ML20010B617
| ML20010B617 | |
| Person / Time | |
|---|---|
| Site: | Surry, North Anna  |
| Issue date: | 07/31/1981 |
| From: | Bowling M, Rhodes J, Rodes J VIRGINIA POWER (VIRGINIA ELECTRIC & POWER CO.) |
| To: | |
| Shared Package | |
| ML18130A343 | List: |
| References | |
| VEP-FRD-20A, NUDOCS 8108170343 | |
| Download: ML20010B617 (80) | |
Text
W VEP-FRD-20A JULY, 1981 Vepco THE PDQ 07 ONE ZONE MODEL F
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VEP-FRD-20 A THE PDQ07 ONE ZONE MODEL l
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.i. R. RODES NUCLEAR FUEL ENGINEERING GROUP FUEL RESOURCES DEPARTENI VIRGINIA ELECTRIC AND POWER COMPANY RICEMOND, VIRGINIA July, 1981 Retou::: tended for Approval:
Md [- k M. L. Bowling, Supervisof Nuclear Fuel Engineering Group Approved :
l J.'T.' Rhodes, Director Nuclear Fuel Engineering and j
Operation l
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!,Yp ;.f',g NUCLEAR REGULATORY COMr.11SSION is, WASHING TON, D. C. 20555 g.; A,,,,c,}j C V,r u
E y*m.y y t'Ay 9 01981 Mr. W. N. Thomas, Vice President Fuel Resources Virginia Electric Power Company Richmond, Virginia 23261
Dear Mr. Thon'as:
SUBJECT:
ACCEPTAflCE FOR REFERENCIllG OF TOPICAL ' REPORT VEP-FRD-20 "THE PDQ07 ONE ZONE MODEL" The Nuclear Regulatory Commission (NRC) staff has completed its review of
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the Virginia Electric and Power Company (Vepco) Topical Report number VEP-FRD-20 entitled "The PDQ07 Or.c Zone Model". The Vepco developed a coarse mesh (i.e., scyeral mesh lines per fuel assembly), two-dimensional, two neutron energy group, diffusion-depletion calculational model, designated as the PDQ07 one zone model. This model is similar to the previously NRC accepted Vepco PDQ07 discrete (i.e., one mesh line per fuel rod) model in that it uses the NULIF, PDQ07, SHUFFLE, and HAFIT computer codes which are part of the Fuel Utilization and Performance Analysis Code (FUPAC) system obtained from the Babcock and Wilcox Company.
The purpose of the one zone model is to provide a supplementary model to the PDQ07 discrete model for the more efficient (1.e., less compu-tational time) perfomance of reactor physics, fuel management, and operational support analyses for the Surry and North Anna nuclear reactors.
The accuracy of the one zone model is demonstrated through comparisons with both the Vepco PDQ07 discrete model predictions and measurements taken at Surry Units No.1 and 2.
Our sunnary of the evaluation is enclosed.
As the result of our reviews we conclude that the Vepco Licensine Topical Report VEP-FRD-20 entitled "The PDQ07 One Zone Model" dated January 1977 is acceptable for referencing in licensing actions b,t Vepco to the extent specified and under the limitations in the report and the enclosed evalua-tion.
We do not intend to repeat the review of the safety features described in the report as found acceptable herein. Our acceptance applies only to the use of features described in the topical report as discussed herein.
In accordance with established requirements, it is requested that Vepco issue a revised version of this report within three months of the receipt y
of this letter. This evaluation letter and its enclosure is to be included in the revised version between the title page and the abstract and the approved report will carry the identifier VEP-FRD-20.
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Mr. W. N. Thomas ;g.
Should NRC criteria or regulations change'such that our conclusions as to the acceptability of the report are invalidated, Vepco will be expected to revise and resubmit the topical report or submit justification for the continued effective applicability of the topical report without revi-sion.
If you have any questions about the review or our conclusion, please contact us.
Sincerely, I *Ecb L + c~'
Robert L. Tedesco, Assistant Director j
for Licensing Division of Licensing
Enclosure:
Evaluation of Report i
VEP-FRD-20 i
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\\ FAY d 1981 Enclosure EVALUATION OF VEPC0 TOPICAL REPORT VEP-FRD-20 Report Number >
VEP-FRD-20 Report
Title:
The PDQ07 One Zone Model Report Date:
January 1977 Originating Organization: The Virginia Electric and Power Company Reviewed By:
Core Perfomance Branch /W. Brooks The Virginia Electric and Power Company (VEPCO) has presented a number of licensing topical reports for our review in preparation for performing their own reload analysis, VEP-FRD-20 is one of the series. The Core Performance Branch has reviewed this report. Our evaluation follows.
1.
Description of Report The report includes the following:
1.
A description of the Surry Units 1 and 2 cores including the fuel and burnable poison Icadings for Cycles 1 and 2 of eich unit.
2.
A brief description of the calculational model including the homogenization procedure, the cross-section preparation tech-niques, and the core geometry representation for the diffusion theory code.
3.
A comparison of calculated results from the one zone model to those calculated by the discrett model and those treasured in the Surry reactors.
4.
A sumary of the results of the comp'arisons yielding uncertainty values to be assigned to the various calculated parameters.
Verification of the one zone model for the calculation of the following parameters is presented:
1.
Assembly average radial power distributions.
2.
Stuck rod power distributions.
3.
Assembly and batch burnup.
4.
Control bank worths.
5.
Shutdown worth and stuck rod worth.
6.
Critical baron concentration vs burnup and control rod con-figuration.
7.
Differential baron worth.
8.
Isothermal temperature coefficients.
4
. In contrast to the discrete model (described in VEP-FR-19 which has been reviewed and appro--d) which has one mesh point for each fuel rod, guide tube or 4-
, _nientation tube, the one zone model is restricted to a few mesh points per assembly.
In practice, the assembly is divided into mesh blocks which all have the same distribution of fuel and non-fueled locations. Thus each mesh block in a particular fuel assembly has the same homogenized nuclear parameters at beginning of life. This accounts for the use of the term one zone model. Because the core can be modeled with far fewer mesh points a solution can be obtained with the one zone model much more rapidly than with the discrete model. For this reason the one zone model is oftca used for scoping calculations with the discrete model being used for the final analyses.
In addition, the one zone model is used when the whole core must be represented as in perfaming stuck rod calculations.
Comparisons between measured and calculated assembly average power distributions in the form of standard eviations are presented for both the one zone and the discrete models. Representative examples of core maps showing comparisons of measurement and one zone calcu-lations are also given. Comparisons between one zone and discrete calculations of the flux distribution for a stuck rod configuration are presented along with examples of comparisons between measured and calculated end of cycle burnup distributions.
Comparisons are presented between calculated and measured values of certain reactivity parameters including
- D and C bank works at beginning of cycle, HZP conditions;
- total shutdown worth (all rods in) and stuck rod worth;
- critical boron concentrations for the first three cycles of Surry Units 1 and 2 as a function of burnup;
- critical boron concentration as a function of control rods inserted for the first three cycles of Surry, Unit 1;
- differential boron worths for all rods out configuration for the first three cycles of Surry, Unit 1; and
- isothemal temperature coefficients as a function of rods inserted for the first three cycles of Unit 1.
For all but the last of those parameters, the results of comparisons between measurement and discrete model calculations are also given.
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. Firjally the comparison data are summarized to obtain uncertainty values to be used for production calculations. Except as noted camparisons are to measurements. These uncertainty values are:
- assembly average power distribution - maximum standard deviatic.n of s 6 percent;
- stuck rod peak assembly pownr to within 3 percent of the discrete calculation;
- batch burnup value - maximum difference of 4.2 percent;
- stuck rod worths durin., 'nitial startup of Units 1 and 2 were predicted to within 5 percent; and
- isothermal temperature coefficients are typically predicted to within 1 pcm per degree Fahrenheit with a maximum difference of 2.2 pcm. A value of 3 pcm per degree Fahrenheit is assumed for this uncertainty.
In addition to these conclusions it is also concluded that the one zone model provides adequate values for control rod banx worths in normal sequence, critical boron concentrations 37d differential baron worths, although the model is not intended for production calculations of these parameters.
2.
Summary of Evaluation We have reviewed the model description in the topical report and conclude that the procedures emplo data inputs (cross-section, etc.) yed in the homogenization and the are state-of-the-art and acceptable.
We have reviewed the data presented as support for the assignment of uncertainties to the various calculated parameters listed in Section 1 above. Enough data are presented to permit the conclusions relating to calculational uncertainties to be made. We concur with the values i
for the uncertainties as presented in the report.
3.
Evaluation Procedure The review of topical report VEP-FRD-20 has ' beer. 'ondt e.sthin the guidelines provided for analytical methods in the _t=nds d Review Plan, Section 4.3.
Sufficient information is providec ',o permit a knowledgeable person to conclude that the VEPCO model described in this report is state-of-the-art and is acceptable. EJfficient data are presented to permit the conclusion.that the derived uncertainties are reasonable and are acceptable.
b 4-4.
Regulatory Position Based on our review of licensing topical report VEP-FRD-20 we conclude that it is acceptable for reference in licensing actions by VEPC0. Such reference may be made for the purpose of describing the calculational model and as support for the stated values of uncertainties in the following quantities:
- assembly average power distributions;
- assembly power distributions in the neighborhood of stuck or potentially ejected rods;
- batch and assembly burnup values;
- stuck rod worths; and
- isothermal temperature coefficients.
We further conclude that this model is an acceptable substitute for vendor calculations of the above named quantities.
We endorse the commitment made in the report by VEPCO to continue verification and model improvenents in the one zone model as more data are obtained from the Surry and North Anna Reactors.
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CLASSIFICATION /DISCLADER The data and analytical techniques described in this report have been prepared for sp<teific application by the Virginia Electric I
and Power Company. The Virginia Electric and Power Company makes no claim as to the accuracy of the data or technique contained in this report if used by other organizations.
In addition, any use of this i
j report or any part thereof must have the prior written approval of the Virgisia Electric and Power Company.
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l' I-ABSTRACT l
The Virginia and Electric Power Company (Vepco) has developed a coarse mesh (i.e., several mesh lines per fuel assembly), two-dimensional, two neutron energy group, diffusion-depletion calculational model, designated as the PDQ07 one zone model. This model is similar to the previously deve-loped Vepco PDQ07 discrete (i.e., one mesh line per fuel rod) model in that it uses the NULIF, PDQ07, SHUFFLE, and RAFIT computer codes which are part of the Fuel Utilization and Performance Analysis Code (FUPAC) system obtained from the Babcock and Wilcox Company. The purpose of the one zone model is l-to provide a supplementary model to the PDQ07 discrete model for the more efficient (i.e., less computational time) performance of reactor physics, fuel management, and operational support analyses for the Surry and Nerth Anna nuclear reactors. The accuracy of the one zone model is demonstrated through comparisons with both the Vepco PDQ07 discrete model predictions and measurements taken at Surry Units No. 1 and 2.
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ACKN%1EDGEMENTS The author would like to thank Mr. C. B. Franklin for his assis-cance in performing the computer calculations and data preparation required for this report and Ms. Cathy Loving for her typing of the draft and final manuscript. Special thanks is given to Mr. M. L. Smith whnse technical assistance and direction greatly aided the development of the one zone model. Finally, the author wishes to acknowledge the u ntributions made by the many people who reviewed and provided comments on the preparation
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of this report.
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TABLE OF CONTENTS
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CLASSIFICATION 1
ABSTRACT 11 ACKNOWLEDGEMENTS 111 l
TABLE'0F CONTENTS iv LIST OF FIGURES v
LIST OF TABLES v11 SECTION 1 - INTRODUCTION 1-1 t
SECTION 2 - CORE DESCRIPTION 2-1 1
2.1 Introduction 2-1 ll 2.2 Core Design 2-1 2.3 Fuel Ioadings 2-3 SECTION 3 - MODEL DESCRIPTION 3-1 3.1 Introduction 3-1 3.2 Cross Section Preparation 3-3
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3.3 Diffusion Theory Calculation 3-14 SECTION 4 - COMPARISON OF ONE ZONE PREDICTIONS TO DISCRETE PREDICTIONS 1ND MEASUREMENT DATA 4-1 4.1 Introduction 4-1 4.2 Analytical Calculations 4-1 4.3 Measurement Data 4-4 l
4.4 Results 4-5 1
SECTION 5 -
SUMMARY
AND CONCLUSIONS 5-1 l
SECTION 6 - REFERENCES 6-1 iv
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LIST OF FIGURES Figure Title Page No.
2-1 Cross Sectional View of Surry Fuel Assemblies 2-6 2-2 Control Rod Bank Locations 2-7 2-3 Surry Units 1 and 2 - Cycle 1 Fuel Loading 2-8 2-4 Surry Unit 1 - Cycle 2 Fuel Loading 2-9 2-5 Surry Unit 2 - Cycle 2 Fuel Loading 2-10 2-6 Surry Unit 1 - Cycle 3 Fuel Loading 2-11 2-7 Surry Unit 2 - Cycle 3 Fuel Loading 2-12 2-8 Surry Units 1 and 2 - Cycle 1 Burnable Poison Rod Loading 2-13 2-9 Surry Unit 1 - Cycle 2 Burnable Poison Rod Loading 2-14 2-10 Surry Unit 2 - Cycle 2 Burnable Poison Rod Loading 2-15 2-11 Surry Unit 1 - Cycle 3 Burnable Poison Rod Loading 2-16 2-12 Surry Unit 2 -- Cycle 3 Burnable Poison Rod Loading 2-17 3-1 Flowchart for the PDQ07 One Zone Model 3-4 3-2 Typical One Zone Quarter Core Geometry Represent-ation 3-16 4-1 Assemblywise One Zone Vs. Incore Relative Power Distri-bution For Surry 2, Cycle 2, HZP ARO, at 0 5'D/MIU 4-9 4-2 Assemblywise One Zone Vs. Incore Relative Power Distr-bution For Surry 2, Cycle 2, HZP, D-Bank In at 0 MWD /MTU 4-10 4-3 Assemblywise One Zone vs. Incore Relative Power Distri-bution For Surry 2, Cycle 2, HFP, ARO, at 3000 5'D/MIU 4-11 4-4 Assemblyvise One Zone Vs. Incore Relative Power Distri-bution For Surry 2. Cycle 2, HFP, ARO, at 9000 MWD /MTU 4-12 4-5 Assemblywise Average Power Distribution For Hot Zero Power, All Rods Out, at Beginning of Initial Cycle For Surry Unit 1 4-13 v
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4-6 Assemblywise Average Power Distribution For Hot
~ero Power, All Rods In With Rod H-14 Out At l
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Beginning of Initial Cycle For Surry Unit 1 4-14 5
3 4-7 AssemblywisgAccumulatedBurnupandBatchBurnup j'
i Shart.ng (10 MWD /MTU) For the Cycle 1 Operation of Surry Unit 1 4-15 h
4-8 AssemblywisgAccumulatedBurnupandBatchBurnup Sharing (10 MWD /MTU) For the Cycle 2 Operation of Surry Unit 1 4-16 o
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LIST OF IABLES Table Title Page No.
l 2-1 Surry Core Description 2-4 3-1 Contents of Fine-Energy Group Cross Section Library 3-6 3-2 Fine Energy Group Cross Sections I.abrary Constituents 3-7 3-3 Depletion Equations Used in PDQ07 3-18 4-1 Summary of Comparie'ns For Both the Initial and Reload Cycles 4-7 4-2 Comparison of Predicted and Measured Assembly Average Power Distributions for Surry Units 1 and 2, Cycles 1 and 2 4-8 4-3 Comparison of Predicted and Measured D and C Bank Control Rod Worths For BOC, HZP Conditions 4-17 4-4 Comparison of Predicted and Measured. Total Shutdown Worth and Stuck Rod Worth For Cycle 1 Surry Units 1 and 2, BOC, HZP Conditions 4-18 4-5 Representative Critical Boron Concentration Vs. Burnup Comparisons For Surry Unit 1 4-19 4-6 Representative Critical Boron Concentration Vs. Burnup Comparisons For Surry Unit 2 4-20 4-7 Covparison of Predicted and Measured Critical Boron Concentration Tor various Control Rod Configurations For Surry Unit 1, Cycles 1, 2, and 3 4-21 l
4-8 Comparison of Predicted and Measured Differential Boron Worth For Various Control Rod Configurations For Surry Unit 1, Cycles 1, 2, and 3 4-9 Comparison of Predicted cnd Measured Isothermal Temper-ature Coefficients For Various Rod Configurations for Surry Unit 1, Cycles 1, 2, and 3 4-23 vii
SECTION 1 - INTRODUCTION The Virginia Electric and Power Company (Vepco) is currently deve-loping the capability to perform nuclear reactor analyses for the Surry and North Anna nuclear power stations. The objective of this topical report is
- 1) to describe one of the computational models developed at Vepco for the purposes of reactor physics analyses and fuel management evaluation and 2) t'o demonstrate the accuracy of this model by comparing analytical results generated with the model to alternate calculations and to actual measure-ments from Surry Units No. 1 and 2.
The computational model to be described is a coarse mesh (several mesh lines per fuel assembly), two-dimensional, two neutron energy group, diffusion-depletion (with thermal-hydraulic feedback) calculational package and is designated as the PDQ07 one zone calculational model. The PDQC7 one 2
3 4
zone model uscs the NULIF, PDQ07, SHUF'lLE, and HAFI1 computer codes which P
are part of the Fuel Utilization and Performance Analysis Code 5 (FUPAC) system obtained from the Babcock and 411cox Company. The.?UPAC system is currently
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used by Babcock and Wilcox to perform production reactor analysis and design.
A detailed description of the input / output, functioning, and physical model of the above computer codes can be obtained from the referenced Babcock and Wilcox computer code manuals. The FUPAC system is maintained by Vepco and updated through contractual arrangements between Vepco and Babcock and Wilcox.5 The PDQO7 one zone model is similar to the PDQ07 discrete mode 16 and was designed to provide a two-dimensional reactor physics analysis capa-I bility presently impractical or impossible with the discrete model because of excessive computer usahe requirements. The one zone cods 1 was developed to require much less computer usage than the discrete model by virtue of using a fewer number of spatial mesh lines to represent the geometry of the reactor core. Reduction in running time by a factor of 5 to 12 an be realized 1-1 4
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r depending on the number of mesh lines used in the one zone model. The one zone model has also been developed to be consistent with the discrete model while:
1.
making as few changes as possible to the one zone code input relative to the discrete model input, and t
2.
benchmarking one zone calculations to discrete calculations where practical.
Since the one zone model has many aspects which are identical to the discrete nodel, this topical repert frequently references the PDQO7 Discrete Model Report.
(See Reference 6.)
The purpose of this report is 1) to describe those aspects of the one zone model which differ significantly from the discrete model as well as to summarize the basic similarities, 2) to present the types of calculations that are intended to be performed by the one zone model, and 3) to demonstrate the model's accuracy by comparison to discrete model calculations and actual measurements performed at Surry Units No. 1 and 2.
The types of calculations that can be performed by the one zone model include:
I 1.
Reactor Physics Analysis IB Two-dimensional assembly average radial power distributions a.
b.
Critical soluble boron concentrations as a function of burnup c.
Nuclide concentrations as a function of burnup d.
Integral control rod bank worths e.
Rod worth values for abnormal positioned control rods.
f.
Moderator and doppler coefficient and defects as a function of soluble boron, buraup, average moderator temperature and control rod bank position.
2.
Fuel Management Analysis c.
Batch power and burnup sharing b.
Fuel isotopics as a function of burnup l-2
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Scoping studies for the evaluation of alternative future cycle loading patterns and fuel loading requirements.
Of the above types of calculations, the ones that are of primary interest for one zone model application are the rod vorth and power distri-I bution values for abnormal positioned control rod (i.e., stuck, dropped, misaligned, and ejected rod worths), moderator and Doppler coefficients and defects, and the evaluation of alternative future cycle loading patterns and fuel loading requirements. These calculations, which are computer usage intensive, can be performed to within acceptable accuracy with the one zone model. Rod worth and power distribution values for abnormal positioned con-l trol rods generally require full core calculations which translate to very long computing requirements if the discrete model were to be used. Moderator and Doppler coefficients are needed for a wide range of reactor core condi-tions so that a very large number of calculations must be performed and, l
therefore, using the one zone model greatly reduces the overall computer usage requirement relative to the discrete model. Finally, it is planned to use the one rone model for scoping studies to generate alternate near and long term tuel cycle leading patterns and fuel loading requirements in order to ide cify a group of potentially acceptable loadings which can then be further analyzed by the discrete model for the purpose of selecting the most opera-tionally and economically optimum loading.
The remainder of this report describes the Surry Units No. I and 2 reactor core to be modeled, the purpose and interrelationships of th'e various I
computer codes which comprise the-PDQ07 one zone model, che specific modeling of the reactor core, and the comparison of calculatel results with calculated results from the discrete model and/or selected reactor measurements from Cycles 1 through 3 of Surry Units No. I and 2, as appropriate.
1-3
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l SECTION 2 - CORE DESCRIPTION l
2.1 IN Q UCTION The Surry Nuclear Power Station, which currently consists of two operating units, has been selected as the operating system to be modeled fce verification of the PDQ07 one zone model. The Surry Units No.1 ar'.
2 are identical Westinghouse designed three coolant loop pressurized water reactors with thermal ratings of 2441 Mwt.
Initial criticality wae achieved for Surry Unit No. 1 on July 1, 1972 and for Surry Unit No. 2 on March 7, 1973.
The initial cycle for Surry Unit No. 1 was completed on October 24, 1974 and for Surry Unit No. 2 on April 26, 1975. Second cycle operation commenced on January 30, 1975 and June 14, 1975 and was completed on September 26, 1975 and April 22, 1976 for Surry Units No. 1 and 2, respectively. Third cycle operation began for Unit 1 on December 6, 1975 and was completed on October 17, 1976. For Unit 2, third cycle operation began on June 1, 1976 and is presently planned to be completed in the fall of_1977.
2.2 CORE DESIGN The Surry cores consist of 157 fuel assemblies surrounded b'y a core baffle, barrel, and thermal shield and enclosed in a steel pressure vessel.
The pressure inside the vessel is maintained at.a nominal 2250 psia. The coolant (and moderator) is pressurized water which enters the bottom of the core at 532 F and undergoes an average rise in temperature of 65.5 F before 0
exiting the core. The average coolant temperature is 566 F and the average t
linear power density of the core is 6.2 kw/ft.
Each of the 157 fuel assemblies consists of 204 fuel rods arranged in a 15 by 15 square array. The fuel used in the Surry cores consists of slightly enriched uranium dioxide fuel pellets contained within a lircaloy-4 clad. A small gap containing prescarized helium exists between the pellets and the inner diameter of the clad. For the positions in the 15 by 15 array not occupied by 2-1
fuel rods, there are 20 guide tube locations for either solid burnable poison rods or control rods and one centrally located instmmentation tube.
(See Figure 2-1.) The fuel rods in each fuel assembly are supported by seven Inconel-718 grids located along the length of the assembly. These grids are mechanically attached to the guide tubes, which are, in turn, welded to the upper acd lower nozzles, and thus provide for assembly structural support.
There are 48 full-length Rod Cluster Control Assemblies (referred to as control tods) used to control core reactivity as well as five part-length rods for axial power shaping.. (It should be noted that the part-1 length control rods are physically present but are not currently allowed to f
be inserted into the core.) The absorber material of the control rods is an alloy consisting of 80% silver, 15% indium, and 5% cadmium. The various con-trol rods are arranged in and move in symmetrically located groups, or banks, as depicted in Figure 2-2.
Banks D, C, B, and A are denoted as the control banks and are moved in a fixed sequential pattern to control the reactor over the power range of operation. The remaining rods, Banks SA and SB, are denoted as shutdown banks and are used to provide shutdown margin.
In addition to the control rods, a chemical (boric acid) shim is used to control excess core reactivity and to facilitate operational flexibility.
Above certain concentrations of chemical shi'a, burnable poison rods are also used to control excess reactivity. Fresh ad/or depisted burnable poison rods can also be used to shape (i.e., improve) the core power distribution.
The burnable poison rods contain borosilicate in the form of Pyrex glass clad in a stainless steel tube. Burnable poison rods which may be used in any fuel assembly not under a control rod bank locatioti, consist of clusters of either 1
8, 12, 16, or 20 rods which are inserted into the Zircaloy-4 control rod guide tubes.
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Specific values of the principal mechanical and thermal-hydraulic
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parameters of the Surry core are provided in Table 2-1.
A complete deterip-tion of the Surry units is given in Ref6rence 7.
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2.3 FUEL LOADING The initial and reload quarter core fuel loadings (i.e., initial enrichments and density, previous cycle location if appropriate, beginning of cycle burnup, and number of fresh or depleted burnable poison rods pre-sent) for both Surry units are provided in Figures 2-3 through 2-12.
It l-f should be note'd thtt the fuel loadings for Cycle 1 of both Surry units are l
identical. The fuel management strategy employ *d in the initial cycle of operation of each un?.c was the checkerboard loading of the two lower enriched 4
fuel batches in the center of the core and the highest enriched fuel batch ti around the periphery of the core.
After the first cycle, the fuel manage-I ment became more complicated as the result of the need to minimize the impact i
of fuel densification (which was most severe in the lower density, lower b
prepressurization Batches 1, 2, and 3). Generally a modified out-in strategy was followed wherein higher enrichment fresh fuel was loaded on the core Y
periphery with lower enrichment fresh fuel (one-burned fuel and twice-burned L
fueV checkerboard loaded in the inner region of the core. An exception to I
this was in the third cycle of Unit No. 1 where no fresh fuel was loaded on the periphery. The only fresh fuel was 16 lower enrichment assem*olies loaded in the inner region of the core.
2-3
t-1 Table 2-1 t
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SURFY CORE DESCRIPTION t
,l THERMAL AND HYDRAULIC DESIGN PARAMETERS Total core heac output, Hut 2441 Heat generated in fuel, %
97.4 System operating pressure, psi 2250 Total coolant flow rata, lb/hr (spm) 100.7 x 106 (265,500)
Coolant Temperatures, OF (@l00% power)
Nominal inlet 532 Average rise in the core 65.5 Average in the core 566
'l Nominal outlet of hot channel 642 d
Average linear power density, Kw/ft 6.2 MECHANICAL DESIGN PARAMETERS i
Fuel Assemblies 3
Design Canless 15 x 15 a
Number 157 I
Rod pitch, inches 0.563 Overall dimensions, inches 8.426 x 8.426 I
Number of grids per assemly (material) 7 (Inconel-718)
Number of instrumentation tubes 1
h Fuel Rods j
Number 32,028 Number of rods / assembly 204 Batch 1.2.4.5 Batch 3 Outside diameter, inches 0.422 0.422 Diametrical gap, inches 0.0075 0.0085 Clad thickness, inches
. 0.0243 0.0243 i
Clad material Zircaloy-4 Fuel Pellets j
Material Sintered UO2 l
Density (% of theoretical) and See Figures 2-4 through Enrichment (w/o U235) 2-12 l
Batch 1.2;4.5 Batch 3 Outer diameter 0.3659 0.3649 Control Rod Assemblies Neutron absorber 5% Cd-15% In-80% Ag Cladding Material Type 304 SS-Cold worked Clad thickness, inches 0.019 Number (full length) 48 Number of rods per assembly 20 2-4
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Burnable Poison Rods Material Pyrex glass Content B 02 3 (w/o) 12.5 Core Structure Core barrel I.D./0.D., inches 133.875/137.875 Thermal shield 1.D./0.D., inches 142.625/148.000 Core diameter, inches.. approximate)*
119.5 Reflector thickness (approximate) a d composition Top - Water plus steel,'in.
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Bottom - Water plus steel, in'.
10 Side - Water plus steel, in.
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FIGURE 2-1 CROSS SECTIONAL VIEW OF SURRY FUEL ASSEMBLIES l
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FIGURE 2-2 CONTROL ROD RNK LOCATIONS R
P N
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-a 2
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15 CONTROL ROD ASSEMBLY BANKS Function Number of Assemblies Control Bank D b
Control Bank C 8
Control Bank B 8
Control Bank A S
Shutdown 'S}
16 Part Length (P) 5 53 O =
sau ce ^sse<>'r tocir o==
2-7
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Figure 2-3
- SURRY UNITS 1 AND 2 - CYCLE 1
~
ll FUEL LOADING 08 09 10 11 12 13 14 15 1
2 1
2 1
2 1
3 H
0 0
0 0
0 0
0 0
Fresh Fresh Fresh Fresh Fresh Fresh Fresh Fresh J
(
0 0
0 0
0 0
0 0
Fresh Fresh Fresh Fresh Fresh Fresh Fresh Fresh l
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1 2
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2 1
2 1
3 g
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0 0
0 0
0
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l Fresh Fresh Fresh Fresh Fresh Frech l
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1 2
3 3
Initial N
Batch Enrichment Density 0
0 0
0 0
(#F.A.'s) w/o U235
%TD l.
Fresh Fresh Fresh Fresh Fresh 1 (J3,1 1.85 94 1
3 3
~
3 2 (52) 2.55 93 3.10 92 0
0 0
0 l
Fresh Fresh Fresh Fresh I
R
'O O
Fresh Fresh LEGEND xx
- Batch No.
YY --Initial Burnup (MWD /MTU) zb
- Previous Location (If applicable)
~
e e
2-8
~...
Figura 2-4 SURRY UNIT 1 - CYCLE 2 FUEL LOADING 08 09 10 11 12 13 14 15 1
4B 1
4B
,2 4B 1
4C 1:
H 15231 0
12373 0
15398 0
14546 0
H08 Fresh H14 Fresh H13 Fresh H12 Fresh
(
4B 2
4A 2
2 2
4C 4C l
O 16557 0
14339 16191 14438 0
0 Fresh LO8 Fresh K13 Kil L12 Fresh Fresh 1
4A 1
4A 2
1 4C f
K 12373 0
11120 0
16031 14053 0
P08 Fresh M12 Fresh J12 K12 Fresh I
4B 2
4A 2
2 4C 4C 0
14339 0
16883 167.73 0
0 Fresh N10 Fresh JC8 J10 Fresh _
l Fresh 2
2 2
2 4A 4C M
15398 16191 16031 16723 0
0 N08 L10 M09 K09 Fresh Fresh
~
Initial 43 2
1 4C 4C Batch Enrichment Density N
O 14438 14053 O
O
'~
L Fresh M11 M10 Fresh Fresh 1 (21) 1.85 94 2Z 2 (52) 2.55 93 1
4C 4C 4C I
4A (20) 1.85 95 p
4B (12) 2.60 95 14546 0
0 0
4C (52) 3.35 95 s
MOS Fresh Fresh Fresh 4C 4C R
0 0
Fresh fresh LECEND xx
- Batch No.
yy --Initial Burnup (MWD /MTU)
Previous Location (If applicable) zz 2-9
. - ~.. _ _.. _ _
Figure 2-5 SURRY UNIT 2 - CYCLE 2 FUEL LOADING r
08 09 10 11 12 13 14 15 l
1 3
3 2
- 4A 2
2 4B l
H 16535 15490 11309 18101 0
18399 16912 0
l i
B08 Fresh Fresh 3
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15490 0
17745 0
15805 14745 0
0 P09 Fresh K11 Fresh K13 N11 Fresh Fresh l
?
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11309 17745 15490 18257 0
17582 0
ROS L10 J14 J10 Fresh J12 Fresh 2
4A 2
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18101 0
18257 0
15929 0
0 108 Fresh K09 Fresh L12 Fresh Freshj i
4A 2
4A 2
4L 4B M
0 15805 0
15929 0
0 Fresh N10 Fresh M11 Fresh Fresh l
Initial 2
3 2
4B 4B Batch Enrichment Density
(
.A.'s) wio U235 2TD 18399 14745 17582 O
O J08 L13 M09 Fresh Fresh 1 (1) 1.85 94 2 (52) 2.55 93 l
2 HiB 4B 4B 3 (20) 3.10 92 l
P 4A (32) 2.60 94 l
16112 0
0 0
I 4B (52) 3.10 95 N08 Fresh Fresh Fresh 4B 4B l
R c
0 l
Fresh Fresh LEGEND xx
- Batch No.
yy - Initial Burnup (MWD /MTU) zz
---Previous L> cation (If applicable) 2-10
Figura 2-6 SURRY UNIT 1 - CYCLE 3 FUEL LOADING L
?
08 09 10 11 12 13 14 15 1
3 1
3 3
3 3
4C H
15107 10312 14044 14088 12099 12099 8266 6273 Cy1 KCB Cy1 H01 Cv1 Ell Ovl Cl4 Cvl J14 Cv1 K14 2v1 L14 cv2 H01 3
4B 3
4A 3
1 4C 4C J
10312 8647 8880 7897 13341 12709 7123 4901 cv1 inA cv2 tes y1 C12 cv2 J10 Cv1 E03 Cy1 J13 Cy2 F14 Cy2 G01 1
3 4A 5
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14044 8880 6358 0
0 8062 7253 Cvl Lil Cv1 M03 Ov2 M12 Cvl J15 cv2 G02 3
4A 5
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12099 7403 7646 5619 Cvl P09 gg,2 K09 cvl PIO lCv2 K11 Cy2 E03 Cy2 D03 t
3 3
5 4A 3
4C 14088 13341 0
7403 8266 5193 Cy1 P07 Cy1 C05 Cy2 L10 gCy1 B05 Cy2 E02 Initial 3
1 3
4C 4C Batch Enrichment Lensity N
12099 13709 8062 7646 5193
(#F.A.'s) w/o U235
%TD Cy1 P06 Cy1 N09 Cy1 R09 Cy2 E05 Cy2 BOS 1 (13) 1.85 94 3 (52) 3.10 92 3
4C 4C 4C 4A (20) 1.85 95 p
8266 7123 7253 5619 4E (4) 2.60 95 4C (52) 3.35 95 Cy1 P05 Cy2 P00 Cy2 B07 Cy2 C04 5 (16) 2.10 95 4C 4C R-6273 4901 Cy2 A08 Cy2 A07 LEGEND xx Batch No.
yy Initial Burnup (MWD /MTU) zz Previous Location (If applicable)
Previous Cycle nn 1
2-11
9 5
Figura 2-7 I
SURRY UNIT 2 - CYCLE 3 FUEL LOADING 08 09 10 11 12 13 14 15 1
4B 4A 3
,1 4B 1
4B H
16480 10349 10870 13293 15061 10349 13597 6969 Cyl K08 Cy2 J14 Cy2 G09 Cyl K14 Cyl J13 Cy2 G14 CylH14 Cy2 H01 4B 1
4B 4A 4B 4A 4B 5
J 10349 15061 10303 11092 8540 11040 5730 0
- y2 po7 Cy1 309
- y2 L13 Cy2 K12 Cy2 gl4 Cy2 J11 Cy2J15 Fresh l
4A 4B 4A 3
1 3
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'K 10870 10303 10874 9118 15441 8867 6031
- y2 JO9 Cy2 N11
- y2 M08 Cyl L14 Cyl K12 Cyl J15 Cy2 L14 3
4B 3
1 3
4B 5
L 13293 11092 9118 16227 9805 6889 0
l Cy1 206 l Cy2 gio
- yl pli Cyl tog Cyl M13 Cy2 M13 Fresh 1
4B 1
3 3
'S M
15061 8540 15441 9805 13293 0
Cyl N07 Cy2 P10 21 7
M10 Cy1 N12 Cyl P10 Fresh 4B 4A 3
4B 5
Batch Enrichment Density N
10349 11040 8867 6889 0
(#F.A.'s) w/o U235
%TD Cy2 po9 Cy2 tog
- y1 R09
- y2 N12 Fresh 1 (25) 1.85 94 i
1 4B '
4B 5
3 (32) 3.10 92 4A (24) 2.60 94 13597 5730 6031 10 4
5) 0 95 5
0 5
cv1 P08 Cv2 R09
- v2 P11 Fresh 4B 5
E 6969 0
Cy2 A08 Fresh LEGEND xx
- Batch No.
yy -Initial Burnup (MWD /lfIU)
Previcu. Cycle - nn s
2-11
~
, Figure 2-8 SURRY UNITS 1 AND 2 - CYCLE 1 Burna'ble Poison Rod Loading 08 09 10 11 12 13 14 15 1
2 1
2 1
2 1
i 3
H 12 12 12 i
2 1
2 1
2 1
3 3
12 12 12 12 0
0
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=
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2 3
3
,N 12 12 12 1
1 3
3 3
12 R
r i
i I
i LEGEND l
xx Batch No.
l yy No. of Fresh Burnable Poison Rods 1
e p
2-12
^
Figure 2-9 SURRY UNIT 1 -- CYCLE 2 BURNABLE POISON ROD LOADING 08 09 10 11 12 13 14 15 1
4B 1
4B 2
4B 1
4C H
8 8
12
~.
4B 2
4A 2
2 2
4C 4C 3
8 20 fr 1
4A 1
4A 2
1 4C K
-a.
4B 2
4A 2
2 4C 4C 8
12 r
2 2
2 2
4A 4C M
i-i 4B 2
1 4C 4C N
12 12 1
4C P
4C 4C 20 4C 4C R
~
i l
l
- Batch No.
xx
- No. of Fresh Burnable Poison Rods yy zz
--No. of Depleted Burnable Poison Rods e
i
)
2-13 l.
Figure ?.-10 SURRY UNIT 2 - CYCLE 2 BURNABLE POISON ROD LOADING 08 09 10 11 12 13 14 15 1
3 3
2 4A 2
2 4B H
12 c-a 3
3 4A 2
! 4A 2
3 4B 4B J
s
_' l 3
2 3
2 4A
.2 4B K
l I
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4A 2
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g 4A 2
4A 2
4A I l 4B 2
3 2
4B 4B B
12 12 2
4B 4B 4B P
l I
~
4B 4B R
LEGEND xx
- Batch No.
~
zz
- No. of Depleted Burnable Poison Rods
~
8#
2-14'
~
1 Figura 2-11 SURRY UNIT 1 - CYCLE 3 BURNABLE POISON ROD LOADING 08 09 10 11 12 13 14 15 1
3 1
3 3
J 3
4C H
12 s
3 l
4B 3
4A 3
1 4C 4C J
1 3
4A 5
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K 12 3
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3 1
3 4C 4C t1 12 12 3
4C 4C 4C P
4C 4C R
TVN xx
- -Batch No.
zz
---14. of Depleted Burnable Poison Rods
~
2-15
. ~. -.
Figurs 2-12 SURRY UNIT 2 - CYCLE 3 Btr'WABLE POISCN ROD LOADING 08 09 10 11 12 13 14 15 1
4B 4A 3
1 4D L
4B H
12 4B 1
4B 4A 4B 4A 4B 5
J 12 12 4A 4B 4A 3
1 3
4B K
12 12 12 i
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L 12 I?
i 1
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l 12 12 i
l 4B 4A 3
4B 5
N 12 12
~
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4
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l R
LZGEND xx
- Batch No.
-No. of Depleted Burnable Poison Rods zz 9
2-16 P
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SECTION 3 - MODEL DESCRIPTION
3.1 INTRODUCTION
The PDQ07 one zone model incorporates a few-group, diffusion-depletion theory model, with thermal-hydraulic feedback, to perform spatial neutron flux and material distribution calculations in two-dimensions (x-y) throughout the reactor core as a function of burnup. This calculation is performed at each mesh point represented in the geometry of the reactor core.
Furthermore, each fuel assembly is represented by a specified array of nesh blocks formed by the intersection of the mesh lines in the x and y di.rections (i.e., mesh points). Each mesh block is used to represent c material composi-tion whereas the neutron flux is calculated at each mesh point.
The material compositions of esch assembly are homogenized so that each mesh block within an assembly represents an equal number of fuel rods, guide tubes, etc.
Therefore, the concentrations of the various nuclides would be initially the same in all mesh blocks within a fresh fuel assembly. Henes, when PDQ07 is using this type of representation, it is called a one zone model.
The initial concentrations of nuclides in the homogenized compositions are in-dependent of the number of mesh blocks used to represent an assembly because
~
changing the mesh block size (and hence, the number of mesh points per assembly) only changes the number of points where the neutron flux is eticulated. As the assembly undergoes depletion with power operation, however, the material compositions change in each mesh block according to the neutron flux associated with that mesh block. Thus, the calculated flux is dependent to suce extent on the mesh block size.
The one zone model performs calculations in several steps. First, a fine-group neutron flux spectrum and the appropriate cross sections as a function of neutron energy are calculated for each material composition by a cross section generating code, such as NULIF. Then the fine-group flux 3-1
spectrum is used to spectrum weight and collapse the fine-group cross sections into two neutron energy groups (denoted as the fast and thermal groups or simply two group). The spectrum weighted two-group cross I
sections associated with each material composition as well as for the baffle L
j and reflector are then used to perform an iterative diffusion theory calcul-ation of the neutron f3"x as a function of spatial position. Solution of the diffusion theory equations consists of estimating an initial source distribu-tion and eigenvalue, computing the flux in each group at each mesh point, and then recomputing the source and eigenvalue. This process is repeated until the change in flux and/or eigenvalue between successive iterations meets a predetermined convergence criterion. From the converged neutron flux and cross sections, the core power distribution is determined, and subsequently the fuel and moderator temperature distributions are calculated. Thermal feedback effects are included in the diffusion theory calculation by recalculating the neutron cross sections, power distribution, and fuel and moderator temperature distri-bution iteratively until both the required nuclear and thermal convergence are achieved.
The neutron flux in the core is not only a function of energy and position but is also a function of changes in the nuclide concentrations and cross sections which vary with burnup. The initial nuclide depletion calcula-tion is performed with the intial two-group fluxes and microscopic absorption and fission cross sections for the nuclides in each mesh block that vary with l
burnup. The neutren flux is then recalculated based upon these new values of nuclide concentrations and cross sections. This process is repeated'over an interval of depletion steps until the desired burnup is achieved.
Theoretically, a simultaneous calculation of the neutron flux ( at each depletion step) as a function of both space and energy should be per-formed since the leakage into or out of a given mesh block affects the neutron energy spectrum and, consequently, the spectrum-weighted two-group cross 3-2 ww-y
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I sections. However, the leakage effect can be approxirated by applying a funda-mental mode axial buckling to the calculations used to generate the spectrum-weighted two-group cross sections. This approximation allows for the calcul-acional separability of spatial and energy offects and is appropriate since the leakage effect generally has a much smaller effect on the neutron flux calculation than does the properties of the material composition ( particularly in large PWR cores where the flux spectrum does not change substantially between adjacent fuel assemblies). Therefore, the separability treatment of space and energy is a valid and accepted assumption for large PWR cores.
Several interrel'ated computer codes are used to perform the cal-culations outlined above. The computer codes comprising the PDQ07 one zone o
model and their interrelatienchips are presented in the flow chart of Figure 3-J.
The PDQ07 computAr code itself is the principal reactor analysis calcula-tional tool in the PDQ07 ene zone modal and is used to perform the two-group, two-dimensional diffusion theory calculations. The other codes provide either input data, data manipulation, or use the PDQ07 code output. As indicated in Figure 3-1, the NULIF computer code is used to calculate the required two-group spectrum-weighted cross sections. The HAFIT computer code formats these cross se:.:tions for use in the PDQ07 code (as HARMONY tablesets). The SHUFFLE com-puter code is a lata sanipulation code that takes appropriati end-of-cycle nuclide concentrations from the PDQ07 computer code and shuffles this data in the reactor core according to a specified scheme which duplicates calculationally the actual repit. cement and movement of fuel assmeblies in the reactor core as the result of a refuelf.ng.
The tcmainder of this section describes in greater detail the func-tioning of each of the conputer codes used in the PDQ07 one zone model.
3.2 CROSS SECTION PREPAEATION 3.2.1 FINE ENERGY cn'JP CROSS SECTION DATA:
The source of basic nuclear cross section data for the NULIF computer 3...
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code calculations is the standard fine-group cross section library used by Babcock and Wilcox (see Reference 1).
This cross section library was supplied by Babcock and Wilcox as part of the FUPAC system.
The library contains cross sections for 31 fast and 80 thermal energy groups with a thermal energy cutoff of 1.85 eV.
The fast library contains smooth cross sections, resonance parameters, and an (n, 2n) inelastic scattering matrix for each nuclide. The thermal library contains temperature-dependent oss sections for each thermal energy group and temperature-dependent thermal scattering kernels (both isotropic and anistropic kernels for the bound atom model). The cantents of the files in the cross section library are listed in Table 3-1.
The standard fine-group cross section library contains cross section data for all structural materials, fissionable isotopes, fission products, and the moderator-coolant (water) used in the reactor core. The constituents of the library are listed in Table 3-2.
The NULIF code is used to calculate composition-dependent energy spectra and then collapse the fine-energy group cross sections to produce two-group.
cross sections for each unit cell.
3.2.2 FEW-GROUP CROSS SECTION PREPARATION:
The NULIF computer code calculates two-group spectrum-weighted cross sections for each type of unit cell or groups of unit cells that are present in the reactor core. A unit ca.ll cars be either a fuel rod, a control guide tube, a control rod, or a burnable poison rod, and the moderator associated with each rod. A supercell is defined as a representative group of unit cells comprising, for instance, a fuel assembly. For the supercell group, the fuel rod unit cell is designated as the central cell (or cell) and any other unit cell types present in a particular fuel assembly are designated as subregion-X cells (or subcells).
The supercell option is used to represent the fuel assembly in the one zone 3-5
Table 3-1 CONTENTS OF FINE-ENERGY GROUP CROSS SECTION LIBRARY FILE 1 GENERAL LIBRARY DATA TAPE LABEL
{
~
~
MATERIAL CONTENTS EPITHERE\\L GROUP STRUCTURE THERMAL GROUP STRUCTURE DELAYED NEUTRON PRECURSOR DATA FISSION SOUltCE DISTRIBUTION DATA GENERAL MATERIAL PARMETERS TEMPERATURE LIST FISSION PRODUCT YlELDS RESONANCE ISOTOPE DATA FISSION SPECTRUM DATA DELAYED NEUTRON DATA FILE 2 FAST CROSS SECTION DATA GROUP DATA GENERAL MATERIAL PARA 1ETERS GENERAL UNRESOLVED RESONANCE DATA UNRESOLVED RESONANCE PARMETERS RESOLVED RESONANCE PARAMETERS SMOOTH CROSS SECTION DATA FILE 3 THERMAL CROSS SECTION DATA GENERAL MATERIAL PAiUL'ETERS SLOWING-DOWN SOURCE DATA SMOOTH CROSS SECTION DATA ISOTROPIC SCATTERING KERNEL ANISOTROPIC SCATTERING KFANEL I
\\
3-6
M O
Table 3-2 FINE ENERGY GROUP CROSS SECTION LIBRARY CONSTITUENTS HYDROGEN-1 PROMETHIUM-149 BORON-10 SAMARIUM-149 BORON-ll URANIUM-234 CARBON-12 URANIUM-235 NITROGEN-14 URANIUM-236 OXYGEN-16 i!RANIUM-238 SODIUM-23 NEPTUNIUM-237 NATURAL MAGNESIUM NEPTUNIUM-239 ALUMINUM-27 PLUTONIUM-239 NATURAL SILICON PLUT0NILT-240 NATURAL CHLORINE PLUTONIUM-241 NATURAL POTASSIUM PLUTONILH-242 NATURAL CALCIUM AMERICIUM-241 NATURAL CHROMIUM AMERICIUM-243 MANGANESE-55 BURNABLE POISON (B10)
NATURAL IRON NON-SAT U233 FISSION PRODUCTS NATURAL NICKEL RAP-SAT U233 FISSION PRODUCTS NATURAL ZIRCONIUM SLOW-SAT U233 FISSION PRODUCTS NATURAL MOLYBDENUM NON-SAT U235 FISSION PRODUCTS SILVER-107 RAP-SAT U235 FISSION PRODUCTS SILVER-109 SLOW-SAT U235 FISSION PRODUCTS CADMIUM-113 NON-SAT PU239 FISSION PRODUCTS 10 DINE-135 RAP-SAT PU239 FISSION PRODUCTS XENON-135 SLOW-SAT PU239 FISSION PRODUCTS i
e e
G 3-7
model because only homogenized groups of unit cells can be represented due the larger-than-discrete mesh description used in the one zone geometry i
i representation of the reactor core. The homogenization is performed in a i
manner that results in all the mesh blocks within a given assembly initially having the same material composition. All the cross. sections used in the one zone model are generated with either the supercell option (fuel assemblies) or -
the heterogeneous cell option (baffle and reflector) of the NULIF computer code with the exception of burnable poison and control rod cross sections. The technique used in the calculation of these cross sections will be discussed in Sections 3.2.5 and 3.2.6 below.
The calculation of the neutron energy spectrum and the spectrum-weighted two-group cross sections for each supercell is described in detail in Reference 1.
Those aspec:s which involve calculations using the supercell option are described below.
With the supercell option of the NULIF code, the material compos.itions of the central cell and the various subregion-X cells must be homogentzed togeth-i er before th( fine-group neutron flux is calculated, since the NULIF code does not perform a spatial calculation for the various subt egions. Because of this, l
a method must be employed to represent the heterogeneous nature of the supercell.
This is done by inputting appropriate thermal flux depression factors for each l
subregion-X cell relative rs che supercell. There flux depression factors are l
generated by a detailed spatial calculation (i.e., a quarter assembly discrete PDQ07 calculation where each fuel rod, thimble cell, and water channel asso-ciated with the fuel assembly is explicitly represented). From this detailed spatial calculation, the ratios of the thermal flux in the average fuel cell, thimble cell, and water gap relative to the thermal flux in the entire assembly are determined. The above flux depression factors are then combined in NULIF along with those normally calculated by NULIF for the central cell (i.e., the n
flux distribution in the fuel pellet, clad, and moderator regions of the central 3-8 E
m
cell) to give the overall flux depression factors to be applied over each of che 80 thermal fine-groups for each nuclide in the supercell.
NULIF calculates the neutron flux in the supercell for each of 31 fast f
l and 80 thermal c.nergy fine groups. Macroscopic and microscopic cross sections are then determined for one fast and one thermal energy group by collapsing these l
111 fine groups based on the neutron flux and cross sections calculated for each l
fine group. Cross sections are collapsed into two groups for use in PDQ07 calculations. (It has been determined thtt the use of two groups is adequate I
for large thermal reactors-such as the Surry and North Anna reactors so that the use of more energy groups in PDQ07 would result in substantially longer com-l puter execution times without a corresponding benefit in accuracy.)
1 The neutron energy spectrum caluulated by NULIF for a supercell depends l
l on the material concentrations (i.e., the nuclide concentration or number density) in ths unit cell. The material concentrations change during the operation of the reactor as a result of:
I l
- 1) Depletion of the material
- 3) Changes in material temperature l
I' lie neutron spectrum is also dependent on the temperature of the fuel due to Doppler broadening of the resonance absorption peaks. The NULIF code is used to calculate the effect of both changes in material concentrations and in the fuel l
and moderator temperatures on the neutton spectrum and spectrum-weighted two-group cross sections.
NULIF calculates the depletion of surarcells based on the spectrum-weighted neutron cross sections and the neutron flux. As the material is depleted, the material concentrations change. This change in concentrations affects both the neutron flux and the neutron spectrum and therefore, requires the frequent recalculation of the spectrum-weighted cross sections.
3.2.3 GENERATION OF FUEL ASSEMBLY FEW-GROUP CROSS SECTIONS:
Fuel.ssembly cross sections are generated using the supercell option 3-9
l in NULIF for an assembly with no burnable poison or control rods present.
The NULIF input consists of:
- 1) Fuel cell dimensions (pellet diameter, clad inside diameter, clad outside d'ameter, and fuel rod pitch) control rod guide tube and instrument channel dimensions, and the assembly water gap area.
- 2) Material concentrations for the fuel pellet, clad, gap and moderator as well as the various subregions.
- 3) Average temperature for the fuel, clad, and moderator
- 4) Average power density
- 5) Description for depletion calculations l
- 6) Description for other calculations to obtain cross sections as a function of moderator and fuel temperature, soluble boron,
'and xenon NULIF calculations are then made for the supercell to determine the dependence of the two-group cross sections for each fuel enrichment on:
- 1) Burnup
('
- 2) Soluble boron concentration 1
- 3) Xenon concentration
- 4) Moderator temperature l
- 5) Average fuel temperature Sets of HARMONY cross section tables based on these NULIF calculations are prepared by the HAFlT code. These tables represent:
- 1) Microscopic fast and thermal energy group absorption and fission cross sections as a function of burnup, soluble boron concentration, and xenon concentration.
- 2) Macroscopic fast transport and removal, and thermal transport cross sections as a function of burnup, soluble boron concentration, and xenon concentration i
- 3) The effect of fuel and moderator temperature changes on the macro-scopic cross sections 3.2.4 GENERATION OF BURNABLE POISON (BP) FEW-GROUP CROSS SECTIONS The burnabis poison (BP) cross sections are not calculated directly by NULIF with the supercell option because of calculational inefficiencies.
3-10
Normally, the BP cross sections would be calculated using the two-group cross sections for fuel assemblies containing BP by performing a NULIF supercell cal-culation (as described in Section 3.2.3 above).here one of the subregions con-talu; the appropriate amount of BP.
In other words, the cross sections would be generated in the same straightforward manner as for assemblies without BP How-ever, the fact that the heterogeneous effect of the various subregions are accounted for by applying thermal flux depression factors determined from quarter assembly discrete PDQ calculations must be considered. In general, for assemblies containing no BP, these flux depression factors do not change significantly as a function of burnup so that the flux depression factors calculated at zero burnup are adequate at any stage of depletion. However, this is not the case for subregions containing burnable poison rods because the BP burns out rapidly with increasing burnup causing the flux depression factors to vary significantly with burnup. Since a large number of quarter-assembly PDQ runs would have to be made to calculate these factors for input to NULIF, it was decided to use only the quarter assembly runs themselves to generate the BP cross sections. This calculational technique was performed in accordance with the following procedure:
- 1) Set up a discrete quarter assembly PDQ07 calculation with a 12BP rod cluster inserted in an assembly of the desired fuel enrichment
- 2) Perform a depletion calculation at the core average power density
- 3) At appropriate burnup steps during the depletion, perform a cal-culation with the BP rods removed from the assembly
- 4) Determine the change in assembly average, flux-weighted, two-group macroscopic cross sections (or " delta" cross sections) resulting from the removal of the BP rods
- 5) These delta cross sections are then incorporated into the same cross section tablesets for a non-BP assembly to give HARMONY tablesets that are applicable to assemblies containing BP (as represented in the one zone nodel)
Even though the delta cross sections are actually macroscopic quantities, they are incorporated in the one zone RARMONY tables as " microscopic" cross sections.
Then, a nuclide is defined to represent the presence or absence of BP.
If a 3-11
f I
given fuel assembly in the core has 12 BP rods then the BP nuclide concen-tration is set equal to unity in that assembly. Macroscopic cross sections for the BP are than determined during execution of the one zone calculation by taking the product of the " microscopic" delta cross sections and the BP nuclide concentration. Thus, the cross section contribution of the BP is effectively added to the total cross sections for each mesh block within the assembly. If no burnable poison is present in a fuel assembly then the BP concentration is set equal to zero so that the macroscopic cross section contribution is also zero.
BP clusters comprised of other than 12 rods are modeled by taking the ratio of the number of rods to 12 rods as the BP concentration. For instance, the BP concentration for 20 rods would be 20/12 x 1 or 1,667 while the BP concentration for 8 rods would be 8/12 x 1 or 0.667.
This approach was adopted because it was found that the delta cross section values were directly pro-portional to the number of BP rods present in a fuel assembly to within an acceptable degree of accuracy.
3.2.5 GENERATION OF CONTROL ROD FEW-GROUP CROSS SECTIONS The control rod cross
- u. cions are generated in a similar manner as the BP cross sections. The procedure for calculating the control rod cross sections l
is outlined in the following steps:
- 1) Set up a discreta quarter asstably PDQ07 calculation (for a given fuel enrichment) with no control rods inserted.
- 2) Perform a bipletion calculation at the core average relative power density.
- 3) At appropriate burnup steps during the depletion, perform a calcul-ation with the control rods inserted.
- 4) Determine the change in assembly average flux-weighted, two-group macroscopic cross vections resulting from the insertion of the control rods.
- 5) In the same manner as was done with the BP delta cross sections, the control rod delta cross sections are then incorporated into the appropriate HARMONY cross section tablesets.
3-12
l 3.2.6 GENERATION OF REFLECTOR FEW-GROUP CROSS SECTIONS-i The cross sections in the reflector region are calculated by NULIF using the unit cell option. The reflector region extends from the outside of the core baffle to the reactor vessel wall, including the thermal shield and core barrel. The stainless s, teel and water in this region of the reactor are homogenized (volume-weighted) in NULIF, and a neutron spectrum and spectrum-weighted cross sections are calculated for this region. These calculations are performed for several soluble boron concentrations, and tables representing the cross sections of the reflector region as a function of soluble baron concen-tration are prepared by HAFIT for use in the HARMONY tablesets of the PDQ07 code.
3.2.7 GENERATION OF BAFFLE FEW-CROUP CROSS SECTIONS The cross sections for the stainless steel baffle region were obtained from cross sections identical to those used in the discrete model. (See Reference 6).
The discrete model baffle cross sections were generated by unit cell NULIF csiculations for stainless steel. Then the cross sections were adjusted to provide a discrete model calculated radial power distribution that closely agreed with the corresponding measured power distribution for Leginning of Cycle 1 of Surry Un.: No. 1.
However, since the baffle cannot be explicitly repre-sented in the one zone mode'_ (i.e., the mesh spaciug is about twice the actual b.ffle thickness) some of the reflector region must also be included. Therefore, cross section values for each of these material compositions (baffle and reflector) were appropriately volume weighted to produce cross sections to represent this region. Also, the standard modification of the. macroscopic thermal absorption cross section was made to bring the one zone model calculated core power distri-bution into closer agreement with the discrete model calculated core power distri-bution. This was done by first performing a one zone calculation with the same cross sections (appropriately volume weighted) as used in the discrete model. If the one zone model then predicted a higher power on the core periphery, for instance, 3-13 p
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then the macroscopic thermal absorption cross section was adjusted upward to force lower peripheral assembly powers. A trial and error process was employed until the one zone predicted overall radial power distribution was equivalent to the discrete model prediction. The need for the endif% cation was not unex-pected, since the relative overall radial power distribution is influenced by char.ges in mesh spccing and cross section differences In addition, diffusion theory codes do not predict as well in regions of rapidly changing fluxes, such as is found near the core periphery, since the basic assumption in diffusion theory requires an essentially isotropic flux distribution.
.i.2.i FORMATING OF FEW-GROUP CROSS SECTIONS:
The HAFIT computer code is a data manipulation code which is used to prepare HARMONY cross section tablesets for input to PDQ07. The input to the HAFIT program consists of a magnetic computer tape containing the spectrum-weighted two-group cross sections calculated by the NULIF code, and a descrip-tion of how these cross sections are to be used to create a set of HARMONY tables for input to PDQ07. An automated data processing code like PAFIT must be used to prepare the HARMONY tablerats for PDQ07 because of the substantial volume of data involved. More detaf.ed information on HAFIT and the HARMONY system is contained in References 2, 4, and 6.
3.3 DIFFUSION THECRY CALCULATION a.
3.1 INTRODUCTION
The PDQ07 computer code, as used in the PDQ07 one zone calculational model, is a two-dimensional, two group, diffusion-depletion program which is used to calculate the neutron flux, power, and nuclide concentrations as a function of radial (x-y) position and burnup. The PDQ07 computer code utilizes the appro-triate and properly formated cross sections along with the initial description of the reactor core (i.e., geometry and material composition description) to 3-14
calculate the neutron flux distribution at spatial mesh points (and for two l
energy groups) at the desired core power. The spatially dependent neutron flux is then combined with the appropriate nuclide concentrations and cross sections to obtain the spatially dependent power distribution. Once the initial spatially dependent flux and power dis ~cributions are ob:ained, the depletion of the nuclide concentrations is calculated.
3.3.2 GEOMETRY DESCRIPTION The size of the mesh spacing used in the one zone model to represent a fuel assembly may vary. The exact size of the mesh spacing selected depends on the type of calculation to be performed, the accuracy desired, and the computer resources available. In the one zone w,ael, the material compocitions of the fuel rod cells, instressnt channel, control rod guide tubes and assembly water gap are all homogenized together in aach assembly. A typical quarter core geo-metry representation showing the mesh spacing over tha region of soittion is shown in Figure 3-2.
This representation depicts a 6 x 6 mesh spacing per assem-bly where there are 55 mesh lines (45 fuel,1 baffle, 9 reflector) equally spaced in both x and y directions, resulting in a total of 3025 mesh points. Ly com-parison, the number of mesh points used to represent the same core uith a discrete model is 132 x 132 or 17,424 which explicitly represents each fuel rod, guide tube and water gap in the core. Since the computer calculational time is almost directly proportional to the nuxber of mesh points, the result is that the running time can be reduced by a factor of 5 to 12 (depending on the particular type of cal-culation and the mesh spacing used) with the one zone relative to the discreta model.
The boundary conditions used in the quarter core solution of the two-dimensional diffusion theory equation are:
- 1) Zero curtsnt for the boundaries located along the core axis
- 2) Zero neutron flux for the boundaries located at the reactor vescel wall 3-15
nGURE 3-2 Typical One Zone Quarter Core Geometry Representation (6 x 6 mesh / assembly) l l
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The boundary conditions used in the full core geometry representation are zero flux at the boundaries located at the reactor vessel wall.
3.3.3 DEPLETION EQUATIONS:
Each mesh block in the PDQ07 code contains a single homogenous composi-tion. The volume-weighted nuclide concentrations for each mesh block in the core are input to PDQ07 for beginning of life core conditions. In addition, a set of equations, which is used by PDQ07 to calculate the change in nuclide con-centrations with barnup, is input to PDQ07 for each different composition in the core.
It t appropriate set of material (nuclide) depletion equations is assigned in PDQ07 to each mesh block. These equations are used by PDQ07 to deplete the nuclide concentrations in each mesh block based on:
- 1) The average fast and thermal energy group neutron fluxes calculated by PDQ07 for the mesh block
- 2) The spectrum-weighted fast and thermal group absorption cross sections determined by PDQ07 from the cross section table-set assigned to the mesh block The depletion chains described with these depletion equacions in the one zone model for each fuel cell type are summarized in Table 3-3.
A detailed description of how ths depletion equations are input to PDQ07 describing these depletion chains is given in Section 5 of Reference 2.
3.3.4 THERMAL-HYDRAULIC FEEDBACK PARAMETERS:
The input to PDQ07 required for thermal-hydraulic feedback consists of:
- 1) Coolant inlet enthalpy
- 2) Heated perimeter per unit area of flou
- 3) Hydraulic diameter of the channels
- 4) Flow area of the fuel assembly per total area of flow
- 5) System pressure
- 6) Difference between average fuel temperature and moderator teaper-ature as a function of relative power density 3-17
=
Table 3-3 Depletion Equations used in PD007 1.
Neutron Absorptions Not Leading to Fission 230 a.
0
, Pu depletion chain 238 n
239 g
P 239 n
240 n
241 n
242 n
243 m
s m
Pu Pu Pu m Pu e Am 241 35 b.
U depletion chain 235 n
m 236 n
237 m
U U
< Np 2.
Neutron absorptions which produce fission are represented with the following fission products:
.f35,h
,h
, and Sus which are represented explicitly 135 149 149 a.
b.
Two groups of fission products which eventually build up to an equilibrium concentration (since they are created by fission reactices and destroyed by decay reactions). One group is characteristic of fission reactions by uranium isotopes and the other group is characteristic of fission reactions by plutonium isotopes.
c.
Two groups of non-saturating fission products which are either stable isotopes or have half-lives greater than a few years.
.Again, one group is characteristic of fission reactions by uranium isotopes and the other group is characteristic of fis-sior reactions by plutonium isotopes.
3-18 iiii
1 The strategy used in the feedback calculation consists of first making l
an initial estimate of the fuel and moderator temperature for each coolant channel. Based on this initial estimate and the cross section tables for each fuel cell, the PDQ07 code calculates the two-group, spectrum-weighted cross sections for each mesh block. These crot* sections are used in a diffusion theory calculation of gewer density in each fuel rod cell. This power density is then used in a calculatio'n of the fuel and moderator temperature for each fuel cell. In turn, the neu fuel and m6de ator temperaturer are used to calculate new two-group, spectrum-weighted cross :ections for another diffusica theory power distribution calculation. This process is continued until the power density for each fuel rod in the Nth iteration differs from the power th density in the N-i iteration by less than the convergence criterion.
Thermal-hydraulic feedback effects are represented in the PDQ07 model in order to more accurately calculate the power and burnup distributions.
O 3-19
SECTION 4 - COMPARISON OF ONE ZONE PREDICTIONS TO DISCRETE MODEL PREDICTIONS AND EXPERIMENTAL DATA
4.1 INTRODUCTION
The purpose of this section is to present a comparison of analytical predictions from the PDQO7 one zone model with PDQ07 discrete model predictions and experimental data obtained from Surry Units No. 1 and 2.
These compari-sons encsepass both initial and reload cycles of operation in order to demonotrate both the accuracy and flexibility of the one zone model.
Since it is planned to perform calculations with the one zone model that would have otherwise been performed by the discrete model, it is impor-tant that the results compare well. Therefore, the accuracy of the one zone model is established by benchmarking against this model whose accuracy has been previously verified (see Reference 6).
In areas where the discrete model has not been applied extensively, such as the calculations of temperature reactivity coefficients, the one zone model is compared to available measured data.
4.2 ANALYTICAL CALCULATIONS The types of calculations described in this section fall into two general groups: power distribution calculations and reactivity calculations.
Power distribution calculations include:
1.
Fuel assembly average relative radial power distributions as a function of cycle depletion.
2.
Power distributions resulting from various symmetric and non-symmetric control rod bank positions.
3.
Batch and assembly tverage burnup sharing.
Power distribution calculations as a function of burnup are performed to assure that the assemblywise relative powers are within acceptable limits for the entire cycle depletion (power distributions for various redded configurations are typically performed at beginning of cycle (BOL) and end of cycle (EOC) at 4-1 hemi m
hot full power (HFP) or hot zero power (C??). Cycle depletions are run with all rods out (ARO) cver a series of depletioa intervals, typically 1000 or 2000 MWD /MTU incrementra The flux and power distributions are calculated at the beginning of each interval and is assumed constant for the entire depletion in cerval. The change in nuclide concentrations over the depletion interval is calculated based on this flux distribution and provides the nuclide concentra-tions that are to be input to the next depletiot step. Then the flux and power distributions for the next time. step are determined based upon the nuclide concentrations input from the previous time step. This process is repeated until the end of cycle buruup is attained. From the last time step, the batch and assembly average burnups and the isotopic data for fuel assemblies which are eo be either per=anently discharged or shuffled to the next cycle of operation are obtained.
Reactivity calculations include:
1.
Integral control rod bank worths 2.
Stuck and ejected rod worths 3.
Critical boron cc:centrations and differential boron worthe 4.
Isothermal tsmperature coefficients Integral control rod bank worths are calculated by holding all reactor parameters constant (including soluble boron concentration) except for the rod bank (s) whose worth is to be determined. First, a calculation is performed for then for D bank fully inserted, then C and D banks fully inserted, all rods out, The change in core reactivity resulting from each of the rod bank con-etc.
figuration changes is a direct measure of the control red bank worth.
Stuck rod worths are calculated to assure that there is adequate The shutdown margin with the mest reactive control red stuck out of the core.
methed for calculating stuck rod worth is to perform two full core one zone cal-culations at hoe zero power (HZP): one with all rods in (ARI), and the other with 4-2
ARI less one tod removed from the core. The change in reactivity resulting from thes t-two cases is the stuck rod worth. Calculations for ejected rod worths are similar to stuck tod worth calculations except that the initial conditions are different, i.e., ejected rod worth calculations would typically be per-formed for EZP or HFP operation with the control rod bank (s) at approximate insertion limits. The ejected rod worth is then determined by calculating the reactivity change resulting from the removal of one control rod. Misaligned control rod conditions can also be simulated in a similar manner.
Core criticality is maintainAC by adjusting the boron concentration as a function of burnup, power level, etc.
The boron concentration at which the reactor is just critical is called the critical baron concentration. This value is calculated by first using a best-estimate boron concentration to determine the core keff and then correctin'g this boren concentration to a value which cotresponds to the just critical condition. Since the one zone model does not represent the core explicitly, it will not necessarily compute a core k gg equal e
to one with the boron concentration set at the just critical condition (as ~would be determined from measured data). Therefore, it is necessary to establish a
" target" keff oc beginning of life (BOL) based on measured data or discrete model PDQ calculations for the critical boron concentration. This target k gg e
is then used as a basis throughout the cycle depletion to predict the critical boren concentration.
It has been found that the target keff does not deviate l
l l
significantly during the cycle or from one cycle to another so that the need
~
to update this value is not usually necessary.
The isothermal temperature coefficient is defined as the change in core reactivity per degree change in the moderator, clad, and fuel temperature (1 9., the sum of the moderator and Doppler temperature coefficients). The celculation of the isothermal temperature coefficient values at the hot :ero power (HZP) condition is important because they can be compared to plant 4-3
measuraments taken during startup physics testing. and therefore, can provide a basis for evaluating the accuracy of isothermal temperature coefficient, moderator temperature coefficient, and Doppler coefficient design predictions.
At HZP conditions (547 F for the Surry Units) the isothermal temperature coe-fficient is calculated by determining the change in reactivity, ap, for +20F I
and -20F around 5470F. In other words, one calculation is performed at 545?F I
and another at 549*F, where these temperatures are held uniform across the core.
Then the isothermal temperature coefficient is derived by '.ividing Ap by AT.
At part or full power operation the calculational method is different because the moderator and fuel temperature are not uniform over the core. For this situation, two calculations (e.g., at HFP) having different core inlet modera-tor enthalpies are made. The isothermal temperature coefficient is then Ao divided b'y the change in core average moderator temperature resulting from the change in inlet enthalpy. In these calculations, the change in the core average fuel temperature is assumed to be the same as the change in moderator reaperature.
4.3 MEASUREMENT DATA e.
Measurement data is obtained for the Surry Units from routine physics testing conducted during the startup of each cycle of operation as ve,ll as from routine core performance monitoring conducted during the depletion of each cycle.
The methods used for measuring core power distribution, burnups, control rod bank worths and critical boron concentrations are described in Reference 6.
The procedure-for measuring stuck rod worths and isothermal temperature coefficients were not covered in Reference 6 and will be discribed briefly below.
Stuck rod worths were measured during the initial startup physics testing for Cycle 1 of each of the Surry Units. The value of the stuck rod worth was measured by manually tripping one of the control rods from step 228 (out of the core)', observing the average flux level change indicated by the source range det.ectors, and calculating the resulting change in reactivity from the point-kinetics equation.
4-4
Iscthermal temperature coefficients are m4asured during the startup cf each cycle by adjusting the reactor coolant system (RCS) heat gains and losses through the use of condenser steam dump valves to establish uniform heatup and cooldown rates, and then monitoring the resulting reactivity changes.
Specifically, the measurements are performed during approximately a 100F/hr RCS heatup and/or cooldown ramp during which the RCS temperature changes up to i l'.
Reactivity is determined using the reactivity computer and is plotted against RCS temperature on an x-y recorder. The temperature coefficient is then determined from the slope of the plotted line. Normally, both post {.ve and negative temperature swings are used to negate the effe:ts of any inadver-tant reactivity additions to the system (i.e., boron concentration mismatches between pressurizer and/or volume control tank and the main coolant). The measurecants are done at very low power levels to insure that nuclear heat is not added, thereby saintaining the moderator and fuel at approximately the same temperature and minimizing Doppler feedback.
4.4 RESULTS Representative results of the one zone model power distribution and reactivity predictions compared to the discrete model calculations and measure-ments obtained from the Surry Power Station are presented in this section. The I
specific types of results compared are summarized in Table 4-1 Table 4-2 pre-l l
sents the standard deviation between predicted (one zone and discrete models) l -
and measured assembly average relative power distributions for representative reactor conditions forboth initial and reload cycles of Surry Units 1 and 2 The standard deviation (a) between predicted and measured power distribution is given by:
157 1
o. (- - I (Xe - X")2)l/2 156 11 1
4-5 n.
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,-m-
---,.-e.
w--,y.-.
.- ~
,p-a
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Xyisthemeasuredassemblyaveragepowerfortheith
(
assemoly I
Figures 4-1 through 4-4 provide representative (i.e., of the cases l
delineated in Table 4-2) quarter core comparisons of individual assembly relative power distributions between measurement and one zone model predic-tions at various core conditions during Cycle 2 of Surry Unic No. 2.
Also given for each fuel aasembly is the percent difference which is defined as:
% dif f e'.ence (%A) = l * ""* ""d*'
"""*"*d X 100 Measured Figures 4-5 and 4-6 provide a comparison between the one zone and discrete models for calculating full core power distributions. Figure 4-5 gives the one zone and discrete calculated assembly average relative power
.=asities (and percent differences) for Surry Unit No. 1, Cycle 1 at a BOC, HZP, and ARO condition. Figure 4-6 gives the assembly average relative power distributions (and percent differences for the assembly relative powers j
greater than unity) for the same conditions except that all rods are inserted with rod H-14 assumed to be stuck out of the core.
A comparison of the assembly average end of cycle burnup distribu-tions between the one zone model and measurement is given in Figures 4-7 and 4-8 for an initial and reload cycle, respectively. Also included is the corresponding comparison of the batch average burnup sharing.
The reactivity comparisons are given i-tables 4-3 through 4-9.
All comparisons were made at HZP, BOC conditions with the exception cf the critical boron concentratna versus burnup given in Tables 4-5 and 4-6 which were calculated at EFP at the indicated burnup. Both one zone model and dis-crete model predictions were compared to the measured reactivity values except fer the isothermal temperature coefficient predictions (Table 4-9) where only one zone.model predictions and measured values were compared.
4-6 e
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TABLE 4-1 ONE ZONE MODFt. COMPARISONS REACTOR CONDITION TYPE OF COMPARISON AT WilICH COMPARISON IS_MADE REFERENCE FOR COMPARISON Power Distribution Assembly Average Units 1 & 2. Cycle i & 2 Operation Table 4-2 Unit 2, Cycle 2, ll2P,'ARO, BOC Figure 4-1 Unit 2 Cycle 2 HZP, D-bank in. BOC Figure 4-2 Unit 2, Cycle 2, HFP, ARO, 2790 MWD /MTU Figure 4-3 Unit 2 Cycle 2. HFP, ARD, 8850 AWD/MTU Figure 4-4
- Unit 1 Cycle 1. HZP, ARO, BOC Figure 4-5 Stuck Rod Unit 1, Cycle 1. HZP, ARI less rod H-14, BOC Figure 4-6 Assemblywise Burnup and Unit 1, Cycle 1, EOC Figure 4-7 Batch Burnup Sharing Unit 1, Cycle 2, EOC Figure 4-8 Reactivity D & C Bank Control Rod Unit 1 & 2. Cycle *a 1, 2, & 3, HZP, BOC Table 4-3 Worths Total Shutdown and Unit 1 & 2. Cycle 1. HZP, BOC Table 4-4 Stuck Rod Worths Critical Boron Concentration Unit 1, Cycles 1, 2, & 3 Table 4-5 vs. Burnup Unit 2. Cycles 1, 2, & 3 Table 4-6 Critical Boron concentration Unit 1. Cycles 1, 2, & 3, BOC Table 4-7 for Various Control Rod Configurations Differential Boron Worth Unit 1. Cycles 1, 2, & 3 BOC Table 4-8 Isothermal Temperature
'.;'t 1 Cycles 1, 2, & 3, BOC Table 4-9 Coefficients
I t
TABLE 4-2 COMPARISON OF PREDICTED AND HEASURED ASSEMBLY AVERACE POWER DISTRIBUTIO6S FOR SURRY UNITS 1 AND 2, CYCLES 1 AND 2 i
Standard Deviation f
H/D Hap Power Control Rod Cycle Burnup Between Naasured And I
Unit Cycle Number Level (%)
Configuration (HWD/ situ),__
one-Zone Discrete 1
1 40 75 ARO 1150 0.021 0.015 1
1 59
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2 1
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l Tiguro 4-5 ASSEMBI.TWISE AVERAGE POWER DISTRIBUTION FOR HOT ZERO POWER. ALL RODS OUT AT BEGINNING 0F INITIAL CYCLE FOR SURRY UNIT 1.
R P
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15
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-1.1 AVERAGE PERCENT DIFFD2NCE = 1.3 4-13
Figure 4-6 ASSDGLYWISE AVERACE POWER DIST7.IBURION FOR HOT ZERO POWER, ALL RODS IN WITH M-14 OUT AT BEGINNING OF INITIAL CTCLE FOR SURRY LMIT 1 R'
P N
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A 0.023 0.029 0.023 0.027 0.035 0.027 1
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0.u59 0.Or4 0.072 0.045 0.033 0.111 0.129 0.111 0.083 0.045 0.072 0.094 0.059 0.067 0.105 0.083 0.047 0.096 0.128 0.145 0.128 0.096 0.047 0.083 0.105 0.067 5
0.059 0.096 0.081 0.148 0.0d2 0.123 0.081 0.123 0.082 0.148 0.081 0.098 0.059 0.060 0.1 11 0.084 0.167 0.085 0.139 0.083 0.139 0.085 0.167 0.084 0.111 0.060 6
I 0.096 0.118 0.096 0.264 0.288 0.218 0.126 0.224 0.126 0.218 0.288 0.264 0.096 0.118 0.096 O.103 0.133 0.099 0.290 3.321 0.243 0.128 0.247 0.128 0.243 0.320 0.290 0.099 0.133 0.108 7
0.139 0.092 0.220 0.379 0.461 0.218 0.351 0.417 0.351 0.218 0.461 0.379 0.220 0.092 0.139 0.157 0.094 0.245 0.416 0.493 0.218 0.382 0.454 0.382 0.218 0.493 0.416 0.245 0.094 0.157 8
0.129 u.187 u.139 0.429 p.545, 0.547 0.399 0.676 0.399 p.547 0.545 0.429 0.159 0.187 0.129 u
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Figure 4-7 ASSEMBLY 1TISE ACCUMULATED BURNUP AND BATCH BURNUP SEARINC (103 15iD/tfrU) FOR THE CYCLE 1 OPERATION OF SURRY UNIT 1 1
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CORE AVERACE BURNUP = I3,547.WD/tfrU Oce Zone One Zone Model Discrete Discrete Model Measured Model Percent Difference _ Model Percent Difference Batch 1 14.25 14.06
-1.3 14.20
+0.4 Batch 2 15.46 15.71
+1.6 15.62
-1.0 Batch 3 10.93 10.75
-1.6 10.81
+1.1 4-15 1
Figure 4-8 ASSEMBLYWISE ACCUMUIRED BURNUP AND BATCH BU"NUP SHARING (103 MWD /MTU) For. DE CYO!12 CPERATION OF SURRT UNIT 1 R
F N
M
- t
'k J
g *- C F
E D
C B
A 4.90 0.27 4.90 5.00 6.16 4.82
-2.0
+1.8
+1.7
~
1 5.19 7.12 7.25 20.35 7.25 7.12 5.19 5.47 7.28 6.35 20.19 6.22 7.05 5.38 2
-5.1
-2.2
+4.2
+0.8 F16.6
+1.0
-3.5 5.62 7.65 19.86 21.52 8.75 21.52 19.86 7.65 5.62 6.02 7.44 20.19 21.59 8.27 21.41 20.03 7.39 6.04 3
-6.6
+2.8 -1.6
-0.3 d5.8
+0.5
-0.8
+3.5
-7.0 5.62 6.36 23.28 22.78 23.22 22.89 23.22 22.78 23.28 6.36 5.62 6.02 6.85 23.11 22.47 22.73 22.34 22.92 22.63 23.14 6.79 6.04 4
-6.6
-7.2
+0.7
+1.4
+2.2
+2.5
+1.3
+0.7
+0.6
-6.3
-7.0 5.19 7.65 23.28 23.72 7.40 22.10 8.65 22.10 7.40 23.72 23.28 7.65 5.19 5.48 7.42 22.97 23.64 7.54 21.98 8.25 21.95 7.67 23.53 22.98 7.43 5.77 5
-5.3
+3.1
+1.3
+0.3
-1.9
+0.5
+4.8 0.7
-3.5
+0.8
+1.3
+3.0
-10.1 7.12 19.86 22.78 7.40 18.13 7.90 19.46 7.90 18.13 7.40 22.78 Lt.S6 7.12 7.22 19.82 22.61 7.56 18.44 8.04 19.42 8.17 18.47 7.62 22.84 L9.94 7.61 6
-1.4
+0.2
+0.8
-2.1 -1.7
-1.7
+0.2
-3.3
-1.8
-2.9
-0.3
-1.4
-6.4 1
4.90 7.25 21.52 23.22 22.10 7.90 24.14 8.86 24.14 7.90 22.10 23.22 21.52 7.25 4.90 5.16 6.48 21.29 2; 47 21.92 8.11 24.39 8.70 24.34 8.2G 21.96 22.93 21.07 6.6G 5.11 7
-5.0 +11.9
+1.1
+3
+0.8
-2.6 -0.6
+1.8
-0.8
-3.)
+0.6
+1.3
>2.1
+9.8
-4.1 6.27 20.35 8.75 22.89 8.65 19.46 8.56 22.09 8.86 19.46 8.65 22.89 8.75 20.33 6.27 6.48 20.60 8.49 23.03 8.41 19.86 8.73
,22.09 8.59 19.72 8.50 22.99 8.60 20.67 6.38 8
' 1. 2
+3.1
-0.6
+2.9
-2.0 1+1.5
-0.0
+3.1 l-1.3
- +1.8
-0.4
>1.7
-1.5
-1.7 L
-3.2 4.90 7.25 21.52 23.22 22.10 7.90 24.14 8.86 24.14 7.90 22.10 23.22 21.52 7.25 4.9C 5.16 6.49 21.47 23.04 21.70 8.10 24.26 8.53 23.69 7.95 21.92 22.67 21.34 6.51 5.07 9
-5.0
+11.7 m.2
+0.8 1.8
-2.5 -0.5
+3.9
+1.9
-0.6
+0.8
+2.4
-0.1 11.4
-3.4 7.12 19.86 22.78 7.40 18.13 7.90 19.46 7.90 18.13 7.40 22.78 19.86 7.12 7.25 19.82 22.60 7.64 18.69 8.09 19.39 7.90 18.40 7.49 22.52 19.94 7.39 10
-1.8
+0.2
- 4. 8
-3.1 -3.0
-2.3 4.4
-0.0
-1.5
-1.2
+1.2
-0.4
-3.5 5.19 7.65 23.28 23.72 7.40 22.10 8.65 22.10 7.40 23.72 23.38 7.65 5.19 5.53 7.48 23.08 23.55 7.65 21.85 8.33 21.76 7.61 23.43 22.85 7.44 5.53 11
-6.1
+2.3
+0.9 0.7
-3.3 +1.1
+3.8
+1.6
-2.8
+1.2
+1.9
+1.9
-6.1 5.62 6.36 23.28 22.78 23.22 22.89 23.22 22.78 23.28 6.36 5.62 6.17 6.95 22.91 22.35 22.85 22.31 22.72 22.25 22.86 6.94 6.07 12
-8.9
-8.5
+1.6
+1.9 1.6 2.6
+2.2
+2.4
+1.8
-8.4
-7.4 5.19 7.65 19.86 21.52 8.75 21.52 19.86 7.65 5.62 6.11 7.42 19.97 21.63 8.35 21.44 19.81 7.41 6.11 13
~
-8.0
+3.1
-0.6
-0.5 44.8
+0.4
+0.3
+3.2
-8.0 5.19 7.12 ' ?.25 20.35 7.25 7.12 5.19 5.49 7.43 6.53 20.16 6.71 7.46 5.41 l'
one Zone
-5.5l-4.2 11.0 A.9
+8.0
-4.6
-i.!
,g 4.90 6.27 4.%
,Diff*
^
5.20 6.57 5.28 15
-5.8
-4.6
-7.2 CORE AVERACE BURNUP = 6915 MWD /MTU One Zone One Zone Model
- iscretc Discrete Model Measured Model Percent Diftertnce Model Percent Difference Batch 1A 19.63 19.64
+0.1 19.82
+1.0 Batch 2 22.60 22.83
+1.0 22.80
+0.9 Batch 4A 7.60 1,y9
-2.8 7.49
-1.4 Batch 4B 8.40 8./5
+4.2 8.19
-2.5 Bat.d 4C 6.25 6.29
+0.6 6.27
+0.3 4-16
TABLE 4-3 COMPARISON OF PREDICTED AND HEASURED D AND C BANK CONTROL ROD WORTHS FOR BOC, HZP CONDITIONS Rod Worths, pcm*
Surry Cycle Control One Zone Percent Discrete Percent Unit No.
Bank Hodel Measured Difference **
Model Difference **
l I
1 1
D 1407 1480
-4.9 1379
-6.8 l
C (with D in) 1278 1300
-1.7 1234
-5.1 1
2 D
1157 1051 10.1 1079 2.7 C (with D in) 1216 1331
-8.6 1202
-9.7 1
3 3
1255 1129 11.2 1176 4.2 C (with D in) 1159 1055 9.9 1068 1.2 l
7' 2
1 D
1407 1435
-2.0 1379
-3.9 t'
C (with D in) 1278 1309
-2.4 1234
-5.7 2
2 D
935 880 6.3 931 5.8 C (with D in) 1309 1244 5.2 1249 0.4 2
3 D
1082 1098
-1.5 1067
-2.8 C (with D in) 1242 1213 2.4 1196
-1.4 ePco Model - Heasured
- P rcent Diffe ence =
X 100 Heasured
TABLE 4-4 COMPARISON OF PREDICTED AND HEASURED TOTAL SHUTDOWN WORTH AND STUCK ROD WORTH FOR CYCLE 1, SURRY UNITS 1 AND 2 BOC, HZP CON'?TIONS Rod Worths, pcm*
Surry One Zone Percent Discrete Percent Unit Control Bank Model Measured Difference **
Model Difference **
,1 D
1401 1480
-4.9 1379
-6.8 C (with D in) 1278 1300
-1.7 1234
-5.1 B (with D + C in) 1943 1920
+1.2 A (with D + C + B in) 1481 1440
+2.9 ARI 10223 10460
-2.2 10051
-3.9 Rod H-14 out (with ARI) 2336 2300 1.6 2215
-3.7 i
- j-2 D
1407 1435
-2.0 1379
-3.9 g;
C (with D in) 1278 1309
-2.4 1?34
-5.7 B (with D + C in) 1943 1929
+0.7 A (with D + C + B in) 1481 1508 al.8 3
ARI 10223 10440
-2.0 10031
-3.7 Rod H-14 out (with ARI) 2336 2425
-3.7 2215
-8.7 ePeo Ho
~
- P r ent Dif e ence =
X 100 M
ue
- This data has not been calculated.
I m_
TABLE 4-5 REPRESENTATIVE CRITICAL D RON CONCENTRATION VS. BUENUP COMPARISONS TOR SURRY UNIT 1 One Zona Discrete Burnup at Burnup M6 del Model Measured Measured Cycle pjWD/MTU)
(PPM)
(PPM)
(PPM)
(MWD /MTU) 1 BOC 1100 1094 150 817 810 738 270 7000 537 512 531 7000 13000 154
'131
- 102 13000 2
BOC 898 895 150 626 626 636 145 3000 421 421-425 3010 6915 134 102 132 6810 3
BOC 1221 1202 150 948 932 923 265 3000 687 672 684 3065 7000 327 316 318 7070
4-19
TABLE 4-6 l
REPRESENTATIVE CRITICAL BORON CONCENTRATION VS BURNUP COMPARISONS FOR SURRY UNIT 2 One Zone Discrete Burnup At Burnup Model Mods 1 Measured Measured Cycle (MWD /MTU)
(PPM)
(PPM)
(PPM)
(MWD /MTU) 1 BOC 1100 1094 150 817 810 7000 537 512 543 6995 13000 154 131 131 13015 2
BOC 1309 1303 150 1021 1017 970 160 5000 588 587 593 5000 9000 226 230 246 8985 3
BOC 1152 1113 150 875 836 898 170 5000 423 397 8000 161 140
- S2C3 has not reached these burnup levels at the time of this writing.
l 4-20
. ~..
~
~
w gy.
.w
~.
W
7 i
e TABLE 4-7 COMPARISON OF PREDICTED AND MEASURED CRCTICAL BORON CONCENTRATION FOR VARIOUS CONTROL ROD CONFICURATIONS FOR SURRY UNIT 1 CYCLES 1, 2, AND 3 Measured Discrete Model One-Zone Model Critical Boron Critical Boron Discrete Model Critical Boron One-Zone Model Control Rod Concentration Concentration Percent Concentration Percent Cycle Bank Position (PPM)
(PPM)
Difrerence (PPM)
Difference 1
1 ARO 1196 1168
-2.2 1207
+0.9 1
D-Bank In 1077 1050
-2.5 1080
+0.3 1
C and D-Banks 957 942
-1.6 967
+1.0 In 4
2 ARO 1033 997
-3.5 1032
-0.1 2
D-Bank In 917 899
-2.0 921
+0.4 2
C and D-Banks 800 787
-1.6 799
-0.1 In
' y 3
ARO 1311 1322
-0.1 1355
+3.4 p
3 D-Bank In 1196 1207
-0.1 1229
+2.8 3
C and D-Banks 1095 1101
-0.1 1113
+1.6 4
l In 1
i !
A 1
i 5
TABLE 4-6 COMPARISON OF PREDICTED AND MEASURED DIFFERENTIAL BORON WORTH FOR VARIOUS CONTROL ROD CONFIGURATIONS FOR SURRY UNIT 1, CYCLES 1, 2 AND 3 One Zone Model Measured Discrete Model Control Rod Boron Worth Boron Worth Boron Worth Cycle Bank Position (PCH/ PPM)
(PCM/ PPM)
(PCM/ PPM) 1 ARO 11.3 12.1 11.9 1
D-Bank In 11.2 1
C and D-Banks 11.1 In 2
ARO 10.5 10.2 10.8 2
D-Bank In 10.4 2
C and D-Banks 10.2 In d
3 ARO 9.9 11.0 10.2 y,
3 D-Bank In 10.0 N
3 C and D-Banks 10.0 l
In i-O P
9 6
I TABLE 4-9 COMPARISON OF PREDICTED AND HEASURED ISOTHERMAL TEMPERATURE COEFFICIENTS FOR VARIOUS ROD CONFICURATIONS FOR SURRY UNIT 1. CYCLES 1, 2, AND 3 Heasured One-Zone Model Isothermal Temperature Isothermal Temperature Control Rod Ccefficient Coefficient Difference 0
Cycle Bank Position (PCM/0F)
(FCM/0F)
(PCH/ F) 1 ARO
-0.3
+0.2
-0.5 1
D-Bank In
-3.5
-2.60
-0.9 1
C and D-Banks
-7.9
-6.88
-1.0 In 1
2 ARO
-2.88
-2.8
-0.1 2
D-Bank In
-5.27
-7.43
+2.2 2
C and D-Banks
-9.61
-11,38
+1.8 In 7
i
[l 3
ARO
+1.68
+0.6
+1.1 3
D-Bank In
-0.93
-2.05
+1.1 3
C and D-Banks
-4.67
-5.30
+0.6 In
l -.
SECTION 5 - SLTfARY AND CONCLUSION The Vepco PDQ07 ene zone model has been developed from the Vepco PDQ07 discrete model for the purpose of performing two-dimensional (x-y) reactor physics calculations. The coarse (i.e., as opposed to discrete) mesh representation allows calculations to be performed both faster and with smaller computer memory requirements, since fewer mesh lines are required to represent the geometry of the reactor core. In general, it is intended to use the more efficient one cone model to' perform fuel management and reactor physics sceping calett 4tions, and then perform the final production calculations to support react?r operations with the discrete model. However, for the calculational evaluation of abnormal control rod positioning, assembly average radial power distributions, assemblywise and batch burnup distributions, and reactivity coefficients, it is intended to use the one zone model for final production calculations to support reactor operations.
The accuracy of the one zone model has been demonstrated for each of the above production calculations through comparisons with both analytical PDQ07 discrete model calculations and with measurements taken at Surry Units No I and 2.
Th'e results of these comparisons are:
1.
Assembly average power distributions are generally predicted within a 0.02 to 0.03 standard deviation range relative to measurement, with a maximum standard deviation of 0.058 for a low power measurement. For the stuck rod calculation at HZP, the one zone model predictes the peak assembly relative power density to within 3% of the discrete model predictions.
Power distribution. calculations to the above accuracies are acceptable for preduction use.
2.
Batch burnup values are typically predicted within less than 2% of the measurement value with a maxinum difference of 4.2%.
Batch bur:up distributions to the above accuracies are acceptable for preduction use.
3.
The stuck rod worth vtlues measured during initial startup of Cycle 1 of both Surry Unit 1 and 2 was adequately predicted by the one zone model (2336 pcm predicted vs. 2300 and 2425 pcm for Units 1 and 2, respectively). Control rods bank worths are typically within 5% of the measured values with the 5-1
maximum deviation being approximately 11% of the measured values.
Total shutdown worth was predicted within approximately 2% of the
(
measured value. The accuracy of the one zone model for use La normally positioned control rod worth production calculations are adequate (i.e., predicted average control rod worths are within 10% of the measured values) even though the primary application is for scoping calculations.
4.
Critical boron concentrations as a function of burnup were typically predicted within 25 ppm with a maximum deviation of 51 ppm. The predicted critical boron concentration for various rodded configurations was generally aithin 1% of the measured values with a maximum deviation of approximately 3%.
Differ-ential boron worths were predicted within 1.1 pcm/ ppm (approx-imately 10%) of measurement.
The" accuracies of the above critical boron concentrations and the differential boron worths are adequate (i.e., within 4% cf measurement and conservative to the values assumed in appropriate accident analyses res-pectively) for production use even though the primary applica-tion is for scoping calculations.
5.
Isothermal temperature coefficients are predicted within an average of 1.0 pcm and with a maximum difference of 2.2 pcm relative to the measured values. Temperature coefficients to the above accuracy are acceptable (i.e., within 3 pem of the measured values) for production use.
Verification and model improvements will continue to be made as more experience is gained through continued application of the Vepco PDQ07 one zone model to the Surry and North Anna reactors.
e 5-2
l SECTION 6 - REFERENCES 1.
W. A. Wittkopf, et. al., NUUF
" Neutron.. S;e.ctrum Generator, Few Group Constant Calculator, and Fuel Dipletion Code", BAW-10ll5, June 1976.
2.
H. H. Hassan, et. al., " Babcock add Wilcox Version of PDQ07 - User's Moual", BAW-10ll7P, December 1975.
3.
H. H. Hassan, et. al., " SHUFFLE - Program to Perform Fuel Shuffle in Nuclear Reactor Core", BAW-422, Rev. 1, July 1975.
4.
H. H. Hassan, W. A. Wittkopf, et. al., "EAFIT", BAW-425, July 1973.
5.
Private contractual correspondence from the Babcock and Wilcox Company to the Virginia Electric and Power Company dated February 3, 1971, and October 6, 1971.
6.
M. L. Smith, "The PDQ07 Discrete Model," Virginia Electric and Power C mpany, VEP-FRD-19, July 1976.
7.
Final Safety Analysis Report - Surry Power Station Units 1 and 2, Virginia Electric and Power Company.
i l
l i-1 e
1 i
1 6-1 m-+-
c- - - - - -
._v_g m
-