of the spatial nuclide inventory for CASMO.

The core average neutron lifetime depends on adjoint flux weighting of local absorption lifetimes.

If a conservative estimate of the error in regional power sharing (7%) is used in determining the impact on the core average lifetime, the error in lifetime is on the order of 1.0%.

Combining all of these uncertainties linearly results in a total uncertainty of 1.8% for CASMO-3.

Therefore, a 4% reliability factor es will be applied to the neutron lifetime calculation when applied to

~J safety related calculations.

O NSPN AD-8609-A Rev. 3 Page 27 of 76

' C) i 1

Table 3.6.1 Full Power Statopoints Cycle Cycle Power (%)

Rod Density K,

dD.

Exposure

(%)

I (GWD/MTU) 11

.388 99.9 11.71 0.9989

.819 100.0 8.26 0.9981 1.331 99.9 8.75 0.9980 1.759 100.0 7.85 0.9981 2.251-100.0 7.71 0.9981 4D l 2.659 100.0 7.61 0.9983 3.223 100.0 7.37 0.9985 3.716 100.0 7.30 0.9980 4.128 100.1 7.23 0.9987 4.631 100.0 6.71 0.9990 5.301 99.9

-4.58 1.0003 5.624 100.0 4.17 1.0009 6.352 98.6 0.03 1.0017 (D j 6.756 92.1 0.03 1.0016 7.256 83.5 0.03 1.0015 7.764 74.0 0.03 1.0014.

8.159 66.4 0.03 1.0016 12 0.535 100.0 2.89 1.0006 1.063 100.0 3.17 0.9994 1.736 99.9 5.23 0.9988 gg i 1.945 99.9 5.23 0.9993 2.478 99.9 7.82 0.9992 2.858 100.0 7.30 0.9998 4.497 99.9 7.02 1.0000 4.880 99.9 5.54 0.9998 5.478 99.8 3.03 1.0002 6.830 95.7 0.96 1.0004 7.148 91.1 0.00 0.9999 gg 13 0.783 100.0 7.58 0.9963 1.408 100.0 8.26 0.9956 2.149 100.0 9.09 0.9952 2.672 100.0 10.47 0.9961 3.351 100.0 10.74 0.9959 3.967 99.9 10.47 0.9965 4.956 99.9 8.26 0.9966 6.165 100.0 6.06 0.9973 III 6.707 100.0 3.58 0.9976 7.373 99.9 0.00 0.9975 8.229 86.8 0.00 0.9970 8.724 77.8 0.00 0.9968 9.103 70.6 0.00 0.9969 9.729 58.9 0.00 0.9969 10.165 50.9 0.00 0.9968 l

(D 14 0.751 100.0 6.20.

0.9970 1.296 100.1 6.37 0.9962 1.977 100.0

'.02 0.9955 7

2.648 100.1 8.26 0.9958 3.325 100.1 8.68 0.9956 4.170 99.9 8.68 0.9962 5.284 100.1 8.75 0.9970 5.904 100.0 6.61 0.9969 6.530 100.0 4.58 0.9983 UD 7.454 100.0 1.89 0.9992 8.237 92.7 0.00 0.9990 8.882 82.5 0.00 0.9988 0

NSPNAD-8609 A Rev. 3 Page 28 of 76

b Table 3.6.1 Full Power Statepoints (Continued)

I Cycle Cycle Power (%)

Rod Density k,,

Exposure

(%)

(GWD/MTU) 15 0.187 99.8 7.51 0.9979 0.954 99.9 6.23 0.9963 1.790 99.8 7.92 0.9958 2.735 99.8 8.68 0.9947

)

3.591 99.7 8.95 0.9943 4.518 99.7 9.54 0.9944 5.409 99.7 9.33 0.9959 6.802 99.8 8.13 0.9971 7.636 99.8 6.30 0.9971 8.349 99.5 5.51 0.9977 9.332 99.7 2.86 0.9982 10.301 91.1 1.10 0.9972 11.197 73.4 0.00 0.9960

)

D D

D i

i B

D l

NSPN AD-8609-A Rev. 3 Page 29 of 76

_.m.

i o

Table'3.6.2 Axial Power Distribution Comparison Peak to Peak to O

Rod cycle Location Average Average

% Difference TIP Calculated 11 20-29 Out 1.185 1.143 3.5 11 28-13 Out 1.272 1.297

-2.0 12 28-29 Out 1.241 1.255

-1.1 12 20-21 out 1.182 1.192

-0.8 12 12-21 out 1.183 1.194

-1.0 13 44-29 Out 1.405 1.406

-0.1 13 12-29 Out 1.438 1.393 3.1 el 4

J 13 28-21 Out 1.155 1.153

' -0.6 14 20-29 Out 1.318 1.302 1.2 14 44-29 Out 1.256 1.231 1.9 14 12-37 Out 1.289 1.275 1.1 15 36-29 Out 1.161 1.193

-2.8 (B

15 36-37 Out 1.415 1.326 6.3 J

15 12-37 Out 1.361 1.349 0.9 11 20-37 In 1.611 1.598 0.8 12 20-21 In 1.225 1.259

-2.7 O

13 28-45 In 1.173 1.115 5.0 14 20-37 In 1.500 1.434 4.4 14 12-29 In 1.324 1.333

-0.6 7

15 28-29 In 1.195 1.181 1.1 L

0 e

)

l el e

NSPN AD-8609-A Rev 3 Page 30 of 76

s Table 3.6.3 Radial Power Distribution Comparisons

)

Cycle Location Exposure TIP Calculated

% Difference 11 20-37 0.388 1.118 1.103 1.4 11 36-13 1.331 1.151 1.185

-3.0 11 28-37 2.251 1.179 1.157 1.9 11 20-29 3.223 1.141 1.122 1.7 g

11 12-21 4.631 1.230 1.242

-1.0 11 12-29 7.764 1.228 1.176 4.2 12 36-29 1.063 1.159 1.139 1.7 l

12 36-29 2.478 1.187 1.150 3.1

)

12 12-21 4.880 1.155 1.131 2.1 12 28-21 6.830 1.131 1.199

-6.1 12 28-29 6.830 1.190 1.208

-1.6 12 28-37 7.148 1.159 1.208

-4.2 i

13 20-21 2.150 1.217 1.278

-5.0 g

13 28-37 2.672 1.136 1.149

-1.2 13 36-29 6.165 1.117 1.150

-3.0 13 36-29 6.707 1.125 1.147

-1.9 13 28-21 7.374 1.155 1.163

-0.7

)

13 28-37 10.165 1.120 1.127

-0.6 14 12-29 1.297 1.129 1.144

-1.3 14 36-29 1.977 1.117 1.168

-4.5 14 20-37 3.325 1.153 1.121 2.7 14 28-21 5.904 1.121 1.130

-0.8 g

14 28-13 7.454 1.110 1.130

-1.8 14 20-37 8.882 1.181 1.193

-1.0 15 12-29 0.954 1.111 1.168

-5.2 15 36-13 2.735 1.181 1.157 2.0 15 28-21 5.409 1.148 1.118 2.7 15 20-37 8.349 1.168 1.151 1.5 15 36-21 10.301 1.140 1.199

-5.2 15 20-37 11.197 1.233 1.201 2.6 4

9 NSPNAD-8609-A Rev. 3 Page 31 of 76

() !

i Table 3.6.4 Power Distribution Standard Deviations in 20 Axial Planes Planar Standard II ;

Planes Deviation j

3 0.062 4

0.061' 5

0.056 6

0.054 III 7

0.055 8

0.054

-9 0.056 1

10 0.060 II i 11 0.058 r

12 0.060 1

13 0.062 14 0.064 15 0.062 16 0.060 17 0.066 18 0.061 19 0.060 gg 20 0.062

~

21 0.063 22 0.074 O!

ID i OI I

l> l NSPN AD-8609-A Rev. 3 Page 32 of 76 j

m m

w

O O

O O

O O

O O

o 0

s Figure 3.6.1 Measured and Calculated Detector Responses BOC Cycle 11 S

../

2 2

34, 2

vs 1237 3037 2937 3537 4G7

?

• s g

}

?

1

?

m 429 1229 20f9 2029 M29 4429

'N

'~

N E

y

=

u 3

1

\\

m

~

9, m,

==,

2.i mi of.

g s

8 1213 20t3 30t3 38 3

.see oworr g

.3

. esse 9 2006 AVE I

STATEPOtNT1103 AT 0.3882GWDMTU l

SIMULATE-3 O

Measured

!l k

i

>i!

-f h-f " a 7

s 5

f 3

2 2

D 5

4 4

4 N

3 4,

4, 4_

1 "

09 G

e 1

S.

3 6

4 s

1 e

1 1

8 7

e 1

3 3

t 2

1 8

6 s

5 8

e 3

3, 3,

3, 3,

l s

.s cy C

C O

M

, i e

s 4

e s

n r

op S'

7 e

t 3

3 r

t 1

s e

e e

0 I.

l, r_

t, 2

e R

r O

o T

t N

c DW e

i't ll 2-t

. E

.*)*

G l

e a

1 1

c D

3

.e 4

e,d 63 d

4 e

TE d t

A Te 4

a 8

7 t

3 5

e, 1A r t

1 1L u l

1^

8 e

0 t

3 1

e u

TU s c

NM a l

I e

OI a

PS M C

ETA d

T L

n s*)

S O

2.

.i s

a d

e r

4 u

sa 3

M 1^

e, 7

9 1

3 2

e 2

2_

2, 1

1 t

t 2

f E 6

3 eru e:

g 4

iF t - i r:-

y9Es > $<. w T ?O g

j, i!;i l

!??

.Pi[

,l; r

t T 9 N f

E D % i% 5 V

=.

2.

G 0

N s 5 5 A

a 1

e 9 0 1

0 5

5 u

1 8

S g_

1 1

u

=

m ts e

l

=

s 3s cy C

CO 8

E

.i:

s s

e

.4

.=

.a u

s n

r op i

3 e

.=.

m.

t

=,

s 02, R

ro U

t T

1 N

c v

D e

8 f

. 1 W

t a

e G

6 D

85

.=

.a 1

3 d

8 e

t T

Ed A Te a

3 1

Ar u

=.

=.

10 Lu l

2 1

2_

Us 1

c T Ma N

l t

SM I e a

O C

PE u

T d

A

.I:

n t

TS O

2 a

.I der

.a

.a

.a us a

i 3

e 7$

m.

1 M

r 2

1 U

• .I

• .a.

3

.I.I 6

3

.a.

eru L

g iF 3

~J T.

M3 >9gSi ??

m.Mog

Figure 3.6.4 Measured and Calculated Detector Responses BOC Cycle 12 l.

2 noes sees ases Is

)

2 g

w I

g sost inst

, rear asar m3r 9

s a

s S

3 N

t s

[

u es tare zers zero asse une

k..

N f

}

o im soas seri asas g

urs I

1 i

t 1213 fois 2st3 3s13 ass sworr 99 %P 92 %W 120067 sees awe STATEPOINT 1201 AT O.5350 GWDMTU SIMULATE-3 l

O Measured O

g o

e 6

9 e'

~

e

O O

O O

O O

O O

U U

Figure 3.6.5 Measured and Calculated Detector Responses MOC Cycle 12 so.s n.s mes 8

J

/

z mr son men mn un 2

9 3

8 8

?

}

5

[

un as

/

<n sm un un t

2

[

i-T

=

}

mi non nu.

m, g

m, 3!

2 h*g 1213 2013 Mt3 M13 4 sao owwr g

nw St%W

.99984 h

2006 AVE STATEPOINT 1208 AT 4.8804 GWOMTU SIMULATE-3 O

Measured

i f'

l r

i f P W E

f V

s r

D %1 5 se A

4 4

4,

?

y W9 9 s G

o 0

s.

4 1

7

.i L

I 2

1 e

i s

t I

a e

m r

t s

l n

c m

s a

y C

CO E

.I 1

s es n

ops n

i S

t s

n y-s a

y m

O e

e e

s e

R ro t

U c

T M

e I

D t

W e

D G

l 97 3 d

4 7 Ed 1

e t

Te T

a A Ar l

Lu s

s 1

t u

m c

o Us t

i 2

1 se c

l a

s Ma t

1 T Ie N

a I

SM C

O P

d ET n

A O

a I

T 13}j%

S d

/..

eru s

ae i

s M

t s

r r

a e

r, t

t t

6

)I i.

6 I

3 e

r ug iF I

2$gpE?>F5m 7M

i Figure 3.6.7 Measured and Calculated Detector Responses BOC Cycle 13 5

4 I

I I

i

/

. /.

==

==

6

/

==

t im n

==

==

z 2

t A

5

'}

{8 F

l s

i i,

.I 6

i Y

M o

mi

>=i mi mi o.

~

i I

l n.-

M %P t

N %W

.9 08 r

J STATEPOINT 1301 AT 0.785 GWDNTU SIMULATE-3 l

0 Measured

=

s Figure 3.6.8 Measured and Calculated Detector Responses MOC Cycle 13 d

t

~

1 I

2 im aest nest soar 3r i

i i

,4 i

4 j-i 1

7 1

8 4

8 mi mi mi mi n

3 4

^

k I.

I L

I 1213 to13 2913 3sts t

4998OWtW 99 %P j

t.sw i.

.90887

/ _

~

STATEPOINT1308 AT 4.9558GWDNTU SIMULATE-3 O

Measured O

9 4

S S

W 8

8

e<

k i

t W

o"%

r E

7 I

i V

3 I

n 4

5 A

a S

a a"9 w

0 4,

O 4,

00 s

9 e

i.o n

v 2

i

.i..

3 1

7 M,

m, t

i s

3 a

3_

s s3 v

e l

i, cy C

es

./

C

/.

O 2

E

'E-se s

v no 7

S 3

5 9

I n

t 0

p 8

I e

0 8

s 2,

I, t,

2, 2,

eR U

r e

T o

s N

t O

.8, W

c 8

e G

t 1

5 v

De 6

1 0

3 1

d T

e A

Ed t

7 M_

1 8

Te t

3 r

1 3

a 0

o 0

3 Ar s,

3 l

2, 1

Lu u

TN Us c

l Ma l

c P

Ie a

E SM

~.i

.'s

,ts-T C

A T

U d

S n

O f.

a der us 7

I t

3 a

3 I

r 1

1 I

a 1

2, t,

1 e

M U

5 s

.,e 9

6 3

er 9

u 2

U 4

g iF 5

U U

2

,ok?> n3 w 7,, o t

b

• \\

l i

i O

f e W E

3 2

fD s%

V 7

9 e

A 4

4 W o e e

c B r 4,

4 G i o

9 n.

57 e

t

~

4 1

3 7

N 1

e-3 8

5 B

e 3

3-3 l

.I' cy C

CO

=

B t

se s

e n

I f

o N-N.

t 6

F 9

3 p

I 2

0 N

2, 0

seR r

U o

T t

M c

D e

W t

I G

e g:

e 0

D 1

5 3

d 7

0

-Ed e

T t

A Te Ar a

3 1

7 H

N, Us 1

0 Lu 3

l o

o 4

f-f.

u 1

T Ma c

N I e l

I SM O

a P

C E

T e_

A d

T n

S O

a I

s I

d e

r u

I f

sa 3

7 9

2 1

3 2

e 2

2 1

1, M

1 e

0 1

s k

6 8

3 e

r f

u o_

9 g

2 i

4 F

e e

2$2 98?> N0.

2TgRg

s

=

n i

f P W f

E a

D %%

v 9 5 a

~.

u, m

w9 0 8 1

G 9 0

0 9

15 e

4 8

s e

s.

4 t

a n

M.

=.

1 e

t a

n a

s s

s e

8 l

c y

C CO I

M s

esn s

i 3

5 o

=

M.

=.

r t

0 a

a N

0 p

l r

2 s

eR U

r 4

T o

N t

D 9

c W

1.I G

e t

3 e

07 D

1 4

3 d

T e

A Ed t

e s

3 6

r 1

0 Te

=

M.

=

m a

o 0

4 Ar n

2 1

l Lu T

u N

Us c

I Ma O

l P

I e a

E SM C

T A

T d

.S k*:

S l7 n

S O

o 8

a d

e r

us e

s 3

=

n 1

e a.

i_

in 2

a 1

M

.8 1

5 e

1 S

e 6

3 e

r n

u e

g i

F s

s.

33>9

@> y<. u P

• I 23

Figure 3.6.12 Measured and Calculated Detector Responses EOC Cycle 14 3045 Itet 3s49 N

g g

h 1

h.

i

/

}

s t

d ersi soar naar assy 4437 g

3 y

=

S i

(

e

{.,

/

<n m,

m.

m, m,

an t

• l e

)

i m

i i

t im mi mi mi un O

d a

M.-

-s 3

3 I

1

=

93%9 g

,i sw e

t H05 AVE L

STATEPOINT 1413 AT 8.8822 GWDNTU SIMULATE-3 O

Measured O

9 9

e e

e e

4 S

e i

l s

W%~

T P 7

9 t

s 2

2 4

4 4

4, 4

4_

W H ~

7, G

7 0

1

)O I*

5 s

r 9

1 s

1 e

u 2

2 t

8 s

a ss_

s, 3

s_

s

)

e N

l cy C

I.

C OB s

es

]

N.

no s

7 9

1 3

e 3

2 2

t p

s 3

8 t

2, 2_

2, 2

f s

e R

r U

T o

M t

/D c

W e

G t

.3, 0

e 78 D

1 0

3 d

T e

A Ed Te t

s 7

9 1

3 1

s 3

2 2

1 0

Ar a

o 0

0 0

0 5

t 2,

2_

2_

2_

Lu l

1 u

T Us c

N Ma I

l O Ie P

E SM a

C TA T

d S

x O

n a.

a derus

?

9 1

3 a

s 2

2 9

2 2

2 e

i 1_

1 2

M 1

I 3

.s 1

6 3

er 9

u 2

i 4

g iF y

,3s > M$L 4 t o]

l l

1 li1)

I\\

P W

- i 5 A

E V

t n

r r

o a

a 0

nS f

f 59 9

g 8

5 1

1 i

s s

r

=

r t

e i

e e

m

=

s.

s e

e y

l cy C

O 8 -

88 C

M s

e s

sno 6

0 i

=

p r

s 0

r e

s e

0 0

m n.

s.

2 2_

e s

y eR r

U o

T M

t c

8 D

e 1

W 8

t G

e 68 D

0 4

3 5

d e

T Ed A

t Te 7

u 0 Ar a

e r

o ie m.

m.

c o

5 Lu l

e a.

s 1

s Us u

T c

N Ma I

Ie l

O a

P SM E

C T

1 A

d E.

T n

S O

a der usa r

e i

s e

m m

m.

m M

4

.t 2

1 58 g

6 3

erug

=

iF 2 3>9&S5 r<. m

,i**,,

ll l

l:l.

I.l!lI1ll1,J l1[

l1\\

1 l

3 r p W E

7 n

e3s%

V 3

7 4

A 44 o

v 7 9 59 o

9 r

9 t

i.

u g

i.

5 1

5 7

i s

3 3

3 m

i 5

8 sa S

e lcy C

C

}.I.

O 2

g E

.I

[

se s

U no i

s p

'2; m.

i N

5 73 s

9 a_

s eR U

r T

..2 o

M

/

t t*

D

• .f'l t

W c

e G

2 7

U e

69 D

1 1

3 1

d T

Ed e

A n

t 3

Te t

3 5

7 M

Ar a

1 a

o 5

l 2,

m s_

Lu 1

u T

Us c

N Ma I

l O

I e a

P SM C

E T

A U

d 2

S T

O n

a d

er u

i s

s a

M i -

m.

i 7

3 e

i r

2 U

5 1

6

.//.

3 eru 9

O g

i F

2 O

O z&d$<5 n

7 t,,3 c

?

O Figure 3.6.16 Observed Differences Density Function Comparison 8000 l

i i

I I

i i

I i

I 7000

.i I

i 1

l i

I i

I e

6000 i

i l

l l

5000

~

i g

C t

.9 l

l l

oca i

I

'i k

4000 x

+'

i g

m l

l C

i l

0 i

l O

j l

3000 i

r i

i i

l i

i I

9 l

1 2000 l

i I

i 1000 i

I I

l O

-4

-3

-2

-1 0

1 2

3 4

e Error '(in standard deviations frorn the rnean) e NSPN AD-8609 A Rev. 3 Page 48 of 76

k Figure 3.6.17

)

Cumulative Distribution Function (CDF)

Comparison 1.0 7

?

/J 0.s 1

f 0.6 r

u_

Oo

?

l 0.4 4

?

0.2 1

/

b 0.0

)

-5

-4

-3

-2

-1 0

1 2

3 4

5 Error (in standard deviations from the mean)

NSPNAD-8609-A Rev. 3 Page 49 of 76

O Figure 3.6.18 CDF in the Region of the 95th Percentile Model Comparison 0.95015 i

O, i

O e

/

O.95010 i

I l

l O

l' 0.95005 I

i O!

f O

O.95000 e

O 3

0.94995 v

_)

l I

I O

0.94990 1

O e

l 0.94985 0 l 0.94980 e'

I l

I l

l 0.94975 I

1.6875 1.6880 1.6885 1.6890 1.6895 1.6900 gl Error (in standard deviations from the mean)

.I NSPN AD-8609 A Rev. 3 Page 50 of 76

!)

Figure 3.6.19 Observed Differences Density Function l

r l

Integrated Reaction Rates Comparison D

l 350 l

l l

i

\\

3 i

I 300

?

I l

250 i

C S

200 1

o I

l I

C t

a a.

b l

1 a

i J

g 150 o

l 100 D

I i

l l

I l

50 6

D I

l i

o i

-4

-3

-2

-1 0

1 2

3 4

D Error.(in standard deviations from the rnean)

NSPN AD-8609 A Rev. 3 Page 51 of 76 l

O.

Figure 3.6.20 Cumulative Distribution Function (CDF) e integrated Reaction Rates Comparison 1.0 0.8 0.6 Lt Oo el 0.4 e

0.2 7

e 0.0

-3

-2

-1 0

1 2

3 4

e Error (in standard deviations from the mean) e NSPN AD-8609-A Rev. 3 Page 52 of 76

3 Figure 3.6.21 CDF i'n the Region of the 95th Percentile g

For Integrated Reaction Rates 0.956 I

i O

l

~~

l

/

0.954 O

O j

C i

O l

0.952 O

O l

l l

i u_

O 0.950 o

l 1

a l

O O

0.948 i

O I

I.

0.946 0

I O

i l

1 i

l 1

l l

0.944 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 O

Error (in standard dsviations from the mean) l l

O NS PN AD-8609. A Rev. 3 P ;c 53 of 76

0:

Figure 3.6.22 Standard Deviation vs Measured Instrument Response g

Absolute Differences (Meas-Calc) 0.10 i

i i

i i

i, 0.09 g-0.08 0.07

~5 0.06 0.05 G

!!!!!PJ J

0.00 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Measured Response 9

Relative Differences (Meas-Colc)/ Meas 0.10 i

i i

i i

ii 0.09 0.08 p

.j 0.07

'f 0.06 0.05 7

0.0 0.00 9

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Measured Response NSPN AD-8609 A Rev. 3 Page $4 of 76

4.0 HODEL APPLICATIONS TO REACTOR OPERATIONS This section describes the methods used in applying the reliability

)

factors and biases to reactor operations.

It is not the intent of this section to define the procedures used.

However, some aspects of these procedures are presented in order to clarify the approach taken in applying the model reliability factors and biases.

The model will be applied to reactor operations in two primary modes, predictive and monitoring. Cold critical comparisons, including few rod and in-sequence criticals; and hot criticals at power are given below to

}

verify this mode of application.

In the monitoring mode, process computer support and isotopic inventory calculations must be considered.

4.1 Predictive Applications 4.1.1 Cold Criticals D

NSP has predicted few rod cold criticals around the high worth rod for each cycle of operation in order to verify the predicted model. The resultant cold critical km for all few rod criticals calculated for cycles 11 through 15 ist km = 0.9929 i'.0023 lg NSP has predicted in-sequence withdrawals to cold critical for each cycle of operation to verify the rod withdrawal pattern and to prevent the withdrawal of a high notch worth rod that could scram the reactor.

The resultant cold critical k,for all in-sequence criticals calculated for cycles 11 through 15 is:

]

km = 0.9922 i.0028 The combined statistics of few rod and in-sequence criticals calculated for cycles 11 through 15 is:

km = 0.9923 i.0027 Table 4.1.1 gives the detailed information for each critical.

7 Figure 4.1.1 gives the graphical representation of the criticals for each c}cle.

4.1.2 Hot Full Power Criticals NSP has piedicted the hot at-power critical conditions throughout each cycle.

)

The resultant hot critical ka for all criticals calculated for cycles 11 through 15 is:

km = 0.9979 t.0019 Table 3.6.1 gives the detailed information for each critical.

Figure 4.1.2 gives the graphical representation of the criticals for each cycle. Circled points indicate coastdowns.

e 4

NSPN AD-8609-A Rev. 3 Page 55 of 76

() i 4.2 Monitorino Aeolications 4.2.1 Process Comouter The General Electric 3D-Monicore System recently installed at Monticello will be retained. NSP is currently evaluating several options for support of this system for cycles 18 and beyond. GE will supply support for cycle 17.

The support options are as follows:

1.

Continue to have GE supply all support.

2.

NSP will support with system as installed.

II 3.

NSP will support with system modified by replacing Panacea with an approved core model (i.e. SIMULATE-3 or NDH).

4.2.2 Isotoolc Inventory The isotopic inventory calculation will be performed by NSP if either option 2 or 3 is decided upon in Section 4.2.1.

The calculation of the isotopic inventory for Monticello is based upon dB a two-dimensional, CASMO-3 calculation.

This is the same model as is used to calculate the TIP trace design input.

Therefore, the accuracy of the burnup distribution can be verified by the agreement of the measured and calculated reaction rates which is used to evaluate the measurement uncertainties, see Section 3.6 above. The accuracy of the isotopics versus local exposure is described in references 4 and 36 based on measurements at Yankee Rowe.

O 9

O!

9.

9 9

NSPN AD-8609-A Rev. 3 Page 56 of 76

e TABLE 4.1.1 Few Rod and In-sequence Cold Criticals e

Cycle Cycle Temperature F = Few Rod k,,

Exposure

(*F)

S = Sequence (GWD/MTU) 11 0.000 85 F

0.9921 1

0.000 106 F

O.9936 0.000 106 S

0.9948 0.000 113 S

0.9936 g

12 0.000 129 F

O.9964 0.000 128 S

0.9928 0.000 128 S

0.9938 i

3.256 141 S

0.9903 6.260 203 S

0.9896 13 0.000 91 F

0.9905 2,

0.000 91 F

0.9904 0.000 91 S

0.9897 0.000 91 S

0.9908 8.853 201 S

0.9876 9.764 164 S

0.9851 14 0.000 109 F

O.9907 O.000 111 S

0.9913 e',

0.000 118 S

0.9936 4.569 122 F

O.9924 4.569 123 S

0.9919 5.811 152 S

0.9895 6.647 209 S

0.9905 8.510 154 S

0.9923 8.510 142 S

0.9920 15 0.000 108 F

O.9933 k'

O.000 108 F

O.9963 0.000 113 S

0.9939 O.000 107 S

0.9963 0.093 200 S

0.9979 0.093 147 S

0.9962 1.616 182 S

0.9939 4.151 137 S

0.9922 6.202 129 S

0.9928 Statistics Type N

Mean a

Few Rod 9

0.9929 0.0023 O

Sequence 24 0.9922 0.0028 Combined 33 0.9923 0.0027 0

o'

NSPN AD-8609-A Rev. 3 Page 57 of 76 I

Figure 4.1.1 Cold Criticals vs Core Average Exposure 1.000 g

i i

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4 4

0.999 i

0.998

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+-

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)

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0.984 O.983 14 A

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+

0.981 i

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i 5.0 MODEL APPLICATIONS TO SAFETY EVALUATION CALCULATIONS This section describes the methods used in applying the reliability factors and biases to the results of safety related physics ID !

calculations.

It is not the intent of this section to define the procedures to be used in performing the physics calculations.

However, some aspects of these procedures are presented in order to clarify the approach taken in applying the model reliability factors and biases.

In such applications, the question is generally:

Will the reload core maintain a safe margin to established safety limits (i.e., peak linear heat generation rate, minimum CPR, shutdown margin, etc.) under normal l$ t and non-normal or accident conditions? The question is usually answered by performing cycle specific safety analyses for the limiting transients and accidents.

For each parameter of intrerest, RFx and Bias are given in Table 3.0.1.

x and Bias : for each parameter of interest is The application of the RFx x

shown below.

GB,

5.1 Linear Heat Generation Rate (LHGR and APLHGR) i The Linear Heat Generation Rate (LHGR) and the Average Planar Linear Heat Generation Rate (APLHGR) are calculated directly in SIMULATE-3.

The model reliability factor and bias listed in Table 3.0.1 are then 1

applied as follows:

j GB -

LHGR(model) (1 + Bias + RFny)

LHGR

=

APLHGR = APLHCR(model) (1 + Bias + RFny) q where model signifies the best estimate value directly calculated with the 3D simulator.

5.2 Critical Power Ratio-(CPR) lp l The Critical Power Ratio is defined as the ratio of the bundle power required to produce onset of transition boiling somewhere in the bundle (critical power) to the actual bundle power, i.e.:

Pc(I, J ) / P(I,J)

CPR(I,J)

=

where:

gp Pe(I, J ) is the critical bundle power in assembly (I,J)

P(I,J).is the actual bundle power in assembly (I,J)

The minimum critical power ratio, MCPR, is defined as the minimum value of.CPR in the' core, i.e.:

(Pe(I,J) / (P(I,J)),

() '

HCPR

=

The model reliability and bias listed in Table 3.0.1 are then applied as follows:

[ Pc(I, J ) / P(I,J)) (1 + Bias + RFan))

CPR =

5.3 Control Rod Worth GD Rod worth are calculated using the three-dimensional nodal model. Worth 1

are determined by varying the rod position while the independent core parameters such as core power, flow, and void distribution are held constant.

UD '

NSPNAD-8609 A Rev. 3 Page 60 of 76

)

1 l

l The model reliability factor and bias listed in Table 3.0.1 are then l

applied as follows:

1)

AK,oo AKaon(MODEL) (1 + Bias) (1 i RFaoo)

=

The reliability factor is either added or subtracted, whichever is most i

conservative for each particular application.

l I

5.4 Void Reactivity i

The model reliability and biaces listed in Table 3.0.1 are applied to Ak/ AU as Ak/AU (1 + Bias) (1 1 RFe) l The reliability factor is either added or subtracted, whichever is most l

conservative, for each application.

l) l 5.5 Fuel Temperature (Doppier) Coefficient The Doppler coefficient is a measure of the change in neutron J

multiplication associated with a change in fuel temperature. Reactivity is changed mainly due to Doppler broadening of the U-238 parasitic 1

resonance absorption cross section due to increases in fuel temperature.

i

]

The model reliability factor and bias listed in Table 3.0.1 are then i

i applied at each point as follows:

Ak/ Atr" (1 + Bias) (1 RFo)

Again, the reliability factor is either added or subtracted, whichever is most conservative for each particular application.

5.6 Delayed Neutrons The delayed neutron constants; B,,i and A, are assumed to be constant in time during a transient.

The use of constant delayed neutron constants corresponding to the initial conditions is justified by the results in Reference 29 which show that B.tr does not change significantly during a transient until the scram is over.

Adjoint flux weighting is used to j

obtain these constants.

l The reliability factor listed in 3.0.1 is applied as shown:

B.n l (model) (1 + Bias) (1 1 RFe) 5.7 Prompt Neutron Lifetime The prompt neutron lifetime A is assumed to be constant in time.

The reliability factor listed in Table 3.0.1 is applied as follows:

A(model) (1 + Bias) (1 i RF )

4 O

O I

NSPN AD 8609-A Rev. 3 Page 61 of 76

C) l i

6.0 REFERENCES

1.

FSP Topical " Qualification of Reactor Physics Methods for Application to PI Units", NSPNAD-8101P, Rev.

1, December, 1982.

II 2.

NSP Topical " Qualification of Reactor Physics Methods for Application to Monticello", NSPNAD-8609, Rev.

1, April, 1992.

3.

NSP Topical "Monticello Nuclear Generating Plant Safety Evaluation Methods," NSPNAD-8608, Rev.

1, August, 1988.

4.

A.

S. DiGiovine, K.

B. Spinney, D. G.

Napolitano, J.

Pappas, 4>

"CASMO-3G Validation and Verification", YAEC-1653-A, Yankee Atomic Electric Company, 1990.

5.

A.

S.

DiGiovine, J.

P. Gorski, M. A.

Tremblay, " SIMULATE-3 Validation and Verification", YAEC-1659-A, Yankee Atomic Electric Company, 1990.

6.

B.

Y. Hubbard, D.

J. Morin, J. Pappas, R.

C.

Potter, "MICBURN-G 3/CASMO-3/ TABLES-3/ SIMULATE-3 Benchmarking of Cycles 9 Through 13,"

YAEC-1683-A, Yankee Atomic Electric Company, 1990.

7.

M. Edenius, and B.

H.

Forssen, "CASMO-3 A Fuel Assembly Burnup Program User's Manual", Studsvik AB, NFA-89/3 Rev.2, March, 1992.

8.

M.

Edenius, H. Huggblom, and B. H. Forssen, "CASMO-3 A Fuel Assembly Burnup Program Methodology", Studsvik AB, NFA-89/2 Rev.1, (b

January, 1991.

9.

M.

Edenius, A. Ahlin, and H. Huggblom, "CASMO-2 User's Manual, Studsvik AB, NR-81/3, 1981.

10.

M.

Edenius, and C. Grugg, "MICBURN-3 Microscopic Burnup in Burnable Absorber Rods User's Manual", Studsvik AB, NFA-89/12, November, 1989.

gg 11.

J.

A. Umbarger, A.

S.

DiGiovine, K.

S.

Smith, and J.

T.

Cronin,

" SIMULATE-3 Advanced Three-Dimensional Two-Group Reactor Analysis Code Users Manual", Studsvik of America, SOA-92/01 Rev.0, April, 1992.

12.

K.

S.

Smith, J. T.

Cronin, and J. A. Umbarger, " SIMULATE-3 Advanced Three-Dimensional Two-Group Reactor Analysis Code gg Methodology", Studsvik of America, SOA-92/02 Rev.0, April, 1992.

13.

J.

A.

Umbarger, and K.

S.

Smith, " TABLES-3 Library Preparation Code for SIMULATE-3", Studsvik of America, SOA-92/03 Rev.0, April, 1992.

14.

"S3 POST SIMULATE-3 Summary File Postprocessor",

Studsvik of America, SOA-91/04, 1991 gg 15.

I.

B.

Fiero, M.

A.

Krammen, H.

R. Freeburn, et al, "ESCORE-The EPRI Steady-State Core Reload Evaluator Code: General Description", Electric Power Research Institute, EPRI NP-5100-L-A, April, 1991.

16.

M.

A.

Krammen, H. R. Freeburn, et al, "ESCORE-The EPRI Steady-State Core Reload Evaluator Code Volume 1: Theory Manual",

Electric Power Research Institute, EPRI NP-4492-CCMP Volume 1, gg August, 1986.

17.

M. A.

Krammen, R.

B.

Fancher, N. T. Yackle, et al, "ESCORE-The EPRI Steady-State Core Reload Evaluator Code Volume 2: User's Manual", Electric Power Research Institute, EPRI NP-4492-CCMP O

NSPN AD-8609-A Rev. 3 Page 62 of 76

-~

()

i Volume 2, August, 1986.

18.

M.

A.

Krammen, R.

B.

Fancher, M. W. Kennard, et al, "ESCORE-The

(]

EPRI Steady-State Core Reload Evaluator code Volume 3:

Programmer's Manual", Electric Power Research Institute, EPRI NP-

[

4492-CCMP Volume 3, August, 1986.

t 19.

D. B. Jones, "ARMP-02 Documentation Part II, Chapter 7-MICBURN-E Computer code Manual Volume 1: Theory and Numerics Manual",

Electric Power Research Institute, EPRI NP-4574-CCM, Part II, Ch.

7 Volume 1, December, 1986.

20.

D. B. Jones, "ARMP-02 Documentation Part II, Chapter 7-MICBURN-E Computer Code Manual Volume 2: User's Manual", Electric Power Research Institute, EPRI NP-4574-CCM, Part II, Ch. 7 Volume 2, December, 1986.

21.

D. B. Jones, "ARMP-02 Documentation Part II, Chapter 7-MICBURN-E Computer Code Manual Volume 3: Programmers Manual", Electric Power

O Research Institute, EPRI NP-4574-CCM, Part II, Ch. 7 Volume 3, A

December, 1986.

22.

M. Edenius, and H. Huggblom, " Benchmarking of CASMO Resonance Integrals for U-238 Against Hellstrand's Measurements", Studsvik of America, SOA-91/05, December, 1991.

23.

M. A. Edenius, " Benchmarking of CASMO Resonance Integrals for U-C) 238 Against Hellstrand's Measurements. Comparison between CASMO-3

)

Versions 4.4 and 4.7",

Studsvik of America, SOA-93/04, March, j

1993.

24.

M.

A.

Edenius, "CASMO Doppler Coefficients versus McNP-3A Monte l

Carlo Calculations", Studsvik of America, SOA-93/06, October, 1993.

s

2..

M. Edenius, " Studies of the Reactivity Temperature Coefficient in j

5 C)

Light Water Reactors," AE-RF-76-3160, AB Stomenergi, 1976.

26.

M. Edenius, " Seminar on U-238 Resonance Capture," S.

Pearlstein, j

Editcr, page 87, BNL-NCS-50451, 1975.

]

27.

M. Edenius, " Temperature Effects in Thermal Reactor Analysis,"

Internal Report presented to Oskarshamnuerkets Kraftgrupp AB(OKG),

Stockholm, Sweden, employed by AB Stomenergi Studsvik, Sweden.

28.

M. Edenius, and A. Ahlin, "CASMO-3: New Features, Benchmarking, 1

and Advanced Applications," Nuclear Science and Engineering, 192, No. 3, p. 342, November, 1988.

29.

J. M. Holzer, et.al.

"A Code System to Produce Point Kinetics Parameters for LWR Calculations," ANS Trans, 29, 946-7, 1981.

()

30.

M.G.

Kendall, A. Stuart, "The Advanced Theory of Statistics," Vol.

1, 5th. ed., Hafner Publishing Co. N.Y.,

1987.

31.

D.B.

Owen, " Factors for One-Sided Tolerance Limits and for Variables Sampling Plans" Sandia Corporation, March 1963.

32.

K.

S. Smith, " SIMULATE-3 Pin Power Reconstruction: Benchmarking Against B&W Critical Experiments," Trans. Am. Nuc. Soc., 16, p.

531, San Diego, CA, June, 1988.

33.

M. Edenius, "CASMO-3 Benchmarking," Trans. Am. Nuc. Soc., 16, p.

536, San Diego, CA, June, 1988.

34.

K.

R.

Rempe, K.

S.

Smith, and A. F. Henry, " SIMULATE-3 Pin Power O

useuxD_ 609 3 a. 3 p.s. 63 or v6

() 1 Reconstruction: Methodology and Benchmarking," Nuclear Science and Engineering, 191, No. 4,

p. 334, December, 1989.

35.

T. Uegata, E. Saji, and M. Tanaka, " Verification of the CASMO-II 3/ SIMULATE-3 Pin Power Accuracy by Comparison with Operating Boiling Water Reactor Measurements," Nuclear Science and Engineering, 111, No. 1,

p. 81, May, 1993.

36.

P. J. Rashid, "CASMO-3 Benchmark Against Yankee Rowe Isotopics",

~

Studsvik of America, SOA-86/05, September, 1986.

37.

" Nuclear Design Methodology Using CASMO-3/ SIMULATE-3P," Duke Power QD Company DPC-NE-1004A, November, 1992.

38.

D. J. Edwards, L. E. Kostynak, F. A. Honger, R.

M.

Rubin, and C.

E. Willingham, " Steady State Reactor Physics Methodology," Texas Utilities Electric Company, RXE-89-003-NP, July, 1989.

39.

R.

Y. Chang, C. W. Gabel, "PWR Reactor Physics Methodology Using CASMO-3/ SIMULATE-3," Southern California Edison Company, SCE-9001-(D A,

September, 1992.

40.

M. Edenius and P.

J.

Rashid, " Benchmarking of the Gamma-TIP Calculation in CASMO Against the Hatch BWR," Trans. Am. Nuc. Soc.,

49, p. 431, Boston, MA, June, 1985.

41.

K.

S.

Smith and K. R. Rempe, " Testing and Applications of the QPANDA Nodal Model," Nuclear Science and Engineering,1QQ, No. 3, qp

p. 324, November, 1988.

42.

A. S. DiGiovine and D. G. Napolitano, " SIMULATE-3 Pin Power Reconstruction and Comparison to Fine-Mesh PDQ," Trans. Am. Nuc.

Soc., 1A, p. 361, Dallas, TX, June, 1987.

43.

K. R. Rempe and K.

S.

Smith, " SIMULATE-3: Power Distributions and Detector Response Modeling," Trans. Am. Nuc. Soc., 14, p. 355, gg.

Dallas, TX, June, 1987.

44.

D. G.

Napolitano, A.

S.

DiGiovine, K. R.

Rempe, and K.

S.

Smith,

" SIMULATE-3: Pin Power Reconstruction Applied to Seabrook Station," Trans. Am. Nuc. Soc., 15, p. 590, Los Angeles, CA, November, 1987.

45.

R. Hakanson and E. Kurcyusz-Ohlofsson, "Forsmark 1 Core Analysis gg.

with the Studsvik Code Package," Proceedings of the 1968 International Reactor Physics Conference, Jackson Hole, WY, September, 1988.

46.

A. S.

DiGiovine, J.

P. Gorski, and M. A. Tremblay, " Verification of the SIMULATE-3 Pin Power Distribution Calculation.," Nuclear Science and Engineering, 103, No. 4,

p. 324, December, 1989.

47.

E. Kurcyusz-Ohlofsson, " Analysis of Advanced PWR Cores with CASMO-3/ SIMULATE-3," PHYSOR 90, Vol.2, p. XIV-1, Marseille, France, April, 1990.

48.

K.

S.

Smith and K.

R.

Rempe, " Mixed-Oxide and BWR Pin Power Reconstruction," PHYSOR 90, Vol.2, p. VII-11, Marseille, France, April, 1990.

49.

H. Grubel, R.

Rippler, G.

Skoff, B. Wikes, and G.

Wupperfeld, gg i "Umstellung der nuklearen Kernausleng fur das KKW MQ1heim-Kurlich (KMK) auf das Studsvik-Programmsystem CASMO/ SIMULATE,"

Tagungsbericht Proceedings, Jahrestagung Kerntechnik '91, p. 3, Bonn, Germany, May, 1991.

O NSPN AD-8609-A Rev. 3 Page 64 of 76

-. -... ~ ~ -.. -..... -........ -....... _. _.. _ -...

.. ~.. _ -

i 4

O j

i I

50.

Y. Wang, J.

Yang, Y. Yeh, and S. Yaur, "Neutronic Model Verification for Maanshan Power Plant with Advanced In-core Fuel Management Package," Proceedings of the 1992 Topical Meeting on

.O Advances in Reactor Physics, p. 1-13, Charleston, SC, March, 1992.

i 51.

A. Jonsson, D.

R. Harris, R.

Y. Chang, O.

J. Thomsen, " Analysis of Critical Experiments with Erbia-Urania Fuel," Trans. Am. Nuc.

Soc., kl,

p. 415, Boston, MA, June, 1992.

O 1

O O

1 O

i

)

I O

o o

i NSPN AD-8609 A Rev. 3 Page 65 of 76

.=

.... - ~ -... - - - -.. _ _. -..

O.

I APPENDIX A Statistical Methods for the Determination and Aeolication of Uncertainties Oi I

The purpose of using statistical methods is to determine the value Xe (calculated) such that there is a 95% prcbability at the 95% confidence level that Xe will be conservative with respect to XT (true value) when applying the calculational 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.1 are used.

If the distribution cannot be treated as normal, but the distributions are 9~

known, then the methods described in Section A.2 are used.

If neither of the above methods apply, then the parameter in question is conservatively bounded.

O, O.

O i

i O'

1 4;

l i

I O

l 9

NSPN AD-8609-A Rev. 3 Page 66 of 76 m

1

)

e 1

i 1

A.1 Acolication of Normal Distribution Statistics Seoaration of Measurement and calculational Uncertainties

)

comparison of measured and calculated reactor parameters includes 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:

Xi = true reactor parameter

}

X, = measured reactor parameter X, = calculated reactor parameter e, = ( X, - X,) / X, = measurement error e, = ( X, - X,) / X, = calculation error j

]

e, = ( X, - X,) / X, = observed dif ferences 1

a i

1 01

,.-1

)

i o=(

(eg-p3)2 ) / (#-1)) * = scandard devlacion If e, and e, are independent, then the following relationships exist.

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

]

well).

oi=oie-ci 9, = p,- 9.,

D once the o, and,have been calculated from historical data, they could be used to apply conservatism to future calculations of reactor parameters, X,,

as follows:

24 - X,(1 + p,) (12140,)

[)

The factor K, is defined as described in Table A.1.14 to provide a 95%

probability at the 95% confidence level that X, is conservative with j

respect to the true value, X,.

l Reliability Factors It is the objective to define reliability factors which are to be used to increase / 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 reactor parameters.

For any given application, there is concern only with one side of the component; that is, if the calculated value is too large or too small.

NSPN AD-8609-A Rev. 3 Page 67 of 76 l

O,!

Therefore, one-sided tolerance limits based on normal distributions may be used to find a K, which will give a 954 probability at the 95%

confidence level to the reliability factor defined by s

Si RF = K,0c i

Numerical values of K, for various sample sizes used to calculate o, are provided on Table A.l.

9i 9-O:

j O'

i i

O i

Oi b

4 i

O-NSPN AD-8609-A Rev. 3 Page 68 of 76

I TABLE A.1 Single-Sided Toleranc, Factors (Reference 31)

D n

K, 2

26.26 3

7.66 4

5.15 5

4.20 6

3.71 7

3.40 g

8 3.19 9

3.03 10 2.91 11 2.82 12 2.74 15 2.57 20 2.40 25 2.29 g

30 2.22 40 2.13 60 2.02 100 1.93 200 1.84 500 1.76 m

1.645 S

n = Number of data points used for o D

D D

D NSPNAD-8609-A Rev. 3 Page 69 of 76

() '

s A.2 Apolication of Non-Normal Distribution Statistics If a distribution is determined to be other than normal, the requirement is that there is a 95% confidence level that X, will be conservative db -

with respect to the true value X.

(In the following, the notation used is consistent with that defined in Section A.1).

It is thus required that a 95% upper confidence limit be determined for the 95th percentile of the distribution of errors.

In the calculation, a set of error observations ( ei) are determined.

The mean (p.) and the standard deviation (o.) are calculated using the following formulation:

GD aei p,, = ' ' 2 as o,, = ( ([ (eg - p,,) ') / (n-1) )

• 2e1 Note that the ei above are determined from the following:

O' ei = e,, = (X,-X,) /X, = observed differences Generally, the e, are taken from several cycles of operation; thus, they represent the true distribution. The ei are then transformed to standard measure by the following formula: ' ' ~ Z, = Cac and the resulting variates (Z) are sorted into ascending order and the kth (such that k 2.95n) variate is chosen as an estimate of the 95th percentile of the distribution (See reference 30, page 50-51). This gives a 95th percentile of Z to be On. This implies that 95% of the errors are likely to be less than Qe. gp It remains to calculate a 95% confidence interval on Qu. (The formula for this calculation is taken from reference 13 page 236-243 (See references section 6.0). Var On = 7II-7I nf e 1 where: q the quantile (.95) j = number of independent observations in the sample n = f i ordinate of the density function of the distribution of I = observed differences at abscissa q l It is necessary to determine if the observations are independent. If they are not independent, it is necessary to reduce the sample size to gp account for the dependence in the determination of the 95% confidence level. Gl NSPNAD-8609-A Rev. 3 Page 70 of 76

B D i B D 2 D3 D4 Ds g D, D 3 D, Figure A.2.1. Differences for Nearby Positions D To set notation, let 6,3 be the population 95th percentile for the observed differences, that is P [ D; s 6 ,,5 ) .95. We wish to determine a = 95% upper confidence limit for 6.,3 when some of the differences are dependent. For differences observed at adjacent positions, the appropriate measure of association for our analysis can be shown to be C(1) = P(D s 6,,, and Da ' O.ss) - (.95) 8 3 We also consider the association of differences observed at locations two apart C(2) = P[D s 6,,3 and D s 6,,5) - (.95): 3 3 and, more generally, C(k) = P[D s 6,,3 and D.3 s 6,,5) - (. 9 5) 2 3 3 for k = 1,2,3,4,5,6,7 locations apart. In this example, there are 8 differences D, 7 adjacent pairs (D, D.,), 6 pairs with indices two i i i (D,D +2) g apart 1 pair D,D,. i i Let d be the sample 95th percentile with a selected to be the smallest w integer not less than.95n. The large sample distribution of dm depends on that of T(x) number of differences, D, that are less than or equal x. = i g Even with dependence among the D, i 1 - -- ( T(x) -nF(x) ) T(x) -nF(x) /T2 s.d.[T(x)) __1-s. d. [T(x) ) /n 3 will be approximately standard normal. Here F(x) = P(D; s x) and f(x) is the probability density function for the observed differences. m U NSPNAD-8609-A Rev. 3 Page 71 of 76

...m. O It follows that P[@(d,3 -0,,3) s z) = 1 -P[T(6,,3 + n~*z) s s-1] e-t -f(6,,5) z 1 s.d [T(6,,3)) where , [

s. d. [T(6,,5) ] ] 2 = f [n(.95) (.05) + 2 nC(1) + 2 nC(2) +...

nC(7 ) ) C(3) +... - f C(7) = (.95) (. 05) + C(1) + C(2) + Under independence 0 = C(l) = C(2) =... = C(7) and this expression 9-reduces to its customary value (.95)(.05). If the differences are 4 dependent, the variance of d is e (.95) (.05) 2 (8-k) C(k) 1 9, nf2(6,,3) 8 (.95) (.05) ,.3 e In order to apply this result, we estimate C(l) by number of adjacent pairs (D,D.1) where both s dq,, _(,5y, i i Total number of adjacent pairs The~ estimate of C(2) is g: , number of pairs (Ds,D 2) where both s d,, _ (,S), i q t Total number of pairs (Dj,Dj,2) and e' , number of pairs (D,D.9) where both s de,, _ (,5), i i 20 cal numver of pairs (Dj,D.g) i v 2 for k = 3,4,5,6,7. The value of f ( 6,,3) can be estimated as previously suggested. Then, the large sample upper 95% confidence limit for 6,3, adjusted for dependence among differences by location is given by .g. cw ] 1.645 (.95) (. 05) 2 (8-k) C(k) d + 1 { 8(.95) (.05) {d f 2 (6,5) j g ,.2 I one interpretation of this confidence limit, or the variance expression, is that the total sample size n is effectively reduced by the j dependence. We estimate the effective sample size to be gp, 1 i e1 NS PN AD-8609-A Rev. 3 Page 72 of 76

1 O n 2 (8-k) C(k) 3 O 8 (.95) (.05) 1 If only two terms are used, the effective sample size is estimated to be (.95) (.05) n (.95) (. 05) + C(l) + C(2) It is necessary to obtain an estimate of f, (.95) on a short interval of the cumulative distribution function of Z in the region of the 95th percentile. The slope of the cumulative distribution function is an estimate of the ordinate of the density function since the density function is simply the derivative of the cumulative distribution function. Thus ok, = Var 0,3 This value then allows an estimate of the 95% confidence limit on Q,3 Even though nothing is known about the distribution of Q,3, the distribution can be shown to be normal using the following derivation. P(D 5 0,,5 and D 8 0.ss) f 3 2 where 6.,5 is the 95th percentile of the distribution of differences. If q the dif ferences D, and D are independent O Pto s a.., and a s o. s1 = r[D s 6.,31 FID s 6.,5) i 1 = (.95) (.95) = (.95): The difference P[D s 8,,5 and D 5 0.ss) - (.9 5)' 3 2 O is a measure of association (dependence) from position to adjacent position. Note that if il if D s6 i 5 I(D s 5,,3) = 1 0 if D > 6l,3 3 i 0 1 1 f 4 5 6.s I(D 5 0.ss) 0 if D > 6 ',5 2 2 then the covariance is C(1) = Cov(I(D 5 6,,3),I(D 5 0.95) ) = P[D s 6,,3 and D 50.s51 - (.95)8 3 2 3 2 O we assume the same covariance for 5 6.,5)... I ( D, s 6.,3) and I ( D, s 6.,5). I(D2 s 6.95 ) and I(D3 There are about n 7/8 such pairs among the whole set of n observed NSPNAD 8609 A Rev. 3 Page 73 of 76

. ~.. _.... -.- -. ~. - - .~... - ~ -.... - ~. O; differences. Let d,3 be the sample 95th percentile where s is the smallest integer not less than n(.95). When n is large O! number of pairs (Dg,Dg.1) where both 5 d,, _ t _9 5, Tocal number of pairs (Dj,Dg.1) .is a good estimate of c(1). Similarly, for the approximately 6n/8 pairs (D,, D +2) 9-i i C(2) = Cov[I(D s 6,,3), I(D s 6,,5) ] 2 3 is estimated by number of pairs (D,Dg,,) where both s d<,p _(,S)2 Q. s Total number of pairs (Dg, Dg.2) and (*> -(.95)3 C(k) = Total number of pairs (Dg,Dg.g) y Let us now see how to modify the proof that d,is asymptotically normal u in order to account for the dependence among adjacent differences. It is still true that I

1. ~
   1. * ~

(A1) (*) (8) 4 = 1-P[T(x) < s) ) where T(x) I(Dj s x)

1. differences Di s x.

Moreover, T(x) - nF(x) = = has mean 0 and, for large samples, is approximately normal under a wide range of dependence structures. consequently, the g b I(Dj s x) are independent of one another and each has the same sums 4.t distribution. Since T(x) is just the sum of these group sums, the central limit theorem gives ~ ( is approximately standard normal. 9 T(x) Consequently, from (A1) and the normal approximation i P(fn(d,3 - 6,,,) s 2] = P[d<,3 56,,5 + n ~*2] t = 1-P[T(6.95

• D' 2) < 83 (A2) s-nF(6.,s + n

) e! ,g

s. d. (T(6,,3 + n-*z) ]

Now, note that j O' NS PN AD-8609-A Rev. 3 Page 74 of 76

O 1 (s-nF(6,,3 + n ~*z) ) = 1 (s-nF(6,,5) - nf(6,,5) n ~*z+0 (1) ) O = 2 (s-n(.95) - n*zf(6,,) ) + 0 (1) = -zF(6,,5) + 0 (1) Furthermore, O $"'rIT(0.ss*"~"")1""*rII(D 5 0 s + ""~*)] 2 s 7 2(8 *} COVII( 2 5 0.es + D'*2) e I(U.x 8 0.ssD -* 2) I + 2 8 which converges to O 2(8 *) F(6,,5) -p2 (6,,5) + (P(D ' O.s s, D.3 s 6,,3] - (. 9 5 ) 2) 2 3 8 2(8 *) C(k) = lim 1-Var [ T(6,,5) ) = (.95) (.05) + 8 O Therefore, by (A2), ~ P(# (d,3 - 6,,5) s z) 4 g - s. d. (T(6,,5) ] O or vn(d(s) - 6.,, ) is approximately normal with mean 0 and variance i 7 (.95) (.05) + { 2 (8-k) C(k) /8 1_ r.1 D f a (6,,5) As was indicated above, the C(k) may be estimated by C(k) and the large sample normality will still hold. Therefore using Table A.1 to obtain K,2 A,, = K, ( Var 0,3)

• p O

Thus it is 95% certain that o,, lies in the interv.1 Oss s Oss +A00,s therefore it is safe to say that we are 95% confident that the 95th percentile of the differences is: ) 0 p,,.,,,,,,, p,,. ( g,,. x, p,, ),,,, j NSPN AD-8609-A Rev. 3 Page 73 of 76

C) APPENDIX B Computer Code Summary Descriotion II - COMPUTER CODE DESCRIPTION CASMO-3 CASMO-3 is a multigroup two-dimensional transport theory code for depletion and branch calculations for a single assembly. It calculates the cross sections, nuclide concentrations, pin power distributions, and other nuclear data used to calculate input to the SIMULATE-3 program. Some of the characteristics GD of CASMO-3 are: 1. 40 energy group cross section library. 2. 7 energy groups are used during the two-dimensional transport calculations. 3. Gadolinium effective cross sections are generated by the ($ MICBURN-3 program. 4. The predictor-corrector approach is used for depletion. 5. Effective resonance cross sections are calculated individually for each pin. ESCORE ESCORE is a steady-state fuel performance code capable of gg i modeling the thermal and mechanical response of LWR fuel and used to provide fuel temperature inputs. MICBURN-3 MICBURN-3 calculates the burnup of a fuel pin containing gadolinium and generates 40 group effective cross sections as a function of number density for gadolinium to be input to CASMO-3. SAMULATE-3 A two-group 3D nodal program based on the QPANDA neutronics model. Some of the features of SIMULATE-3 are: 1. Explicit reflector cross model. 2. Pin power reconstruction. 3. Fourth order expansion of intranodal flux distribution. gg 4. No input normalization from higher order calculations or benchmark results. SPM Receives input from S3 POST of the predicted, measured, and difference of the TIP reaction rates and calculates the biases and reliability factors. S3 POST Reads output SIMULATE-3 and generates summaries and comparisons to measured incore TIP response. Modified by NSP to generate a file containing measured and predicted incore TIP response for input to the SPM program. TABLES-3 Reads CASMO-3 output files and generates the input tables and curve fits for each fuel type for the SIMULATE-3 computer program. O O NSPN AD-8609-A Rev. 3 Page 76 of 76}}