ML031690108
| ML031690108 | |
| Person / Time | |
|---|---|
| Site: | Surry, North Anna  |
| Issue date: | 06/11/2003 |
| From: | Hartz L Virginia Electric & Power Co (VEPCO) |
| To: | Document Control Desk, Office of Nuclear Reactor Regulation |
| References | |
| 03-366, NL&OS/GDM: R0 DOM-NAF-1 | |
| Download: ML031690108 (158) | |
Text
VIRGINiA ELECTRIC AND POWER COMPANY RICHMOND, VIRGINIA 23261 June 11, 2003 United States Nuclear Regulatory Commission Serial No.03-366 Attention: Document Control Desk NL&OS/GDM: RO Washington, D.C. 20555 Docket Nos.
50-280/281 50-338/339 License Nos. DPR-32/37 NPF-4/7 VIRGINIA ELECTRIC AND POWER COMPANY SUBMITTAL OF APPROVED TOPICAL REPORT DOM-NAF-1 -REV. 0.0-P-A QUALIFICATION OF THE STUDSVIK CORE MANAGEMENT SYSTEM REACTOR PHYSICS METHODS FOR APPLICATION TO NORTH ANNA AND SURRY POWER STATIONS In a letter dated June 13, 2002 (Serial No.02-334), as supplemented by letters dated November 25, 2002 (Serial No. 02-334A) and January 30, 2003 (Serial No.03-084),
Virginia Electric and Power Company (Dominion) requested approval of Topical Report DOM-NAF-1 for qualification of the Studsvik Core Management System reactor physics methodology for application at North Anna and Surry Power Stations.
The NRC approved the topical report in a letter dated March 12, 2003. In that letter the NRC requested that Dominion "...publish an accepted version of this topical report..." in accordance with the specifics noted in their letter. In response to the NRC's request, Dominion has prepared an accepted version of the topical report consistent with NRC requirements, and the report is included in the attachments to this letter.
As noted in the June 13, 2002 letter discussed above, Dominion considers a portion of Topical Report DOM-NAF-1 -Rev. 0.0-P-A proprietary. To conform to the requirements of 10 CFR 2.790 conceming the protection of proprietary information, the proprietary information provided in Attachment 1 is contained within brackets. The report title also includes the P" designator indicating its proprietary status.
Where the proprietary information has been deleted in the non-proprietary version, only the brackets remain (i.e., the information that was contained within the brackets in the proprietary version has been redacted). Attachment 2 has been redacted to provide a non-proprietary version of the topical report (DOM-NAF-1-Rev. 0.0-A) and does not include the P" designator in the title. Pursuant to 10 CFR 2.790(b)(1), the basis for redacting certain information as proprietary in this correspondence is addressed in the application for
- 1 1/444 It
withholding and affidavit provided in our June 13, 2002 letter and is applicable to this accepted version of the topical report as well.
If you have further questions or require additional infomiation, please contact Mr. Gary D.
Miller at (804) 273-2771.
Very truly yours, Leslie N. Hartz Vice President - Nuclear Engineering Attachments Commitments made in this letter: None cc:
U.S. Nuclear Regulatory Commission Region II Atlanta Federal Center 61 Forsyth Street, SW Suite 23 T85 Atlanta, Georgia 30303 Mr. M. J. Morgan NRC Senior Resident Inspector North Anna Power Station Mr. R. A. Musser NRC Senior Resident Inspector Surry Power Station Mr. C. R. Gratton NRC Senior Project Manager U. S. Nuclear Regulatory Commission One White Flint North 11555 Rockville Pike Mail Stop 8-G9 Rockville, MD 20852 Mr. S. R. Monarque NRC Senior Project Manager U. S. Nuclear Regulatory Commission One White Flint North 11555 Rockville Pike Mail Stop 8-H12 Rockville, MD 20852
DOM-NAF-1 -Rev. 0.0 -A Dom U nionS T
Qualification of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations Nuclear Analysis and Fuel June, 2003
DOM-NAF-1-Rev. 0.0 -A Qualification of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations NUCLEAR ANALYSIS AND FUEL DEPARTMENT DOMINION RICHMOND, VIRGINIA June, 2003 Prepared by:
Robert A. Hall Rebecca D. Kepler James G. Miller Christopher J. Wells Wafter A. Peterson Recommended for Approval:
. LaRoe Supervisor, Nuclear Core Design Approved:
k L Xii,w K. L. Basehore Director, Nuclear Analysis and Fuel I
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UNITED STATES NUCLEAR REGULATORY COMMISSION M
t WASHENGTON, D.C. 20555001 March 12, 2003 SERIAL f 3
Kco MAR X8 2003 Mr. David A. Christian Sr. Vice President and Chief Nuclear Officer Virginia Electric and Power Company NUCLEAR LMOSttG Innsbrook Technical Center 5000 Dominion Boulevard Glen Allen, Virginia 23060-6711
SUBJECT:
VIRGINIA ELECTRIC AND POWER COMPANY - ACCEPTANCE OF TOPICAL REPORT DOM-NAF-1, "QUALIFICATION OF THE STUDSVIK CORE MANAGEMENT SYSTEM REACTOR PHYSICS METHODS FOR APPLICATION TO NORTH ANNA AND SURRY POWER STATIONS" (TAC NOS. MB5433, MB5434, MB5436, AND MB5437)
Dear Mr. Christian:
By letter dated June 13, 2002, as supplemented by letter dated November 25, 2002, Virginia Electric and Power Company (VEPCO) requested approval of Topical Report DOM-NAF-1, entitled QualificatiOn of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations.*
The NRC staff has found that Topical Report DOM-NAF-1 is acceptable for referencing in licensing applications for the North Anna and Surry Power Stations, Units I and 2, to the extent specified and under the limitations delineated in the report and in the associated NRC Safety Evaluation (SE). The SE defines the basis for acceptance of the report.
Pursuant to Title 10 of the Code of Federal Regulations (10 CFR) Section 2.790, we have determined that the enclosed SE does not contain proprietary information. However, we will delay placing the SE in the public document room for a period of 10 working days from the date of this letter to provide you with the opportunity to comment on the proprietary aspects only. If you believe that any information in the enclosure is proprietary, please identify such information line by line and define the basis pursuant to the criteria of 10 CFR 2.790.
Our acceptance applies only to matters approved in the subject report. We do not intend to repeat our review of the acceptable matters described in the report. Ucense amendment requests that deviate from this topical report will be subject to a plant-specific review in accordance with applicable review standards.
In accordance with the guidance provided on the NRC website, we request that VEPCO publish an accepted version of this topical report within 3 months of receipt of this letter. The accepted version shall incorporate this letter and the enclosed SE between the tile page and the abstract. It must be well indexed such that information is readily located. Also, it must contain in appendices historical review information, such as questions and accepted responses, and original report pages that were replaced. The accepted version shall include an -A*
(designated accepted) following the report Identification symbol.
March 12, 2003 1
If the NRC's criteria or regulations change such that its conclusions as to the acceptability of L
the topical report are invalidated, then VEPCO will be expected to revise and resubmit its respective documentation, or submit justification for the continued applicability of the topical report without revision of the respective documentation.
Sincerely, Scott Moore, Acting Director Project Directorate II Division of Licensing Project Management Office of Nuclear Reactor Regulation l
Docket Nos. 50-280,50-281, 50-338, and 0-339
Enclosure:
Safety Evaluation cc w/end: See next page
[
Mr. David A. Christian Virginia Electric and Power Company cc:
Ms. Lillian M. Cuoco, Esq.
Senior Nuclear Counsel Dominion Nuclear Connecticut, Inc.
Millstone power Station Building 475, 5th Floor Rope Ferry Road Rt. 156 Waterford, Connecticut 06385 Mr. Richard H. Blount, f Site Vice President Surry Power Station Virginia Electric and Power Company 5570 Hog Island Road Surry, Virginia 23883-0315 Senior Resident Inspector Surry Power Station U. S. Nuclear Regulatory Commission 5850 Hog Island Road Surry, Virginia 23883 Chairman Board of Supervisors of Surry County Surry County Courthouse Surry, Virginia 23683 Dr. W. T. Lough Virginia State Corporation Commission Division of Energy Regulation P. O. Box 1197 Richmond, Virginia 23209 Robert B. Strobe, M.D., M.P.H.
State Health Commissioner Office of the Commissioner Virginia Department of Health P.O. Box 2448 Richmond, Virginia 23218 Office of the Attorney General Commonwealth of Virginia 900 East Main Street Richmond, Virginia 23219 Mr. Stephen P. Sarver, Director Nuclear Ucensing & Operations Support Innsbrook Technical Center Virginia Electric and Power Company 5000 Dominion Blvd.
Glen Allen, Virginia 23060-6711 Mr. David A. Heacock Site Vice President North Anna Power Station Virginia Electric and Power Company P. 0. Box 402 Mineral, Virginia 23117-0402 Mr. C. Lee Lintecum County Administrator Louisa County P.O. Box 160 Louisa, Virginia 23093 Old Dominion Electric Cooperative 4201 Dominion Blvd.
Glen Allen, Virginia 23060 Senior Resident Inspector North Anna Power Station U.S. Nuclear Regulatory Commission 1024 Haley Drive Mineral, Virginia 23117 Mr. William R. Matthews Vice President - Nuclear Operations Virginia Electric and Power Company lnnsbrook Technical Center 5000 Dominion Boulevard Glen Allen, Virginia 23060-6711
UNITED STATES NUCLEAR REGULATORY COMMISSION 0
WASHINGtON, D.C. 205554001 SAFETY EVALUATION BY THE OFFICE OF NUCLEAR REACTOR REGULATION RELATING TO TOPICAL REPORT DOM-NAF-1 QUALIFICATION OF THE STUDSVIK CORE MANAGEMENT SYSTEM REACTOR PHYSICS METHODS FOR APPLICATION TO NORTH ANNA AND SURRY POWER STATIONS. UNITS 1 AND 2 DOCKET NOS. 50-280.50-281, 50-338. AND 50-339
1.0 INTRODUCTION
By letter dated June 13, 2002, as supplemented by letter dated November 25, 2002, (References 1 and 2), Virginia Electric and Power Company (the licensee) requested approval of Topical Report DOM-NAF-1, Oualification of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations." This approval would permit the use of the Studsvik Core Management System (StudsviklCMS) code package to support the reload design analyses for North Anna and Surry Power Stations, Units 1 and 2. The Studsvik/CMS primarly consists of the CASMO-4 and SIMULATE-3 computer codes. This report demonstrates the validity and accuracy of the Studsvik/CMS package at North Anna and Surry for core reload design, core follow, and calculation of key core parameters for reload safety analysis.
2.0 REGULATORY EVALUATION
10 CFR 50.34, "Contents of applications; technical information," requires that safety analysis reports be submitted that analyze the design and performance of structures, systems, and components provided for the prevention of accidents and the mitigation of the consequences of accidents. As part o1 the core reload process, licensees perform reload safety evaluatons to ensure that their safety analyses remain bounding ior the design cycle. To verity that the analyses remain bounding, the licensees confirm that the inputs to the safety analyses are conservative with respect to the current design cycle. These inputs are checked by using core design codes and methodologies.
3.0 TECHNICAL EVALUATION
Currently, the North Anna and Surry Power Stations use the NOMAD computer code and model, PDQ two-zone model, TIP/CECOR computer code package, and various methodologies. In its submittal, the licensee requested to replace its codes with the Studsvik/CMS. The CASMO-4, CMS-LINK, and SIMULATE-3 computer codes comprse the Studsvik/CMS package.
Enclosure The CASMO-4 computer code is the Studsvik Scandpower, Inc. lattice code. The CASMO-4 computer code, a multi-group, two-dimensional transport theory code used for depletion and branch calculations for a single assembly, is used to generate the lattice physics parameters.
These parameters include the cross sections, nudide concentrations, pin power distributions and other nuclear data used as Input to the SIMULATE-3 program for pressurized-water reactor core performance analyses. CASMO-4, which is an Improved version of CASMO-3, incorporates the microscopic depletion of burnable absorbers Into the main calculations, introduces a heterogeneous model for the two-dimensional calculation, and incorporates the L
use of the characteristics forn for solving the transport equation.
Studsvik/CMS also supplies the SIMULATE-3 code. It is a two-group, 3-dimensional nodal program based on the NRC staff-approved QPANDA neutronics model that employs fourth-order polynomial representations of the intranodal flux distributions in both the fast and thermal neutron groups. This code is based on the modified coarse mesh (nodal) diffusion theory calculational technique, coupled with thermal hydraulic and Doppler feedback. This program explicitly models the baffle/reflector region, eliminating the need to normalize to higher-order fine mesh calculations. It also includes the following modeling capabilities:
solution of the two-group neutron diffusion equation, fuel assembly homogenization, explicit reflector cross-section model, cross-section depletion and pin power reconstruction.
In order to ensure flux continuity at nodal interfaces and perform an accurate determination of pin-wise power distributions, SIMULATE-3 uses assembly discontinuity factors that are 1
pre-calculated by CASMO-4. These factors are related to the ratio of the nodal surface flux in the actual heterogenous 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 CASMO-4 to combine the global (nodal) flux shape and the assembly 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 normalization or other adjustment at the core/reflector interface.
The SIMULATE-3 uel depletion model uses tabular and funclionalized macroscopic or microscopic, or both, cross sections to account for fuel exposure without tracking the individual nuclide concentrations. Depletion history effects are calculated by CASMO-4 and then processed by the CMS-LINK code for generation of the cross-section library used by SIMULATE-3. SIMULATE-3 can be used to calculate the three-dimensional pin-by-pin power distribution in a manner that accounts for individual pin bumup and spectral effects.
Furthermore, SIMULATE-3 calculates control rod worth and moderator, Doppler, and xenon feedback effects.
3.1 Model Benchmarking The licensee's June 13, 2002, submittal compared the CASMO-4 and SIMULATE-3 predictions of key physics parameters against plant data, critical experiments, and Monte Carlo calculations. As part of the development o1 the North Anna and Surry models, the licensee compared CASMO and Monte Carlo code calculations of reactivity worth for soluble boron, bumable poison rods, silver-indium-cadmium control rods, hafnium flux suppression rods, temperature defect, and Doppler defect.
For the SIMULATE-3 benchmarking, the licensee performed most of the calculations using full-core, 32 axial node, 2x2 X-Y mesh per assembly geometry. The comparison of SIMULATE predictions to measured data incorporates bias and uncertainty for both the predictions and the measured data. The licensee used statistical methods to account for these uncertainties. The licensee also used the CASMO, SIMULATE, and Monte Carlo code calculations In combination with the normalized flux map reaction rate comparisons to determine appropriate peaking factor uncertainty factors.
The licensee intends to use the CASMO-4 and SIMULATE-3 programs in licensing applications, including calculations for core reload design, core follow, and calculation of key core parameters for reload safety analyses of North Anna and Surry Power Stations, Units 1 and 2.
The licensee used data from the North Anna, Units 1 and 2, operating cycles 1 through 15, and Surry, Units 1 and 2, operating cycles 1 through 17 to benchmark the CASMO-4 and SIMULATE-3 models. These cycles covered core design changes over more than 60 cycles of operation, including transitions in fuel enrichment, fuel density, fuel loading pattem strategy, spacer grid design and material, fuel vendor, core operating conditions (full-power average moderator temperature and rated thermal power), and burnable poison material and design.
The fuel loading pattem variations include out-in and low-low-leakage designs, axially zoned fixed poison rods for reactor pressure vessel fluence reduction, transition to axially and radially zoned burnable poisons, and a range of operating cycle lengths from 202 to 582 effective full-power days with and without temperature and power coastdown. The licensee used critical boron concentration measurements, startup physics testing data, estimated critical position information, flux maps, and operational transient data to conduct model benchmarking. The good agreement between the measured and the calculated values presented in the June 13, 2002, submittal, is used to validate the licensee's application of these computer programs for analysis of the North Anna and Surry Power Stations, Units 1 and 2. For the parameters compared, the licensee calculated a sample mean and standard deviation of the observed differences. In addition, the licensee determined bias to describe the statistical difference between predicted and reference values.
The licensee demonstrated that the CASMO-4 and SIMULATE-3 models, n conjunction with the indicated reliability factors, adequately represent the operating characteristics of the North Anna and Surry Power Stations. Additionally, the licensee did not change key aspects of Its core design and analysis methodology, while maintaining code and quality assurance practices that provided assurances that future changes to the core, fuel, and burnable poison design will be modeled with accuracy and conservatism. Since the StudsviWCMS package adequately represents the operating characteristics, and the licensee will maintain this code and methodology with its existing quality assurance practices, the NRC staff finds the use of the Studsvik/CMS package acceptable for the North Anna Power Station Units 1 and 2, and Surry Power Station Units 1 and 2.
However, the licensee did not include benchmarking or physics information for mixed oxide fuels at the North Anna and Surry Power Stations. Additionally, the NRC staff has yet to approve of the Studsvik/CMS code package for use with mixed oxide fuels. Therefore, the NRC staff does not approve this topical report for use with mixed oxide fuels. Similarly, introduction of new fuel designs or fuel designs that are significantly different from those p
-1 analyzed in this topical report will require further validation of the above-stated physics methods for application to the North Anna and Surry Power Stations and will require NRC staff approval.
3.2 Statistics The NRC staff reviewed VEPCO's application for statistical content. The statistical issues revolved around the 95/95 tolerance limit calculations for each parameter of interest. The calculations give 95-percent assurance that at least 95 percent of the population will not exceed the tolerance limit.
The procedure used in the tolerance limits depended on whether the data could be assumed to be distributed normally. The licensee used several established techniques for testing normality and assumed normality only if the majority of the techniques validated that assumption. This approach is acceptable to the NRC staff.
When the normal distribution was applicable, the licensee used the traditional one-sided tolerance calculations (Ref. 3). Otherwise, they used the nonparametric method of Summerville (Ref. 4). Both the parametric and the nonparametric approaches, in their proper context, are acceptable to the NRC staff.
4.0 CONCLUSION
The licensee has performed extensive benchmarking using the CASMO-4 and SIMULATE-3 methodology. Its effort consisted of conducting detailed comparisons of calculated key physics parameters with measurements obtained from over 60 operating cycles of the North Anna and Surry Power Stations, Units 1 and 2. These results were then used to determine the set of 95/95 tolerance limits for application to the calculation of the stated physics parameters.
Based on the review of the analyses and results presented in the June 13, 2002, submittal, the L
NRC stafi has concluded that the CASMO-4 and SIMULATE-3 methodology, as validated by the licensee, can be applied to the North Anna and Surry steady-state physics calculations for reload applications as described in the above technical evaluation.
Based on the considerations discussed above, the NRC staff has concluded that: (1) there is reasonable assurance that the health and safety of the public will not be endangered by operation in the proposed manner, (2) such activities will be conducted in compliance with the Commission's regulations; and (3) the issuance of this amendment will not be inimical to the common defense and security or to the health and safety of the public.
5.0 CONDITIONS AND LIMITATIONS The NRC staffs approval of this topical report does not apply to the use of mixed oxide fuel.
Furthermore, introduction of significantly different or new fuel designs will require further validation of the above-stated physics methods for application to North Anna and Surry by the licensee and will require NRC staff approval.
I
4,
6.0 REFERENCES
- 1. Letter from Leslie N. Hartz, Vice President Nuclear Engineering, Virginia Electric and Power Company to-the USNRC, "Virginia Electric and Power Company Request for Approval of Topical Report DOM-NAF-1, Qualification of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations,"
June 13, 2002.
- 2.
Letter from Leslie N. Hartz, Vice President Nuclear Engineering, Virginia Electric and Power Company to the USNRC, "Virginia Electric and Power Company Request for Additional Information, Topical Report DOM-NAF-1, Qualification of the Studsvik Core Management System Reactor Physics Methods for Application to North Anna and Surry Power Stations," November 25, 2002.
- 3.
R. E. Odeh and D. B. Owen, "Tables for Normal Tolerance Umits," Marcel Dekker, Inc.,
New York, 1980.
- 4. Summerville, "Annals of Mathematical Statistics," Vol. 29, p. 599, 1958.
Principal Contributors: A. Attard S. Peters Date: March 12, 2003
CLASSIFICATION/DISCLAIMER The data and analytical techniques described in this report have been prepared specifically for application by Dominion. Dominion makes no claim as to the accuracy of the data or techniques contained in this report if used by other organizations. Any use of this report or any part thereof must have the prior written approval of Dominion. All items denoted by [ ] indicate information proprietary to Dominion.
ABSTRACT As part of Dominion's continuing effort to improve its reload design methods, the StudsvikJCMS core modeling code package has been validated for use in the reload design process for the North Anna and Surry Power Stations. The primary codes in the CMS system are CASMO-4 and SIMULATE-3. The accuracy of the CMS system is demonstrated through comparisons with measurements from over 60 cycles of operation taken at the Surry and North Anna Nuclear Power Stations and through comparison with higher order Monte Carlo neutron transport calculations. The CMS system has been shown to meet or exceed the same standards for accuracy as models currently used by Dominion.
2
Table of Contents CLASSIFICATIONIDISCLAIMER..........................................................
2 ABSTRACT.........................................................
2 TABLE OF CONTENTS..........................................................
3 LIST OF TABLES.........................................................
4 LIST OF FIGURES.........................................................
5 SECTION 1 - INTRODUCTION..........................................................
7 SURRY NUCLEAR POWER STATION OPERATING HISTORY................................................. 11 NORTH ANNA NUCLEAR POWER STATION OPERATING HISTORY..................................... 12 SECTION 2-CODE AND MODEL DESCRIPTION..........................................................
13 2.1 CASMO-4..........................................................
13 2.2 CMS-LINK..........................................................
14 2.3 SIMULATE-3.........................................................
15 2.4 AUXILIARY CODES.........................................................
16 2.4.1 Monte Carlo Codes - Cross Section LIbrary Benchmarking................................... 16 2.4.2 ESCORE - Fuel Temperature Data..................
..................................... 16 2.4.3 CECOR - Flux Map Reaction Rate Data...........................
............................ 18 SECTION 3-MODEL BENCHMARKING.........................................................
19 3.1 CASMO BENCHMARKING.........................................................
19 3.2 SIMULATE BENCHMARKING TO HIGHER ORDER CALCULATIONS.............................. 22 3.3 SIMULATE BENCHMARKING TO MEASURED CYCLE DATA.......................................... 27 3.3.1 Crtical Boron Concentration........................................................
27 3.3.2 Control Rod Worth........................................................
34 3.3.3 Isothennal Temperature Coefficient.......................................................
42 3.3.4 Differential Boron Worth....................................................... 45 3.3.5 Estimated Crtical Position.......................................................
51 3.3.6 Reaction Rate Comparisons....................................................... 55 3.3.7 Normal Operafion Power Transienfs.......................................................
67 3.3.8 Xenon Oscillation Demonstrafon.......................................................
90 SECTION 4-UNCERTAINTY AND RELIABILITY FACTORS...................................................
92 4.1 DEFINITIONS..........................................................
92 4.2 STATISTICAL METHODS.........................................................
95 4.3 DETERMINATION OF NUCLEAR UNCERTAINTY FACTORS........................................... 99 4.3.1 Critical Boron Concentration........................................................
99 4.3.2 Integral Confrol Rod Worth.......................................................
101 4.3.3 Peak Differential Control Rod Worth...........................................
105 4.3.4 Isothermal Temperature Coefficient...........................................
106 4.3.5 Differential Boron Worth...........................................
107 4.3.6 Estimated Critical Position...........................................
109 4.3.7 Reaction Rate Comparsons...........................................
112 4.3.8 Doppler Coefficients and Defects...........................................
114 4.3.9 Delayed Neutron and Prompt Neutron Lifetime...........................................
1 115 SECTION 5 -
SUMMARY
AND CONCLUSIONS............................................
119 SECTION 6 - REFERENCES............................................
121 APPENDIX A - RAI SET 1 QUESTIONS AND RESPONSES.
125 APPENDIX B - RAI SET 2 QUESTIONS AND RESPONSES.
137 APPENDIX C - REPLACED PAGES FROM ORIGINAL SUBMITTAL.
140 3
List of Tables Table Title Page 1
Surry Nuclear Power Station Operating History 1 1 2
North Anna Nuclear Power Station Operating History 12 3
CASMO-4 Reactivity Benchmarking Versus MCNP-4B and KENO-V.a 20 4
CASMO-4 W-prime and Pin-to-Box Ratio Comparisons 26 5
SIMULATE Critical Boron Comparisons 32 6
SIMULATE Integral Control Rod Worth Comparisons 38 7
SIMULATE Peak Differential Control Rod Worth Comparisons 38 8
SIMULATE HZP BOC ITC Comparisons 44 9
SIMULATE HZP DBW Comparisons 49 10 SIMULATE ECP Error 53 11 Flux Map Database for Reaction Rate Comparison 59 12 Flux Map Reaction Rate Statistics 66 13 N 1C 11 Power Ascension Flux Map Reaction Rate Statistics 85 14 Approved NRF Values for Previous Design Models 94 15 SIMULATE Critical Boron NUF 100 16 SIMULATE Integral Rod Worth NUF 102 17 Rod Worth Measurement Uncertainty Estimate 104 18 SIMULATE Peak Differential Rod Worth NUF 105 19 SIMULATE Isothermal Temperature Coefficient NUF 106 20 SIMULATE Differential Boron Worth NUF 108 21 SIMULATE Estimated Critical Position NUF 111 22 Approximate Uncertainty Components for ECP Calculations 111 23 SIMULATE Reaction Rate NUF 113 24 SIMULATE FAH and FQ NUF 113 25 Validation of CASMO-4 Prompt Neutron Lifetime Calculations 118 4
List of Figures Figure Title Page 1
Surry (15x15) Temperature Defects; CASMO-4 Versus MCNP-4B 21 2
North Anna (17x17) Temperature Defects; CASMO-4 Versus MCNP-4B 21 3
N2C5 Boron Letdown Curve 30 4
N2C12 Boron Letdown Curve 30 5
North Anna Critical Boron Difference; Simulate Minus Measured 31 6
Surry Critical Boron Difference; Simulate Minus Measured 31 7
Combined Critical Boron Difference; Simulate Minus Measured 33 8
North Anna Rod Worth Comparison 36 9
Surry Rod Worth Comparison 36 10 Combined Rod Worth Comparison 37 11 Combined Peak Differential Rod Worth Comparison 39 12 North Anna Unit 1, Cycle 4 Bank B Differential Rod Worth 40 13 North Anna Unit 2, Cycle 15 Bank B Differential Rod Worth 40 14 Surry Unit 2, Cycle 10 Bank B Differential Rod Worth 41 15 Surry Unit 1, Cycle 17 Bank B Differential Rod Worth 41 16 North Anna HZP BOC ITC Comparison 43 17 Surry HZP BOC ITC Comparison 43 18 Combined Reactivity Computer Bias Influence 49 19 Combined Differential Boron Worth Comparison 50 20 Combined DBW Error vs. Critical Boron Concentration 50 21 Combined ECP Results 54 22 Combined ECP Error Versus At-Power Critical Boron 54 23 In-core Moveable Detector Locations 58 24 Flux Map Thimble Reaction Rate Comparison; Integrated Trace Data 65 25 Flux Map Thimble Reaction Rate Comparison; 32 Axial Regions 65 26 S2C2 Load Follow Transient; Power and D-Bank Position Versus Time 69 27 S2C2 Load Follow Transient Delta-I Comparison 69 28 S2C2 Load Follow Transient Critical Boron Comparison 70 5
List of Figures (continued)
Figure Title Page 29 S2C2 Load Follow Transient; Peak Core Average Axial Power Comparison 70 30 N1C3 Power Transient 1; Power and D-Bank Position Versus Time 72 31 N1C3 Power Transient 1 Delta-I Comparison 72 32 N1 C3 Power Transient 1 Critical Boron Comparison 73 33 N1C3 Power Transient 2; Power and D-Bank Position Versus Time 73 34 N1C3 Power Transient 2 Axial Offset Comparison 74 35 Ni C3 Power Transient 2 Critical Boron Comparison 74 36 NIC6 Power Transient; Power and D-Bank Position Versus Time 76 37 N1 C6 Power Transient Delta-I Comparison 76 38 N1C6 Power Transient Critical Boron Comparison 77 N1C9 MTC Measurement Transient; Measured Inlet Temperature and 80 Critical Boron Concentration 40 N1C9 MTC Measurement Transient; Delta-I Change from Beginning of 80 Measurement 41 N1C9 MTC Measurement Transient; SIMULATE K-effective Drift 81 42 N1Cl 1 Initial Power Ascension; Power and D-Bank Position Versus Time 83 43 N1C 1 Initial Power Ascension Delta-I Comparison 83 44 N1C 1 Initial Power Ascension Critical Boron Comparison 84 45 Core Average Axial Power Comparison; N1C 1 Flux Map 1, 29.9% Power, 84 Dg124 46 Core Average Axial Power Comparison; NIC 1 Flux Map 2, 74.0% Power, 85 D@179 8
47 N2C14 Power Transient; Power and D-Bank Position Versus Time 88 48 N2C14 Power Transient Delta-I Comparison 88 49 N2C14 Power Transient Critical Boron Comparison 89 50 N2C14 Power Transient Delta-I Comparison; Sensitivity to Moderator Flow 89 51 N1C15 Xenon Oscillation Demonstration 91 52 Control Rod Worth Comparison; SIMULATE Versus Measured 103 6
SECTION 1 - INTRODUCTION Virginia Electric and Power Company (Dominion) is updating its capability to perform nuclear utility reactor analyses in support of the Surry and North Anna nuclear power stations. The objectives of this report are to briefly describe the computational models to be validated, to describe the intended applications of the models in the reload design process, and to demonstrate the accuracy of the models by comparing calculated data to measurements from Surry and North Anna Units 1 and 2.
The updated models use the Studsvik Core Management System (CMS) core modeling code package, consisting primarily of the CASMO-4 (CASMO, references 1-4) and SIMULATE-3 (SIMULATE, references 5-6) codes. The CMS package was developed by Studsvik AB and Studsvik of America (currently Studsvik Scandpower, Inc.). The CMS package is used and accepted in the nuclear industry both in the United States and worldwide in its current and previous versions. A brief description of the theory and function of the computer codes used for core modeling and for verification of model accuracy is presented in Section 2.
The primary focus of this report is to demonstrate the validity and accuracy of the CMS package as implemented at Dominion for core reload design, core follow, and calculation of key core parameters for reload safety analysis. An integral part of the implementation is a rigorous modeling approach that begins with higher order computer codes to identify and eliminate significant model bias prior to performing core calculations. The types of calculations that can be performed by the CMS model include:
Three-dimensional assembly power and flux distributions, relative radial peaking factors (Fxy(Z)), enthalpy rise hot channel factors (FAH(X,Y)), assembly average axial power distribution, core average axial power distribution (F(Z)),
and heat flux hot channel factor (FQ(X,Y,Z))
Soluble boron concentration and boron worth Fuel and bumable poison nuclide concentrations as a function of fuel bumup Integral and differential control rod bank worths Abnormally positioned control rod worths 7
Moderator and Doppler temperature coefficients and defects Power coefficients and defects Operational transient simulation Delayed neutron parameters and prompt neutron lifetime Detector reaction rates, coupling coefficients, and peaking factors for flux map analysis Fuel bumup Scoping studies for the evaluation of alternative fuel management strategies, fuel design changes, bumable poison product changes, and alternate control rod designs These calculations are currently performed with other core models (References 7-10) as described in those and other Topical Reports (References 11-13, 18, 39). The benchmarking data presented in this report demonstrate that the CMS models, including appropriate uncertainty factors derived herein, are fully capable of and acceptable for performing these types of calculations. Use of the CMS models does not change the essential methodology of those reports, but may alter details of the methodology. For example, because SIMULATE models the entire core in three dimensions, it is no longer necessary to perform 1 -D/3-D peaking factor synthesis. Due to the efficient run-time of the SIMULATE models, 1 -D calculations formerly required due to computer time limitations are no longer necessary. These cases may now be run directly in full-core 3-D geometry, eliminating approximations inherent in quarter-core modeling and the synthesis process.
The Surry Nuclear Power Station and the North Anna Nuclear Power Station, each consisting of two operating units, have been selected for verification of the CMS model.
Measurements from Surry cycles S1C1-SIC17 and S2C1-S2C17 and from North Anna cycles N1C1-N1C15 and N2C1-N2C15 will be used for model benchmarking and determination of model reliability factors.
These cycles represent evolutionary changes in core design over more than 60 cycles of operation including transitions in fuel enrichment, fuel density, fuel loading pattem strategy, spacer grid design and material, fuel vendor, core operating conditions (full 8
power average moderator temperature and rated thermal power) and bumable poison material and design. Loading pattern strategy variations include out-in and low-low-leakage designs, axially zoned fixed poison rods for reactor pressure vessel fluence reduction, transition to axially and radially zoned burnable poisons, and a range of operating cycle lengths from 202 to 582 effective full power days (EFPD) with and without temperature and power coastdown.
Types of core measurements used for model benchmarking include:
Critical boron concentration Hot full power (HFP)
Hot zero power (HZP) beginning of cycle (BOC)
HZP for restarts following reactor trips or mid-cycle outages Startup Physics Tests (HZP, BOC)
Integral control rod worth (via boron dilution and rod swap methods)
Differential control rod worth (boron dilution method)
Isothermal temperature coefficient (ITC)
Differential boron worth (DBW)
Estimated Critical Position (ECP)
Retum to HZP critical conditions following an outage Verification of reactivity effect of control rods, power defect, soluble boron, xenon and other isotopic changes Flux maps Instrument thimble reaction rates Operational transients Similar to load follow maneuvers Verification of reactivity effects (critical boron vs. time)
Verification of correct axial power distribution effects (axial offset or delta-I versus time)
Verification of undamped xenon oscillation axial power distribution behavior (correct balance between Doppler feedback and axial xenon oscillations)
The Surry Units I and 2 are identical Westinghouse designed three coolant loop pressurized water reactors with thermal ratings of 2546 MWt (Initially rated 2441 MWNt).
Initial criticality was achieved for Surry Unit I on July 1,1972 and for Surry Unit 2 on March 7, 1973. Cycle operating summaries for the Surry units are listed in Table 1.
The North Anna Unis 1 and 2 are identical Westinghouse designed three coolant loop pressurized water reactors with thermal ratings of 2893 MNt (initially rated 2775 MW%t).
Initial criticality was achieved for North Anna Unit I on April 5, 1978 and for North Anna 9
~~~_
_ I Unit 2 on June 6, 1980. Cycle operating summaries for the North Anna units are listed in Table 2.
10
Table I Surry Nuclear Power Station Operating History On Line Off Line Length Rating Loading Load Cycle Date Date (Months)
(MWt)
(MTM)
EFPD MWDIMTU Factor SICI 09/12/72 10/2474 25.4 2441 70.45 391 13548 51 SIC2 02/03/75 09/26/75 7.7 2441 71.27 202 6919 86 SIC3 12108/75 10/17/76 10.3 2441 70.83 260 8960 83 S1C4 01/24/77 04/22/78 14.9 2441 71.65 385 13116 85 S1C5 07/09/78 09/14/80 26.2 2441 71.7 423 14401 53 SIC6 07/06/81 02/07/83 19.1 2441 71.75 485 16500 83 SIC7 05/30183 09/26/84 15.9 2441 71.81 353 11999 73 S1C8 12/26/84 05/10/86 16.4 2441 71.91 414 14053 83 SIC9 07/12/86 04/09/88 20.9 2441 72.18 475 16064 75 SICIO 07/14/88 09/14/88 2
2441 72.33 53 1789 85 SICIOA 07/05/89 10/06/90 15 2441 72.33 417 14073 91 SIC11 12/17/90 02/29/92 14.4 2441 72.41 414 13956 94 S1C12 05/01/92 01/22/94 20.7 2441 72.47 582 19603 92 S1C13 03/24/94 09/08/95 17.5 2441 72.38 483 16289 91 S1C14 10/19/95 03/07/97 16.6 2546 72.31 485 17077 96 SIC15 04/28/97 10119/98 17.7 2546 72.38 495 17412 92 SIC16 11/19/98 04/16/00 16.9 2546 72.43 499 17540 97 S1C17 05/08/00 10/14/01 17.2 2546 72.45 512 17992 98 S2C1 03/19173 04/26/75 25.2 2441 70.46 429 14862 56 S2C2 06/19/75 04/22/76 10.1 2441 71.03 263 9038 85 S2C3 06/10/76 09/10/77 15 2441 71.21 275 9427 60 S2C4 10/12/77 02/04/79 15.8 2441 71.86 403 13689 84 S2C5 08/19/80 11/07/81 14.6 2441 71.88 411 13957 92 S2C6 12/31/81 06130/83 17.9 2441 71.87 471 15997 86 S2C7 09/25/83 03/20/85 17.8 2441 71.89 437 14838 81 S2C8 06/27/85 10/04/86 15.2 2441 71.95 394 13367 85 S2C9 11/30/86 09110/88 21.4 2441 72.12 464 15705 71 S2C10 09116/89 03/30/91 18.4 2441 72.21 442 14941 79 S2C11 06/05/91 03/06/93 21 2441 72.28 551 18608 86 S2C12 05/04/93 02/03/95 21 2441 72.38 550 18549 86 S2C13 03/19195 05/03/96 13.5 2546 72.37 377 13055 92 S2C14 06/05/96 10/06/97 16 2546 72.42 464 16312 95 S2C15 10/30/97 04/18/99 17.6 2546 72.43 518 18208 97 S2C16 05/25/99 10/01/00 16.3 2546 72.41 474 16666 96 S2C17 10/30/00 Operating Operating 2546 72.48 Operating Operating Operating 11 Note: Data from Reference 14. MWD/MTU and loading is approximate.
Table 2 North Anna Nuclear Power Station Operating History On Line Off Line Length Rating Loading Load Cycle Date Date (Months)
(MWt)
(MTM)
EFPD MWDIMTU Factor NlCl 04/23178 09/25/79 17.1 2775 72.15 413 15885 79 N1C2 01/24/80 12/28/80 11.1 2775 72.18 279 10726 82 N1C3 04/10/81 05/17/82 13.2 2775 72.27 347 13324 86 N1C4 11/18/82 05/12/84 17.8 2775 72.12 350 13467 65 N1C5 09/25/84 11/04/85 13.3 2775 72.29 349 13397 86 N1C6 12/23/85 04/19/87 15.8 2893 72.41 401 15694 83 N1C7 06/29/87 02/25/89 19.9 2893 72.62 423 16851 70 N1C8 07/15/89 01/12/91 17.9 2893 72.74 485 19289 89 N1C9 03/07/91 01/04/93 22.0 2893 72.78 503 19994 75 NICIO 04/09/93 09/09/94 17.0 2893 72.74 494 19647 95 NlCll 10/08/94 02/11/96 16.1 2893 72.81 474 18834 97 N1C12 03/10/96 05/11/97 14.0 2893 72.78 419 16655 98 N1C13 06/10197 09/13/98 15.1 2893 72.78 452 17967 98 N1C14 10/07198 03/12/00 17.1 2893 72.87 509 20208 98 NiC15 04/07/00 09/09/01 17.1 2893 72.91 498 19760 96 N2C1 08/23/80 03/07/82 18.4 2775 72.06 376 14480 67 N2C2 06/02/82 04102/83 10.0 2775 72.2 220 8456 72 N2C3 05/29/83 08/02/84 14.2 2775 72.26 383 14708 89 N2C4 11/02/84 02/20/86 15.6 2775 72.5 416 15923 88 N2C5 04/01/86 08/24/87 16.8 2893 72.61 443 17455 87 N2C6 11103/87 02/20/89 15.6 2893 72.74 449 17858 95 N2C7 05/07/89 08/21/90 15.5 2893 72.83 454 18034 96 N2C8 11/01/90 02/26/92 15.8 2893 72.75 459 18253 95 N2C9 04/22192 09/07/93 16.5 2893 72.74 469 18653 93 N2C10 10/26/93 03/25/95 16.9 2893 72.8 485 19273 94 N2C11 05/31/95 09/08/96 15.3 2893 72.74 458 18215 98 N2C12 10/12/96 04/05/98 17.7 2893 72.73 487 19372 90 N2C13 05/03/98 09/12/99 16.3 2893 72.79 491 19515 99 N2C14 10/09/99 03/11/01 17.0 2893 72.81 499 19827 96 N2C15 04/09/01 Operating Operating 2893 72.89 Operating Operating Operating 12 Note: Data from Reference 14. MWD/MTU and loading is approximate.
SECTION 2 - CODE AND MODEL DESCRIPTION 2.1 CASMO-4 CASMO4 (CASMO) is a multigroup two-dimensional transport theory code for bumup calculations on BWR and PWR assemblies or simple pin cells. The code handles a geometry consisting of cylindrical fuel rods of varying composition in a square pitch array.
Fuel rods may be loaded with integral poisons such as gadolinium or boron. The fuel assembly model may contain bumable absorber rods, cluster control rods, in-core instrument channels, water gaps, boron steel curtains, and cruciform control rods in the regions separating fuel assemblies. Typical fuel storage rack geometries can also be handled. Some characteristics of CASMO are listed below:
Nuclear data are collected in a library containing microscopic cross sections in 70 energy groups. Neutron energies cover the range 0 to 10 MeV.
CASMO can accommodate non-symmetric fuel bundles containing up to 25 by 25 rods. Full, half, quadrant or octant symmetry (mirror symmetry) can be utilized in the calculations.
Absorber rods or water holes covering lxl, 2x2 pin cell positions or larger areas are allowed in the assembly.
Effective resonance cross sections are calculated individually for each fuel pin.
A fundamental mode calculation Is performed to account for leakage effects.
The microscopic depletion is calculated in each fuel and burnable absorber pin.
Isotopic depletion as a function of irradiation is calculated for each fuel pin and for each region containing a bumable absorber.
Discontinuity factors are calculated at the boundary between bundles and for reflector regions.
In order to generate a neutronic data library for SIMULATE-3 a series of CASMO depletions and branch cases is required. This series of calculations is defined within CMS as the "SIMULATE-3 Case Matrix." This case matrix consists of a series of depletions and instantaneous branch cases vs. exposure as a function of varied boron concentration, moderator temperature, fuel temperature, and shutdown cooling time, as well as cases with control rods and without removable burnable poison in guide tube locations.
13
2.2 CMS-LINK CMS-LINK (Ref. 33) is a linking code that processes CASMO card image files into a binary formatted nuclear data library for use by SIMULATE-3. The code collects the following data from CASMO card image files:
Two-group macroscopic cross sections Two-group discontinuity factors Fission product data Detector data Pin power reconstruction data Kinetics data Isotopics data Spontaneous fission data CMS-LINK is capable of processing data for the following segment types:
Standard hot and cold PWR segments (fuel regions) with and without burnable poison Pulled and reinserted burnable poison for PWR segments Standard cold and hot PWR reflector segments Functional dependencies for key core condition variables are predefined in the code. A diverse set of CASMO cases provide data covering a range of reactor conditions between hot or cold shutdown and full power operation. Branch cases include changes in soluble boron, moderator temperature, fuel temperature, insertion and removal of burnable poison rods, insertion of control rods, and isotopic decay after shutdown. The cumulative effect of long term changes in individual variables such as soluble boron, moderator temperature or fuel temperature are treated as "history" effects by CMS-LINK and subsequently in SIMULATE.
14
2.3 SIMULATE-3 SIMULATE-3 (SIMULATE) is an advanced two-group nodal code for the analysis of both PWRs and BWRs. The code is based on the QPANDA neutronics model (Ref. 6) which employs fourth-order polynomial representations of the intranodal flux distributions in both the fast and thermal groups. Key features of SIMULATE are:
Pin power reconstruction No normalization required against higher order calculations Explicit representation of the reflector region Coupled neutronicstthermal-hydraulics Internal calculation of the effect of spacer grids on axial power distributions Calculation of intra-nodal axial power distribution effect on FQ SIMULATE cross-section input is provided from CASMO with linkage through CMS-LINK.
15
2.4 AUXILIARY CODES 2.4.1 Monte Carlo Codes - Cross Section Library Benchmarking Monte Carlo method codes such as KENO-V.a (Ref. 15) and MCNP4C (Ref. 16) are used to benchmark CASMO and SIMULATE calculations. Monte Carlo fuel assembly models are used to identify any biases in the CASMO model key parameters (such as control rod worth, burnable poison worth, fuel temperature (Doppler) defect, and soluble boron worth). [
Monte Carlo models are also used to verify the accuracy of peak-to-average pin power calculations in CASMO and SIMULATE. In conjunction with comparisons of measured and predicted flux thimble reaction rates, the Monte Carlo models support the derivation of overall uncertainty and reliabililty factors for peaking factor predictions using the CMS system.
2.4.2 ESCORE - Fuel Temperature Data In SIMULATE, the average temperature of the fuel pellets in a node is calculated by:
TFU = TMO +A (x,y) xP+ B x P 2 16
where TMO is the moderator temperature, P is the nodal power density relative to core-averaged power density at 100% of rated power, A is the linear coefficient of the fuel temperature with respect to nodal power density (this can be a table that is a function of up to two state variables, x and y ), and B is a quadratic coefficient of fuel temperature with respect to nodal power density. For the North Anna and Surry models, fuel temperature data based on the EPRI ESCORE code (Ref. 17) are represented via A(x,y) in the above equation. The coefficient A is a function of local burnup and power level.
Model benchmarking which supports the use of ESCORE fuel data coupled with CASMO cross sections [
l includes:
- 1) Comparison of HZP and HFP critical boron (measured versus predicted).
Doppler feedback is a major contributor to the power defect near BOC.
Consistency between the HZP and HFP boron agreement supports a conclusion of accurate power defect predictions.
- 2) Comparison of measured and predicted axial offset during undamped xenon oscillations following operational transients and return to full power. Axial xenon variations tend to cause unstable axial offset oscillations. Doppler feedback is the primary damping force. Comparison of the measured and predicted axial offset behavior demonstrates whether the model has the proper xenon / Doppler balance.
- 3) Comparison of measured and predicted critical conditions for mid-cycle reactor restarts (also known as Estimated Critical Position or ECP calculations). ECP calculations are a reactivity balance (typically between HFP and HZP) which incorporate changes in control bank position, soluble boron, xenon, power defect, and other less significant changing isotopic concentrations to predict conditions for the retum to criticality following a reactor trip or shutdown. The power defect is a significant component in all ECPs, and the Doppler feedback is a large portion of the power defect.
17
2.4.3 CECOR - Flux Map Reaction Rate Data CECOR (Ref. 10, 18) is used for movable in-core detector flux map analysis. The primary use in the benchmarking of the North Anna and Surry SIMULATE models is to provide instrument thimble detector reaction rate data for comparison to predicted reaction rates.
A Dominion post-processor code reads SIMULATE and CECOR reaction rates and provides normalized comparisons.
Reaction rate comparisons are a key component used to determine peaking factor uncertainty factors.
18
SECTION 3 - MODEL BENCHMARKING 3.1 CASMO BENCHMARKING CASMO-4 has been extensively benchmarked against critical experiments and Monte Carlo calculations. These benchmarks encompass criticality, pin power predictions, fuel isotopic concentrations, new LEU fuel, bumed LEU fuel, and MOX fuel. A sampling of relevant papers are listed in References 19 through 22. As part of the development of the North Anna and Surry models, Dominion has performed a comparison of CASMO and Monte Carlo code calculations of reactivity worth for soluble boron, bumable poison rods (BP), AIC (silver-indium-cadmium) control rods, Hafnium flux suppression rods, temperature defect, and Doppler defect. [
Table 3 and Figures 1 and 2 show the results of the CASMO reactivity benchmarking.
Statistical uncertainty associated with each Monte Carlo calculation was limited to a range of 0.0001 to 0.00037 AK (one standard deviation). For all but the Doppler defects, the data represents a range of fuel enrichments from 2.6 to 5.0 w/o U-235, soluble boron concentration from 0 to 2000 ppm, and temperature from 100 to 547 F. Doppler comparisons are for enrichments of 3.0 and 4.0 wlo U-235 (bumed and new fuel) over a fuel temperature range of 300 to 900 K. [
19
Table 3 CASMO-4 Reactivity Benchmarking Versus MCNP-4B and KENO-V.a Component Fuel Type Mean Std. Deviation Number of
(% difference)
(% difference)
Observations AIC Control North Anna (17x17)
[
]
[
]
12 Rods Surry (15x15)
[
I
[
]
12 Hf Rods Surry (15x15)
[
]
[
]
12 Soluble Boron North Anna (17x17)
[]
36 Surry (15x15)
[
]
[
]
24 8 BP Rods @
North Anna (17x17) 12 20 BP Rods North Anna (17x1 7)
[
]
[
12 0.95 w/o B4C NorA (1x1)
[
]
[
l 8 BP Rods @
North Anna (17x17)
[
]
[ l 12 3.0 w/o B4C Surry (15x15)
[
]
[
1 12 20OBP Rods@
North Anna (1 7x17)
[][]12 3.Ow/o B4C Surry (5x1 5) 11112 North Anna (17x17)
[
3
[
]
3 Doppler Defect Surry (1 5x1 5)
I 1
I 1
3 Note: % Difference is 100 x (CASMO WORTH - MONTE CARLO CARLO WORTH)
WORTH) I (MONTE 20
Figure 1 Figure 2 21
3.2 SIMULATE BENCHMARKING TO HIGHER ORDER CALCULATIONS Comparison of CASMO/SIMULATE and Monte Carlo code calculations of pin-to-box ratios and flux thimble instrument reaction rate ratios are used in combination with normalized flux map reaction rate comparisons to determine appropriate peaking factor (FAH and FQ) uncertainty factors. Comparison of pin-to-box ratios and flux thimble reaction rate ratios (W-primes) exercises the entire CMS system (CASMO, CMS-LINK, and SIMULATE).
Pin-to-box ratios are defined here to be the ratio of pin power to assembly average power.
W-prime is defined as the normalized ratio of assembly power to flux thimble instrument reaction rate.
When assessing the ability of core design codes to predict pin powers, predicted pin powers would ideally be compared directly to measured values. Unfortunately, in most power reactors there is no method available to directly measure individual pin powers.
Power reactor measured pin powers are reconstructed using measured instrument thimble reaction rates, predicted W-prime values, and predicted pin-to-box ratios. The key components associated with measured and predicted peaking factors are described as follows:
Predicted peak pin power = Predicted assembly power x predicted pin-to-box ratio Measured peak pin power = Measured thimble reaction rate x predicted W-prime x predicted pin-to-box ratio Uncertainty associated with predicted peak pin power is therefore different than the uncertainty associated with measured peak pin power. The uncertainty factor for predicted peaking factors will be derived by combining the uncertainty factor from measured and predicted thimble reaction rate comparisons with the pin-to-box uncertainty factor derived from comparisons of SIMULATE and MCNP.
Thimble reaction rate comparisons will be used to determine a conservative approximation of the predicted assembly power uncertainty. It is conservative because it 22
inherently includes not only predicted power uncertainty, but measurement uncertainty and uncertainty associated with reconstructing the predicted thimble reaction rate (W-prime uncertainty). Appropriate uncertainty for measured peaking factors is composed of a combination of the W-prime uncertainty (from comparisons of SIMULATE and MCNP),
the pin-to-box uncertainty, and any other desired factors (such as the effect of manufacturing tolerances on FQ).
In order to estimate the W-prime and pin-to-box uncertainty for the Surry and North Anna models, two-by-two assembly models have been constructed using both SIMULATE and MCNP. These models are comprised of identical fresh fuel assemblies with two diagonally opposite assemblies containing control rods. Periodic boundary conditions were used. The fuel assembly designs and operating conditions include North Anna and Surry fuel assembly designs, a range of fuel enrichments, and a range of soluble boron concentrations. The SIMULATE model setup, to the extent possible, paralleled that of the North Anna and Surry CMS core models to ensure that the results of these calculations are applicable to the production models.
The set of cases modeled (six 22 cases for 1 5x1 5 fuel and six 2x2 cases for 1 7x1 7 fuel) is not exhaustive in scope. However, extreme inter-assembly and intra-assembly flux and power gradients are caused by the presence of the control rods. Strong gradients increase pin-to-box factors and result in challenging and conservative conditions for both W-prime and pin-to-box uncertainty determinations.
Additional conservatism results from different treatment of the gamma contribution to the pin power distribution in SIMULATE and MCNP. CASMO/SIMULATE uses a gamma smoothing technique to account for redistribution of fission energy released as gamma radiation. This method redistributes approximately 7% of the assembly power, effectively flattening the intra-assembly pin power distribution. Various references (Ref. 27, 28) support long range (- 100 cm) gamma energy contributions from prompt fission gammas, capture gammas, and fission product decay gammas of 7% - 12% of total recoverable energy. Gamma smoothing was not incorporated into the MCNP model. MCNP will therefore conservatively model the variation in intra-assembly pin powers, resulting in a 23
conservatively larger pin-to-box uncertainty for CMS as determined by comparison to MCNP. Statistics will also be provided for SIMULATE predictions without gamma smoothing, which effectively provides a comparison of fission rates.
Results of the SIMULATE / MCNP 2x2 model comparisons are presented in Table 4. All W-prime data was determined to be normal and all pin-to-box ratio data was determined to be non-normal using the Shapiro-Wilk W-test. Because the W-prime data is normal and simple tests of the mean and variance (simplified versions of the T-test and F-test, Ref. 25) indicated that there is no reason to believe that the Surry and North Anna samples are from different populations, the data were pooled. Due to the non-normality of the pin-to-box data, no pooling was performed. One-sided tolerance intervals (95%
probability, 95% confidence) were calculated based on the sample size, mean and standard deviation (Ref. 25) for W-prime and based on the sample size (Ref. 26) for pin-to-box. Additional discussion on statistical tests and tolerance intervals is provided in Section 4.2.
The pin-to-box cases of primary significance in Table 4 are the statistics for the unrodded assemblies, because in none of the cases does the rodded assembly have an RPD (relative power density) above unity. In fact despite the larger pin-to-box ratios in the rodded assemblies, typically only one or two pins in the rodded assembly exceeded an RPD of one, whereas typically all of the pins in the unrodded assembly exceeded an RPD of one. The pin-to-box errors of the rodded assemblies would not play a role in determining the maximum core-wide peaking factors. The range of standard deviations in Table 4 for pin-to-box ratio [
] is consistent with pin power RMS (root mean square) differences for CASMO-4 comparisons to three sets of critical experiment measurements (Ref. 20). The reported RMS differences range from I
and represent typical pin fission rate measured-versus-predicted differences for the small cores. Note that RMS and standard deviation are directly comparable if the population mean associated with the RMS value is zero.
MCNP statistical uncertainty for W-prime is approximately 0.8% (one standard deviation).
The MCNP uncertainty contribution to the tolerance limit is relatively small for the pin-to-24
box ratio, but is significant for the W-prime, resulting in a very conservative estimate of
[
I for the W-prime tolerance interval. Excluding the MCNP uncertainty reduces the W-prime uncertainty to [1.
MCNP statistical uncertainty for pin-to-box ratios is approximately 0.4% (one standard deviation), therefore its contribution to the pin-to-box ratio tolerance interval is modest.
Because the magnitude of the SIMULATE gamma smearing (7%) appears to be reasonable compared to values previously referenced, the statistics from Table 4 without the influence of gamma smearing are taken to be the most appropriate for determining the pin-to-box tolerance interval. The tolerance interval for assemblies with pin powers above unity is [
3 for both fuel types. The cases modeled here represent extreme inter-assembly flux gradients due to the rodded assemblies. However, it is possible that less significant insert components (such as discrete burnable poison rods) which have not been modeled here could result in assemblies with above average power and pin-to-box uncertainty larger than for the unrodded assemblies. In consideration of this possibility, the tolerance interval is chosen to be [
- 1. The RSS (root sum square) combination of W-pfime and pin-to-box uncertainty for use in determining measured peaking factors is [
] using the conservative W-prime tolerance and
[
using the W-prime tolerance with the MCNP uncertainty removed.
25
Table 4 CASMO-4 W-prime and Pin-to-box Ratio Comparisons FuelType/
Assembly Sample Mean Std. Dev.
Normal Tolerance Parameter Sz SdDe.Limit Rodded 6
l
]
Yes
[
SurryIxl5 Unrodded 6
]
[
]
Yes
[
Combined 12
[
]
[
]
Yes
[
]
North Anna Rodded 6
[
1
[
1 Yes
[
17x17 Unrodded 6
[
]
[
]
Yes
[
W-prime Combined 12
[
]
[
]
Yes
[
]
Combined data Combined 24
[
l
[
]
Yes
[
]
W-prime Pin-to-box Ratio Statistics (Including Gamma Smearing)
Surry 15x15 Rodded 186
[
]
[
]
No
[
Pin-to-box Unrodded 186
[
]
[
]
No
[
]
ratio Combined 372
[
]
[
]
No
[
]
North Anna Rodded 234
[
]
[
]
No
[
Pin-to-box Unrodded 234
[
]
[
]
No
[
]
ratio Combined 468
[
]
[
]
No
[
]
Pin-to-box Ratio Statistics (Excluding Gamma Smearing)
Surry 15x15 Rodded 186
[
]
[
I No
[
Pin-to-box Unrodded 186
[
]
[
I No
[
]
ratio Combined 372
[
]
[
]
No
[
]
North Anna Rodded 234
[
]
[
I No
[
17xPi7 Unrodded 234
[
]
[
]
No
[
]
ratio Combined 468 l
]
[
No
[
]
Note: Difference is ((SIMULATE - MCNP) / SIMULATE) x 100%
- Eliminating the MCNP W-prime uncertainty component (conservatively set at [
root sum square results in a W-prime tolerance interval of [
].
]) by 26
3.3 SIMULATE BENCHMARKING TO MEASURED CYCLE DATA The following sections present the results of comparisons of SIMULATE-3 predictions with measurements from the North Anna and Surry power stations. Most calculations were performed using full core, 32 axial node, 2x2 X-Y mesh per assembly geometry.
Depending on the type of calculation, this geometry can sometimes be relaxed to a lower level of detail without significantly changing the results.
All comparisons of SIMULATE predictions with measured data will by nature represent a combination of SIMULATE bias, SIMULATE uncertainty, measurement bias, and measurement uncertainty. These comparisons will be used to derive appropriate uncertainty factors for SIMULATE predictions. In cases where the comparison data lead to unrealistically high estimates for SIMULATE uncertainty, aftempts to quantify and account for measurement bias and uncertainty will be made. Statistical methods are discussed in Section 4.2. Specific uncertainty factors based on the results given in this section are developed in Section 4.3. In the statistics presented, the sign convention used is such that a positive value indicates over-prediction of the magnitude of a parameter by SIMULATE, and a negative value indicates under-prediction by SIMULATE.
3.3.1 Critical Boron Concentration Critical boron concentrations were obtained from three sources. Startup physics tests provided measured critical boron at HZP, ARO conditions. HFP critical boron concentrations were obtained from routine daily boron measurements. Measured HZP boron concentrations for plant restarts (ECPs) were also used for cases near BOC and EOC.
Sources of boron concentration uncertainty unrelated to SIMULATE include titration (used to measure the boron concentration) and B10 depletion. B depletion is a reduction in the natural B10/B atom ratio caused by loss of Bl0 by neutron capture as boron in the coolant passes through the operating core. If there is little boron inventory tumover in the primary 27
system then the B'01B ratio can decrease continuously. Because only the B in boron contributes to the boron worth and the boron concentration measured by titration includes both B10 and B", the measured and predicted boron concentrations may not reflect the same B'°/B ratio assumptions and should not be compared without consideration of the B'° depletion effect.
Only equilibrium HFP data near BOC (up to 700 MWD/MTU) and EOC (between 50 and 5 ppm critical boron concentration) was used for the comparisons due to the complication of accounting for B10 depletion. The B10/B atom ratio is typically equal to the ratio for fresh boron (0.198 - 0.2) at BOC due to the addition of fresh boric acid during refueling. Near EOC, B depletion is not significant due to the low boron concentration. All SIMULATE calculations assume 0.198 B'°/B ratio.
Soluble boron measurement uncertainty is approximately +/-10 ppm for titration. In addition, near BOC there is potential Bl 0/B variation of approximately +/-1% (equivalent to approximately +/-10 to +20 ppm) due to natural boron isotopic ratio variation. Near EOC, the B'1/B isotopic ratio variation is estimated to contribute about +5/-0 ppm measurement uncertainty (0 to 10% B'1 depletion). The BOC B'° isotopic content can range high depending on the source of fresh boron used and can range low due to a limited amount of B10 depletion that can occur for the near-BOC data (up to 700 MNWD/MTU). B depletion can reduce the B10/B ratio to 0.18 or less at EOC (approximately 10% reduction in boron worth). To minimize the effect of B10 depletion, EOC data is limited to measured boron concentrations of 50 ppm or less.
Figures 3 and 4 demonstrate the effect of B'° depletion on boron letdown curve agreement. Figure 3 is representative of a cycle with relatively little B depletion effect.
The B'°/B ratio tends to be re-established to the natural boron ration by relatively high primary system leakage (continuous) or outages (periodic). Figure 4 is representative of a cycle with significant B'1 depletion effect (due to low primary system leakage and few outages). The effect of an outage (partial restoration of the B'°/B ratio by mixing with fresh boron) is visible in Figure 4 at about 15 GWD/MTU burnup.
28
Figures 5 and 6 present the difference between SIMULATE and measured boron concentrations in histogram format. Each histogram bin represents +/- 5 ppm about the indicated bin midpoint value. Table 5 presents boron difference statistics. Data is based on SIMULATE core models for 29 North Anna cycles and 33 Surry cycles. Figure 7 presents a histogram of all Surry and North Anna data combined.
29
Figure 3 N2C5 Boron Letdown Curve HFP, ARO Critical Boron Versus Cycle Burnup 0
2 4
6 8
10 Cycle Bumup (GWDIITU)
Figure 4 N2C12 Boron Letdown Curve HFP, ARO Critical Boron Versus Cycle Burnup I
~
12 14 16 0
2 4
6 8
10 12 Cycle Bumup (GWDIMTU) 14 16 18 20 30 a.
06 06 E
,o 0
0
<D C
0 m
E a.
U c
0 m
- l mi
- I
Figure 5 North Anna Critical Boron Difference SIMULATE Minus Measured
-50
-40
-30
-20
.10 0
10 20 30 40 50 Boron Differene Bln (ppm)
Figure 6 Surry Critical Boron Difference SIMULATE Minus Measured
-50
-40
-30
-20
-10 0
10 20 30 40 s0 Boron Difference Bin (ppm) 31 1406 100i-S 80 A
60-0 40 Y 20 0-ij 0
Table 5 SIMULATE Critical Boron Comparisons Note: Critical boron difference is (SIMULATE - Measured) (ppm)
Yes - Passed all tests Yes* - Failed the D' test but passed the K-S and Kuiper tests Yes' - Failed the D' and K-S tests but passed the Kuiper test YesA - Failed the K-S test but passed the D' and Kuiper tests 32 Mean Sigma D'
D' D'
D' D'
K-S Kuiper CaIc.
0.05 Plant Condition (ppm) (ppm) Obs. Max. Min. Normal P=.025 P=.05 P=.95 P=.975 Sig L Sig L W
W NRF NRF NA BOC HZP
-8.1 20.3 30 30
-53 Yes 0.8179 0.9995 0.9653 0.927 1
3.3 BOC HFP
-7.2 16.4 228 30
-51 Yes*
948.2 955.7 958.6 980.7 982.3 0.1868 0.6974 1
0.4 EOC HFP
-5.9 14.6 199 24
-39 Yes 792.3 777.8 780.3 799.7 801 0.0872 0.4539 0
0.0 ECP
-10.1 13.2 5
4
-31 N/A 0
0.0 A
p X
4 8.:2it¢w:
.30 3
276.270 277 2821.2.8.
O.0Z, 0
1
_.4 SY BOC HZP
-5 23.4 35 48
-49 Yes 0.7569 0.9982 0.9758 0.934 0
0.0 BOC HFP -11.2 16.5 212 35
-54 Yes*
854.9 856.4 859.1 879.7 881.1 0.079 0.4264 5
2.4
=___ EOC HFP -14.8 14.6 305 16
-48 Yes*
1518 1482 1486 1516 1517.5 0.175 0.6761 0
0.0 ECP 2.8 24.4 4
30
-29 N/A 0
0.0 ALL BOC HZP
-6.4 21.9 65 48
-53 Yes 148 142.7 143.7 149.9 150.1 0.7423 0.9979 1
1.5 BOC HFP
-9.1 16.5 440 35
-54 Yes' 2550 2574 2579 2622 2625 0.0315 0.2276 6
1.4 EOC HFP -11.2 15.2 504 24
-48 Yes*
3227 3158 3164 3213 3217 0.1003 0.497 0
0.0 ECP
-4.3 18.9 9
30
-31 N/A 0
0.0
.iO; 184 1018 4
-54.
Ys se ~09~ w9iO 921 9t18 0,01:1 0:244 7
0.7 w
Figure 7 Combined Critical Boron Difference SIMULATE Minus Measured 300-250 200-M North Anna a
A Surry a
I iIM
.0 00
-50
-40
-30
-20
-10 0
10 20 30 40 50 Boron Difference Bin (ppm) 33
3.3.2 Control Rod Worth The methods used for measuring control rod bank worth for Startup Physics Testing are described in Reference 13, and include the boron dilution method and the rod swap method. Measured rod swap bank worth accuracy is dependent on the accuracy of the reference (highest worth) bank worth measurement determined via the boron dilution method.
Sources of measurement uncertainty using the boron dilution method include boron measurement (titration) uncertainty, reactivity computer bias, and reactivity computer uncertainty. Reactivity computer bias and uncertainty is presumed to result primarily from the calculated delayed neutron data used in the kinetics equations. Delayed neutron data uncertainty is generally considered to be about +/-5% (Ref. 23 and Section 4.3.9) and has been estimated by indirect means to add significantly to the variance between predicted and measured rod worth (Section 3.3.4). Additional sources of measurement uncertainty include reactivity computer drift due to uncompensated background current and the manual measurement of each partial segment of the reference bank worth (roughly 20 segments per bank measurement which are also used to determine the differential rod worth).
Figures 8, 9, and 10 present the difference between SIMULATE and measured integral control rod worth for North Anna, Surry, and data for both units combined.
Each histogram bin represents +/-1% about the indicated bin midpoint value. Table 6 presents the same data in statistical format.
For control rod banks measured using the boron dilution method, the differential rod worth (DRW) is also measured. Statistics for the difference (%) between the SIMULATE and measured peak differential rod worth for 65 measurements are shown in Table 7. There is a significant tendency for SIMULATE to over-predict the peak DRW.
No distinction is made concerning the rod position at which the peak DRW occurs because the most important use of the DRW is for the rod withdrawal from subcritical accident. That accident is terminated after a few seconds and the 34
maximum DRW is usually conservatively assumed to occur for the entire withdrawal sequence. Previous assessments of DRW uncertainty (Ref. 23) developed an uncertainty factor based on the DRW difference in units of pcm/step. However, it is more appropriate and conservative to determine the uncertainty in terms of %
difference, because it results in a much larger DRW conservatism for accident conditions at which the predicted DRW is much higher than any of the cases in the measured database.
A histogram for the Table 7 data is shown in Figure 11 with each bin representing the indicated midpoint +/- 0.25 pcm/step. A sampling of four differential rod worth curve comparisons (DRW vs. rod position) is presented in Figures 12 through 15.
35
Fi~gure 8 North Anna Integral Rod Worth Comparison
-12
-10
-8
-6
-4
-2 0
2 4
6 8
10 12 14 16 Difference (%)
Figure 9 Surry Integral Rod Worth Comparison Simulate versus Measured
-18
-16
-14
-12
-10
-8
-6
-4
-2 0
2 4
6 8
10 12 14 16 Difference (%/)
36 II a
C 0
(I
.0 0
ac0 ii 0
0
Figure 10 Integral Rod Worth Comparison Combined Surry and North Anna 80-70-60 60 C
i_l
-18
-16 12
-10
-8
-6
-4
-2 0
2 4
6 8
10 12 14 16 Difference (%)
37
Table 6 SIMULATE Integral Control Rod Worth Comparisons Plant Type Mean Sigma Nobs Max.
Min. Normal D'
D' D'
D' D'
K-S Kulper Ca.
0.05 I(%)I
(%)___
P=.025 P=.05 P=.95 P=.975 Sig L Sig L W
W NRF NRF NA Dilution 2.4 4.3 39 16.1
-7.3 Yes 0.4678 0.9532 0.9621 0.939 2
5.1 Rod Swap 0.6 4.1 139 13.4
-12.4 Yes*
449.4 452.1 454 467.5 468.3 0.6507 0.9927 6
4.3 ALL 0
B.9 42 1
18.1 412.4
- 64.
- 78 0,3 SU Dilution 1.7 5.2 54 13.6
-17.4 Yes*
104.9 107.5 108.4 113.5 113.7 0.7026 0.9961 3
5.6 Rod Swap 1.8 3.7 130 10.4
-9.7 Yes 415.5 409.4 411.2 423.8 424.5 0.9823 1.0000 1
0.8 77 77~.>7 777>
7772472:f 0*>
ALL Dilution 2
4.8 93 16.1
-17.4 Yes*
238.6 245.9 247.2 256.1 256.6 0.4803 0.9595 4
4.3 Rod Swap 1.2 3.9 269 13.4
-12.4 Yes*
1224 1226 1230 1256 1258 0.7952 0.9992 8
3.0 7777 L
- 1.
4.2
.1 7
- i.
1883 1
1923 1958 16 0
.8971' Note: Rod worth difference is ((SIMULATE - Measured)/SIMULATE) x 100%
Yes* - Failed the D' test but passed the K-S and Kuiper tests Table 7 SIMULATE Peak Differential Control Rod Worth Comparisons Plant Mean Std. Dev.
Number Max.
Min.
Normal Plant
(%)
(%
Of Obs.
Ma.
M.
Nrl North Anna 5.0 8.0 39 30.6
-12.2 Yes Surry 6.0 8.3 54 20.1
-17.0 Yes Combined l
5.6 l
8.1 l
93 30.6
-17.0 l Yes I
Note: Differential rod worth difference is ((SIMULATE - Measured)/SIMULATE) x 100%
38 I
~~~
~~~~i r
I I
I I
I I
Figure 11 Combined Peak Differential Rod Worth Comparison 25-20-J Nor
- 15 N
-20
-16
-12
-8
-4 0
4 8
12 16 20 24
% Difference 39 28 32
Figure 12 North Anna Unit 1, Cycle 4 Bank B Differential Rod Worth 9
a 7
2
.C
'S t:3z 3 2
I 0
0 26 50 75 100 126 150 Bank B Position (steps withdrawn) 176 200 226 Figure 13 North Anna Unit 2, Cycle 15 Bank B Differential Rod Worth 0
26 s0 76 100 125 10 175 200 225 Bank 8 Position (steps withdrawn) 40 12 10 6
S 0
1-Z I
az
Figure 14 Surry 2, Cycle 10 Bank B Differential Rod Worth
£ 0
I 0
25 50 75 100 125 10 Bank B Position (steps withdrawn) 176 200 225 Figure 15 Surry 1, Cycle 17 Bank B Differential Rod Worth t6 4
2 0
0 25 60 76 100 125 150 Bank B Position (steps withdrawn) 175 200 225 41
3.3.3 Isothermal Temperature Coefficient The isothermal temperature coefficient is measured at BOC, HZP as part of startup physics testing. Earlier core measurements included unrodded as well as several rodded configurations for the ITC measurement. Later cycles typically include only the ARO condition. The temperature change for the ITC is usually 3-5 F.
Sources of measurement uncertainty for the ITC include reactivity computer bias, reactivity computer uncertainty, and uncertainty in the measurement of the temperature change. Reactivity computer accuracy is determined during startup physics testing by verifying that measured and predicted doubling and halving times for a given reactivity insertion match within +/- 4%. Using assumed uncertainty values of 4% for the reactivity computer and 0.1 °F for the temperature change (about 2.5%) leads to a root sum square (RSS) estimate of ITC measurement uncertainty of about 5%. The measured ITC is usually determined using the average of a heatup measurement and a cooldown measurement. Ideally, the two measurements should be the same. In practice, they can vary and are considered acceptable measurements if they agree within 1 pcm / F. An estimate of measurement uncertainty based on acceptable differences between heatup and cooldown measurements is therefore +/- 0.5 pcm / F.
Figures 16 and 17 present the SIMULATE versus measured ITCs for North Anna and Surry, respectively. Uncertainty bands of +/- 3 pcm/OF about the 450 line (measured = predicted) are shown for reference. A least squares fit through the pairs of points (SIMULATE, measured) shows excellent correlation of the slope, but with a slight SIMULATE bias of less than +1 pcm/°F. Table 8 presents the same data in statistical format, including the data for Surry and North Anna combined.
Although only the ITC is measured, the same comparison statistics are used for the MTC. The Doppler coefficient portion of the MTC is small (between 1 and 2 pcm/OF) and nearly constant at all reactor operating conditions, whereas the MTC component is highly dependent on fuel enrichment, soluble boron concentration, and moderator density.
42
Figure 16 North Anna HZP BOC ITC Comparison
-9
-6
-1 Predicted ITC (pcnF)
Figure 17 Surry HZP BOC ITC Comparison 8.00
-4.00 0.00 Predicted ITC (pcm/F) 43 3
41 I
i 6I
-9
-9
-13
-17
-13 3
4.00 0.00
.4.00
-8.00
-12.00
-12.00 (I
4.00
Table 8 SIMULATE HZP BOC ITC Comparisons Plant Mean Sigma Nobs Max.
M.
Normal D'
D DI D'
K-S l Kuiper l Caic.
0.05 (pcmlF) (pcmlF) -__j__-___
P=.025 P=.05 P=.95 P=.975 Sig Lj Sig L JW W
NRF NRF NA 0.84 0.73 38 2.24
-1.72 Yes' 0.5773 0.9825 0.9148 0.938 2
5.3 SU 0.44 0.55 49 1.49
-1.64 Yes' 0.5557 0.9787 0.9325 0.947 0
0.0 ALL 0.62 0.66 87 12.24
-1.72 Yes*
215.2 *222.2 223.5 231.8 232.2 0.3182 10.8651 1 i
2 2.3 Note: ITC difference is (SIMULATE - Measured) (pcm/F)
Yes' - Failed the W test but passed the K-S and Kuiper tests Yes* - Failed the D' test but passed the K-S and Kuiper tests 44
3.3.4 Differential Boron Worth The differential boron worth (DBW) is measured at BOC, HZP as part of startup physics testing. Measured differential boron worth is determined by dividing the measured control rod worth (boron dilution method) by the change in critical boron from the same bank worth measurement. Prior to the use of the rod swap technique, several bank worth measurements were made in sequence (i.e. D-bank, D+C-bank, D+C+B-bank, etc.) using the dilution method. These measurements can be collapsed into a single total rod worth and total boron change, or can be treated as multiple measurements of essentially the same quantity (the differential boron worth is only a weak function of boron concentration). Later cycles typically include only the reference bank worth measurement.
Assessment of DBW Measurement Uncertainfv Sources of measurement uncertainty for the DBW include reactivity computer bias and uncertainty (contained in the measured rod worth), uncertainty in the manual measurement of each partial segment of the measured bank worth, and measurement of the two critical boron concentration endpoints. Uncertainty in the boron measurement has varied over time with procedural changes (number of multiple measurements and measurement consistency requirements) as well as equipment changes (manual versus automatic titration).
An estimate of critical boron measurement uncertainty can be made based on ANSI/ANS Standard 19.6.1-1997 (Ref. 24), which recommends continuing boron sampling until three consecutive samples are obtained which (1) show no trend and (2) are within 10 ppm of the three sample average. This implies a maximum acceptable boron measurement uncertainty of approximately +/- 10 ppm. The boron change for single bank measurements has averaged roughly 175 ppm at North Anna and Surry. For two endpoint measurements (three-sample average), the RSS uncertainty for two boron endpoint measurements is 14 ppm, which represents a maximum measurement uncertainty in the boron worth measurement due to boron measurement uncertainty alone of about 8%. For early cycles with multiple dilution-45
type rod worth measurements, the use of the total rod worth and boron change for multiple banks will reduce this uncertainty by approximately a factor of 3. However, only a few cycles used the dilution method for multiple rod banks. It is therefore likely that an uncertainty factor for the predicted boron worth derived from comparison to measurements will be unrealistically high by several percent.
Effect of Reactivity Computer Bias on DBW Measurement Uncertaintv A technique for estimating the magnitude of the reactivity computer bias can be developed using the following observations.
46
] Figure 19 is a histogram of the raw DBW data. Each bin represents +/- 1% about the indicated midpoint % difference value.
47
Indirect Evidence of DBW Uncertainty Indirect indication of the SIMULATE DBW uncertainty comes from the critical boron data discussed in Section 3.2.1. The raw DBW data in Table 9 indicates a 2ca SIMULATE DBW uncertainty of about 7% and a maximum observed difference of 9.6%. These data were measured for soluble boron concentrations ranging from approximately 1000 ppm to over 2000 ppm. Figure 20 confirms that there is no significant trend of DBW error with critical boron concentration, therefore the SIMULATE integral boron worth can be expected to exhibit bias and uncertainty similar to the SIMULATE differential boron worth. Based on this observation, critical boron differences due to boron worth error alone in the range of 70 ppm (7% x 1000 ppm) to 192 ppm (9.6% x 2000 ppm) are expected to be observed in the critical boron data. However, the largest observed boron difference for all BOC measurements due to all sources of bias and uncertainty combined is 54 ppm (absolute value from Table 5). This suggests that the true DBW uncertainty is significantly lower than the DBW statistics indicate.
48
Figure 18 Table 9 SIMULATE HZP DBW Comparisons Note: DBW % difference is 100 x (SIMULATE - Measured) / SIMULATE 49 Plant Data Mean St.
Number Plant lAdjustment l(% diff.)
D d.
Of Obs.
Max.
Min.
Normal North Anna None 0.0 3.2 30 7.6
-6.1 Yes Surry None 0.3 4.2 35 9.6
-7.8 Yes Combined None 0.2 3.7 65 9.6
-7.8 Yes Combined e[
[ I C
[
1 [
1 Ys
Figure 19 Combined Differential Boron Worth Comparison a,ca it 0
-10
-8
-6
-4
-2 0
2 4
6 8
10 DBW % Difference Figure 20 Combined DBW Error vs. Critical Broron Concentration 50 10.0 S
C cS a
C ma C-aa
-10.0 I
I I
I I
I 600 800 1000 1200 1400 1600 1800 2000 Average Critical Boron (ppm) 2200
3.3.5 Estimated Critical Position An estimated critical rod position (ECP) calculation is required prior to restarting a reactor after a period of time at zero power (such as after a trip or maintenance outage). All reactivity elements of the CMS model are tested in this calculation because soluble boron worth, power defect, partially inserted control rod worth, axial flux redistribution effects, transient fuel isotope and fission product worth (such as Xe135, Sm'49, Np239 decay to Pu239, and others) are all involved. The xenon concentration and boron concentration may be higher or lower than the HFP equilibrium value depending on the power history, down time, and desired control rod position.
There are two primary sources of measurement uncertainty for an ECP calculation.
The largest is the measurement uncertainty of the critical boron concentrations for a critical condition prior to the outage and for the critical re-start condition. A second source of uncertainty is the exact timing and power history for the ramp down or trip prior to the outage. For long outages, xenon completely decays away and the timing uncertainty is negligible. For short outages, xenon can change at the rate of about 150 pcm / hour. Although there is no reliability factor associated with the ECP calculation, an administrative limit of +/-500 pcm is typically used to screen for unexpected reactivity anomalies. The ECP calculation is a useful indicator of overall model accuracy for reactivity calculations.
A total of 71 ECP calculations were run for seven Surry Unit 1 cycles, ten Surry Unit 2 cycles, ten North Anna Unit I cycles, and eight North Anna Unit 2 cycles. For the Surry cycles, core bumup ranged from 78 to 16653 MWD/MTU, D-bank position at restart ranged from 82 to 212 steps withdrawn (ARO position is 225 steps), and down time ranged from 7.8 to 1798 hours0.0208 days <br />0.499 hours <br />0.00297 weeks <br />6.84139e-4 months <br />. For the North Anna cycles, core burnup ranged from 225 to 14632 MWD/MTU, D-bank position at restart ranged from 16 to 215 steps withdrawn (ARO position is 225 steps), and down time ranged from 6.3 to 2150 hours0.0249 days <br />0.597 hours <br />0.00355 weeks <br />8.18075e-4 months <br />. Two SIMULATE cases were run for each ECP. The first represents a critical condition (typically HFP, equilibrium Xe) measured just prior to the outage.
51
The second represents the measured critical restart condition. The ECP error is calculated as follows:
ECP Error (pcm) = (Kstartup - Kprevous)/(Kstartup*Kprevious)*100000 where Kprevious is the SIMULATE K-effective for the critical at power condition prior to the outage and Kstartup is the SIMULATE K-effective for the restart critical conditions.
Note that because the error is calculated relative to a known previous critical condition, the ECP error is free of overall reactivity bias. The startup K-effective can also be used directly to estimate critical boron difference (see Table 5).
Table 10 presents the ECP error statistics. Figure 21 is a histogram of the same ECP error data. There is a slight positive bias (SIMULATE restart K-effective higher than measured). Figure 22 demonstrates that the source of the bias is primarily in the middle of the boron range (the critical boron of the critical condition prior to the outage). This is most likely due to reduced Bl0 depletion effects for the restart condition caused by boration and dilution during the outage. B depletion effects are not significant at high boron concentration (near BOC) or at low boron concentration (insignificant boron reactivity). The data used for ECP error statistics has not been adjusted to eliminate the effect of Bl0 depletion. Inclusion of the effects of B'° depletion will tend to increase the bias and standard deviation of the ECP error. A more complete discussion of B' 0 depletion effects is provided in Section 3.3. 1.
The results presented in Table 10 and in Figures 21 and 22 indicate excellent SIMULATE agreement with measured data and preclude any large bias or uncertainty related to power defect, xenon worth, control rod worth, or boron worth.
52
Table 10 SIMULATE ECP Error Mean Std.
Number Ma.
M.
Nrl Plant (pcm)
Dev Of Obs.
Max.
Min.
Normal North Anna 22 107 38 297
-231 Yes Surry 42 142 33 322
-213 Yes COMBINED 31 124 71 322
-231 Yes Note:
ECP Error (pcm) is (Kstartup - KPre00ous)(Kstartup*0Kpre00s)*1 0000 where Kpm,,i.. is the SIMULATE K-effective for the critical at power condition prior to the outage and Kstartup is the SIMULATE K-effective for the restart critical conditions.
53
Figure 21 Combined ECP Results 0
1 U
02 1 00 E
z IiG e z 5 2 T
wI
-300
-200
-100 0
100 200 300 400 ECP Error (pcm)
Figure 22 Combined ECP Error Versus At-Power Critical Boron
-1.............
I.............
0 200 400 600 800 1000 1200 1400 1600 Critical Boron {Prior to shutdown; ppm)
E 100 2
0 L
LU -100 54
3.3.6 Reaction Rate Comparisons Flux mapping is routinely performed using movable in-core fission chamber detectors for each cycle on a monthly basis and at approximately 30% and 70%
power durng initial power ascension following a refueling. Figure 23 shows the in-core detector flux thimble locations (identical for North Anna and Surry). For routine flux mapping, the CECOR code (Ref. 18) is used to align, calibrate, and normalize the reaction rate data obtained using five independent detectors so that the core power distribution and peaking factors can be synthesized.
Each axial flux trace (a pass) is obtained by withdrawing the detector and drive cable through the flux thimble from the top of the fuel assembly to the bottom at a fixed rate. A total of 61 or 610 "snapshots" are collected at equally spaced time intervals during each pass. CECOR performs a synthesis of measured reaction rate data, predicted reaction rate data, and predicted assembly power and peaking factor data to obtain the core power distribution, including RPD, F(z), FAH, and FQ(z). RPD (relative power density) is the average of the axially integrated power of all fuel pins in a fuel assembly divided by the core average axially integrated fuel pin power. F(z) is the core average axial power distribution. FAH is the enthalpy rise hot channel factor (also referred to as the "peak pin") and represents the highest axially integrated fuel pin power divided by the core average axially integrated fuel pin power. FQ(z) is the ratio of the highest local pin power at each elevation divided by the core average axially integrated fuel pin power.
In the flux mapping process described above, only the reaction rates are directly measured. Therefore, in order to determine an appropriate reliability factor for FAH, FQ(z), and peak FQ, the uncertainty of the following components of the process must be assessed and combined:
- 1) Thimble reaction rate uncertainty (integral for RPD and FAH, 32 node for FQ(z)). This uncertainty will be derived using SIMULATE predictions and measured thimble reaction rates from the flux maps for each cycle.
55
- 2) Uncertainty in the reconstruction of measured assembly RPD (and local RPD(z)) from the thimble reaction rates. This component is discussed in Section 3.1.
- 3) Uncertainty in the reconstruction of FAH and FQ(z) from the RPD. This component is also discussed in Section 3.1.
Two separate sets of reaction rate comparison statistics are needed. Axially integrated reaction rates are needed to develop uncertainty factors for 2-D quantities RPD and FAH. Reaction rates at multiple axial locations are needed to develop uncertainty factors for FQ.
For each flux map, measured reaction rates are normalized to the average of all measured reaction rates in instrumented assemblies. For the same set of fuel assemblies, predicted reaction rates are normalized to the average of all predicted reaction rates. The normalized measured and predicted integral reaction rates are then accumulated for all maps for the calculation of integral difference statistics.
Normalized integral reaction rates of 1.0 or less are discarded because they represent fuel assemblies with less than core average relative power. Low power assemblies not only have higher measurement uncertainty, but they are also not of interest for the determination of peaking factor uncertainty factors, because high peaking factors are found in high power assemblies.
Reaction rates at multiple axial locations are needed to develop uncertainty factors for FQ. Normalized measured and predicted reaction rates at 32 axial locations are accumulated for all maps for the calculation of difference statistics. These reaction rates correspond to the "mini" integrals over 32 equally spaced axial core regions (with a 1:1 correspondence with each SIMULATE axial node). The measured axial reaction rates are collapsed from 61 measured points to 32 integrals by trapezoidal integration of the measured data. As with RPD and FAH, reaction rates of 1.0 or less are discarded.
56
A listing of flux maps used to develop the reaction rate comparison statistics is provided in Table 11. Flux mapping is typically only performed when the core is axially stable (no more than 1% per hour axial offset change). SIMULATE predictions are also normally based on equilibrium xenon conditions. However, transient modeling of the N C11 startup in Section 3.3.7 demonstrates that maps (particularly during initial power ascension) are sometimes taken at relatively stable but non-equilibrium xenon conditions, and that the axial offset can vary significantly from the equilibrium value. Therefore, to get a valid comparison of measured and predicted reaction rates, both the core and the model need to be close to equilibrium conditions (as with most full power flux maps), or the reactor history needs to be modeled in detail (as with the NIC 1 startup). Because detailed operating history modeling is impractical for the large number of flux maps needed to develop the uncertainty factors, a tolerance of +/- 4% axial offset difference was used as a filter for probable mismatches between measured conditions and the assumed equilibrium SIMULATE conditions.
Figure 24 is a histogram of the thimble integral differences. The difference is defined as the (Predicted - Measured) / Predicted (%) for all normalized reaction rates > 1.0. Figure 25 is a corresponding histogram of the 32 node differences. In both Figures, each bin represents +/- 0.5% about the value indicated. Table 12 contains the difference data statistics for Surry maps, North Anna maps, and for all maps combined.
57
Figure 23 In-core Moveable Detector Locations R
P N
M L
MD K
J H
G F
E D
C MD Mn MDIMD lMni MD MD MD MD-MD MD IMD MD MD I
MDMD MD MD MDI IIIMDI I IMD MDIMD MD MD MD MD MD IMD MD - Moveable Detector 58 MD MD
_ _ M--
MD MD __
_MD
_ M MD MDI M
_M _
D MD
_M
_=
M 4
+ -
4-4
---
4-
+
1 -4-
B A
1 2
3 4
5 6
7 8
Table 11 Flux Map Database for Reaction Rate Comparison D-bank AIO Map Bumup Core CECOR SIMULATE CYCLE (steps Difference (MWDIMTU) wid)
Power fO(
)
fO(
%)
(C - S)
NICI 9
50 210 49
-2.6
-4.1 1.5 25 300 216 96
-8.3
-8.6 0.3 N1C2 12 110 192 45 6.7 5.8 0.9 21 1129 220 99 0.5
-0.1 0.6 30 4490 215 100
-1.7
-3.5 1.8 47 8811 228 100
-0.4
-2.2 1.8 NIC3 87 12433 214 99
-1.9
-2 0.1 N1C4 5
41 188 52 4.2 1.2 3.0 7
305 221 100 0.2
-0.5 0.7 18 6834 214 100
-4.6
-3.6
-1.0 29 12241 222 100
-2.7
-2.4
-0.3 NIC5 23 6831 224 100
-2.3
-2.8 0.5 34 12983.2 228 100
-0.9
-1.2 0.3 N1C6 3
55 170 49
-3.2
-3.2 0.0 6
69 181 75
-4.8
-4.8 0.0 9
378 219 100
-1.6
-2.2 0.6 19 8170 228 96
-2.0
-1.9
-0.1 29 14340 228 100
-1.2
-1.6 0.4 N1C7 2
37 179 49 2.8 1
1.8 19 7404 228 100
-2.6
-2.9 0.3 29 15400 228 100
-1.6
-1.7 0.1 N1C8 1
14 163 29
-1.7
-0.3
-1.4 2
47 192 74 0.5
-0.5 1.0 6
1243 228 100 0.2
-1 1.2 13 9462 228 100
-2.5
-2.6 0.1 21 16201 228 100
-0.6
-1.8 1.2 N1C9 1
14 133 24
-13.7
-11.8
-1.9 6
305 228 99
-2.4
-5.7 3.3 19 9842 228 100
-2.7
-2.7 0.0 29 16830 228 95 0.5
-1 1.5 NlClO 1
6 137 30
-7.3
-8.9 1.6 4
1452 225 100
-2.0
-4.2 2.2 12 9513 225 100
-2.4
-2.5 0.1 18 16233 225 100
-0.9
-1.2 0.3 NlCll 1
4 124 30
-12.7
-13.7 1.0 2
37 179 74
-6.3
-6
-0.3 4
1908 225 100
-1.7
-3.9 2.2 11 9852 225 100
-2.1
-2.7 0.6 17 16963 225 100 0.0
-1 1.0 59
Table 11 (continued)
D-bank A/O Map Burnup Core CECOR SIMULATE CYCLE (steps Difference (MUWD/MTU) w/)
Power (%) A/O (%)
A1O (%)
(C-S wid)
(C -S)
N1C12 1
5 152 30
-3.4
-3.5 0.1 2
25 213 74 3.3 2.2 1.1 4
1792 225 100
-1.1
-2 0.9 10 8698 225 100
-2.4
-2.7 0.3 16 15591 225 100
-1.0
-1.7 0.7 N1C131 2 36 189 74
-2.3
-4.4 2.1 4
1758 225 100 0.6
-1.9 2.5 10 8590 225 100
-1.0
-2 1.0 19 16618 225 100
-0.7
-1.3 0.6 N1C14 1
8 156 29
-2.5
-3.6 1.1 2
31 183 71
-1.6
-3.3 1.7 4
1553 227 100 0.3
-1.2 1.5 11 9782 227 100
-1.5
-2.5 1.0 18 17911 227 100
-1.4
-1.3
-0.1 NIC15 2
30.3 194 70
-0.5
-3.2 2.7 1 4 1303 225 100
-1.2
-4.2 3.0 10 8678 225 100
-1.6
-2.5 0.9 17 17073 225 100
-0.9
-0.9 0.0 N2C1 19 280 186 76
-14.1
-10.9
-3.2 40 8011 203 100
-3.7
-3.3
-0.4 N2C2 17 1700 223 100 2.6 0.3 2.3 21 4110 228 100
-0.8
-1.7 0.9 30 7844 218 100
-2.4
-3.4 1.0 N2C3 2
0 177 3 1 1.0 1.9
-0.9 1 3 671 228 100
-3.6
-4.1 0.5
_25 7647 217 100
-2.3
-3.8 1.5 38 13299 221 100
-0.5
-1.7 1.2 N2C4 2
65 162 50
-3.9
-5.8 1.9 7
230 216 100
-1.3
-3.3 2.0 23 7906 222 100 X_-2.3
__X_-2.7 0.4 34 14612 228 100
-1.2
-1.4 0.2 N2C5 2
5 145 27
-8.1
-8.3 0.2 8
250 228 100
-0.4
-1.9 1.5 22 8370 228 100
-2.6
-3.0 0.4 35 15295 228 100
-1.4
-1.6 0.2 N2C6 4
222 1
228 100
-1.3
-3.5 2.2 16 8586 228
_100
-2.9
-3.0 0.1 24 15516 228
_100 I-1.1_
-1.6 0.5 60
Table 11 (continued)
D-bank A10 Map Burnup Core CECOR SIMULATE CYCLE (steps Difference (MWDIMTU) wld)
Power (%) AO (%)
O (%)-
S)
N2C7 1
19 123 30
-11.0
-9.7
-1.3 8
800 228 100
-0.2
-2.4 2.2 15 8339 228 100
-1.6
-1.8 0.2 24 15823 228 100
-1.3
-1.7 0.4 N2C8 1
18 150 28
-2.6
-5.1 2.5 7
1505 228 100
-0.5
-2.2 1.7 14 9129 228 100
-2.5
-2.9 0.4 25 16640 228 100
-0.9
-1.7 0.8 N2C9 3
159 225 100 2.3 0.3 2.0 11 8571 225 100
-2.1
-2.9 0.8 21 16086 225 100
-1.3
-1.9 0.6 N2CIO 3
46 173 73
-4.1
-6.5 2.4 6
1782 225 100
-2.7
-3.4 0.7 14 10811 225 100
-2.6
-2.7 0.1 20 17126 225 100 0.8
-1.2 2.0 N2C11 1
8 130 29
-6.5
-8.6 2.1 2
46 192 74
-2.3
-1.9
-0.4 4
1517 225 100 0.0
-2.2 2.2 11 9713 225 100
-1.9
-2.6 0.7 17 16107 225 100
-1.1
-1.6 0.5 N2C12 1
4 125 30
-10.0
-11 1.0 2
27 186 72
-1.5
-1.3
-0.2 4
1109 225 100 0.8
-0.5 1.3 12 10449 225 100
-1.9
-2.5 0.6 19 16589 225 100
-1.2
-1.7 0.5 N2C13 2
20 191 70
-2.2
-2.7 0.5 4
1445 225 100
-0.5
-3 2.5 12 9985 225 100
-1.5
-2 0.5 18 17042 225 100
-0.8
-1.3 0.5 N2C14 3
56 190 75
-0.6
-2.2 1.6 4
289 225 100 0.8
-0.8 1.6 12 9429 225 100
-1.9
-2.4 0.5 19 17746 225 100
-0.8
-1.4 0.6 61
Table 11 (continued)
D-bank NO Map Burnup Core CECOR SIMULATE CYCLE (steps Difference (MWDIMTU) w/d)
Power (%) NO (%)
A/O (%)
(C - S)
S1C04 19 6968 207 100
-4.7
-4.8 0.1 SICO5 10 150 221 100
-0.3
-3.4 3.1 S1CO6 56 7518 228 100
-0.9
-2.0 1.1 74 14752 226 100
-0.1
-1.5 1.4 S1C07 3
6 180 51 0.7
-3.1 3.8 11 1612 227 100 1.0
-1.9 2.9 24 9593 225 100
-1.9
-2.5 0.6 S1CO8 36 6873 227 100
-1.8
-2.5 0.7 50 13212 212 99
-0.6
-3.6 3.0 S1CO9 2
14 168 50
-0.1
-3.6 3.5 6
240 220 100 1.0 0.8 0.2 29 8640 228 100
-0.9
-2.1 1.2 SlCl0A 19 3373 217 100
-1.0
-2.8 1.8 29 7419 224 100
-0.1
-2.4 2.3 1 48 13908 224 94 2.9 0.6 2.3 SiCi 7
626 219 100
-0.1
-3.5 3.4 15 6670 224 100
-1.1
-2.4 1.3 21 12640 224 100
-1.0
-1.5 0.5 S1C12 3
28.4 163 69
-5.1
-7.1 2.0 5
178 220 100 4.1 0.6 3.5 14 9266 224 100
-1.0
-1.8 0.8 23 16789 223 100
-0.5
-1.8 1.3 S1C13 2
19 196 70
-3.1
-6.5 3.4 13 7836 224 96 0.9 0.1 0.8 24 14678 224 100 1.8 1.0 0.8 S1C14 2
28 181 54
-5.1
-7.0 1.9 4
1500 224 100
-2.8
-5.2 2.4 14 8600 226 100
-0.2
-1.0 0.8 22 15978 225 100 1.1 1.3
-0.2 S1C15 4
88 192 68 0.0
-2.1 2.1 5
238 225 100
-0.5
-1.8 1.3 13 8723 225 100
-0.4
-0.9 0.5 20 15870 226 100 0.6 0.0 0.6 S1C16 3
35 193 69 0.2
-3.0 3.2 5
1332 227 100
-0.2
-2.3 2.1 13 8705 228 100
-0.7
-1.2 0.5 19 14098 228 100 0.7 0.0 0.7 62
Table 11 (continued)
D-bank A10 Map Bunup Core CECOR SIMULATE CYCLE (steps Difference (MWDIMITU) wi)
Power (%) N{O (%t NtO (%)
(C-S wld)
(C -S)
S1C17 2
22.5 200 68
-1.0
-2.5 1.5 6
2243 225 100
-1.3
-3.0 1.7 12 8551 225 100
-0.7
-1.1 0.4 20 16856 225 100 1.0 0.5 0.5 S2C04 17 4524 218 100
-1.0
-3.1 2.1 36 13200 222 100 0.5
-1.6 2.1 S2C05 13 450 215 100 2.3 0.5 1.8 24 6653 227 100 0.5
-1.7 2.2 S2C06 4
17 180 59
-5.3
-5.3 0.0 7
1116 228 100
-0.9
-2.8 1.9 18 7390 228 100
-1.5
-2.3 0.8 31 15326 228 100
-0.5
-1.1 0.6 S2C07 2
10 178 47 0.9
-3.0 3.9 5
198 228 100
-0.1
-2.1 2.0 45 14150 223 100
-0.6
-1.4 0.8 S2C08 3
31 157 46
-7.5
-9.9 2.4 S2C09 17 6887 223 100 0.3
-2.0 2.3 S2C1O 22 8016 222 100
-1.3
-2.6 1.3 50 13935 222 90 0.3 0.0 0.3 S2C11 3
43 182 68
-1.0
-3.1 2.1 13 2986 221 100 0.0
-1.2 1.2 22 9650 223 100
-1.2
-2.2 1.0 32 17246 223 100
-0.6
-1.6 1.0 S2C12 2
28 165 57
-2.8
-5.4 2.6 4
646 224 100 1.5
-0.9 2.4 16 9368 217 94
-0.5
-0.8 0.3 28 17575 224 100 0.0
-0.9 0.9 S2C13 2
20 177 69
-3.4
-5.1 1.7 4
890 225 100
-0.2
-1.6 1.4 10 4876 224 100
-1.6
-1.8 0.2 11 5416 224 100
-1.7
-1.9 0.2 18 12044 226 100
-1.5
-1.6 0.1 S2C14 2
19 184 71 0.7
-1.9 2.6 4
1126 226 100 1.8 0.7 1.1 11 8204 225 100
-1.6
-1.5
-0.1 19 15356 223 100
-1.3
-1.5 0.2 S2C15 4
178 228 100 0.2
-3.3 3.5 13 8514 227 100
-0.7
-1.2 0.5 20 15909 228 100
-0.1
-0.6 0.5 63
Table 11 (continued)
D-bank NO Map Burnup Core CECOR SIMULATE CYCLE (steps Difference (MWDIMTU) wid)
Power (%)
A/O (%)
AJO (%)
(C - S)
S2C16 4
1412 225 100 0.2
-1.8 2.0 11 8762 225 100
-1.8
-2.0 0.2 X 19 15314 225 100
-0.4
-0.9 0.5 S2C17 2
34.8 185 66 2.0
-1.2 3.2 64
Figure 24 Flux Map Thimble Reaction Rate Comparisons Integral Trace Data
-6
-C
-4
-3
-2
-1 0
1 2
3 4
5 6
Reaction Rate Difference (%)
Figure 25 Flux Map Thimble Reaction Rate Comparisons 32 Axial Regions 0-Mo' 0/
0-0 0 9 -8
-7
-6 4 2
-1 0 1
2 3
4 5
6 7
8 9 10 Reaction Rate Difference (%)
65 I0 1800 1600 1400 1200
.1000 Io 0
600 400 200
Table 12 Flux Map Reaction Rate Statistics Plant Data Mean Std.
Number Max.
Min.
Pant Type
(% Diff.)
Dev.
Of Obs. (% Diff.)
(% Diff.)
Normal North Anna Integral
-0.02 1.34 3453 5.8
-6.2 No Surry Integral 0.07 1.34 2322 5.1
-6.1 No Combined Integral 0.01 1.34 5775 5.8
-6.2 No North Anna 32 Node 0.14 2.41 93070 16.4
-12.8 No Surry 32 Node 0.38 2.79 64354 13.8
-15.1 No Combined 32 Node 0.24 2.58 157424 16.4
-15.1 No Note:
Reaction rate difference is ((SIMULATE - Measured) / SIMULATE) x 100% for all normalized reaction rates > 1.0.
66
3.3.7 Normal Operation Power Transients Normal operation plant transient modeling provides an opportunity to test the performance of the SIMULATE model in a dynamic manner. Operational transients involve all reactivity components of the model, including thermal-hydraulic feedback, power and temperature defects, boron worth, control rod worth, and transient xenon worth. Reactivity performance can be assessed using measured critical boron concentrations. These reactivity components also have an impact on the core axial power distribution, which can be monitored via the ex-core instrumentation (measured delta-I or axial offset). In some cases, a limited amount of in-core flux map information is also available.
Measured plant transients were modeled for the following:
S2C2 - 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> 100-50-100 load follow test on 8/1-8/2/75.
NIC3 - two EOC return to power scenarios on 4/16-4/20182 and 4/30-5/2/82.
N1 C6 - power transient initiated on 12/26/86.
NIC9 - 95% power EOC MTC measurement on 6/15/92.
NIC 1 - BOC power ascension to 100% 10/8/94-10/17/94.
N2C14 - power transient initiated 10/14/00.
Comparison to measured data includes critical boron concentration, axial offset, delta-I, and peak F(z).
Axial offset (AO) is a measure of axial core power imbalance. AO is defined as the power in the top half of the core minus the power in the bottom half of the core divided by the total core power. Delta-is equal to AO times the core relative power (fraction of full power). Peak F(z) is the maximum point in the core average relative axial power distribution F(z).
67
S2C2 Load Follow Demonstration A twenty-four hour 100-50-100 load follow test was conducted for S2C2.
Measured data was gathered every twenty minutes for delta-1, peak core average axial power F(z), and critical boron concentration.
Figure 26 provides the core power and D-bank position as a function of time.
Figures 27, 28, and 29 show the comparison of SIMULATE and measured delta-1, critical boron concentration, and peak F(z), respectively. SIMULATE calculated delta-I versus time follows the measured values to within about +3% / -1 % after accounting for an initial bias of roughly -2%.
SIMULATE critical boron values follow the measured values within about +14 ppm / -20 ppm after accounting for an initial bias of -34 ppm. SIMULATE calculated peak F(z) values are low by 0.01-0.04, but follow the trend well.
Comparison of Figures 27 and 29 demonstrates that delta-I agreement based on calibrated ex-core detectors is a relatively good indicator of axial power shape agreement (represented by peak F(z) from in-core measurements).
68
Figure 26 S2C2 Load Follow Transient Power and D4Bank Position Versus Time 200 -
4 8
12 16 20 24 Time (hours)
Figure 27 S2C2 Load Follow Transient Delta-I Comparison 0
4 8
12 16 20 24 Time (hours) 69 110 100 90 80 70 60 60 40
-r U-
Figure 28 S2C2 Load Follow Transient Critical Boron Comparison 4
8 12 16 20 Time (hours)
Figure 29 S2C2 Load Follow Transient Peak Core Average Axial Power Comparison 0
4 8
12 16 20 Time (hours) 70 980 960 E
- a. 940 ca c 920 00 4
900 a0
=0 880 840 0
24 1.32 IL a
51 4a a,
'U 24
NIC3 Tnp and Return to Power Two sets of measured data were recorded near the end of North Anna unit 1, Cycle 3 during power escalations following reactor trips. The first incident (transient 1) occurred on April 16-20, 1982, and the second (transient 2) on April 30 -
May 2, 1982. Hourly readings of delta-I and eight critical boron measurements were taken during transient 1. During transient 2, both ex-core delta-I readings and in-core axial offset measurements were performed, because delta-I cannot be measured accurately at very low power levels. Note that in-core measurements were performed on only four or five assemblies each time and may therefore not be completely representative of core average behavior.
The delta-f readings have been converted to axial offsets in order to compare SIMULATE results to both types of data.
Figure 30 provides the core power and D-bank position as a function of time for case 1. Figures 31, and 32 show the case 1 comparison of SIMULATE and measured delta-I and critical boron concentration respectively.
Figure 33 provides the core power and D-bank position as a function of time for case 1.
Figures 34, and 35 show the case 2 comparison of SIMULATE and measured delta-I and critical boron concentration respectively. The two N1C3 transients are very wide ranging in both reactivity (critical boron) and delta-I.
For both transients the SIMULATE delta-I (or axial offset) and critical boron predictions are in excellent agreement with the measured data. In the transient 1 delta-I plot, a small difference that oscillates from positive to negative and back with a period of about 30 hours3.472222e-4 days <br />0.00833 hours <br />4.960317e-5 weeks <br />1.1415e-5 months <br /> is apparent. This could be due to a pre-existing xenon oscillation.
71
Fiqure 30 NIC3 Power Transient I Power and D-Bank Position Versus Time 220 200
-180 160 c 140 1 120 a 100 aS e
-80,
-60 '
m0 40 20 0
-20
-10 0
10 20 30 40 50 60 70 80 Time (hours)
Figure 31 NI C3 Power Transient I Delta-I Comparison 10 20 30 40 50 60 70 80 lime (hours) 72 110 100 90 80 70 60 o
50 t
40 30 20 10 0
-10 25 20 15 10 5
Ia a
0
-5
-10 0
Figure 32 N1C3 Power Transient I Critical Boron Comparison 0
10 20 30 40 50 60 70 80 Time (hours)
Figure 33 NIC3 Power TransIent 2 Power and D-Bank Position Versus Time 220 200 180 160 140 120 100 I S
E0 z
so E, m
60 D 0
10 20 30 40 S0 60 Time (hours) 73 300 EF 250 Q
C.
C.
i 200 C
2 10 0I so 90 80 70 i
60 940 U
Figure 34 NlIC3 Power Transient 2 Axial Offset Comparison 0
10 20 30 40 50 Time (hours)
Figure 35 NIC3 Power Transient 2 Critical Boron Comparison 0
10 20 30 40 50 Time (hours) 74 s0 0
60 350 E 250 c 200 ca C
.i 100 C
0 0
= 100 U
60
NIC6 Pipe Insnection During NIC6 operation, power was reduced from 100% to 20% during a secondary side pipe inspection on December 25 through December 29, 1986. The reactor was at HFP, ARO equilibrium conditions prior to the inspection. Power was reduced at a rate of about 15% per hour down to approximately 17% but was soon stabilized at 20% power. This power level proved to be low enough that the water flow through the pipe to be inspected could be stopped for the testing procedure. However, at 20% power with control rods deeply inserted, power was forced to the top of the core.
During this event, the axial power distribution changed dramatically due to changing thermal hydraulic feedback (core power changes), control rod insertion for both reactivity and axial power control, and an induced axial iodine and xenon transient.
Figure 36 provides the core power and D-bank position as a function of time. Figures 37, and 38 show the comparison of SIMULATE and measured delta-I and critical boron concentration, respectively.
SIMULATE calculated delta-I versus time follows the measured values to within about +2% / -3% after accounting for an initial bias of roughly
+2%. SIMULATE critical boron values follow the measured values within about +18 ppm
/ -15 ppm after accounting for an initial bias of -24 ppm.
An interesting feature of this transient is the full-power xenon oscillation beginning at about 50 hours5.787037e-4 days <br />0.0139 hours <br />8.267196e-5 weeks <br />1.9025e-5 months <br /> (see Figure 37). The measured delta-I indicates stable or slightly naturally damped behavior. The good agreement of the measured and predicted magnitude and timing of the axial oscillation over more than one full period indicates that the tradeoff of xenon and Doppler reactivity is in proper balance. If the Doppler feedback were too small the xenon oscillation would be divergent. If the Doppler feedback were too large, the xenon oscillation would damp out too rapidly.
75
Figure 36 NIC6 Power Transient Power and D-Bank Position Versus Time 110 100 90 80
?
70 o
60 0
4 o 40 30 20 10 0
10 20 30 40 50 Time (hours)
_ua
~
230
-210 l
- ~190
-Power 1550 R
X
.- ^-D Bank
-130 e 110 oi CL
_1_ =
-~~~~~70 i___
0S 30 so 70 0
90 100 Figure 37 NI CS Power Transient Delta-I Comparison 12 10 8
6 4
a a0
-2
-4
-8 0
10 20 30 40 S0 60 Time (hours) 70 80 90 100 76
Figure 38 NIC6 Power Transient Critical Boron Comparison 0
20 40 60 so 100 Time (houms) 77 600 650
.e 600 c.2 j 450 p0 c 400 C
5 350 300 250 120
NIC9 HFP MTC Measurement Modeling of the N1C9 HFP MTC measurement provides verification of the ability of SIMULATE to correctly calculate a moderator temperature driven axial transient in which no rod movement or significant power change occurs. Boron, temperature, and axial xenon effects are important contributors to this transient.
The measurement was performed on 6/15/92 at 95% power.
Figure 39 provides the measured moderator inlet temperature and critical boron concentration versus time.
Figure 40 shows the comparison of measured and predicted delta-I change versus time (set to zero at the beginning of the MTC measurement to eliminate bias).
SIMULATE closely matches the measured delta-I change, indicating good performance of the Doppler, xenon, and moderator temperature components of the model.
Figure 41 shows the SIMULATE K-effective drift over time for each of the three statepoints of the MTC measurement (nominal, heatup, cooldown).
Each statepoint is composed of four individual measurements. The reference K-effective for Figure 41 is the average SIMULATE K-effective for the four points in the nominal statepoint.
Each statepoint represents a critical core condition with different combinations of individual reactivity components (primarily soluble boron and moderator temperature).
Perfect agreement between measurement and prediction is indicated by eigenvalue drift of zero.
SIMULATE eigenvalue drift for the individual measurements comprising the three statepoints varies from +5 pcm to -8 pcm. The maximum difference between statepoint averages is less than 7 pcm.
This indicates that the tradeoff between soluble boron reactivity and HFP near EOC moderator temperature reactivity in SIMULATE closely matches the N1C9 core. The total reactivity worth for each component of this tradeoff (boron change and temperature change) is approximately 200 pcm.
In Section 3.3.4, the HZP BOC boron worth bias for SIMULATE was found to be negligible. Therefore, we can reasonably assume that the 7 pcm eigenvalue drift for the 78
HFP MTC measurement may be due to bias in the MTC. The core average moderator temperature change for this measurement between the first two statepoints is approximately 5 F. Therefore for this measurement, the MTC difference between SIMULATE and measurement is approximately 7 pcm / 5 F or 1.4 pcm/OF.
The magnitude of this difference is consistent with the HZP ITC differences discussed in Section 3.3.3.
79
Figure 39 NIC9 MTC Measurement Transient Measured Inlet Temperature and Critical Boron Concentration 555 553 Q 552 U
e 551 E5 4:00 5:12 6:24 7:36 8:48 10:00 11:12 Time of Day on 6115192 F-igure 40 NI C9 MTC Measurement Transient Delta-I Change from Beginning of Measurement
-61 i
I i
4:00 5:12 6:24 7:36 8:48 10:00 11:12 Time of Day on 611 5192 80 300 295 290 Xt
.°
-285 t4 0
20c 0
28-25 S
0co 275.2 270 265
-1
- -2 0,
a -3 0
Figure 41 NIC9 MTC Measurement Transient SIMULATE K-effective Drift 4-i 2 -
~
- Nominal Statepoint I -
11 Heatup Statepoint A
ACooldown Statepoint A *8-EE
-10 4:00 6:12 6:24 7:36 8:48 Time of Day on 6115192 10:00 11:12 81
'EK E
I Fb
NIC1 I nitial Power Ascension L
Modeling of the NIC 1 initial power ascension is a test of many aspects of the SIMULATE l
model including thermal feedback (HZP-HFP), xenon (0 to equilibrium HFP), and control rods (D+C in overlap). Data collected on October 8-17, 1994 during startup physics testing was used for comparison of the measured and predicted delta-I and critical boron concentration during the transient. Figure 42 provides the core power and D-bank position as a function of time.
Figures 43 and 44 show the comparison of SIMULATE and measured delta-I and critical boron concentration respectively.
SIMULATE calculated delta-I versus time follows the measured values to within about +/- 2%. SIMULATE critical boron values follow the measured values very closely (within +9 ppm / -13 ppm).
The NlC 1 initial power ascension is of particular interest because full core flux maps were obtained during the power holds at 30% and 74% power (at approximately 21 and 75 hours8.680556e-4 days <br />0.0208 hours <br />1.240079e-4 weeks <br />2.85375e-5 months <br />, l
respectively). Figures 45-46 compare the measured and predicted core average axial power shapes (F(z)) for the two initial power ascension maps. Agreement between measurement and prediction is excellent for both maps, which indicates that SIMULATE is capable of accurate power distribution calculations at low power, rodded configurations with changing
{
xenon concentrations. Table 13 includes comparison statistics for measured and predicted flux thimble reaction rates for the two NlC 1 maps. These data compare favorably with the data from all cycles discussed in Section 3.3.6.
L 82l
Figure 42 NIC1I Initial Power AscensIon Power and D-Bank Position Versus Time 240 220 200 1800 160 140 2 0
120 S 1002 E0 a
F?
4 I
4 I
I I
20 0
20 40 60 80 100 120 140 160 180 Time (hours)
Figure 43 NIC1I Initial Power Ascension Delta-l Comparison 0
20 40 S0 g0 100 Time (hours) 120 140 160 180 200 83 110 100 90 s0
-70 I60 0
8 40 30 20 10 0
Figure 44 NIC1 IInitial Power Ascension Critical Boron Comparison 1900 1800 E6 X5 1700 0
aC Z 16B00 O 1500 a
5 1400 U
1300 1200 0
20 40 60 80 100 120 140 Time (hours)
Figure 45 Core Average Axial Power Comparison NICII Flux Map 1, 29.9% Power, D@124 10 180 200 10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Axial Height (% of core height) 84 I
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I I,Z 1. - _
}1-_
0.8 I
0.8 -
'R 0.
4 o 0.4; j 0.2 0-0%
Figure 46 Core Average Axial Power Comparison N1C1I Flux Map 2, 74.0% Power, D@179 0%
10%
20%
30%
40'h 50%
60%
Axial Height (% of core height) 70%
80%
S0%
100%
Table 13 NIC1I Power Ascension Flux Map Reaction Rate Statistics Data Mean Std Number Max.
Min (%)
Normal Type
(% Duff.)
Dev.
Of Obs.
(%)
Mi.()
Nra
~~(%
Diff.)
Integral 0.4 1.8 61 4.1
-4.7 Yes 32 Node 0.2 2.2 1488 7.5
-6.1 No Note:
Reaction rate difference is ((Predicted - Measured) / Predicted) x 100% for all normalized reaction rates > 1.0.
85 1.4 1.2 air1
- 0.8
.6 9 0.4 0.2 0
1 N2C14 Power Transienf I
North Anna Unit 2 power was reduced from HFP equilibrum conditions to approximately l
27% on 10/14/2000. After holding at low power for approximately 10 hours1.157407e-4 days <br />0.00278 hours <br />1.653439e-5 weeks <br />3.805e-6 months <br />, a ramp to 100%
over about 11 hours1.273148e-4 days <br />0.00306 hours <br />1.818783e-5 weeks <br />4.1855e-6 months <br /> was initiated. Figure 47 provides the core power and D-bank position I
as a function of time.
Figures 48 and 49 show the comparison of SIMULATE and measured delta-I and critical boron concentration respectively.
I SIMULATE calculated delta-I versus time follows the measured values to within about +/-
i 5%. This agreement is not as good as some other transients. One possible explanation is the extremely deep control rod insertions, which cause the ex-core detectors to be I
shadowed by C-bank between about 9 and 22 hours2.546296e-4 days <br />0.00611 hours <br />3.637566e-5 weeks <br />8.371e-6 months <br />. Figure 48 shows SIMULATE delta-I results using both calorimetric (CAL) and ex-core nuclear instrumentation (NI) power.
l Below about 30% power, N power is typically more accurate.
Above 30% power, calorimetric power is considered more accurate. As shown in Figure 48, the difference is significant for the initial ramp down and for the period of low power operation (10-20 hours), but does not change the remainder of the transient.
SIMULATE critical boron values follow the trend in the measured values very closely, with a bias of about 60 ppm. The bias is attributable largely to a high degree of B-10 depletion due to low primary system leakage and very high load factor in N2C14.
A full-power undamped xenon oscillation begins at about 40 hours4.62963e-4 days <br />0.0111 hours <br />6.613757e-5 weeks <br />1.522e-5 months <br /> (see Figure 50). The measured delta-I indicates stable or slightly damped natural axial core power behavior.
The good agreement of the measured and predicted magnitude of the axial oscillation over more than one full period is consistent with results from the N1C6 transient. The A
timing of the oscillation appears to be shifted by several hours. The reason for this shift is not known.
Results of a reduced moderator flow sensitivity case are presented in Figure 50. There is a j
strong correlation between the flow reduction (5%) and the change in the magnitude of the 86
positive and negative delta-I oscillation. These results are not intended to justify use of a value for core moderator flow rate other than measured, but are shown to demonstrate that uncertainty in the measured flow rate for the core is a significant source of uncertainty in transient modeling. The uncertainty in core moderator flow measurement is considered to be of the same order of magnitude as the calorimetric uncertainty (roughly 2%).
87
Figure 47 N2C14 Power Transient Power and D-Bank Position Versus Time 240 220
~~~~~~~200 180 8 /
- + ~~~~~~~~~~D anklo 40 ~
0 10 20 30 40 S0 s1 70 80 90 100 Tim (hours)
Figure 48 N2C14 Power Transient Delta-l Comparison lar
.5 0
10 20 30 40 50 S0 Time (hours) 70 80 90 100 88 I
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Figure 49 N2C14 Power Transient Critical Boron Comparison 0
20 40 60 80 Time (hours) 100 Figure 50 N2C14 Power Transient Delta-l Comparison Sensitivity to Moderator Flow Rate 0
10 20 30 40 60 s0 70 s0 90 100 Time (hours) 89 650 Soo 00 I
cal 450 0
400 350 I
300 250 20 15 10 6
0 8
-6
-10 16
3.3.8 Xenon Oscillation Demonstration L
Verifying the ability of SIMULATE to accurately model plant transients provides evidence I
that SIMULATE can be used to verify acceptable design axial flux difference (AFD) operating bands via load follow simulations (FAC analysis) or via the free xenon oscillation I
technique (RPDC analysis, Ref. 11).
l For RPDC analysis, axially skewed xenon distrbutions saved at different times during an unstable axial xenon oscillation are subsequently used to vary the axial power distributions for a matrix of core conditions at different power levels and control rod insertions.
ns'ability is created by reducing Doppler feedback.
This is normally accomplished by artificially I
changing the relationship between fuel rod power and fuel temperature.
Figure 51 demonstrates an unstable xenon oscillation created using SIMULATE for the N1C15 core.
Note that the nominal SIMULATE model is naturally damped, as is the actual core. The instability in Figure 51 was created by reducing Doppler feedback to 60% of nominal. Note that the change in Doppler feedback causes a large change in the amplitude of the xenon oscillation, but only a small change in the timing. This demonstration, coupled with the results presented in Section 3.3.7 shows that SIMULATE is fully qualified to perform FAC and RPDC analyses.
90
Figure 51 NICI5 Xenon Oscillation Demonstration HFP, ARO 9000 MWDJMTU 20 -
-SIMULATE Nominal tO
--- SIMULATE 60% Doppler 10 A
5 0
0 10 20 30 40 60 60 70 80 90 100 Time (hourn) 91
SECTION 4 - UNCERTAINTY AND RELIABILITY FACTORS 4.1 DEFINITIONS Two terms will be discussed throughout this section. The Nuclear Uncertainty Factor (NUF) is defined as the calculational uncertainty for a core physics model parameter derived from a statistical analysis (where practical) of measurements and predictions of the parameter. If measurements are not available in sufficient quality or quantity to I
determine the NUF directly, comparisons can be made to higher order calculations, or the uncertainty can be inferred indirectly using observations of dependent quantities.
I The Nuclear Reliability Factor (NRF) is defined as the allowance to be applied to a safety l
related core physics model design calculation to assure conservatism. For those parameters for which a NUF has been derived, the corresponding NRF is chosen to be l
equally conservative or more conservative than the NUF. A more complete description of the NRF including values approved for use in previous design models is provided in I
Reference 23.
Ideally, the NUF is determined such that when the NUF is applied to a model prediction, the result will be conservative compared to the corresponding measurement for 95% of I
the sample population with a 95% confidence level (when a sufficiently large sample population is available). The NUF is determined as a one-sided tolerance limit even for L
parameters for which both under and over-prediction may be important for safety analysis.
A one-sided tolerance is acceptable for those parameters (such as differential boron worth) because the corresponding NRF is applied in the conservative direction for each analysis scenario. For example, if a boron dilution key analysis parameter is minimum 4
boron worth and the differential boron worth NRF is 1.05 (max) /0.95 (min), then the predicted differential boron worth is multiplied by 0.95. Another accident scenario may be sensitive to maximum boron worth. For that key parameter the predicted differential boron worth is multiplied by 1.05. Application of the NRF selectively as described meets the intent of 95% probability and 95% confidence. Some NRF's may be applied statistically 92
for safety evaluation calculations, but typically the application is for a one-sided parameter such as FQ, for which under-prediction is the only direction of concem.
It is important to note that when determining the NUF using comparsons of measurement and prediction, measurement uncertainty is inherently included in the statistically determined NUF. Measurement uncertainty can be of similar magnitude to the model uncertainty itself (see Section 3.3.4). Failure to address measurement uncertainty can lead to unreasonably large estimates of model predictive uncertainty. Approved NRF values for previous core design models are provided in Table 14.
Deternination of fhe NUF from Tolerance Intervals In the statistics presented in Section 3.3, the sign convention used is such that a positive value indicates over-prediction of the magnitude of a parameter by SIMULATE, and a negative value indicates under-prediction by SIMULATE. The appropriate interpretation of the statistical data is therefore to determine an uncertainty factor in the opposite direction to be applied to SIMULATE predictions. For example, if a statistically determined tolerance interval for critical boron concentration is determined to be -35 ppm to +45 ppm, then the uncertainty factor to apply to predicted boron worth is +35 ppm when maximum boron concentration is conservative, and -45 when minimum boron concentration is conservative.
Similarly, statistics given in percent difference are defined as (SIMULATE - Measured) /
SIMULATE in units of percent. The uncertainty factor in this case should be a multiplier on the SIMULATE value consistent with this definition. If a tolerance interval for a parameter is indicated to be -5% to +8%, then the appropriate multiplier range for SIMULATE predictions is 1.05 (when the maximum parameter estimate is desired) and 0.92 (when the minimum parameter estimate is desired).
93
Table 14 Approved NRF Values for Previous Design Models Parameter NRF Notes Integral Control Rod Bank
+
Multiply by 0.9 or 1.1, Worth (Individual banks)
_ 10 whichever is conservative.
Integral Control Rod Bank 10%
Bounded by individual bank Worth (Total of all banks)
NRF Differential Control Rod Bank Worth
+/-2 pcm/step No current use.
Critical Boron Add or subtract 50 ppm, Concentration
+50 ppm whichever is conservative.
Differential Boron Worth
+ 5%
Inferred from dilution bank worth measurements Moderator Temperature
+/-3 PF NRF is based on ITC Coefficient pcm measurements.
Doppler Temperature
+ 10%
Not directly measured.
Coefficient Doppler Power Coefficient
+/- 10%
Not directly measured.
Effective Delayed Neutron 5%
Not directly measured.
Fraction Prompt Neutron Lifetime
+/-5%
Not directly measured.
FAH 1.05 One-sided multiplier.
One-sided multiplier. Includes FQ 1.075 bias for models with no explicit spacer grid modeling.
94 I
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4.2 STATISTICAL METHODS The difference between a predicted value, P, and a measured value, mi, for the purpose of deriving the NUFs is defined as either X= p -m or 4= (p -
i) x 100% /p xi is assumed to be an observation of a distribution of size n whose mean xm and variance are defined as:
n xm (xi)/ n i=1 syZ 4 _
u XM)2 / (n - 1 )
i-i In general, 9 includes the statistical uncertainties due to both measurement and calculation. That is, the variance of x, is given as a = am + c2 Therefore, any standard deviation for calculational uncertainty is conservative since an additional margin for measurement uncertainty is included.
In deriving the NUFs, the assumption is made that individual cycle data may be pooled for a given nuclear unit because the data represents the same physical quantity for cores using essentially the same fuel design and undergoing similar operation. In addition, the measured data from various cycles has been derived using the same procedures and compared with predictions from the same computer code. Since the sister units of each station are of similar design, and fuel is often shuffled between sister units, analogous 95
arguments support the pooling of all cycle data for each station. These assertions are l
further supported by inspection of the descriptive statistics for cycles, which indicate that all cycle data for a given station are members of the same population.
Similarly, there is no reason to believe, based on Monte Carlo benchmarking (Section L
3.1), that minor differences in geometry between 15x15 and 17x17 fuel designs cause Surry and North Anna statistical data to represent different populations. As with sister units for a station, the operational procedures and data measurement techniques for both stations are similar. For large samples, uncertainty factors derived from separate Surry and North Anna data support this assertion. For small samples, particularly those that do not pass normality tests, pooling was performed out of necessity because non-parametric methods cannot be used for very small samples.
I Further reason to treat individual cycle data as a subset of a larger population is the
+/-
process by which it will be treated for future use of the models. Uncertainty factors must be based on prior cycle benchmarking and applied to future cycle designs. It is not practical to determine unique uncertainty factors for each cycle design, because the choice of uncertainty factors for future cycles thereby becomes subjective.
j The uncertainty factor is based on a one-sided upper tolerance limit TL defined as I
TL = xm + (K x) l where K is chosen such that 95% of the population is less than the value of TL, applied in a conservative direction, with a 95% confidence level.
The value of K is most readily determined should the distribution, from which xm and a are derived, prove to be normal (Ref. 29). For those parameters whose uncertainty factor is I
derived from a population which is not assumed to be normal, TL is assumed to depend on the sample size n. In this case, TL is based on the mth largest value in a ranking of the observations making up the distribution (References 26, 29).
96
Since no test for normality is foolproof, each having different strengths and weaknesses, the Kolmogorov-Smimov (K-S) test previously used by Dominion (References 23, 30) has been supplemented by additional tests:
- 1. the Kuiper variant of the K-S test (Ref. 31),
- 2. the W test of Shapiro and Wilk (Ref. 32), and
- 3. the D' test of D'Agostino (Ref. 32).
Whereas the K-S and Kuiper tests were applied to samples of all sizes, the W test was applied only to samples of size 50 or less, and the D' test to sample sizes between 51 and 2000 inclusive.
The different normality tests were evaluated using samples whose normality or non-normality was known to a high degree of confidence. Included were normal samples of varying sizes, means and standard deviations generated by Monte Carlo methods.
Consistent with the derivation of the nuclear uncertainty factors, all tests were performed for a 95% confidence level with a 0.05 level of significance being considered as adequate for the rejection of the assumption of normality.
As suspected, the various tests were not always in agreement in their rejection or non-rejection of some of the test samples. Of particular note, for the larger Monte Carlo generated normal distributions, the computed level of significance decreased with increasing sample size. The K-S and Kuiper tests occasionally demonstrated a type I error (rejecting the null hypothesis of normality when it is really true) for sample sizes greater than 100,000. Based on the nature of these tests, it is understandable that they might occasionally "fail" for such large sample sizes, as the probability of producing significant outliers by a random process increases with sample size.
The size of the Dominion data base for nodal reaction rates falls within such a large sample realm, leading to the suspicion that the conclusion that the reaction rate sample was not normal might be a type I error. Fortunately, in this realm the value of K for a non-97
I normal distribution converges with that derived for a normal distribution of similar mean I
and standard distribution.I I
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4.3 DETERMINATION OF NUCLEAR UNCERTAINTY FACTORS The following sections will detail the derivation of NUFs for key core physics design parameters using the statistical methods described above. For parameters that cannot be directly evaluated using statistical techniques, the basis for arriving at conservative estimates for the NUF and NRF will be presented.
4.3.1 Critical Boron Concentration Based on data presented in Table 5, the uncertainty factor for SIMULATE critical boron concentration predictions can be statistically determined. Table 15 presents upper and lower one-sided tolerance interval information (95% confidence) for North Anna data, Surry data, and combined data assuming normality. The NUF assuming normality was determined to be -19 /+39 ppm for the combined data. Therefore, use of the existing Table 14 NRF for critical boron concentration (+/- 50 ppm) is conservative.
99
Table 15 SIMULATE Critical Boron NUF (Normality Assumed)
Std.
Upper Lower Plant Mean Dev.
Number Std. Dev.
Tolerance Tolerance (ppm)
Pem)
Of Obs. Multiplier Limit Limit (ppm)
(ppm)
North Anna
-6.7 15.9 462 1.77 21
-35 Surry
-12.7 16.3 556 1.76 16
-41 Combined
-10.0 16.4 1018 1.76 19
-39 100 I
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4.3.2 Integral Control Rod Worth Based on data presented in Table 6, uncertainty factors can be statistically determined for the SIMULATE control rod worth predictions. Table 16 presents the upper and lower tolerance interval information (95% confidence) for North Anna data, Surry data, and combined data. Normality is assumed based on the results of tests as indicated in Table
- 6. Figure 52 is a plot of measured versus SIMULATE control rod worths along with upper and lower lines +/- 10% about the SIMULATE worth. The measured and predicted values correlate well from very small rod worths to very large rod worths. The integral rod worth NUF range (a multiplier) for Surry and North Anna data combined was determined to be 0.911 to 1.062.
It is also useful to note that two sources of conservatism exist in the calculation of the rod worth NUF under either normality assumption. [
l In addition, an undetermined amount of other measurement uncertainty is inherently included in the measured versus predicted rod worth comparisons. Table 17 compares calculated and measured control rod worth for two pair of essentially identical cycles (N1C1/N2C1 and S1C1/S2C1). Minor differences in predicted rod worth are due to slight variations in as-built fuel enrichments. Measured rod worth differences are much larger than the slight predicted differences, which indicates the influence of measurement uncertainty (including reactivity computer bias). The calculated NUF is therefore estimated to be conservative for SIMULATE predicted rod worth uncertainty.
The NRF for integral rod worth in Table 14 of +/-10% (multiplier range 0.90 to 1.10) bounds the NUF and is therefore also conservative for SIMULATE integral rod worth calculations.
No calculations have been performed to determine the NUF for total rod worth (the sum of all bank worths in the core). However, the uncertainty for the total rod worth cannot be larger than the uncertainty for individual banks, therefore a NRF of +/-10% (multiplier range 0.90 to 1.10) is also conservative for SIMULATE total rod worth calculations.
101
Table 16 SIMULATE Integral Rod Worth NUF (Normality Assumed)
Mean Std.
Number Std. Dev.
Upper Lower Plant Dev.
l Tolerance Tolerance N(%)
Of Obs. Multiplier Limit (%)
Limit (%
North Anna 0.9 4.2 178 1.86 8.7
-6.8 Surry 1.8 4.2 184 1.85 9.6
-6.0 Combined 1.4 4.2 362 1.79 8.9
-6.2 102 A1 I
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j
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r -
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I Figure 52 Integral Control Rod Worth Comparison SIMULATE Versus Measured 2200 2000 1800 E
D. 1600 o 1400 o 1200 X 1000 c0 C)
- 0 800 0
°0 600 0
400 200 0
0 200 400 600 800 1000 1200 1400 SIMULATE Control Rod Worth (pcm) 1600 1800 2000 2200 103
Table 17 Rod Worth Measurement Uncertainty Estimate Cycle Bank Measured Worth (pcm)
Predicted Worth (pcm)
Unit Unit 2
% Diff Unit unit 2
% Diff D
1463 1437 1.8 1433 1434
-0.1 North C w/
D In 1303 1236 5.1 1215 1218
-0.3 Anna B w/ C+D In 2036 2002 1.7 2011 2017
-0.3 Cycles A w/ B+C+D In 1309 1303 0.5 1246 1236 0.8
- 1.
SB w/ A+B+C+D In 1034 1046
-1.2 1037 1061
-2.3 Mean 1.6 Mean
-0.4 Std. Dev.
2.3 Std. Dev.
1.1 Surry D
1480 1435 3.0 1411 1414
-0.2 Cycles c
1300 1309
-0.7 1281 1285
-0.3 1
B 1920 1929
-0.5 1916 1920
-0.2 A
1440 1508
-4.7 1289 1284 0.4 Mean
-0.7 Mean
-0.1 Std. Dev.
3.2 Std. Dev.
0.3 Combined Mean 0.6 Mean
-0.3 Std. Dev.
2.8 Std. Dev.
0.8 104 1
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1 1
4.3.3 Peak Differential Control Rod Worth Based on data presented in Table 7, the uncertainty factor for peak differential rod worth can be determined statistically. Upper and lower one-sided tolerance limits based on Table 7 data are provided in Table 18. The existing Table 14 NRF for differential control rod worth of +/-2 pcm/step is not relevant (see discussion in Section 3.3.2). Based on this data, the NUF multiplier range is 1.10 to 0.79. Considering the significant amount of uncertainty involved in the measurement of the DRW, and the distribution of data shown in Figure 11, it appears to be prudent to set the NRF multiplier range at 1.15 to 0.8. This range bounds 90 of the 93 observations, with only one observation on each side exceeding this range significantly.
Table 18 SIMULATE Peak Differential Rod Worth NUF (Normality Assumed)
Mean Std.
Number Std. iDev.
Upper Lower Plant (%)
(%)
OfOs utpirLimit (%)
Limit (%/)
Combined 5.6 8.1 93 1.94 21.3
-10.2 105
4.3.4 Isothermal Temperature Coefficient Based on data presented in Table 8, the uncertainty factor for ITC can be determined statistically. Upper and lower one-sided tolerance limits based on Table 8 combined data are provided in Table 19. A NRF for ITC of +/-2 pcm/OF conservatively bounds the NUF of
-1.9 / +0.7 pcm/0F and is therefore considered appropriate.
Table 19 SIMULATE Isothermal Temperature Coefficient NUF (Normality Assumed)
Std.
Upper Lower Mean Number Std. Dev.
Tolerance Tolerance (pcm 0F)
(pcmF)
Of Obs.
Multiplier Limit Limit Combined 0.62___
0.66_
87(PCOF) pcn.-m 0 F Combined 0.62 0.66 87 1.95 1.9
-0.7 106 I
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1
4.3.5 Differential Boron Worth Based on data presented in Table 9, the uncertainty factor can be statistically determined for the SIMULATE DBW predictions. [
I It is likely that boron measurement uncertainty, which has not been removed from the boron worth statistics, remains a significant source of uncertainty in these measurements.
Boron measurement uncertainty in the determination of DBW was estimated to be as large as 8% in Section 3.3.4. Therefore, based primarily on the evidence of critical boron concentration difference data, a NUF and NRF of +/- 5% (multiplier range of 1.05 to 0.95) is considered to be sufficiently conservative for SIMULATE differential boron worth predictions.
107
Table 20 SIMULATE Differential Boron Worth NUF (Normality Assumed) 108 F -F -
F -
H-H -
HH Mean Sd.
Number Std. Dev Upper Lower Plant Data Adjustment
)n Dev Of Obs.
ultDple ; Tolerance Tolerance
(%
Limit (%) Limit (%)
North Anna None 0.0 3.2 30 2.22 7.0
-7.0 Surry None 0.3 4.2 35 2.17 9.3
-8.7 Combined None 0.2 3.7 65 2.01 7.6
-7.3 Combined
[
I
[
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i 11
4.3.6 Estimated Critical Position Although there is no NRF for the ECP calculation, it is useful to develop uncertainty estimates based on the ECP data. ECP calculations involve all reactivity components of the SIMULATE model including control rod worth, xenon worth, power defect, and boron worth. The ECP uncertainty factor can be used as an estimator to make inferences about the maximum uncertainty associated with those components. Since uncertainty factors have been developed separately for at least three of the reactivity components (boron worth, control rod worth and moderator temperature coefficient via the ITC statistics), the remaining components can be approximated.
Table 21 presents the upper and lower tolerance interval information (95%
confidence) for North Anna data, Surry data, and all ECP data combined.
Normality is assumed based on the results of normality tests shown in Table 10.
A very crude approximation of the combined uncertainty of SIMULATE xenon and Doppler worth can be performed as follows. Using the assumption of normality, the major contributions to ECP uncertainty (variance) can be expressed as shown in Equation 3.
CY2ECP 2Xe +CT2 DPD + CJ2LM'
+ 2RW + O2BW +
+BC1
+ F2 BC2 (Eqn. 3)
The components, converted into units of pcm by weighting with typical reactivity contributions to the ECP calculation, are defined as follows:
CECP - combined standard deviation for ECP calculations from all sources (Table 21)
CGXe
- standard deviation associated with SIMULATE xenon change COPD - standard deviation associated with SIMULATE Doppler defect amTD - standard deviation associated with SIMULATE moderator defect 109
yRw - standard deviation associated with SIMULATE rod orth change aBw - standard deviation associated with SIMULATE boron change aBc - standard deviation associated with at-power boron measurement aBC2 - standard deviation associated with zero power boron measurement Using uncertainty estimates from previous sections, approximate values can be substituted into Equation 3 for ECP as indicated in Table 22. Note that most of I
the "typical" ECP reactivity components can vary widely depending on time in cycle life, outage duration, and outage recovery strategy.
Substituting the estimated quantities into Equation 3 and rearranging terms results in Equation 4:
CS X+G 2DpD = (1242 - 402 -402 - 872-212-232) = 602 (Eqn. 4) 1 The total Doppler change from HFP to HZP is on the order of 1000 pcm for all I
ECPs, and the xenon worth change can range from about +3500 pcm to -1500 pcm depending on the elapsed outage time. If the remaining 60 pcm standard I
deviation is assumed to be equally distributed between the Doppler defect and the xenon worth change, then the uncertainty of the Doppler component can be estimated. Using a standard deviation multiplier of 1.65, the Doppler uncertainty is estimated to be 1.65 x 30 pcm /1000 pcm or 5%.
1 I
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Table 21 SIMULATE Estimated Critical Position NUF (Normality Assumed)
Upper Lower Mean Std.
Number Std. Dev.
Tolerance Tolerance Plant (pcm)
Dev.
Of Obs.
Multiplier Limit Limit (p om )
__m(p m
North Anna 22 107 38 2.15 252
-208 Surry 42 142 33 2.19 353
-269 COMBINED 31 124 71 1.99 278
-216 Table 22 Approximate Uncertainty Components for ECP Calculations (Normality Assumed)
Component Typical ECP Std. Dev.
Std. Dev.
variable change (pcm)
Control rod worth 500 pcm 4.2 %
21 (From Table 6)
Boron worth (From Table 9; 8 pcmlppm 350 ppm 3.1 %
87 assumed)
Boron measurement (2 per ECP; 8 N/A 5 ppm 40 pcm/ppm assumed)
MTD (From Table 8) 35 F cm/F 23 Total (From Table 21)
N/A N/A 124 111
4.3.7 Reaction Rate Comparisons L
Based on data presented in Table 12, the uncertainty factor can be statistically L
determined for the SIMULATE flux thimble reaction rate predictions. Although histograms of the reaction rate differences (%) appeared well distributed, the hypothesis of normality was rejected. Table 23 presents the one-sided upper tolerance interval information (95% confidence) for North Anna data, Surry data, and combined data for both integral and 32 node reaction rates assuming non-normality.
In order to use the data from Table 23 to determine NUFs for predicted FAH and I
FQ, the tolerance limits must be combined with the CASMO/SIMULATE pin-to-l box uncertainty factor from Section 3.1. Assuming that the reaction rate predictive uncertainty is independent of the Table 4 factors, the combination is performed by calculating the square root of the sum of the squares of the individual components (RSS). Table 24 presents the resulting FAH and FQ NUFs.
l The FAH data supports a NUF of 1.03. This value is less than the 1.05 NRF approved for previous models (see Table 14) and reflects both improved I
modeling techniques (CASMO transport theory versus PDQ diffusion theory, 3D modeling in full core geometry, modeling of detector cross section variations in
[
3D, etc.) and a much larger database of reaction rate comparisons. A NRF for FAH of 1.04 is therefore conservative. The FQ NRF approved for previous models is 1.075 (7.5%). However, this value included a bias of about 2.5% to account for grid effects. Previous models did not include a grid model that could l
account for the effect of grids on the axial power shape. The SIMULATE FQ NUF of 1.05 corresponds to a new NRF of 1.05. Use of SIMULATE with an FQ NRF of 1.05 (with no additional grid bias) is analogous to use of the previous NRF of 1.075 with prior models with no axial grid model.
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I Table 23 SIMULATE Reaction Rate NUF (Non-normality Assumed)
Note: Sign on computed tolerance limits changed to positive for consistency.
Table 24 SiMULATE FAH and FQ NUF Reaction Rate Combined Plant Data Type Tolerance Limit t
Tolerance (Table 23)
Limit (°)
North Anna Integral / FAH
-2.23
[
l
-3.0 Surry Integral / FAH
-2.35
[
1
-3.1 COMBINED Integral / FAH
-2.25 1
1
-3.0 North Anna 32 Node / FQ
-3.96
[ 1
-4.4 Surry 32 Node / FQ
-4.53 f
1
-5.0 COMBINED 32 Node / FQ
-4.17
[
1
-4.6 113 Std.
Number Reported Reported Rigorous Rigorous Number
% of Data Mean d
Number Llmiting One Sided Limiting One Sided f Obs.
Obs.>
Plant Type
(%)
Dev Of Obs.
Tolerance Tolerance Tolerance Tolerance o
( )
Value Limit (%)
Value Limit (
>) NRF NRF N. Anna Integral
-0.02 1.34 3453 150 2.23 152 2.21 20 0.6 Surry Integral 0.07 1.34 2322 98 2.34 99 2.33 9
0.4 N. Anna 32 Node 0.14 2.41 93070 4273 3.96 4544 3.89 1969 2.1 Sur 32 Node 0.38 2.79 64354 2952 4.53 3127 4.42 2270 3.5
4.3.8 Doppler Coefficients and Defects As discussed in a prior submittal (Ref. 23) direct determination of the NRF for Doppler feedback is very difficuft. A value of 1.10 for the Doppler Temperature l
Coefficient and Doppler Power Coefficient was proposed in that submittal and accepted following NRC review. Although it is still very difficult to directly determine Doppler feedback uncertainty, there are three indirect indications (in addition to the development in Section 4.3.6) that support continued use of a
+/-10% NRF (multiplier range 1.10 to 0.90):
I
- 1) Benchmarking of CASMO Doppler Temperature Defects to monte carlo
{
methods enables a best-estimate correction to be performed that effectively eliminates the theoretical CASMO Doppler bias (as determined using higher order calculations) from the SIMULATE model.
- 2) Critical boron data from Sections 3.3.1 (BOC HZP and HFP critical boron data), 3.3.5, and 4.3.6 (ECP data) suggests that total Doppler feedback (HFP to HZP) is well predicted. Comparison of the mean biases for HZP L
and HFP BOC critical boron concentration shows only a 3 ppm (roughly 20 pcm) difference. ECP data spanning all times in core life also shows little HFP-HZP bias (31 pcm in the same direction as the critical boron L
bias). There are three significant reactivity components involved in the HZP-HFP statepoint transition: Doppler temperature defect, moderator temperature defect, and xenon build-in (all offset by reduced boron concentration). The data cited above indicates, at a minimum, that the sum of these factors is well predicted, and therefore that the Doppler defect is probably well predicted.
L
- 3) Several of the operational transients modeled in Section 3.3.7 included undamped xenon oscillations (NIC6, NIC9, and particularly NIC1 1). The degree of axial stability is determined by the relative balance between the axially shifting xenon distribution and opposing power-driven fuel temperature change. This phenomena is demonstrated graphically in Figure 50. The good agreement of the measured and predicted axial offset oscillation magnitude in the modeled operational transients demonstrates that the xenon-Doppler balance is well predicted. Since I
both the combination of xenon and Doppler feedback (item 2 above) and the balance between xenon and Doppler feedback are well predicted, it follows that the individual components are also well predicted.
I 114
4.3.9 Delayed Neutron and Prompt Neutron Lifetime Data The techniques used for calculating effective delayed neutron fractions for the core are described in reference 2 (CASMO, Section 9.7) and reference 6 (SIMULATE, Section 4.2). The treatment in CASMO uses a conventional six delayed neutron group approach based on basic nuclear data (m,i and km,,) for each fissioning nuclide m and delayed neutron group i. The data are weighted by nuclide fission rate and by energy group importance using the cell average adjoint flux in each energy group. CASMO data is passed to SIMULATE via the CMS-LINK cross section library. In the SIMULATE core model, CASMO data is integrated using the relative fission neutron production rate of each assembly weighted by the spatial adjoint flux.
There are three sets of basic delayed neutron data available in CASMO.
ENDF/B-V data is available in a form which assumes a delayed group independent v (neutrons per fission) and in a form which uses a delayed group dependent v (the default data). The Tuttle 1979 evaluation for delayed neutron yield is also available. In practice, there is only a small difference between the Tuttle and ENDF/B-V data as indicated in reference 34.
Based on this review of the data and techniques used to calculate the effective delayed neutron fraction and decay constants for each delayed neutron group, it is reasonable to maintain the existing NRF of +/- 5% for effective delayed neutron fraction. This value is consistent with the +/- 4% value approved for the same use in a similar reactor in reference 35.
The techniques used for calculating prompt neutron lifetime (Lp) for the core are described in reference 2 (CASMO, Section 9.7) and reference 6 (SIMULATE, Section 4.2). Although a variety of ways exist to define and calculate the prompt neutron lifetime, the technique described in reference 2 is similar to the description in reference 36. Reference 2 expands the calculation to a multiple 115
energy groups, and incorporates adjoint importance weighting. One difference is l
that instead of using the macroscopic absorption cross section in the denominator, the CASMO technique employs vEf. The effect of this is that CASMO will tend to produce the value for Lp which would occur in a critical assembly (where vlf = Ea). CASMO data is passed to SIMULATE via the CMS-LINK cross section library. In the SIMULATE core model, CASMO Lp data is weighted using the spatial adjoint flux to obtain the core Lp.
L 116A Il
Based on this review and validation of the techniques used to calculate Lp, it is reasonable to maintain the existing NRF of +/- 5%. This value is consistent with the +/- 4% value approved for the same use in a similar reactor in reference 35.
117
I Table 25 1
Validation of CASMO-4 Prompt Neutron Lifetime Calculations I
I I
I I
I I
I
.1 I
I I
118
SECTION 5 -
SUMMARY
AND CONCLUSIONS Dominion (Virginia Power) has demonstrated in this report the accuracy of CASMO-4/SIMULATE-3 core models as well as Dominion's ability to develop and use these models for a variety of applications. The models have been validated by an extensive set of benchmarks to both higher order calculations and to over 60 cycles of measured data from the Surry and North Anna nuclear power stations. Based on those benchmarks, the following set of nuclear reliability factors (NRF) were determined to account for model predictive bias and uncertainty:
NRF Parameter N
Lw Upper Lower Integral Control Rod Bank Worth (Individual banks) 1.1 0.9 Integral Control Rod Bank Worth (Total of all banks) 1.1 0.9 Differential Control Rod Bank Worth 1.15 0.8 Critical Boron Concentration
+50 ppm
-50 ppm Differential Boron Worth 1.05 0.95 Isothermal and Moderator Temperature Coefficient
+2
-2 pcm/OF pcmP0F Doppler Temperature Coefficient 1.10 0.90 Doppler Power Coefficient 1.10 0.90 Effective Delayed Neutron Fraction 1.05 0.95 Prompt Neutron Lifetime 1.05 0.95 FAH 1.04 N/A FQ 1.05 N/A Dominion concludes that the CASMO-4/SIMULATE-3 models, in conjunction with the indicated reliability factors, are fully qualified for use as equivalent replacements for prior models. Key aspects of core design and analysis methodology described in other Topical Reports (references 11-13, 18, 39) are not changed by the use of CASMO-4/SIMULATE-3 models as replacements.
Furthermore, a robust model development process has been described that 119
benefits in part from the use of higher order models to identify and eliminate significant bias prior to use of the models for core calculations. This process, coupled with code and model quality assurance practices, provides assurance I
that future changes to core, fuel and burnable poison designs will be modeled with accuracy and appropriate conservatism. It is anticipated that additional I
model validation and improvement will continue as the CASMO-4/SIMULATE-3 models are applied to future core designs.
I I
.1 120 I
SECTION 6 - REFERENCES
- 1. M. Edenius, K. Ekberg, B.H. Forssen, D. Knott, CASMO-4 A Fuel Assembly Bumup Program User's Manual," Studsvik of America, Inc. and Studsvik Core Analysis AB, SOA-9511, Rev. 0, September 1995.
- 2.
D. Knott, B.H. Forssen, M. Edenius, CASMO 4 A Fuel Assembly Bumup Program Methodology," Studsvik of America, Inc. and Studsvik Core Analysis AB, SOA-95/2, Rev. 0, September 1995.
- 3.
J. D. Rhodes, K. Smith, "CASMO-4 v2.05 Modeling Changes and Additional Input Cards," Studsvik Scandpower, SSP-00/417, Rev. 0, June 2000.
- 4.
T. Bahadir, A. S. DiGiovine, J. Rhodes, K. Smith, CMS Microscopic Bumable Poison Option," Studsvik of America, SOA-97/36, Rev. 0, November 1997.
- 5.
A. S. DiGiovine, J. D. Rhodes, SIMULATE-3 User's Manual," Studsvik of America, SOA-95/15, Rev. 0, October 1995.
- 6.
J. T. Cronin, K. S. Smith, D. M. Ver Planck, J. A. Umbarger, M. Edenius, USIMULATE-3 Methodology," Studsvik of America, SOA-95/18, Rev. 0, October 1995.
- 7.
R. A. Hall, 'The PDQ Two Zone Model," Virginia Electric and Power Company, Topical Report VEP-NAF-1, July 1990.
- 8.
Letter from W. L. Stewart (Virginia Electric and Power Company) to U.S.
Nuclear Regulatory Commission, Virginia Electric and Power Company, Surry Power Station Units I & 2, North Anna Power Station Units I& 2 Topical Report - PDQ Two Zone Model," October 1, 1990.
- 9.
S. M. Bowman, "The Vepco NOMAD Code and Model," Dominion Topical Report VEP-NFE-1-A, May 1985.
- 10. Letter from W. L. Stewart (Virginia Electric and Power Company) to U.S.
Nuclear Regulatory Commission, "Virginia Electric and Power Company, Surry Power Station Units I & 2, North Anna Power Station Units 1& 2 Topical Report Use Pursuant to I OCFR50.59," November 25,1992.
- 11. K. L. Basehore, et al., Vepco Relaxed Power Distribution Control Methodology and Associated Fq Surveillance Technical Specifications,"
VEP-NE-1-A, March 1986.
- 12. D. Dziadosz, et al., Reload Nuclear Design Methodology," Dominion Topical Report VEP-FRD-42 Rev. 1 -A, September 1996.
121
SECTION 6-REFERENCES (Continued)
L
- 13. T. K. Ross, W.C. Beck, "Control Rod Reactivity Worth Determination by the Rod Swap Technique," Dominion Topical Report VEP-FRD-36A, December 1
1 980.
- 14. R. W. Twitchell, "Fuel Management Scheme 2002," Dominion Technical L
Report NE-1 313, Rev. 0, February 2002.
- 15. "SCALE: A Modular Code System for Performing Standardized Computer I
Analyses for Licensing Evaluation," NUREG/CR-0200, Rev. 6, Oak Ridge National Laboratory, December 1999.
- 16. J. F. Breismeister, "MCNP - A General Monte Carlo N-Particle Transport Code, Version 4C," LA-13709-M, December 2000.
- 17. J. G. Miller, 'The ESCORE Steady State Fuel Performance Code," Dominion Technical Report NE-554, Rev. 0, November 1986.
1
- 18. T. W. Schleicher, Reactor Power Distribution Analysis Using a Moveable In-core Detector System and the TIP/CECOR Computer Code Package,"
I Dominion Topical Report VEP-NAF-2, November 1991.
- 19. [
I 1 9.~~~~~~~~~~~~
- 20. [
l
]
- 21. K. Ekberg, CASMO4 Benchmark Against Yankee Rowe Isotopic l
Measurements," Tagungsbericht Proceedings, ISSN 0720-9207, Jahrestagung Kerntechnik'97, May 1997.
- 22. K. Terazu, et al., "Verification of the CASMO-4 Transport Method Based on BWR High-Burnup 9x9 Fuel Critical Experiments," Transactions of the American Nuclear Society, Volume 73, TANSAO 73 1-522 (1995), ISSN 0003-18X, October 1995.
- 23. J. G. Miller, Vepco Nuclear Design Reliability Factors," Dominion Topical Report VEP-FRD-45A, October 1982.
- 24. "American National Standard Reload Startup Physics Tests for Pressurized Water Reactors," ANSI/ANS-19.6.1-1997, August 1997.
I
- 25. M. G. Natrella, "Experimental Statistics," National Bureau of Standards Handbook 91, August 1963.
1 122
SECTION 6 - REFERENCES (Continued)
- 26. P. N. Somerville, Tables for Obtaining Non-Parametric Tolerance Limits,"
Ann. Math. Stat., Vol 29, 1958.
- 27. J. J. Duderstadt and L. J. Hamilton, "Nuclear Reactor Analysis," Table 2-4, ISBN 0-471-22363-8, John Wiley and Sons, 1976.
- 28. J. R. Lamarsh, "Introduction to Nuclear Reactor Theory," Table 3-10, Addison-Wesley Publishing Company, 1966.
- 29. "An Acceptance Model and Related Statistical Methods for the Analysis of Fuel Densification," U.S.N.R.C. Regulatory Guide 1.126, Rev. 1, March 1978.
- 30. M. A. Stephens, "Use of the Kolmogorov-Smimov, Cramer-Von Mises and related statistics without extensive tables," J. American Statistical Association, 69:730, 1974.
- 31. M. A. Stephens, Biometrika, Vol. 52, pp. 309-321, 1965.
- 32. "American National Standard Assessment of the Assumption of Normality (Employing Individual Observed Values)," ANSI N15.15-1974.
- 33. T. Bahadir, J. Umbarger, M. Edenius, CMS-LINK User's Manual," Studsvik of America, SOA-97/04 Rev. 2, April 1999.
- 34. M. C. Brady and T. R. England, Delayed Neutron Data and Group Parameters for 43 Fissioning Systems," Nuclear Science and Engineering:
103,129-149 (1989).
- 35. Letter from T. Kim, U. S. Nuclear Regulatory Commission to Mr. Joel Sorenson, Prairie Island Nuclear Generating Plant, "Prairie Island Nuclear Generating Plant, Units 1 and 2 - Safety Evaluation on Topical Report, NSPNAD-8101, Revision 2, Qualification of Reactor Physics Methods for Application to Prairie Island Units and 2," September 13, 2000.
- 36. J. R. Lamarsh, "Introduction to Nuclear Reactor Theory, 2nd Edition," Chapter 7.1, Addison-Wesley Publishing Company, 1983.
- 37. M. M. Bretscher, Evaluation of Reactor Kinetic Parameters Wthout The Need For Perturbation Codes," Argonne National Laboratory under DOE contract # W-31-109-ENG-38, Presented at the 1997 Intemational Meeting on Reduced Enrichment for Research and Test Reactors, October 5-10, 1997.
123
SECTION 6 - REFERENCES (Continued)
I
- 38. L. M. Petrie, et al, "KENO-V.a: An Improved Monte Carlo Criticality Program With Supergrouping," NUREG/CR-0200, Rev. 6, Volume 2 Section F11.5.14, Oak Ridge National Laboratory, March 2000.
- 39. C. A. Ford and T. W. Schleicher, "Reactor Vessel Fluence Analysis I
Methodology," Dominion Topical Report VEP-NAF-3A, April 1999.
I I
I I
1 24 1!
DOM-NAF-1-REV. 0.0 -A Page 125 Appendix A: RAI Set I Questions and Responses NRC Request for Additional Information (first set) and Responses
- 1) Page 7, paragraph 2 states that the CMS package is used by the nuclear industry in the U.S. and worldwide. What other utilities or vendors use this methodology in the U.S? Has this methodology been reviewed and approved by the NRC for these vendorslutilities?
Utilities/vendors using CMS (no version specified, list from Studsvik ca. 2000):
AEP, APS, CPL (Progress Energy), (Commonwealth Edison) Excelon, Consumers Energy, Duke Power, Entergy, Illinois Power, Iowa Electric, NYPA, NSP, Omaha Public Power District, Philadelphia Electric, Southem Cal. Edison, TU Electric, Toledo Ed., Union El., Framatome, Siemens Utilities/vendors with licensing approval:
Yankee Atomic (Duke, 1990)
Entergy (CASMO3/S3 9/95)
Duke (CASMO31S3P 12/97)
NSP (CASMO4/S3 9113/00)
Palo Verde (CASMO4/S3 3/20/01)
- 2) Page 16, paragraph I - The subject of bias is brought up. Please provide an example of how bias is calculated for any of the neutronic key parameters, such as those listed for the CASMO model.
Bias refers to the mean of the set of observed differences between predicted (CASMO or SIMULATE) and reference values (measured or Monte Carlo). Using Table 3 for example, the CASMO soluble boron worth bias for 17x17 fuel is [
1, which means that CASMO tends to [
I soluble boron worth relative to KENO-V.a. The bias for some parameters is stated in terms of percent difference, and for others in terms of difference (such as ppm for critical boron concentration). The definition of difference is given below each Table. For comparison of reactivity worth, worth is calculated in units of pcm ((1/K 1-1/K2) x 105).
- 3) On page 19, paragraph 2, the Doppler defect comparisons were only extended to 4.0% enrichment Why was the comparison not extended to 5.0% like the rest of the parameters? Why is this acceptable?
The range of comparisons was not expanded because we did not observe any significant trend with either enrichment or burnup in the 3 and 4 w/o observations. All differences over a 600K AT (900K to 300K fuel temperature) were between [
I with no trend apparent given the statistical uncertainty. In addition, because these are very long running Monte Carlo cases (40 million histories) and each worth calculation requires two cases, we did not perform an exhaustive set. The insensitivity of these comparisons to small changes in U235 enrichment is understandable due to the dominant role of U 238 in resonance absorption for low enrichment fuel.
DOM-NAF-1 -REV. 0.0 -A Page 126 1
Appendix A: RAI Set I Questions and Responses
- 4) On the last two lines of page 20, Table 3, it Is stated that the number of observations for the Doppler defect is only 3 for both North Anna and Surry.
This appears to be relatively few observations. Also, the mean % difference is large compared to the other means listed in the same table. Please provide technical Justification for these differences.
As noted in the answer to question 3, a limited number of comparisons were performed I
because of the long run times for the Monte Carlo cases and the consistency of results.
The mean differences for the Doppler comparisons in Table 3 are large. The standard deviation associated with the Doppler comparisons is relatively small, which indicates that the mean Doppler difference is significant.
Early testing of CMS suggested (based on instability of some xenon transient modeling) that the Doppler feedback in SIMULATE was probably too low.
The CASMO comparisons to Monte Carlo calculations confirm this suspicion. We speculate that the j
Doppler difference is related to the use of ENDF/B-IV cross section data in CASMO versus ENDF/B-V data in KENO. We identify these biases at the CASMO level so that they can be eliminated prior to reaching SIMULATE as discussed in Sections 2.4.1 and 3.1.
- 5) Page 23, paragraph 3 makes a case for "strong gradients increase pin-to-box l
factors that result In challenging and conservative conditions for both W-prime and pin-to-box uncertainties. Please provide additional clarification of this statement. Does challenging and conservative mean that you have I
considered worst case scenarios?
These are not necessarily the worst case scenarios. However, control rod insertion I
introduces a very large inter-assembly and intra-assembly heterogeneity into the core.
CASMO cases are run using single assembly geometry with reflective boundary conditions. The more homogenous the assembly and core design, the more the pin l
powers tend toward unity and the less challenging the problem is to the modeling theory and the reflective boundary condition assumption.
Control rod insertion represents roughly 30% AK reactivity insertion and introduces assembly power differences on the order of a factor of two across neighboring assemblies in the core. This represents not only a challenge to the intra-assembly pin l
power reconstruction in SIMULATE, but also to the inter-assembly flux calculation.
The presence of bumable absorbers (integral or discrete) does increase intra-assembly heterogeneity, however, bumable poisons are used in core design to reduce core-wide heterogeneity and inter-assembly gradients.
Modeling assemblies with burnable poisons therefore would not necessarily be more challenging than the rodded/unrodded l
checkerboard described.
We view the rodded/unrodded checkerboard cases as representing well above average difficulty level for determining pin/box and W-prime uncertainty.
We also note that our results are consistent with critical experiment l
comparisons reported by others (Section 3.2).
DOM-NAF-1-REV. 0.0 -A Page 127 Appendix A: RAI Set I Questions and Responses
- 6) The last paragraph on page 34 talks about differential rod worth (DRW). It states that SIMULATE tends to over-predict the peak DRW. One presumes that this is a conservative effect. Please provide technical justification for this assumption. Also, please provide additional clarification of the last sentence of the same paragraph.
We do not assume that over-prediction of DRW is conservative, rather, we use the data to develop separate upper and lower reliability factors.
The last part of question 6 refers to a statement justifying use of a percent difference NRF for the DRW rather than an arithmetic difference NRF. For some accident analyses, such as the rod withdrawal accident, maximum DRW is limiting. The DRW limit can be 25-100 pcm/step and represent some highly skewed core conditions.
However, measured values used to determine the DRW reliability factor (NRF) are from symmetric core measurements in the range of 8-15 pcmlstep. The DRW upper NRF of 1.15 corresponds to arithmetic differences of roughly 1-2 pcm/step for the typical measured DRW. However, at accident conditions it represents as much as 15 pcmlstep conservatism (15% of 100 pcmlstep), much greater than a 1-2 pcmJstep NRF. Use of a percent dffference NRF is also logical, since the rod worth, the peak DRW and the error in the peak DRW are closely related quantities.
- 7) Figure 22 on page 64 shows significant scatter. Please explain how this data supports your statement that the bias is primarily in the middle of the boron range.
Figure 22 was not intended to demonstrate a strong correlation between boron concentration and ECP error. In fact, no correlation with boron is expected except that which results from the mis-modeling of ECP conditions due to B'° depletion. Figure 22 was included to show that a portion of the ECP data scatter is probably due to B1 0 depletion rather than SIMULATE uncertainty. However, for simplicity, all of the data have been included in the determination of the ECP statistics in Table 10.
B10 depletion introduces mis-modeling because the measured boron before the ECP can have a different Bl1/B1' ratio than the measured boron at the time of the ECP return to critical. SIMULATE boron predictions are based on a constant B'0/B"' ratio. The reactivity comparison between measurement and prediction is skewed by the B'°/B"1 difference. Although it is possible to correct for this mismatch, the process involves a great deal of measured data and was not practical due to the large number of cycles modeled.
B10 depletion mis-modeling is most likely to occur at mid cycle, during which boron concentration tends to be in the middle of the range shown in Figure 22. The bow in the fit is consistent with the expected influence of uncorrected B'0 depletion on an ECP.
The point in demonstrating this is to show that B10 depletion tends to increase the scatter in the ECP data (introduces a positive bias for certain cases but not for others)
DOM-NAF-1 -REV. 0.0 -A Page 128 Appendix A: RAI Set I Questions and Responses leading to a conservative estimate of SIMULATE ECP accuracy. The ECP statistics are presented as a general confirmation of SIMULATE reactivity predictions. These statistics were not used to develop a NRF.
l
- 8) On page 68, you indicate that SIMULATE's calculated peak F(z) values tend to be low by 0.01 to 0.04. Explain how you account for this tendency when conservatively modeling the transient.
Best estimate models are used to determine approprate uncertainty factors. When we perform FAC or RPDC operational transient modeling, we apply the FQ NRF and other factors. The FQ NRF includes the effect of differences between measured and predicted F(Z).
- 9) On page 68 for the S2C2 Load Follow Demonstration, you indicate that SIMULATE has a critical boron concentration initial bias of -34 ppm. On page 71, for the NIC3 Trip and Return to Power, you do not indicate a bias for the critical boron concentration. On page 75, paragraph 2, for the NIC9 HFP MTC Measurement you indicate that the bias is -24 ppm. On page 82, for the NI C1 Initial Power Ascension, you do not indicate a bias. And on page 86, paragraph 3, for the N2C14 Power Transient, you ndicate that the bias is 60 ppm. Describe why these biases vary significantly and why this variation is I
acceptable. In addition, given the variability of the bias, describe how you account for the bias when using SIMULATE in a predictive capacity.
The bias" cited for each transient is actually the initial difference between measured and predicted boron at the beginning of each transient (snapshots for specific times in specific cydes). These observations provide a reference point to demonstrate the l
degree of boron consistency (measured versus predicted) throughout the transient. The initial differences cited are acceptable because they are consistent with the data used to determine the critical boron NRF (+/- 50 ppm). When a conservative estimate of critical j
boron concentration is needed, the NRF is applied to the best estimate SIMULATE prediction in the conservative direction.
In the case of N2C14, we identified a known contributor to the mid-cycle M-P boron difference (B'° depletion) but did not attempt to model it. The presence of B'° depletion complicates the determination of SIMULATE reactivity modeling accuracy. The primary purpose of the transient modeling is to demonstrate that the SIMULATE model is robust and is capable of accurately calculating the time dependent reactivity and power distribution response of the core to complex changing core conditions (control rod I
position, core power, xenon concentration, boron concentration, and moderator temperature). To that end, it is not necessary to correct for Bl0 depletion. However, in order to arrive at absolute reactivity comparisons between SIMULATE and I
measurements, a correction for Bl depletion is required. As noted in the response to question 7, such a correction is possible, but is not practical due to the large number of cycles modeled. It is for this reason that only BOC and EOC comparisons have been i
used for the determination of the critical boron NRF (Section 3.3.1).
I 1
- I I
DOM-NAF-1 -REV. 0.0 -A Page 129 Appendix A: RAI Set I Questions and Responses 10)On page 75, you indicate that the Figure 38 SIMULATE boron values followed the measured values within about +181-15 ppm. However, you only provide 4 data points for comparison purposes during the power transient. Describe how SIMULATE accurately models this transient given the limited data.
Additionally, describe why the +181-15 ppm assessment is accurate.
There are only four critical boron data points available for the NI C6 transient. The
"+18/-15" comment indicates the range of difference (P-M) for those four points after accounting for the initial difference at the beginning of the transient. These results are consistent with the body of data from the other transients and consistent with the critical boron NRF. The good agreement between predicted and measured delta-I data is the best evidence of modeling accuracy for this transient.
11)On page 110, paragraph 2, you state that, "... the remaining 60 pcm standard deviation is assumed to be equally distributed between the Doppler defect and the xenon worth change..." Why is it acceptable to assume the standard deviation can be divided equally between Doppler defect and xenon worth change?
The assessment of Doppler uncertainty based on ECP data is a "very crude approximation" (Section 4.3.6). We attempted to use the ECP data to support or refute as much as possible the conclusions concerning Doppler feedback from other areas (Table 3, Table 5, and transient axial stability). The assumption was used only to arrive at a reasonable estimate of Doppler uncertainty based on the probability that the xenon uncertainty is non-zero and because the Doppler worth is similar in magnitude to the xenon worth. Even if the entire 60 pcm is attributed solely to Doppler uncertainty, the resulting reliability factor is estimated to be +/-10%, which is the same as the NRF chosen.
12)On page 114, paragraph 1, you indicate that a value of 1.10 for the Doppler Temperature Coefficient and Doppler Power Coefficient was proposed in Dominion Topical Report VEP-FRD-45A, dated October 1982 and accepted by the NRC. Describe why this topical report Is still valid given the changes to fuel designs and loading patterns since 1982.
VEP-FRD-45A was cited for historical perspective, but is not assumed to remain valid.
Infonnation summanzed in Section 4.3.8 is intended to support a Doppler feedback NRF of +/-10% based on the benchmarking of the CMS model. The data presented covers all North Anna and Surry cycles up to the time DOM-NAF-1 was assembled.
13)On page 115, paragraph 3, you indicate that there are three sets of basic delayed neutron data available in CASMO. Provide clarifications as to which data set you use for your CASMO modeling.
DOM-NAF-1 -REV. 0.0 -A Page 130 L
Appendix A: RAI Set I Questions and Responses Dominion plans to use the Tuttle delayed neutron data based on calculations of the effect of the various options on startup physics measurements. The specific choice of CASMO delayed neutron data can shift reactivity computer measurements by approximately 3%. Based on the Dominion startup physics measurements available, the Tuttle data provides the most consistent alignment of measured and predicted control rod worth and boron worth. Little or no bias is expected in these worth predictions due to the benchmarking and bias adjustment process described in Sections 2.4.1 and 3.1.
14)Are all tolerance limits calculated as 9595
?
1 All tolerance limits are calcucated as 95/95.
15)Are all statistical tests conducted at the 0.0 level of significance?
All statistical tests are conducted at the 0.05 evel of significance.
16)Please include a column with the number of observations in Table 4, Page 26.
See the attached revision to Table 4 (p. 26 of Report) which includes the sample sizes.
17)Various datasets were tested for normality using more than one test. Since different tests are sensitive to different departure from normality, the more tests one uses, the more likely it is that normality would be acceptable by at L
least one test. Please discuss the use of multiple tests in light of this concern.
This question addresses the issue of using multiple null hypothesis tests for normality as discussed in Section 4.2. Inspection of the histograms found in the Report shows they all exhibit a bell-shaped behavior, that is, a central peak with diminishing tails, indicative of a normal or near-normal distribution. In a prior submission (Topical Ref.
23), Dominion relied on the W test of Shapiro and Wilk for small size samples (up to 50), and the Kolmogorov-Smimov (K-S) test for larger size samples. This use of a single test for any particular sample was viewed as unrealistic, since no test is foolproof, each having certain strengths and weaknesses. Considering the diversity of parameters, measurement procedures, and conditions reflected in the Report, it would be surprising if any single normality test was equally reliable for all parameters.
The decision of which tests to use was complicated by the large number of available candidates, and the ongoing debate over the applicability, meaning and validity of different tests. (See, for examples, Appendices A and B of the ANSI standard (Topical Ref. 32), and the discussion on higher moments and null hypothesis testing in Numencal Recipes in Fortran 77: 2nd Edition.) Since a survey of the literature failed to identify any consensus for a single test, Dominion concluded that the use of more than one test was a reasonable approach in avoiding either a type I or type 11 error. Where normality was assumed in the determinafion of a NRF, normality tests of the combined data (North Anna and Surry together) indicated normality in at least two out of three I
DOM-NAF-1-REV. 0.0 -A Page 131 Appendix A: RAI Set I Questions and Responses tests. Expanded tables for three key parameters are attached: Table 5 critical boron, Table 6 integral control rod worth, and Table 8 HZP BOC isothermal temperature coefficient. These revised tables include:
the calculated D' statistic and the bounding D' one-sided and two-sided D' limits, the calculated significance level for the K-S and Kuiper tests, the calculated W statistic and the W statistic for a 0.05 level of significance, the number of observations outside the 95/95 NRF, and the percent of observations outside the 95/95 NRF.
The attached Table 5 also corrects three typos in the Report table.
It should be noted that
- 1) both the data to be tested and the null hypothesis tests were selected before any testing was performed, thus avoiding prejudicing a conclusion by hindsight, and
- 2) no tests were performed to remove suspected outliers from the data.
It appears ironic that the only comparisons to measurement for which the hypothesis of normality was clearly rejected were the two with the largest sample sizes and the most normal appearing histograms, that is, the integral and peak reaction rates. Although we suspect the results of these tests to be type I errors on the part of the K-S and Kuiper tests, we nevertheless derived the tolerance limits using a non-parametric method.
However, in this realm of sample size, the tolerance limits which would have resulted if the samples were assumed to be normal tend to converge with those based on the non-parametric method.
Finally, should a type 11 error have been committed, that is, if a NUF is calculated assuming a normal distribution when in reality it is not, additional factors reduce the impact of such an error. These are:
- 1) NUFs calculated by comparison of predictions with measurements inherently include measurement uncertainty in addition to model prediction uncertainty, and
- 2) the NRF is chosen to be equally conservative as or more conservative than the NUF.
18)Please indicate which non-parametric tests were used when data normality was rejected. Give an example of the use of such tests.
The NUF for a non-normal distribution was determined based on the non-parametric ranking method of Somerville (Topical Ref. 26) and referenced in USNRC Regulatory Guide 1.126 (Topical Ref. 29). This method was used for determining the tolerance limits for the integral and peak reaction rates (Table 23), and the pin-to-box ratios (Table 4). For example, for the North Anna integral reaction rate sample of Table 23, the number of observations was 3453. Extension of the data in Table 2 of Topical Ref. 29 indicates the 15 0 th most negative value (m) to be the 95195 limiting tolerance value for a
DOM-NAF-1 -REV. 0.0 -A Page 132 1
Appendix A: RAI Set I Questions and Responses non-normal distribution of this size. The tolerance limit corresponding to this value is 2.23%.
As a check on the accuracy of extending the data in Table 2 of Topical Ref. 29, values l
of m were rigorously calculated for the reported sample sizes based on the incomplete Beta function method described in the Somerville paper (Topical Ref. 26). The results, found in the attached update to Table 23 under the column "Rigorous One Sided Tolerance Limit," demonstrate that the tolerance limits presented in the Report are conservative.
19)The last paragraph of page 92 needs to be addressed for conservatism. The multiplier of the standard deviation (used to derive tolerance limits) is smaller for one-sided than a two-sided criterion. Therefore, when we have a two-sided concern (when we are concerned with accedence that is too low as well as too high) a two-sided multiplier is applicable.
The application of a one-sided multiplier is based on the present Dominion methodology for ensuring conservatism for reload safety evaluations. This methodology, which uses a limiting key parameter approach, has been previously reviewed and accepted by the USNRC (Topical Refs. 12, 23). Briefly, the method for determining NUFs (and, by extension, NRFs) is as follows. We desire a value for a NRF such that when applied to a predicted value X, the result Z is expected to bound the "real" value of the parameter 95% of the time with a 95% confidence level. Here the "real" value is the actual value of the parameter which would exist for the core conditions assumed by the prediction.
l In practice, the NRF is developed using measured data (or in some cases Monte Carlo data) as the best available estimate of the "real" value.
The confusion over the use of one-sided versus two-sided multipliers appears to arise from the fact that when considering the complete reload safety evaluation process, both over-prediction and under-prediction may be important for some parameters. However, I
a concem of simultaneous over-prediction and under-predicfon does not apply to a parameter for a given event; that is, a key parameter used in a particular safety event will either be conservative in the high direction or low direction, but never both at the l
same time. For example, for a transient where maximum control rod worth is limiting, increasing the predicted control rod worth by 10% (one-sided multiplier) provides a 95/95 conservative value. The use of a two-sided multiplier would be even more conservative, but would represent a 95/95 conservatism relative to both high and low rod worth simultaneously, and, in addition, would constitute a change to the Dominion methodology previously reviewed by the USNRC.
DOM-NAF-1 -REV. 0.0 -A Appendix A: RAI Set I Questions and Responses Table 4 Page 133 CASMO-4 W-prime and Pin-to-box Ratio Comparisons FuelType Assembly Sample Mean (%)
Std. Dev. '
Norma Tolerance Parameter ss y Size enLimit Rodded 186
[
]
1 ]
Yes
[
I Surry5xl5 Unrodded 186
[
]
[
]
Yes
[
]
W-prime Combined 372
[
]
1 ]
Yes
[
]
North Anna Rodded 234
[
]
[
]
Yes 17x1 7 Unrodded 234 l
1 l
]
Yes
[
]
W-prime Combined 468
[
]
[
]
Yes
[
]
Combined data Combined 840
[
3 Yes
[
W -Prime__
Pin-to-box Ratio Statistics (including Gamma Smearing)
Surry 15x15 Rodded 186
[
]
[
I No
[
]
Pin-to-box Unrodded 186 1
]
[
]
No
[
]
ratio Combined 372
[
]
[
l No North Anna Rodded 234
[
3
[
]
No
[
]
I 7x1 7 Pin-to-box Unrodded 234 1
[
]
No ratio Combined 468
[
l
[
3 No
[
]
Pin-to-box Ratio Statistics (Excluding Gamma Smearing)
Surry 15x15 Rodded 186
[
]
[
3 No
[
]
Pin-to-box Unrodded 186
[
]
[
]
No
[
]
ratio Combined 372
[
1
[
J No I
]
North Anna Rodded 234 3
[
No
[
3 Pin-to-box Unrodded 234
[
]
[
]
No
[
ratio Combined 468
[
]
[
]
No
[
]) by root sum Note: Difference is ((SIMULATE - MCNP) I SIMULATE) x 100%
- Eliminating the MCNP W-prime uncertainty component (conservatively set at [
square results in a W-prime tolerance interval of I
].
DOM-NAF-1 -REV. 0.0 -A Page 134 Appendix A: RAI Set I Questions and Responses Table 5 SIMULATE Critical Boron Comparisons Note: Critical boron difference is (SIMULATE - Measured) (ppm)
Yes - Passed all tests Yes* - Failed the DY test but passed the K-S and Kuiper tests Yes' - Failed the D' and K-S tests but passed the Kuiper test YesA - Failed the K-S test but passed the D' and Kuiper tests Corrections:
- 1. N. Anna EOC HFP normality test results should be 'Yes," i.e., passed all tests instead of 2 out of 3.
- 2. Number of observations for combined EOC HFP should be 504 instead of 521.
- 3. Surry ECP minimum value should be -29 instead of -31.
IL L_
LI L_
L L-L I_-
-,-=
Mean Sigma D'
D' D'
D' D'
K-S Kulper Calc.
0.05 Plant Condition (ppm) (ppm) Obs. Max. Min. Normal P=.025 P.05 P.95 P=.975 Sig L Sig L W
W NRF NRF NA BOC HZP -8.1 20.3 30 30
-53 Yes
=
0.8179 0.9995 0.9653 0.927 1
3.3 BOC HFP -7.2 16.4 228 30
-51 Yes*
948.2 955.7 958.6 980.7 982.3 0.1868 0.6974 1
0.4 EOC HFP -5.9 14.6 199 24
-39 Yes 792.3 777.8 780.3 799.7 801 0.0872 0.4539 0
0.0 ECP
-10.1 13.2 6
4
-31 N/A 0
0.0 SY BOC HZP
-5 23.4 35 48
-49 Yes 0.7569 0.9982 0.9758 0.934 0
0.0 BOC HFP -11.2 16.5 212 35
-54 Yes*
854.9 856.4 859.1 879.7 881.1 0.079 0.4264 5
2.4 EOC HFP -14.8 14.6 305 16
-48 Yes*
1518 1482 1486 1516 1517.5 0.175 0.6761 0
0.0 ECP 2.8 24.4 4
30
-29 N/A 0
0.0
~~~~2i mi dR iE im M
ALL BOC HZP
-6.4 21.9 65 48
-53 Yes 148 142.7 143.7 149.9 150.1 0.7423 0.9979 1
1.5 BOC HFP
-9.1 16.5 440 35
-54 Yes' 2550 2574 2579 2622 2625 0.0315 0.2276 6
1.4 EOC HFP -11.2 15.2 504 24
-48 Yes*
3227 3158 3164 3213 3217 0.1003 0.497 0
0.0 ECP
-4.3 18.9 9
30
-31 N/A 0
0.0 7F7~L 1
- 14R, 4
5 e
1 9099 9
9211 8
0 F__
F__
F__
r r
r -
r -
f r
r-r r
I r
r I
F f
r DOM-NAF-1-REV. 0.0 -A Page 135 Appendix A: RAI Set I Questions and Responses Table 6 SIMULATE Integral Control Rod Worth Comparisons Plant Type Mean Sigma NobS Max.
Min. Normal D
D D'
D 7
Do K-S Kulper CaIc.
0.05 I___
(¶6)
(¶6)
P=.025 P.05 P.95 P.975 Sg L Sig L W
W NRF NRF NA Dilution 2.4 4.3 39 16.1
-7.3 Yes 0.4678 0.9532 0.9621 0.939 2
5.1 Rod Swap 0.6 4.1 139 13.4
-12.4 Yes*
449.4 452.1 454 467.5 468.3 0.6507 0.9927 6
4.3 SU Dilution 1.7 5.2 54 13.6
-17.4 Yes*
104.9 107.5 108.4 113.5 113.7 0.7026 0.9961 3
5.6 Rod SDwa 1.8 3.7 130 10.4
-9.7 Yes 415.5 409.4 411.2 423.8 424.5 0.9823 1.0000 1
0.8 ALL 1>.8,t 4E) 184 13.6 >4 Ye.
878.4 691.3 593.7 711.8 71215.....9804
.2 ALL Dilution 2
4.8 93 16.1
-17.4 Yes*
238.6 245.9 247.2 256.1 256.6 0.4803 0.9595 4
4.3 tW JAAF JAAA
-^ JAPA AtX 7ff^
^^A. Q
^. n3.
Rod Swap 1.2 3.9 269 13.4
-12.4 Yes*
1224 1226 1230 1256 125B Note: Rod worth difference is ((SIMULATE - Measured)/SIMULATE) x 100%
Yes* - Failed the 0' test but passed the K-S and Kuiper tests Table 8 SIMULATE HZP BOC ITC Comparisons Plan Mean Sgma Nobs Max. Mn.
ormal D
0 D'
Dv Do K-S Kulper Calc.
0.05 Plant F
_pcm_F)P=.025 P-=.05 P=.95 P=.975 Sig L Sig L W
W NRF NRF NA 0.84 0.73 38 2.24
-1.72 Yes' 0.5773 0.9825 0.9148 0.938 2
5.3 SU 0.44 0.55 49 1.49 -1.64 Yes' 0.5557 0.9787 0.9325 0.947 0
0.0 ALL 0.62 0.66 87 2.24 -1.72 Yes*
215.2 222.2 223.5 231.8 232.2 1 0.318210.8651 1 2
2.3 Note: ITC difference is (SIMULATE - Measured) (pcm/F)
Yes' - Failed the W test but passed the K-S and Kuiper tests Yes* - Failed the D' test but passed the K-S and Kuiper tests 0.7952 0.9992_
8 3.U0 I
DOM-NAF-1-REV. 0.0 -A Page 136 Appendix A: RAI Set I Questions and Responses Table 23 SIMULATE Reaction Rate NUF (Non-normality Assumed)
Note: Sign on computed tolerance limits changed to positive for consistency.
Correction:
Surry Integral One Sided Tolerance Limit should be 2.34 instead of 2.35.
L -_
L ~=
K -
K V1 K
F -
F F F-H -
F -
F -
Std.
Reported Reported Rigorous Rigorous Number
% of Plant Data Mean D
Number Limiting One Sided Llmiting One Sided of Obs.
Obs. >
Type
()
Of Obs.
Tolerance Tolerance Tolerance Tolerance
> NRF NRF Value Limit (%)
Value Llmit (%)
N. Anna Integral
-0.02 1.34 3453 150 2.23 152 2.21 20 0.6 Surry Integral 0.07 1.34 2322 98 2.34 99 2.33 9
0.4 N. Anna 32 Node 0.14 2.41 93070 4273 3.96 4544 3.89 1969 2.1 Surry 32 Node 0.38 2.79 64354 2952 4.53 3127 4.42 2270 3.5
~ ~~~
~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
DOM-NAF-1 -REV. 0.0 -A Page 137 Appendix B: RAI Set 2 Questions and Responses NRC Request for Additional Information (second set) and Responses
- 1) Please provide a worked example showing how the tolerance limit was calculated for the parametric case. For example, show how the tolerance limit of [
I was obtained.
The W-prime sample sizes provided in the supplemented Table 4 (Attachment I to the initial response to NRC questions, Serial No. 02-334A) were in error. Since W-prime is the normalized ratio of assembly power to flux thimble instrument reaction rate, there are only two W-prime comparison values for each two-by-two assembly case. Therefore, the sample size for each base W-prime sample (for example, Surry rodded) is 6, that for a combined sample for a station is 12, and that for the combined sample for both stations is 24, as found in the attached update to Table 4.
For the Surry rodded case, the standard deviation was I
] for a sample size of 6. From Ref. 25, the one-sided tolerance multiplier for a normal distribution for 95/95 is 3.71.
Therefore, the tolerance limit is:
[
]
In calculating the W-prime tolerance limits, the mean was ignored. The treatment of the mean is academic for the W-prime data considering:
- 1) the W-prime tolerance limit was based on that of the combined station case, which has a near zero mean,
- 2) the mean for any core-wide normalized value should by definition be zero (consistent with the very low values for the Table 4 combined data means), and
- 3) the W-prime tolerance limit is not used in the derivation of NRFs.
- 2) Please provide a worked example showing how the tolerance limit was calculated for the non-parametric case. For example, show how the tolerance limit of [
] was obtained.
The tolerance limit for a non-normal distribution was determined based on the non-parametric ranking method of Somerville (Ref. 26) and referenced in USNRC Regulatory Guide 1.126 (Ref. 29). For the Surry rodded case (including gamma smearing), the sample size was 186.
The Somerville method indicates the 5th most negative value to be the 95/95 limiting tolerance value for a non-normal distribution of this size. The most negative value is used since this is the conservative direction. The first five ranked values for the Surry rodded case (including gamma smearing) are:
Henc, [
]
[
1
[
]
Hence, the value of the 5th most negative ranked comparison is [
].
DOM-NAF-1 -REV. 0.0 -A Page 138 l
Appendix B: RAI Set 2 Questions and Responses
- 3) Why is the tolerance limit for the first block (w-prime) higher than the mean, whereas it is lower for the second and third blocks?
This is due to an oversight in consistency. By one convention, the tolerance limit for power peaking might always be reported as positive since that is the direction in which it is applied to a prediction. For example, see the expanded version of Table 23 (Attachment 1 to the initial response to NRC questions, Serial No. 02-334A) where, for consistency, the sign of the I
reaction rate tolerance limits was changed from negative to positive. The presentation of negative tolerance limit values for the pin-to-box data in Table 4 serves to emphasize the fact that this is the conservative direction in the ranking of the comparison data from which the tolerance limit was derived.
I
DOM-NAF-1-REV. 0.0 -A Page 139 Appendix B: RAI Set 2 Questions and Responses Table 4 CASMO-4 W-prime and Pin-to-box Ratio Comparisons Fuel Type I Sample Mean (%) Std.e Normal Tolerance Parameter Aseby Size j)Limit Rodded 6
]
[
Yes 1
]
Surry5xl5 Unrodded 6
[
]
[
I Yes
[_
]
W_prime Combined 12
[
]
]
Yes
[
]
North Anna Rodded 6
[
]
[
I Yes
[
]
17x17 Unrodded 6
]
[
]
Yes
[
W-prime Combined 12
[
]
[
]
Yes
[
]
Combined data Combined 24
[
]
l
]
Yes
[
1*
W-prime I
Pin-to-box Ratio Statistics (Including Gamma Smearing)
Surry 15x15 Rodded 186
[
]
1 No
]
Pin-to-box Unrodded 186
[
1
]
No l
[
ratio Combined 372
[
]
[
I No
[
]
North Anna Rodded 234
[
]
[
]
No
[
]
I 7x1 7 Pin-to-box Unrodded 234
[
]
[
]
No
[
]
ratio Combined 468
[
]
[
]
No
[
1 Pin-to-box Ratio Statistics (Excluding Gamma Smearing)
Surry 15x15 Rodded 186
[
]
[
I No
[
Pin-to-box Unrodded 186
[
]
[
l No
[
]
ratio Combined 372
[
]
[
I No
[
I North Anna Rodded 234 1
]
[
]
No
[
]
Pin-to-box Unrodded 234
[
]
[
]
No
[
I ratio Combined 468
[
l
[
]
No
[
]
Note: Difference is ((SIMULATE - MCNP) / SIMULATE) x 100%
- Eliminating the MCNP W-prime uncertainty component (conservatively set at [
sum square results in a W-prime tolerance interval of [
1.
]) by root
1-i--
DOM-NAF-1-REV. 0.0 -A Page 140 Appendix C: Replaced Pages From Original Submittal Contents of this Appendix:
Original Original Original Original Original Original Original submittal page 26 submittal page 32 submittal page 35 submittal page 38 submittal page 44 submittal page 109 submittal page 113 L
I I
I I
I I
I I
I 1
1 I1 I
~1 I
Table 4 CASMO-4 W-prime and Pin-to-box Ratio Comparisons
- Eliminating the MCNP W-prime uncertainty component (conservatively set at [
root sum square results In a W-prime tolerance interval of [
].
26 FuelaType Assembly Mean (%)
Std. Dev. (%)
Normal Tolerance Parameter
_______Limit Rodded
[]
[
Yes
[1 SurryISxl5 Unrodded
[ ]
C ]
Yes
[ l W-prlme Combined I ]
1 ]
Yes
[ ]
North Anna Rodded
[ ]
1 ]
Yes
[ ]
17x17 Unrodded
[ ]
[ I Yes
[ 1 W-prlme Combined
[ i
[ ]
Yes
[ 1 Combined data Combined l ]
[ ]
Yes
[ 1 W-prime Pin-to-box Ratio Statistics (Including Gamma Smearing)
Surry 15x15 Rodded 1 ]
1]
No
[I Pin-to-box Unrodded
[ l
[ 3 No
[
]
ratio Combined
[ ]
[ ]
No
[
3 North Anna Rodded
[ I
[ ]
No t
I 7x17 7noddN Pin-to-box Unodded
[ l
[]
No
[1 ratio Combined
[ 1 1
No I]
Pin-to-box Ratio Statistics (Excluding Gamma Smearing)
Surry 15x15 Rodded
[ ]
[
]
No
[
]
Pin-to-box Unrodded
[ ]
_No
[3 ratio Combined
[1[
No
[t NorthAnna Rodded 1 1
[ ]
No
[
3 17x17 Unrodded i
l l No
[
]
Pin-to-box Combined
[
[ ]
No
]
ra tio_
])by
Table 5 SIMULATE Critical Boron Comparisons Note: Critical boron difference is SIMULATE - Measured (ppm)
Yes - Passed all test (D', K-S. and Kulper tests)
Yes* - Failed the D' test bUt passed the K-S and Kuiper tests Yes' - Failed the D' and K-S tests but passed the Kuiper test YesA - Failed the K-S test but passed the D' and Kuiper tests 32 L
L L-L-
I -
[-
L l
L
[
1
-1
[--[
t-- -
F-Plant Condition Mean Std. Dev.
Number Max.
Min.
Normal (ppm)
(ppm)
Of Obs.
BOC HZP
-8.1 20.3 30 30
-53 Yes BOC HFP
-7.2 16.4 228 30
-51 Yes*
North Anna EOC HFP
-5.9 14.6 199 24
-39 YesA ECP
-10.1 13.2 5
4
-31 N/A BOC HZP
-5.0 23.4 35 48
-49 Yes BOC HFP
-11.2 16.5 212 35
-54 Yes*
Surry EOC HFP
-14.8 14.6 305 16
-48 Yes*
ECP 2.8 24.4 4
30
-31 NIA
~
BOC HZP
-6.4 21.9 65 48
-53 Yes BOC HFP
-9.1 16.5 440 35
-54 Yes' Combined EOC HFP
-11.2 15.2 521 24
-48 Yes*
-4.3 18.9 9
30
-31 N/A B(~~k8
maximum DRW Is usually conservatively assumed to occur for the entire withdrawal sequence. Previous assessments of DRW uncertainty (Ref. 12) developed an uncertainty factor based on the DRW difference In units of pcm/step. However, K is more appropriate and conservative to determine the uncertainty in terms of %
difference, because t results in a much larger DRW conservatism for accident conditions at which the predicted DRW is much higher than any of the cases In the measured database.
A histogram for the Table 7 data is shown in Figure 11 with each bin representing the indicated midpoint +/- 0.25 pcmlstep. A sampling of four differential rod worth curve comparisons (DRW vs. rod position) is presented In Figures 12 through 15.
35
Table 6 SIMULATE Integral Control Rod Worth Comparisons Plant Type Mean Std. Dev.
Number Mx
- i.
Nra (en)
(%)
Of Obs.
Max.
Mi.
No==l Dilution 2.4 4.3 39 18.1
-7.3 Yes North Anna Rod Swap 0.6 4.1 139 13.4
-12.4 Yes*
ALL 0.9 4.2 178 16.1
-12A Yes Dilution 1.7 5.2 54 13.6
-17.4 Yes Surry Rod Swap 1.8 3.7 130 10.4
-9.7 Yes ALL 1.8 4.2 184 13.6
-17.4 Yes*
Dilution 2.0 4.8 93 16.1
-17.4 Yes' Combined Rod Swap 1.2 3.9 269 13.4
-12.4 Yese ALL 1.4 4.2 362 16.1
-17.4 Yes*
Note: Rod worth difference is (SIMULATE - Measured) I SIMULATE)
Yes* - Failed the D' test but passed the K-S test and the Kuiper test Table 7 SIMULATE Peak Differential Control Rod Worth Comparisons Plant l
Mean Std. Dev.
Number Max.
Min.
Plant
(%)
(pcmlstep)
Of Obs.
Ma.
M.
orl North Anna 5.0 8.0 39 30.6
-12.2 Yes Surry 6.0 8.3 54 20.1
-17.0 Yes Combined 5.6 8.1 93 30.6
-17.0 Yes Note: Differential rod worth difference is (SIMULATE - Measured)/SIMULATE (%)
38 I
I I
L I
1 I
I I
I I
I 1
I l
1A j
1
Table 8 SIMULATE HZP BOC ITC Comparisons Plant Mean Std. Dev.
Number Max.
Mi.
Normal (pcml0F)
(pcml°F)
Of Obs.
North Anna 0.84 0.73 38 2.24
-1.72 Yes' Surry 0.44 0.55 49 1 A9
-1.64 Yes' COMBINED 0.62 0.66 87 2.24
-1.72 Yes*
Note: ITC difference is (SIMULATE - Measured)
Yes' - Failed the W test but passed the K-S test and the Kulper test Yes* - Failed the D' test but passed the K-S test and the Kulper test 44
I I
1 4.3.6 Estimated Critical Position Although there is no NRF for the ECP calculation, it is useful to develop uncertainty estimates based on the ECP data. ECP calculations involve all reactivity components of the SIMULATE model including control rod worth, xenon worth, power defect, and boron worth. The ECP uncertainty factor can be used as an estimator to make inferences about the maximum uncertainty associated with those components. Since uncertainty factors have been developed separately for at least three of the reactivity components (boron worth, control rod worth and moderator temperature coefFicient via the ITC statistics), the remaining components can be approximated.
Table 21 presents the upper and lower tolerance interval infornation (95%
confidence) for North Anna data, Surry data, and all ECP data combined.
Normality is assumed based on the results of normality tests shown in Table 10.
A very crude approximation of the combined uncertainty of SIMULATE xenon and Doppler worth can be performed as follows. Using the assumption of normality, the major contributions to ECP uncertainty (variance) can be expressed as shown in Equation 3.
1 C?ECP =
X. +C 2DPD +
2MTD + C?RW + C 2?W + C?BC1 + ?BC1 (Eqn. 3)
The components, converted into units of pcm by weighting with typical reactvity contributions to the ECP calculation, are defined as follows:
l CSECP - combined standard deviation for ECP calculations from all sources (Table 21) ax.
- standard deviation associated with SIMULATE xenon change i
ODPD - standard deviation associated with SIMULATE Doppler defect amTD - standard deviation associated with SIMULATE moderator defect 109
Table 23 SIMULATE Reaction Rate NUF (Non-normality Assumed)
Data Mean Std.
Number Limiting One Sided Plant D:
n Dev.
OF Ol Tolerance Tolerance TOValue Limt (%)
North Anna Integral
-0.02 1.34 3453 150
-2.23 Surry Integral 0.07 1.34 2322 98
-2.35 COMBINED Integral 0.01 1.34 5775 257
-2.25 North Anna 32 Node 0.14 2.41 93070 4273
-3.96 Surry 32 Node 0.38 2.79 64354 2952
-4.53 COMBINED 32 Node 0.24 2.58 157424 7233
-4.17 Table 24 SIMULATE FAH and FQ NUF Reaction Rate Combined Plant Data Type Tolerance
[
I Tolerance Lmit (Table Umit (%)
23)
North Anna Integral / FAH
-2.23 t
J
-3.0 Surry Integral / FAH
-2.35 1
-3.1 COMBINED Integral I FAH
-2.25
[ 3
-3.0 North Anna 32 Node / FQ
-3.96
[ ]
4.4 Surry 32 Node I FQ
-4.53
[ 3
-5.0 COMBINED 32 Node / FQ
-4.17
[ 3
-4.6 113