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{{Adams
| number = ML18113A771
| issue date = 10/31/1978
| title = Vepco Flame Model. Util Developed 3 Dimensional(X,Y,Z) Modified Diffusion Therory Calculational Model Designated as Vepco Flame Model.Accuracy of Model Is Demonstrated Through Comparisons Taken at Units 1 & 2
| author name = Beck W
| author affiliation = VIRGINIA POWER (VIRGINIA ELECTRIC &amp; POWER CO.)
| addressee name = 
| addressee affiliation = 
| docket = 05000000, 05000280, 05000281, 05000338, 05000339
| license number = 
| contact person = 
| document report number = VEP-FRD-24, NUDOCS 7901150116
| package number = ML18113A770
| document type = REPORTS-TOPICAL (BY MANUFACTURERS-VENDORS ETC), TEXT-SAFETY REPORT
| page count = 104
}}

=Text=
{{#Wiki_filter:I                                                                VEP-FRD-24 I
I I                         THE VEPCO FLAME MODEL I
BY I                               W. C. BECK I
I                 NUCLEAR FUEL ENGINEERING GROUP FUEL RESOURCES DEPARTMENT I        VIRGINIA ELECTRIC AND POWER COMPANY RICHMOND, VIRGINIA I                                                           50-'2..J)/2B \
OCTOBER, 1978                  Lt<" d*d \-&deg;l-1-9 I                                                           '\qC\\SOl\2..
I I                                    Recommended for Approval:
                                                        , -' - /i                      t;?"
                                                                     **               1   .
                                                                                 ' -J* "
,I                                                      *.. /      .
M. 1.* Smith
                                                                        /,-,.r..J,,,I. I*
Nuclear Fuel Engineer I     .... , .. ... ...              Approved:
I
                                               , Nuclear Fuel Engineering I.
1*
790115               o,, (o I

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-1                            CLASSIFICATION/DISCLAIMER I            The data and analytical techniques described in this report I  have been prepared specifically for application by the Virginia Electric and Power Company. The Virginia Electric and Power Company makes no I  claim as to the accuracy of the data or techniques contained in this I report if used by other organizations. Any use of this report or any part thereof must have the prior written approval of the Virginia ii Electric and Power Company.
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ABSTRACT I           The Virginia Electric and Power Company (VEPCO) has developed I a three-dimensional (x, y, z), one energy group, modified diffusion theory calculational model designated as the Vepco FLAME Model.
I           The model utilizes the NULIF, PDQ07, FLAFIT, and FLAME3 computer
-1 Codes which are part of the Fuel Utilization and Performance Analysis Code (FUPAC) system obtained from the Babcock and Wilcox Company. In addition, I the EDI~QAR, PICCOLO, and FLMSHUFL codes have been written by Vepco for use in the FLAME Model. The model is used to p~rform three-dimensional I reactor physics analysis in support of reactor startup and cycle operation of the Vepco Surry and North Anna nuclear reactors. The accuracy of the I  FLAME model is demonstrated through comparisons with measurements taken I  at Surry Units No. 1 and 2.
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I I                            A~KNOWLEDGEMENTS I            The author would like to thank Messrs. C. B. Franklin, J.
R. Rodes and M. L. Smith for their technical assistance during the I  development of the FLAME model and to Ms. Cathy Langston, Ms. Ivy I  Wilkerson, and Ms. Miranda Cooper for their typing of the draft and final manuscripts. The author would also like to express his appreciation 1* to a number of people who reviewed and provided comments on this report.
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I I                                  TABLE OF CONTENTS Page I   CLASSIFICATION/DISCLAIMER                                       i ABSTRACT                                                        ii I  ACKNOWLEDGEMENTS                                                iii 1* TABLE OF CONTENTS LIST OF FIGURES iv
                                                              '*    V I  LIST OF TABLES SECTION 1 - INTRODUCTION ix 1-1 SECTION 2 - CORE DESCRIPTION      ....                 ..       2-1 2.1 Introduction .                 . . . ...         2-1 2.2 Core Design                                      2-1 2.3 Fuel Loadings                                    2-2 SECTION 3 - MODEL DESCRIPTION * * * *
* 3-1 I              3.1 Introduction.
3.2 Input Preparation 3.3 Thermal-Hydraulic 3-1 3-2 Feedback Parameters                             3-15 I             3.4 Xenon Concentration Calculation . . . * *
* 3-16 I  SECTION 4- CALCULATIONAL TECHNIQUES.
4.1 Power Distribution .,
Normalization 4-1 4-1 a              4.2 Differential and Integral Control Rod Worths as a Function of Bank Position.                                       4-3 I  SECTION 5 - RESULTS *
* 5.1 Introduction.
5.2 Radial Power Distribution * . * .
* 5-1 5-1 5-1 5.3 Axial Power Distribution.                        5-2
-1*            5.4 Differential and Integral Rod Worths
* 5-3 SECTION 6 - 

==SUMMARY==
AND CONCLUSIONS.                            6-1 I  SECTION 7 - REFERENCES                                          7-1 I
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I I                          LIST OF FIGURES I Figure                          Title                            Page No.
Cross Sectional View of Surry Fuel Assembly.
I 2-1 2-2    Control Rod Bank Locations 2-7 2-8 I 2-3 2-4 Surry Units 1 and 2 - Cycle 1 Fuel Loading Surry Unit 1 - Cycle 2 Fuel Loading 2-9 2-10 2-5    Surry Unit 2 - Cycle 2 Fuel Loading                        2-11 2-6    Surry Unit 1 - Cycle 3 Fuel Loading                        2-12 I 2-7    Surry Unit 2 - Cycle 3 Fuel Lading                         2-13 I 2-8 2-9 Surry Unit 1 - Cycle 4 Fuel Loading Surry Unit 2 - Cycle 4 Fuel Loading 2-14 2-15 I 2-10   Surry Units 1 and 2 - Cycle 1 Burnable Poison Rod Loading * *                      * ****..                  2-16 I 2-11 2-12 Surry Unit 1 - Cycle 2 Burnable Poison Rod Loading.
Surry Unit 2 - Cycle 2 Burnable Poison Rod Loading 2-17 2-18 I 2-13 2-14 Surry Unit 1 - Cycle 3 Burnable Poison Rod Loading Surry Unit 2 - Cycle 3 Burnable Poison Rod Loading 2-19 2-20 I 2-15   Surry Unit 1 - Cycle 4 Burnable Poison Rod Loading         2-21 I 2-16 3-1 Surry Unit 2 - Cycle 4 Burnable Poison Rod Loading Flow Chart for Vepco FLAME model 2-22 3-3 I 5-1    Radial Power Distribution Comparison for Surry 1, Cycle 1, HZP, ARO, BOC * * * * * * *                . . . 5-6 5-2    Radial Power Distribution Comparison for Surry 1, I        Cycle 1, HFP, ARO, BOC     * . * . . *              .
* 5-7 5-3    Radial Power Distribution Comparison for Surry 1, I 5-4 Cycle 1, HFP, ARO, MOC * .     . * . . . . . .  .
Radial Power Distribution Comparison for Surry 1, Cycle
                                                                  . 5-8 1, HFP, ARO, EOC * . * . * * . * * . . . * . . .         . 5-9 I
I                                 V I

I I                      LIST OF FIGURES (Continued)
Figure                            Title                     Page No.
I  5-5    Radial Power Distribution Comparison for Surry 1, Cycle 4, HZP, ARO, BOC  ... . .. .                     5-10 I  5-6    Radial Power Distribution Comparison for Surry 1, Cycle 4, HFP, ARO, BOC   .... .. .                     5-11 I  5-7    Radial Power Distribution Comparison for Surry 1, Cycle 4, HFP, ARO, MOC   . ... .
                                     .                           5-12 5-8    Radial Power Distribution Comparison for Surry 1, Cycle 4, HFP, ARO, EOC   . .. ..
                                     .     .                     5-13 5-9    Core Average Axial Power Distribution Comparison for I         Surry 1, Cycle 1, BOC, HZP, ARO * . . * * . . .        5-14 5-10   Core-Average Axial Power Distribution Comparison for I  5-11 Surry 1, Cycle 1, BOC, HZP, D Bank In * . . .
* Assembly B-8 Axial Power Distribution Comparison for 5-15 Surry 1, Cycle 1, BOC, HZP, D Bank In * * . . .        5-16 I  5-12   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 3, BOC, HZP, ARO * . * . , . * . .      5-17 I. 5-13   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 3, BOC, HZP, D Bank In . * . .
* 5-18 I  5-14   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 3, BOC, HFP, ARO * . * . . . . .        5-19 I  5-15   Core Avenage Axial Power Distribution Comparison for Surry 2, Cycle 3, MOC, HFP, ARO . , . . . . . .        5-20 I  5-16   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 3, EOC, HFP, ARO * . . . . . . .
Core Average Axial Power Distribution Comparison for 5-21 5-17 I  5-18 Surry 1, Cycle 4, BOC, HZP, ARO * * . . . . . .
Core Average Axial Power Distribution Comparison 5-22 for Surry 1, Cycle 4, BOC, HFP, ARO .     ...    .
I  5-19   Core Average Axial Power Distribution Comparison 5-23 for Surry 1, Cycle 4, MOC, HFP, ARO    ..   . .
                                                    . .          5-24 I  5-20   Core Aver.age Axial Power Distribution Comparison for Surry 1, Cycle 4, EOC, HFP, ARO      ...  . .      5;-25 I  5-21   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 4, BOC, HZP, ARO       .
                                                   . . . .       5-26 I
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I LIST OF FIGURES (Cq_ntinued)
* I  Figure                            Title                     Page No.
I  5-22   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 4, BOC, HFP, ARO    . . . . . . . . 5-27 I  5-23   Core Average Axial Power Distribution Comparison for Surry 2, Cycle 4, MOC, HFP, ARO    .               5-28 5-24   Control Rod Worth Comparison for Surry 1, Cycle 1, I         BOC, HZP, D Bank .  . ... .. ..
                                   .         .     .               5-29 5-25   Control Rod Worth Comparison for Surry 1, Cycle 1, I  5-26 BOC, HZP, C Bank         .       . . . .
Control Rod Worth Comparison for Surry 1, Cycle 1, 5-30 I  5-27 BOC, HZP, B Bank Control Rod Worth Comparison for Surry 1, Cycle 1, 5-31 BOC, HZP, A Bank  .....       .  ..  . ..... .         5-32 I  5-28   Control Rod Worth Comparison for Surry 1, Cycle 1, BOC, HZP, Banks B-D moving 100 step dverlap      . 5-33 I  5-29   Control Rod Worth Comparison for Surry 1, Cycle 2, BOC, HZP, D Bank  ... .              .
                                          . . . . . .              5-34 I  5-30   Control Rod Worth Comparison for Surry 1, Cycle 2, BOC, HZP, C Bank  ... ..      . . . . . . .            5-35 I  5-31   Control Rod Worth Comparison for Surry 2, Cycle 3, BOC, HZP, D Bank  . ... . .
                                .         . . . . .                5-36 5-32   Control Rod Worth Comparison for Surry 2, Cycle 3, I         BOC, HZP, C Bank  . . .
                                .              . ...     .         5-37 5-33   Control Rod Worth Comparison for Surry 1, Cycle 4, I  5-34 BOC, HZP, D Bank              .
Control Rod Worth Comparison for Surry 1, Cycle 4, 5-38 BOC, HZP, C Bank  ... .  . .     . ..     . .
I  5-35   Control Rod Worth Comparison for Surry 1, Cycle 4, BOC, HZP, B Bank  . ....             . ..
5-39 5-40 I  5-36   Control Rod Worth Comparison for Surry 1, Cycle 4, BOC, HZP, A Bank . .   ... . . .
                                          .        . .              5-41 I  5-37   Control Rod Worth Comparison for Surry 1, Cycle 4, BOC, HZP, Banks A-D moving in 100 step overlap          5-42 I
I  5-38   Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, HZP, D Bank .  ....      . .. ..                   5-43 I                                  vii I

I I                      LIST OF FIGURES (Continued)
.1  Figures 5-39 Title Control Rod Worth Comparison for Surry 2, Cycle Page No.
I' 5-40 4, BOC, HZP, C Bank . * . * . , . . . *
* Control Rod Worth Comparison for Surry 2, Cycle 4, 5-44 BOC, HZP, B Bank    ........       . . ...   . . . 5-45 I  5-41    Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, HZP, A Bank   ..... . ... .      . . . .. 5-46 I  5-42    Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, HZP, Banks, A-D moving in 100 step over-lap * . * . * . . * . *  * * . . * . . . . * . . . 5-4 7 I
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I' I                          LIST OF TABLES I  Table                          Title                     Page 2-4 I  2-1 2-2 Surry Nuclear Power Station Operating History **
Surry Core Description                           . 2-5 I  5-1   Summary of Comparisons
* 5-4 I
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I I                             SECTION 1 - INTRODUCTION The purposes of this report are to describe one of the computational
 .I  models developed at Virginia Electric and Power Company (Vepco) and to demon-strate the accuracy of this model by comparing analytical results generated I   by the model to applicable measurements from Surry Units No. 1 and 2. The capabilities obtained with this model will be directly applicable to Surry I   Units 1 and *2 and generally applicable to all of the units at the North I   Anna Nuclear Power Station.
The model described herein is a three-dimensional (x, y, z), one
 .I  energy group, modified diffusion theory (with thermal feedback) calculational package and is designated as the Vepco FLAME Model. The Vepco FLAME Model I   uses the NULIF(l), PDQ07(2), FLAME3(3), and FLAFIT(3) computer codes which are part of the Fuel Utilization and Performance Analysis Code(4) *(FUPAC)
I   system obtained from the Babcock and Wilcox Company.-   In addition, the I   EDITQAR(S), PICCOLo(S), and FLMSHUFL(6) computer codes have been written by Vepco for use in the Vepco FLAME Model~    A detailed description of the input I   requirements, functioning, physical model,s and output capabilities of the above codes can be obtained from the referenced code manuals.
I             The types of reactor physics calculations which can be performed within the general capabilities of the Vepco FLAME Model include:
I             1. Assembly and core average axial power distribution I             2.
3.
Differential control rod bank worths Integral control rod bank worths as a function of rod bank I                  position
: 4. Control rod bank insertion limits I             5. Axial burnup distribution
: 6. Axial offset I             7. Peaking factors (FQ, Fxy(Z), Fz)
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I I This report is concerned primarily with the documentation of the capability I of the Vepco FLAME Model to accurately compute axial power distributions, axial offset, and differential and integral control rod bank worths.
I           The remainder of this report describes the Surry Units.No .. l.and 2 reactor cores to be modeled, the purposes and interrelationships of the I various computer codes :which comprise the Vepco FLAME Model, the specific I modeling of a reactor core with these codes, and comparison of calculated results with appropriate results obtained with the Vepco PDQ07 Discrete I Model(7) and with core measurements obtained from Surry Units No. 1 and 2.
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I I                          SECTION 2 - CORE DESCRIPTION I 2.1    ~ntroduction I              The Surry Nuclear Power s*tation, which ee:msists.,6f twO-*----
operating units, has been selected as the operating system to be modeled I for verification of the Vepco FLAME Model.      The Surry Units No. 1 and 2 are identical Westinghouse designed three coolant loop pressurized water I reactors with thermal ratings of 2441 Mwt. The operating history of the Surry Power Station is summarized in Table 2-1.
I
: 2. 2   Core Design -
I              The Surry cores consist of 157 fuel assemblies surrounded by a core baffle, barrel, and thermal shield and enclosed in a steel pressure I vessel. The pressure inside the vessel is maintained at a nominal 2250 psia.
I The coolant (and moderator) is pressurized water which enters the bottom of the core at a nominal 532&deg;F and undergoes a nominal average rise in tempera-I ture of 65.5&deg;F before exiting the core.      The average coolant temperature is 566&deg;F and the average linear power density of the core is 6.2 kw/ft.
I              Each of the 157 fuel assemblies consists of 204 fuel rods arranged I 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 Zircaloy-4 I clad. A small gap containing pressurized helium exists between the pellets and the inner diameter of the clad.      For the positions in the 15 by 15 array I not occupied by fuel rods, there are 20 guide tube locations for either solid burnable poison rods or control rods and one centrally located instrumentation I tube.
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(See Figure 2~1). The fuel rods in each fuel assembly are supported by I seven Inconel-718 grids located along the length of the assembly.
are mechanically attached to the guide tubes, which are, in turn, fastened to These grids I the upper     and lower nozzles, and thus provide for assembly structural support.
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'I             There are 48 full-length Rod Cluster Control Assemblies (referred I   to as control rods) used to control core reactivity as well as five part-length rods for axial power shaping.   (It should be noted that the part-I   length control rods are physically present but are not currently allowed to 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 I   control 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 I   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 I   and SB, are denoted as shutdown banks and are used to provide shutdown margin.
I              In addition to the control rods, a chemical (boric acid) shim is I   used to control excess core reactivity and to facilitate operational flexi-bility. Above certain concentrations of chemical shim, burnable poison rods are I   also used to control excess reactivity. Fresh and/or depleted burnable poison rods can also be used to shape (i.e., improve) the core power distribution.
I   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 I   fuel assembly not under a control rod bank location, consist of clusters of I   either 8, 12, 16, or 20 rods which are inserted into the Zircaloy-4 control rod guide tubes.
I              Specific values of the principal mechanical and thermal-hydraulic
   *parameters for the Surry core are provided in Table 2-2. A complete descrip-I   tion of the Surry units is given in Reference 8.
I   2.3   Fuel Loadings The initial and reload quarter core fuel loadings (i.e., initial I   enrichments and density, previous cycle iocation if appropriate, beginning of cycle burnup predicted by the Vepco PDQ07 Discrete Model and number of I                                        2-2

I I  fresh or depleted burnable poison rods present) for both Surry units are
:1  provi~ed in Figures 2-3 through 2-16. It should be noted that the fuel loadings for Cycle 1 of both Surry units are identical. The fuel manage-I  ment strategy employed in the initial cycle of operation of each unit was the checkerboard loading of the two lower enriched fuel batches in the center I  of the core and the highest enriched fuel batch around the periphery of the core. After the first cycle, the fuel management became more complicated I  as the result of the need to minimize the impact of fuel densification (which I  was most severe in the lower initial density, lower prepressurization Batches 1, 2, and 3). Generally, a modified out-in strategy was followed wherein I  higher enrichment fresh fuel was loaded on the core periphery with lower enrichment fresh fuel (and once-burned fuel and twice-burned fuel) checker-I  board loaded in the inner region of the core. An exception to this was in the third cycle of Unit No. 1 where no fresh fuel was loaded on the periphery.
I  The only fresh fuel was 16 lower enrichment assemblies loaded in the inner I  region of the core. Beginning in Cycle 4 of both units, a change was made from the typical 12 month operating cycle to an 18 month operating cycle.
I  However, the basic fuel management strategy (i. e., modified out-'in): :'7aS _not changed fo_r the Cycl~ 4 loading patterns.
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I I                                   TABLE 2-1 I                SURRYNUCLEARPOWER STATION OPERATING HISTORY I Surry Unit Cycle No.
Beginning of Cycle End of Cycle Cycle Burnup (MWD/MTU) 1        1       July 1, 1972         October 24, 1974      13547 I   1        2       January 30, 1975     September 26, 1975     6915 I   1 1        4 3      December 6, 1975 January 17, 1977 October 17, 1976 April 21, 1978 8944 13107 I   2        1       March 7, 1973        April 26, 1975        14870 I   2        2       June 14, 1975        April 22, 1976         9054 2         3      June 1, 1976         September 10, 1977     9422 I   2        4       October 8, 1977      1st Qtr 1979*         14000*
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TABLE 2-"2*
I                                SURRY CORE DESCRIPTION I.
* THERMAL AND HYDRAULIC DESIGN PARAMETERS
* Total core heat output, Mwt                         2441 I             Heat generated in fuel, % .
System operating pressure, psi Total co()lant flow rate, lb/hr (gpm) 97.4 2250 100.7  X 106 (265,500)
I                   Coolant Temperatures, &deg;F (@100% power)
Nominal inlet Average rise in the core 532
                                                               *6s.s Average in the core                     566 I                         Nominal outlet of hot channel Average linear power density, Kw/ft
                                                               . 642
                                                               . 6.2.
I    MECHANICAL DESIGN PARAMETERS Fuel Assemblies
                  . Design                                        Canless 15 x 15 Number                                        157 Rod pitch, inches                             0.563
* Overall dimensions, inches                 . 8.426 X 8.426 Number of grids per assem.bly (material) * .* 7 (Inconel-718)
Number of instrumentation tubes               l Fuel Roos Number*                                       32,028 Number of rods/assembly                       204 1*                   outside diameter, inches Batch 1,2,4,5 ,6 * .Batch 3 0.422        *
* 0 .422 Diametrical gap~ inches                           0.0075 *     <:* 0 .0.085 I                    Clad thickness,, inches Clad material 0.0243 Zircaloy-4 *
                                                                                      , .0~_0243 Fuel Pellets I                    Material *      .
Density(% of theoretical) and
                                                                 *Sintered UOz
* See Figures 2-4 through Enrichment (~/o U235).                    *2-12 I                    Outer. diameter
                                            '*.                    Batch 1,2,4,5,6 -*;*Batch 3 o.3659        . *: .o.:-3'649 I              Control Rod Assemblies Neutron absorber
                   . Cladding Material
* 5% Cd~l5% In-80% Ag Type 304 SS-Cold worked Clad thickness, inches                        0.019 I                    Number (full length)
Number of rods per assembly
                                                             .. 48 20 I
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I TABLE 2-2 (Continued)
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I   Burnable Poison Rods Material Content B203 (w/o)
Pyrex glass 12.5 I   Core Structure
* Core barrel I.D./0.D., inches           133.875/137.875 142.625/148.000 Thermal shield I.D./0.D., inches I        Core diameter, inches (approximate)
Reflector thickness (approximate)
          . and composition 119.5 Top - Water plus*steel, in.    *. 10 -
I              Bottom - Water plus steel, in.
Side - Water plus steel, in.
10
* 15 1*
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1*
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FIGURE *2-1 .
* CROSS SECTIONAL VIEW OF SURRY FUEL ASSEMBLY
                                                                                                               ~   ..,
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2-7

I          .                                                                  *
                                                                                        . F_IGURE 2.:..2
                                                                                             .. .  '.  -~    - *.
1-* .                                                               .
CONTROL ROD BANK LOCATIONS
                         . R . p                      N _- M       L..*         .K. __        J   . H                G      _ F. E        D     c B  A I_, *-               1         .                                                   .        000
     ..               2                         :* ....**        . DGD~DGD *...
1              *
* 3 * .. .                     .*     ** -   DDD~IQIITJDDD
* I * .*                4 .         -       -*        D0D0D~D0DGD *_ .
*1** * .*. s .*. DDDEJDDDDDGJDOD* *                                                                                                                                              .
  .. * . .
* GD0DGDGDGDEJDGJ * *.
b ..                                                                                                                                                     .
I            :   ** 1     ODGDDDGJDGJDDOf~DD *. **-
1... -_-,. a DGD~D~DGOGJOGJD~D 1: .* .*. ~0
~1* *_
* 11         *
                                       ~B~B~~~B~8B~B DDD~DDODD0DDD *. -
0 a .* ....             12
                              . . *..                D0DGJD8DEJDGD . ......
  ._-_._           -*  13 -- * -*             --         . DDDEJfaEJODD *. ***- - *:*_:_ * - .
I                     14                          .*      ..    *.000~000 *. :: ..
* 1.
15       -                                                            DOD -*
                                                                            . *.          CONTROL ROD ASSEMBLY BANKS 1*.. *   .     .   .*  ... *.....*  ** -~ * * *
* Function
                                                              * . . Control Bank D * * . . 8 * . *
                                                                                                               .* * . ~umber of            Ass~mblies
                                                                                                                                                                                      ~
I*. .                                                  * . *.**
* Control Bank C                                              8 ** . .
Control Bank B                                  *         '8 * * -
* Control Bank A                                    .* ..
* 8 I .** *                            . .* ..- *.
                                         .            . * * . * . Shutdown (S). . .                               *. . 16 * . .         .   * * * . .
                                                                   *Part Length (P) * . * . 5 . .                                          *
                                                                                                                           . 5*3 .-
 * *. *. *. . tr~                             SOURCE ASSD!BLY LOCATIONS . ....
I.                                                                                                       .
2-8

I                                                                FIGURE 2-3 I
                                                  "SURRY UNITS l ~ 2 -- CYCLE 1
.1             08                   09             10
                                                         .*
* FUEL LOADING 11          12       13             14           15
 ,I. H 1
0 2
0 1
0 2
0 l
0 2
0 1
0 3.
0 Fresh              Fresh          fresh         Fresh        Fresh    Fresh         Fresh       Fresh I
I J
2 ODD*oDoDoD*oooo.o*
oo*                      *
       -,..~----~-re_s_h_          . .             Fresh         Fr~sh .      Fresh    Fres          Fresh . Fresh I   K 1
Fre:h . Fres: Fies: *Fres:
* Fre:J . Fres:
o**.     -o-           2
                                                                                        --io*
1.
I L
2 o*DD***-o DD*                                ._* o o0- JD*     3 o              o.
0*01*.o o~Ll
_ _-_Fr_e_s_h_.
* Fr~sh         Fresh
* Fresh    Fre~       '* Fresh* _
I   M
         ---1                                               0-        *nnr--.
Fre:h D Fres:r Fres}l Fres:I (U;~;;;s) 0 I   N 2                                12                             3                            Initial Enrichment      Density I               Fresh t:.======~                                Fresh         Fres         Fresh 1 (53) w/o U235 1.85
                                                                                                                         %TD 94 1                                                                                             2.55            93 I
rFres:IDD p
3.10            92 0
_! !m 1*
I R
1==3   =.o=o .
* Fresh Fresh LEGEND
                                                            ~-Batch No.
[3   .
                                                           ---Initial Burnup (MWD/M111)
                                                            ---Previous Location (If applicable) 2-9

I                                                             FiqURE 2-4 SURRY UNIT 1 - CYCLE 2 I                                                         FUEL LOADING ...
08                 09         10            11           12         13         14           15
.1     l                     4B          l            4B             z         4B          l           4C 15358                             12536                                        0    14680 H
                   .                 0                          0      15298                                    0
*I              HOB             Fresh          Hl4       Fresh            Hl3      Fresh         Hl2       Fresh I  J 4B 0
EJDQQQWFh       A:oOOo~oc*                                                            0 D                         ooc sh I
ll'-r~~h
                           ~                                 .   .
1                                                             2 I* K 12536 P08        D             l U216 Ml2
                                        .___~"-=.I 15918 Jl2 Li 0
Fresh 1*
I L
4B Fresh 0
                             \429:10    D~               167~:8      2 1659:10 DD I
M 2
15298 NOS 2
16075 LIO 2
15918 M09 2165::9      DD
___ [JD I  N 4B 0
2 14378 1
14191 C.
o Batch
(#F.A. 's)
Initial Enrichment w/o U235 Den sity
                                                                                                                   %TD I                                  Mll         ___,
MIO                     Fresh DDC                .
Fresh                                                                   1 (21)          1.85             94 1                                                                          2 (52)          2.55 *         .9 3 4A(20)          1.85             95 I  p 14680                                   o   DC        o                  4B(12) 4C(52) 2.60             95 3.35             95 MOS.....,                 Fresh         Fresh I  R I
LEGEND I
I                                      []           ---Batch No.
                                                     ---Initial Burnup (MWD/MTU)
                                                     ---Previous Location (If applicable)
I I                                                               2-10

I                                                                FIGURE 2-5 SURRY UNIT 2 - CYCLE 2 I                                                              FUEL LOADING 08             09             10            11         12         13           14            15
-I       1                      3              3            2          4A          2            2             4B H       16693               15422            11414        17992             0    18295        16805              0 I -----
D J09            G14           HIS          Hll      Fresh          H09             C08     Fresh I
~1 J    \5422
        ,_____P_0~9 n
                             ~
                                               \7635 Kll 2
15755 Kl3 3
14725 Nil~~
nn I  K 3
11414R              :763~
3 154::
2 181;:0   D           7 1 1 74 1:J*:res:          I ooo *D*D 08             10              4 2                                                 4           2                       4 I*
                                               ~
L       17992                                             A   . O     15860                   B     O
        ~--~1*.~n~                                                            Ll2
* Fresh 4                                                                        4 J.i 2                     3 5 75 O:: ';=:===
1=::::::r:::es=h=*            N=\=o::: D. D 2
2158
:1 D4B'o 1  BFreJ             Initial D
Batch        Enrichment        Density
                                                .17470                              UftF.A.'s)         w/o U235        %TD N       18295               14725                                                                                     -
        ,___ _J_0_8_,                 Ll3           M09      _            Fresh        1 (1)           1.85.           94 I P     \6805
____H=J...,3...,
DB r sh O     ~[JB W              Fresh.
0 2 (52) 3 (20) 4A(32) 4B(S2) 2.55 3.10 2.60
                                                                                                    .. 3.10 93 92 94 95 I
:I R
4B Fresh OD                    LEGEND I
G
                                                          ---Batch No.
                                                          ---Initial Burnup (MWD/MTU)
 .I                                                       ---Previous Location (If applicable)
I I                                                                   2-11

I                                                              FIGURE 2-6 SURRY UNIT l - CYCLE 3
:1                                                           FUEL LOADING 08            09            10                 11             12                    13              14               15 I         1           3             1                 3                3                   ~                   3                4C H       15236          10420         14182            14034             14034                12224             8387             6239 I        Cvl Tm~ ,,,.,. HOl *,,,.,     Rl 1   ,,,.. ,   ~1 l.t ,,,.,        Tl li. 'r.vl        Kl l.. r.,.,
                                                                                                                 .      T 1 li. r.,,?
                                                                                                                                  . l-101 3           4B            3                 4A               3                   1                   4C               4C I    J       10420           8568           8973             7946            13334                13859             7142             4903
:I       Cyl     AOl Cv:2      Lot Cyl        Cl2     Cy2      JlO    Cyl         E03     Cyl          Jl3    Cy2       Fl4    Cy2     GO!
I   K 1
Cvl 14182 3
I Ll] Cvl 8973
                                    ~A MO: Cv2
                                               . ooca*G 6462 M12    Fresh 0
Fresh 0
1 8174 Jl5     Cv2 6967 G02                 ,.
3           4A                                               4A                   !+C                4C I
I L
Cvl 3
14034 pQC 14034 Cv2 3
7946 KO<
13334 DB                . _12224 C1 4A
* 7486 Cv2 3
7486 Kll
                                                                             . 8371 Cv2
                                                                                            !+C 7601 E03 5230
* Cv2 5667 D03 I       Cyl     PO, Cyl       CO: rFresh        QI Cy2 LlO Cyl                  BO?      Cy2         E02 Initial I    N j
12224 1
13859 j
* 8174 4(.;
7601 41.;
5230 Batch
                                                                                           <f!F .A.' s)
Enrichment w/o U235 Density
                                                                                                                                                 %TD 1 (13)                     1.85                   94
 *.1. Cvl     POl Cvl       NO< Cvl        R09    Cy2 C05          Cy2        BOS 3 (52)                     3.10                   92 3           4C            4C                4C                                      4A(20)                     1.85                   95 4B(4)                      2.60                   95 I    p Cyl 8377 PO: Cy2 7142 POl Cy2 6967 B07    Cy2 5667 C04 4C(52) 5 (16)
                                                                                                                        *3'_35 2.10 95 95 I:     4C          4C R        6239           4903 I       Cv2     AOI Cv2       AO LEGEND I                                                 ---Batch No.              .                       *          .
I           Previous cycle--     D               ---Initial Burnup (MWD/MTU)
                                                    ---Previous Location (If appHc:able)
I I                                                               2-12

I                                                                     FIGURE 2-7 SURRY UNIT 2 - CYCLE 3 FUEL LOADING I
08               09               10                   11                12              13              14
* 15 I        1               4B              4A                3                      1              4B                1                +B 16635             10342            10943               13414               15214           10342             13761           6985
 .1 H
Cvl T(ns; ~ .. ?
                          .       Tl l.t "'**'>    l"'nO    ~ ... ,    T(l l.t   ,,.. ,    .Tl 1 '"!u?      r-14  1~ .. ?    Rll.t. C.v?   Rfll
[J 4B              1                +B                 4A                   4B              +A               4B I  J        10342            15214            10076             11093                  8505          11101               5739 Cy2       PO, Cyl         N09 ~y2          113 Jy2             K12       Cy2       K14   Cy2         Jll   Cy2       Jl5 I       4A              4B               ~A                 3                    1                                ,4B I
I*
K Cv2
       .3 10943 JQC Cv2 4B 10076 Nll Cv2 3
10916' MOB ~vl 1
9228 114       Cvl 3
15586 Kl2   G
                                                                                                 +B Cv2 5972 114 D
L       13414             11093             9228             16377                  9896            6806
 ~I     Cyl 1
POf Cy2 4B Ml( Cyl 1
Pll Jyl 3
109       Cyl 3
Ml3   Cy2         Ml3 I
M       15214              8505            15586                9896               13414 r
D Cyl       NOi   Cy2       pl( Cyl          MlO Jyl             Nl2       Cyl       PlO       Fresh     OI
                                                                                                                          .Initial I   N 4B 10342 4A 11101 3
8978       4B       6806 * .                  0 Batch UfoF .A.' s)
Enrichment w/o U235 Den sity
                                                                                                                                                 %TD pQC Cy2
  .I    Cy2 1               4B LQC Cyl 4B R09 Jy2 5
N12         Fresh . * .         1 (25) 3 (32)"
4A(24) 1.85 3.10 2.60 94 92 94 4B(52)                3.10                95 I p       13761              5739             5972                       0
  ,.                                                                                                   5 (24)                3.10                95 Cyl      POI Cy2         RQC Cy2          PU         Fresh
  .1 R
4B Cy2 6985 AOE D
I                    . . o---Batch LEGEND No.
                                                . yy ---Initial Burnup (MWD/MTU)
                *                  .            zz       ---Previous Location (If applicable)
I         Previous* Cycle--- nn
* I 2-13 I

I                                                FIGURE 2-8 I                                       SURRY UNIT 1 - CYCLE.4 FUEL LOADING I         08        09          10            11          12          13          14           15 1         6A           5           6A            AB         5            4B            6C I        15236 Cyl H06   ___    0 Fresh*__,
10552 Cy3 Fl        Fresh*
0        8760 Cy2
* H09 10552 Cy3 . ElO. CY2 H13 8615 Fresh 0
I   J 6A I. -----
O 4
                  ~ 17296   CJ            4
                                            ~0529 4
                                                         ~1355 4
c  14951 D C D C    ~           0 I   K Fresh
      -5 10552 Cy3 LlO D bj Cy3   Nll O
2/4A 9890 S2C2 M12 Cy3 AOO O
Cy3 4C N04 16875 Cy3 . Jl4 Cy3 DOC -
F02    Fresh Fresh 0
                                                                                            . Fresh I 6 L
I :resh O::os;:1            D :: ::3 :3 ::: DD 72           11 4B 8760 4C 11355 4C 16875 4C 11267      4C13240     bJ I
I N
Cy2 5
JOB Cy3 4
c Cy:os:1 Cy:49::6 Dl3 o~o Cy3    P09  Cy3     Pll   Cy3    ROB bJ 6:esh o ~#:~:~~:)- -E!/::::;;t Initial        Density
                                                                                                      %TD 94 r-----2/4A (4)                    2.60           95
                                                                       ~~~)            ;: ~~
95 DDD 4B        6C       O 6C        O 6C         O               :~                                  95 8615 5 (8)                2.10           95 I    ::e.:o: ~ Fresh Fresh                                   - ii m:                  n~             95 95 95 LEGEND I                                     ---Batch No.
                                       ---Initial Burnup (MWD/MTU)
I                                     ---Previous Location (If applicable)
I I                                                      2-14

I                                                FIGURE 2-9 I                                        SURRY UNIT 2 - CYCLE 4 FUEL LOADING I     1 08 6A 09 4B 10 4B 11
                                                     ,4B 12 4B 13      14 4B          6B 15 I  H      16635 FOB   Fresh 0
Cy3 21458 GlO  Cy3 13392 Hl5    Cy3 21240 H09 Cy3 20813 Hl3 17227 Cy3 E13      Fresh 0
Cyl I     6A          4B 1*
J.
Fresh 0    *19642 Cy3   M09   D K
I  L 4B 13392 I     Cy3    ROB 4B          5           4B I  M 21240        6678 Cy3    J08                                                                Initial I    4B Enrichment w/o U235 Density
                                                                                                 %TD--
N       20813 I    Cy3 NOB 1.-85 3.10 3.*10 94 95 95 4B                                                                         2.90            95 I p Cy3 17227 Nll 3.20           95 I     6B 0
R I      Fresh d                    .
I                         *.           --~Batch No.
G
                                        ---Initial Bu:rnup (MWD/MTU)
I                                      ---Previous Location (If applicable)
I I                                                      2-1:5

I                                                                               FIGURE 2-:).0 I *.. *                                                                   .
I . ." * *
                                                                 *
* SURRY UNITS l AND 2 - CYCLE l Burnable Foison Rod Loadi:ng *                                            * ** *
                                  .~oa_*,..*.. ___;;:0~9~ 1 0 ~ 1 = - rr.--=.;;12~~13~ 1___                                                       4 ,,---is--,,
I*. . ..               H       1           2                   1              2                 1                    2                    1              3 12                                   12                                   12 I .
0LJLJDDDD 2
12 I *
                                               ~o-~o*                                                            *.
i                           J 1
                                                                                                                         ~~*
K                  LJ LJ LJLJ.
:.*                     L 2
12 DDDDGD.
    ,.:I .-*-;- 12LJLJ1_J
    *              ****. M         dGDLl.DlJ.****r~l.*~~o**  *                                                          ....                            *.
N            *                                                           .........* . <. *.
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    ****.*RJ**[].**                                                                                                                   ..
I i
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t:==::':=!=:=!.J
                                                               . LEGEND. .
  *1 *..                                                            xx             Batch No.*                   *
                                                     *. *.   ,       . *. *. yy  --No. of Fresh Burnable Poison Rods
                                                  .      .       ~
     *' .4' *    *
* I
                                                           '. '' .:\>>::!. . :' .* *'
                                                                                             *2-16
* I                                                                 . FIGURE 2-11 I                                                                         .  :  ;. - '
SURRY UNIT 1 -- CYCLE 2 .
:1* ..... .                                           *.*
* BURNABLE POISON ROD LOADING         .
08                09                 10           11 .                 12      13        14           15 I. -
   .       H 1                 4B                 1               4B            2            4B        1           4C 8                             8 I                                                                                              12 J
4 B
8 DLJDDDL3LJ
:       K   l                LJDCJDD'CJ I_-L        4B            sDLJDDLJLJ 11        M   2                DDLJD[]'                                                                           I
:~       N 4
B 12           DDC3J[J -. _
I        p 1
                      --       ~CJ[].*
I- - -                        P[l . *.-. *. .* *,.- ,*. -*
r        1l 4C_ -* .. --.*
                    -          L=:J
                                     - - - .- - , ~;:. l-.:-~tchN,._ _                              - -, -_ - _ _
I . *.           ....... ;.,.
                                  .* _, --,- -* *, :' }ij/ *--~~~ijo. of Fresh *Burnable Poison Rods       . . . .*
                                     - :;~- - *. <
                                                       ~z*.**.:, -~No.. of *_Deyleted Burnable Poison .~ods.
I*:,                                                                         ,2-17

FIGURE 2-12           -
* SURRY.UNIT 2 - CYCLE 2
 *,I H
1
: 08.
* 3 09
                                            *3
                                               . 10 BURNABLE POISON ROD LOADING
* 11 2                4A 12 2
13 2
* 14 4B 15 I                                                                                          12
  ,. 1----'CJDCJDDEJCJ 3
I        J
 ,*.* . DDDDDD 3
K I.*       L ~
2 tJDEJDrJD
~,,-_      M   4A        u '  2 .* ,1 4A            ** _
1 1LJ*2.     *.** ,LJ14A          1r-i I                                          LJ                                             LJ
           ~             [J[JEJ[J 2
I                12 I.
DOD 2
                        *LJ *: * * ...
p  t==:===!
I R:
4B t:=~.!==!J   '
                      . .*     ' .*    . . . -LEGEND-~   >.:* '.. ' . . .' .' . ... . . . . . ' .
*I                                  **      ~ ---Batch No.                         *     .    . *. _ * *       .
1-**.                             * . *W-No: of                             Depleted Burnable      Foi:o~    Rods I
1*                                                                  .. * '2-18

I                                             .* . FIGURE 2-i.3 .
I.*.                                        . SURRY UNIT 1 - CYCLE 3
                                         . BURNABLE POISON ROD LOADING I
'          .       08      09 * .
1 10 3
11    ..
13 12     13        .. 14        15 1       3                                                       3         4C
*1.            H 12 DDDDDDD 3
:_Jt::::===::
  ',           Kl--**    DDDDDD DDDDDD 3
IL               .
3
:M                       DDDLJtJ DOD['.]
3 I            N      12 Ip 3
DD                   4 c                                   ...
:-R 4C                 D                                                                     * ..~-*
1* ..
I    '..     .
                                . xx          -Batch No.     *
* zz    -No. of Depleted Burnable Po.ison Rods . *.
* I ..
I                                                       . 2-19

                                                    .    . ~IGURE    2:14 SURRY UNIT 2 - CYCLE 3 BUBNABLE POISON ROD LOADING
.I          08        09 4A 10    .          11            12                13
* 14        .. 15 1         4B                              3              ,l                                    1           4B I    H 12 DQDGJDDD 4
:    J    s IK4A            QDQDQD
:LJ             DQDDDD
*l**M   t      *o4B      .. o...         * ** Q          .J. o.*-.*.**u(s***              ... I
                    .      12           ..    .      * . 12         ..
* 12 DQD*D 4
:   N    B Ip     1      DDS . ' .
I      **     n.*.*.
IR            LJ t::::==::::~===:J
                          .*:[]*
                           .        LEGEND
                                *
* xx     *
                                                -Batch No.
                        . .. .*...* ... zz      --4!~*     of Depleted Burnable Poison Rods 2..:.20 .

I                                                 FIGURE 2-15 I                                . SURRY UNIT 1 - CYCLE 4 BURNABLE POISON ROD LOADING I            08   _    09     10               11           12   13     14     15 1          6A      5            6A             .4B    5      4B     6C I  H                      8                        12 12 I
I 6
A 8
J . .._..__.....
5 D[JDDDDD I  K GLJLJDLJD
: L=6A          12[J[][JLJ0D I  M     4B         [JLJLJDO 5
: N=        12      DLJLJ[J 6
I R t=:=======..l I                                  .,..-.,....-Batch No.           *
* I                          D       ~~--No. of Fresh Burnable Poison Rods
                                    ~-~~No. of Depleted Burnable Poison Rods I
I                                                        2-21

I                                             FIGURE 2-16 I                                  SURRY UNIT .2 .,. CYCLE 4 BURNABLE POISON ROD LOADING I'              08     09      10          11          12        13        14      15 I     H   l 4B       4B           ,4B        4B          4B. 6B 12 12
'I I     J. _
6 4B A _
12
[JLJ0DDDD I
I' K
DDDDGD s:=:==DDDDDD 4B L
I DODD.
4B                                                 6 I    M D B      ..
         = DC3DD 4
:    N      B 12
  *,: p-4B            G[]D 6B         [JB.
I   R t======-=====.J I                                 ----Batch No,         .
* I                         D       -,..--No, of Fresh Burn.able Poison Rods
                                     --"--No. of Depleted Burnable Poison Rods I
I                                                  2-22

I I                        SECTION 3 - MODEL DESCRIPTION 3.1   Introduction The Vepco FLAME Model is used to calculate nodal power densities I and core reactivity for three-dimensional geometries in which each fuel assembly is represented by one radial node and by up to 32 axial nodes.
I The method used by the Vepco FLAME Model to perform these calculations is I based on th~ FLARE(9) technique which is derived from modified, one energy group diffusion theory. Effects of nonuniform moderator density and fuel I temperature are accounted for by thermal-hydraulic feedback.
The Vepco FLAME Model performs calculat_ions 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 I composition in the fuel assembly by a cross section generating code (i.e.,
I the NULIF(l) computer code). Then the fine-group flux spectrum is used to spectrum weight and collapse the fine-group cross sections into the one I energy group parameters required (i.e., Koo and M2) ~y the FLAME3( 3 ) computer code. These parameters, as well as any appropriate normalization factors, I are then used by FLM-IE3 to perform an iterative, modified diffusion theory I calculation for the neutron production rate density as a function of position.
The method of solution comprises two levels of iteration:    source (or nuclear)
I and thermal-hydraulic feedback. The source calculation is performed first based on an initial guess for the thermal-hydraulic parameters. Then a new I set of thermal-hydraulic parameters are calculated. Using these new thermal-hydraulic parameters, another source calculation is performed. This process I is continued until both the source and thermal-hydraulic convergence criteria I are satisfied.
I I                                       3-1

I I            Several interrelated computer codes are used to perform the I calculations outlined above. The computer codes comprising the Vepco FLAME Model and their interrelationships are presented in the flow chart in Figure I 3-1. The FLAME3 computer code is the principal analytical tool in the Vepco FLAME Model. FLAME3 is used to perform the three-dimensional, one group, I modified diffusion theory calculations. The other codes provide either I input data or data manipulation. As indicated in Figure 3-1,. the NULIF code is used to generate the required one group data for the non-rodded fuel I assembly. The FLAFIT( 3 ) code formats these data for use by FLAME3.
for burnable poison and control rods are generated with the Vepco PDQ07 Data I Discrete Mode1(7) using a quarter assembly discrete representation.         The in-house codes EDITQAR(S) and PICCOLo(5) format the data from the quarter I assembly PDQ07 calculations* for use by FLAME3. The FLMSHUFL ( 6 ) code is a I data manipulation code that shuffles the appropriate end-of-cycle burnup distributions to duplicate .the movement of fuel assemblies during refueling.
I The shuffled burnup distributions from FLMSHUFL are input to FLAME3 to begin reload cycle analyses.
I            The remainder of this chapter describes in greater detail the input to and functioning of the computer codes used in the Vepco FLAME Model.
I 3.2   Input Preparation I            The Vepco FLAME Model uses the FLARE neutron source option for all calculations with the FLAME3 code. Two physics .parameters are required at I each node by the FLARE(9) option:     the infinite multiplication factor (Koo)
I and the migration area (M2). At peripheral nodes, it may also be necessary to input a leakage parameter (or albedo).
I            The infinite multiplication factor, migration area, and albedoesfor each node are usually functions of one or more variables. Among these are initial I
I                                        3-2

CROSS SECTION       DEPLETION      FUEL ASSEMBLY         CROSS SECTION    1/4-ASSEMBLY          DEPLETION GENERAL LIBRARY            INPUT         DESCRIPTION            TABLE SETS        GEOMETRY             INPUT   :PROBLEM L,.)
I L,.)
Ko., DATA FOR THE NON-RODDED*ASSEMBLY & M2 REACTOR       NORMALIZATION       GENERAL    Kc., MULTIPLIERS FOR DESCRIPTION                                    CONT.ROL *c,. BP RODDED FACTORS          PROBLEM          ASSEMBLIES BURNUP 1--~~.....a.~~~-1DISTRIBUTION1--~~~<>-~~~~w AT BOC AXIAL POWER       ROD WORTH     AXIAL BURNUPi--~~~~--~~~-'
DISTRIBUTION       SHAPES       DISTRIBUTION

I I enrichment, burnup, soluble boron concentration,    xenon concentration, fuel I and moderator temperatures, and the presence or absence of burnable poison or control rods. To represent the functional dependencies, Koo and M2 are I calculated for various combinations of the appropriate variables. The resulting values of Ka, (or M2) are then tabulated for use in the FLAME3 code by using I the FLAFIT and PICCOLO codes. The FLAME3 code uses a Lagrangian interpolation routine for selecting the appropriate input data from the tables constructed I by FLAFIT and PICCOLO. This routine allows any input variable (e.g., Ka,) to I be fit as a function of one, two, or three independent variables. Due to this constraint, it has been necessary to use several tables to properly represent I all the functional dependencies of Ka,.
The leakage parameters cannot   be input in tabular form. However, I the leakage parameters may be changed to reflect changing reactor conditions.
I This is discussed further in Section 4.1.
The processes by which tabular input for Koo and M2 are developed are I described in this section.
I 3.2.1  Method of Calculating Input Data for the Non-Rodded Fuel Assembly The NULIF code is used to generate the non-rodded (i.e., no I control or burnable poison rods are present) fuel assembly input data for the FLAME3 code. The NULIF calculations are performed using the supercell option.
_I A supercell is defined as a group of unit cells comprising," for example, a fuel assembly. For the supercell group, the fuel rod unit cell is designated I as the central cell. Any other unit cell types (e.g., control rod guide tube I cell) present in an assembly are designated as subregion cells (subcells).
The supercell option is used to represent the fuel assembly in the Vepco FLAME I Model because only homogenized groups of unit cells can be represented due the larger-than-discrete mesh description implicit in a nodal representation I of the reactor core. The homogenization is performed in a manner that I                                      3-4

I I results in one node representing each fuel assembly.
The calculation of the neutron energy spectrum and the spectrum-I weighted two-group cross sections for each supercell is described in detail I in Reference 1. Those aspects which involve calculations using the supercell option are described below.
I            With the supercell option of the NULIF code, the material compositions of the central cell and the various subcells must be homogenized together I before the fine-group neutron flux is calculated, since the NULIF code does I not perform a spatial calculation for the various subregions. Because of this, a method must be employed to represent the heterogeneous nature of the I supercell. This is done by inputting appropriate thermal flux depression factors for each subcell relative to the supercell. These flux depression I factors are generated by a detailed spatial calculation (i.e., a quarter assembly discrete PDQ07 calculation where each fuel rod, thimble cell, and I water channel associated with the fuel assembly is explicitly represented).
I 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 I in the entire assembly are determined. The above flux depression factors are combined in NULIF with those normally calculated by NULIF for the central I cell (i.e., the flux distribution in the fuel pellet, clad, and moderator regions of the central cell) to give the overall flux depression factors to I be applied ove.r each of the 80 thermal fine-,-groups for each nuclide in the I supercell.
NULIF calculates the neutron flux in the supercell for each of 31 I fast and 80 thermal energy fine groups. The macroscopic, one-energy group parameters needed as input to the FLAME3 code are then determined from the I neutron flux and cross sections for each fine group.
I                                      3-5 I

I
-1            Assembly (supercell) calculations of      Ko, and M2 with the NULIF code I are performed as a function of:
: 1. Initial enrichment I            2. Burnup I            3.
4.
Soluble boron concentration Moderator specific volume I            5.
6.
Fuel temperature Xenon concentration I An assembly of each enrichment used in the core is depleted with NULIF while maintaining constant soluble boron and xenon concentrations, moderator speci-I fic volume and fuel temperature. Recovery cases are then performed at I selected burnups where these parameters are varied.         Care has been taken to vary each*parameter over the range of values expected to occur during the I types of operation to be modeled with the Vepco FLAME Model.
I 3.2.1.I   K-Infinity The Vepco FLAME Model uses for each enri*chment a basic Ka, which I is a function of burnup, soluble boron concentration, and xenon concentra-tion. This combination of independent variables was chosen for two reasons.
I First, these variables have the largest effects on Ka, for the non-rodded assembly (aside from enrichment which, as stated above, is represented by I generating separate tablesets for each initial enrichment).         Second, the I effects of these variables are relatively insensitive to changes in other parameters. For these reasons, the functional dependencies of K00 on burnup, I boron, and xenon are represented together in the basic Ka,.
Since Ka, cannot be adequately represented as a function of only I  three independent variables (the limit for any table used in the FLAME3 code),
I  other tables (i.e., Koo multipliers) are developed to allow the incorporation of additional functional dependencies. The K.:x, multiplier tables contain I                                         3-6

I I factors which are used to modify the values contained in the basic Koo tables~
These factors are arrived at by taking the ratio of     Koo at some nominal I condition to the K00 generated by the NULIF code after a change in one or two I independent variables. For the non-rodded fuel assembly, two Koo multipliers are used to represent the effects of fuel and moderator temparatures.
I            The first K00 multiplier represents the effects ori Koo of changing moderator temperature. Changes in moderator temperature result in two I important phenomena:    1)   change in moderation (neutron spectrum) and 2) change in parasitic absorption in the moderator.      For these reasons, the I first Koo multiplier is fit as a function of moderator specific volume, I burnup, and soluble boron concentration.
The second Koo multiplier incorporates the dependence of Koo on I fuel temperature. Changing fuel temperature causes a change in resonance absorption. This effect is sensitive only to burnup.      Therefore, the second I Koo multiplier is fit as a function of fuel temperature and burnup.
I 3.2.1.2   Migration Area The migration area, M2 ,   is used by the FLAME3 code as a measure of 2
the leakage from an assembly. As such, M is sensitive only to moderator Therefore, M 2 can be adequately I specific volume, burnup, and enrichment.
represented by a single table fit as a function of these three parameters.
I            In addition, the FLAME3 code permits the use of a M2 multiplier as a normalization factor. The use of M2 multipliers is discussed in Section 4.1.
I 3.2.1.3   Input Parameters for Calculating Xenon Concentration
~            The FLARE neutron source option does not allow the explicit calcu-lation of any material concentrations. However, to accurately represent    Koo I it is necessary to know the xenon concentration at each node in the core.
Onc~thenodal xenon concentrations are found, then      Koo for each node may I be obtained from the appropriate tables.
I                                         ~7

I
-I            To find the nodal xenon concentrations, the FLAME3 code solves the I  differential equations for xenon and iodine based on the assumption of constant power throughout a.burnup step (see Section 3.4 ). This solution requires I  that several parameters be input to the FLAME3 code in tabular form as functions of the appropriate independent variables. These input parameters I  are listed below:
A  =  (K1rhl\+ K2r&#xa3;202H1/02)
YI = (y1rf101+ YILf202)(1/02)
I            YX = (yxrf101+ Yxrf20z)(l/02)
(Jxe = thermal microscopic absorption cross section of xenon, I             a2 SIGM = mu1 tip
* 1 ier
* f or craz
                                      *xe I where:      K = energy released per fission rf = macroscopic fission cross sec~ion I              0 = neutron flux YI = yield per fission of Iodine-135 I           Yx = yield per fission of Xenon-135 and subscripts 1 and 2 refer to the fast and thermal energy groups respectively.
I The parameters are all generated by the NULIF code and :.are tabulated by FLAFIT I for use in the FLAME3 code.
The parameters A, YI, and YX are strongly dependent on burnup and I enrichment. However, variations in other independent varia_bles do not signi-ficantly influence these parameters. For this reason, A, YI, and YX are fit I as a function of burnup and enrichment only.
The thermal microscopic absorption cross section of xenon is I dependent upon the neutro~ energy spectrum in the fuel pellet. The neutron I  spectrum i~ in turn,dependent upon the amounts of absorbing and fissile material in the fuel and the moderation which occurs outside the fuel pellet.
I  Therefore, cr!~ is fit as a function of burnup, xenon concentration and enrich-ment. To account for the spectral effects of the moderator, the multiplier I                                        3-8

I I for axe, (SIGM), is fit as a function of soluble boron concentration and a2 moderator specific volume.
I 3.2.2   Method of Calculating Input Data for the Burnable Poison Rodded Assembly I 3.2.2.1   Introduction
*~            The input data for an assembly containing burnable poison (BP) rods are calculated with the Vepco PDQ07 Discrete Model using a 2-D, quarter-assembly I representation. Theoretically, these data could be obtained by NULIF supercell calculations (as described in Section 3.2.3 above) in which one of the subcells I contains the appropriate amount of BP. However, the fact that the hetergeneous I effect of the various subcells are accounted for by applying thermal flux depres-sion factors determined from quarter assembly discrete calculations must be con-I sidered. In general, for assemblies containing no BP, these flux depression factors do not change significantly as a function of burnup,    so that the flux I depression factors calculated at zero burnup are adequate at any stage of deple-I tion. However, this is not the case for subcells containing BP because the BP depletes rapidly with increasing burnup causing the flux depression factors I to vary significantly with burnup. Since a large number of quarter-assembly discrete calculations would have to be made to calculate these factors for input I to NULIF, it has been decided to use the quarter assembly runs directly to generate Ka, multipliers to account for BP reactivity effects. These multipliers I (in conjunction with the Ka, data for the non-rodded fuel assembly discussed in I Section 3.2~.1) are applied to nodes which contain (or have contained) BP rods.
Four Ka, multipliers are used in the Vepco FLAHE Model to represent I BP rods~   Two multipliers represent the presence of fresh BP in a fuel assembly.
The third multiplier accounts for the presence of depleted BP. The fourth Ka, I                                      3-9 I
I

I I multiplier is used to represent the reactivity "after-effect" resulting from I the depletion of a fuel assembly containing fresh BP rods.
I 3.2.2.2   K-Infinity Multipliers-For Fuel Containing Fresh BP The presence of fresh BP rods in a fuel assembly changes that I assembly's characteristics in two ways. First, a large concentration of non-fissile, neutron absorbing material is added to the assembly.      Second, moderator I is displaced from the assembly. The reactivity effects associated with these I changes depend on initial assembly enrichment, cumulative     burnup of the assembly while BP rods are present, soluble boron concentration, and moderator I temperature. To represent these effects, two~ multipliers are used.
The first Ko, multiplier table for BP accounts for the dependence on I enrichment, cummulative burnup,_and soluble boron concentration.      To generate this table, assemblies of various enrichments are depleted at nominal moderator I and fuel temperatures with and without BP rods using a quarter assembly repre-I sentation of the Vepco PDQ07 Discrete Model. At a number of burnup points, recovery cases are performed during which the soluble boron concentration is I changed. The values of the first Koo multiplier are then obtained by ratioing Koo in the rodded state to Koo  in the non-rodded state. The PICCOLO code is I used   to tabulate these values as a function of cumulative    burnup, initial enrichment, and soluble boron concentration. This procedure is followed to I construct separate tables for configurations of 8, 12, 16, *and 20 BP rods per I assembly.
The second Ko,  multiplier accounts for the variation in the reactivity I effect of fresh BP with changes in moderator temperature. Sensitivity calcula-tions have shown that this multiplier is not significantly affected by enrichment I or number of BP rods per assembly. (lQ)    Therefore, the second K00 multiplier is generated for an assembly of average enrichment (i.e., 2.90 w/o      U235) containing I
I                                        3-10

I I - the most commonly used configuration of BP rods (i.e., 12 fresh BP rods per I   assembly). Again using the Vepco PDQ07 Discrete Model, a 2.90 w/o enriched
_assembly is first depleted with 12 fresh BP rods present and then depleted I  without the presence of any BP. At several burnup points during the above two depletions, additional cases are performed in which moderator temperature I   and soluble boron concentration are varied simultaneously. The values of the second K00 multiplier are obtained in two steps. First, for each set of I   conditions, the value of K00 obtained from the depletion case with BP rods I   is divided by the value of Koo obtained from the depletion case without BP rods. Then the ratios determined in the first step are divided by the ratio I   of Koo with BP rods to K00 without BP rods obtained for the nominal moderator temperature (i.e., 566&deg;F). The PICCOLO code is then used to tabulate these I   values in a form acceptable to the FLAME3 code as a function of cumulative burnup, soluble boron concentration, and moderator temperature.
I 3.2.2.3   K-Infinity Multipliers for Fuel Containing Depleted BP I             To account for the presence of depleted BP in a fuel assembly:, a third~ multiplier is used.      As the BP rods in an assembly are depleted, the I   boron concentration decreases rapidly. At the end of one cycle of burnup, I   the boron concentration in the BP rods may be assumed to be zero. When these depleted BP rods are inserted in other assemblies, their principal I   effects are the displacement of water and absorption of neutrons in stainless steel. Sensitivity calculations have shown that this multiplier is not sig-_
I  nificantly affected by enrichment.(lO)      The only configuration of depleted BP I   rods used in Cycles 1 through 4 of Surry Units 1 and 2 is 12 rods per assem-bly. Therefore, this multiplier is generated for an assembly of average I   enrichment (i.e., 2.90 w/o U235) containing 12 depleted BP rods. Using the Vepco PDQ07 Discrete Model, a 2.90 w/o enriched assembly is depleted both I  with and without    12 depleted BP rods. At several burnup points additional I                                          3-11

I I  cases are performed for which moderator temperature and       soluble boron concen-I  tration are varied simultaneously.      The values of the third Koo multiplier are obtained by dividing K.n* with depleted BP by K;.; without BP. The PICCOLO code I  is then used to tabulate these values for input to the FLAME3 code as a I  function of total burnup, moderator temperature, and soluble boron concentration.
3.2.2.4  K-Infinity Multiplier for the "After Effect".of Fresh BP I            The presence of fresh BP rods in a fuel assembly during depletion I  also affects the reactivity in that assembly after the BP rods are removed.
This BP "after-effect" arises from the change in isotopics accompanying I  depletion of the fuel assembly in the harder neutron spectrum resulting from the presence of fresh BP rods.      Once the BP rods are removed, the after-effect I  diminishes with continued depletion of the assembly.      To represent this effect, assemblies of various enrichments are depleted in two ways using a quarter I  assembly representation of the Vepco PDQ07 Discrete Model.       First, an I  assembly is depleted without BP rods.      Second, an assembly of the same enrich-ment containing 12 BP rods is depleted to various burnups.       Then, the BP rods I  are removed, and the assembly is depleted further.      The values of the fourth Ka, multiplier for BP are obtained by dividing Ka, from the assembly which has I  had BP by :IC.,, of the assembly which has not had BP. The PICCOLO code is used to tabulate these values as a function of cumulative burnup experienced by I  the assembly with BP rods present, total burnup~ and enrichment.
I 3.2.3   Method of Calculating Input Data for the Control Rodded Assembly 3.2.3.1   Introduction I            The input data for assemblies containing control rods are generated I in a manner similar to that used to generate the BP data (Section 3.2.2).
Again, a quarter-assembly representation of the Vepco PDQ07 Discrete Model I is used to perform all the basic calculations, while the PICCOLO code is I                                          3-12

I I used to construct the tables for input to the FLAME3 code.
I            Four K:x, multipliers are used in the Vepco FLAME Model to represent control rods. Three multipliers represent the presence of control rods in a I fuel assembly. The fourth K:x, multiplier is used to account for the reactivity I "after-effect" resulting from the depletion of a fuel assembly containing control rods.
I 3.2.3.2   K-Infinity Multipliers for Fuel Containing Control Rods.
I            The presence of control rods in a fuel assembly has much the same effect as the presence of fresh BP in an assembly.      First, a large con-I centration of non-fissile, neutron absorbing material is added to the assembly.
Second, moderator is displaced from the assembly.       The react~vity effects I associated with the presence of control rods depend on initial assembly enrich-ment,  cumulative burnup of the assembly while the rods are present, total I assembly burnup, soluble boron concentration, and moderator temperature.
I To represent these effects, two Koo multipliers are used.
The first Koo multiplier accounts for the dependence on enrichment, I moderator temperature, and soluble boron concentration.      To generate the values for this multiplier, calculations are performed for assemblies of I various enrichments with and without control rods using the Vepco PDQ07 Discrete Model. These calculations are done at zero burnup and with different I values of soluble boron concentration and moderator temperature.      The values I of the first Koo multiplier are obtained by ratioi,ng Ka, in the rodded condition to K~ in the non-rodded condition.
I            The second K;., multiplier accounts for the variation in the reactivity effect of control rods with changes in assembly burnup.      The values of the I second Koo multiplier are generated by depleting assemblies of various enrichments I at constant soluble boron concentration and moderator temperature using the Vepco PDQ07 Discrete Model. At various burnup points, separate recovery cases I                                         3-13

I I are performed during which control rods are inserted.      To calculate the values of the multiplier, the ratio of K00 with the control rods to K00 without control I rods at each burnup point is divided by the ratio of K00 with control rods to Koo without control rods at *zero burnup *
.1            The third K00 multiplier accounts for the dependence on cumulative burnup of fuel while control rods are present.      The change in isotopics accom-I panying depletion of an assembly containing control rods can result in signi-I ficant reactivity variations while the control rods are still in the assembly.
While the input data for BP include this effect in the first K00 multiplier for I BP (Section 3.2.2.2), a separate multiplier is used to represent this effect for control rods. To generate the values for this multiplier, assemblies of various I enrichments are depleted with constant moderator temperature and soluble boron I concentration in the following manner:
: 1)  an assembly containing control rods is depleted to various I                burnups,
: 2)  at .these burnups, the control rods are removed and the I                assembly is depleted further,
: 3)  recovery cases are performed at various burnup points in I                the non-rodded portion of the depletion for which the control I                rods are reinserted.
The values of the third K00 multiplier for control rods are obtained in two I steps. First, for a particular combination of cumulative     and total burnup, the value of~ with control rods is divided by the value of Kro without I  control rods. Second, these values are divided by the ratio of K00 with and without control rods obtained at zero      cumulative and zero total burnup.
I, 3.2.3.3   K-Infinity Multiplier for the "After Effect" of Control Rods I             The method by which the fourth K00 multiplier for control rods is generated is the same as the method described in Section 3.2.1.4 for the fourth I
I                                       3-14

I I Ka, multiplier for BP.      First, an assembly is depleted without control rods using the Vepco PDQ07 Discrete Model.       Second, an assembly of the same enrich-I ment containing control rods is depleted to various burnups.        Then the rods areremoved, and the assembly is depleted further.        The values of the fourth I Koo multiplier for control rods are obtained by dividing Ka, from the assembly I which has had control rods by Ka, of the assembly which has not had control rods present.
I 3.3      Thermal~Hydraulic Feedback Parameters I               Thermal-hydraulic feedback effects are represented in the Vepco FLAME Model in order to more accurately calculate _the power distribution.
I The thermal-hydraulic feedback model incorporated in the FLAME3 code is the same as the feedback model used in the PDQ07 code portion of the Vepco I PDQ07 Discrete Model. ( )
7 The input required consists.of:
I               1) 2)
Coolant inlet enthalpy, Heated perimeter per unit area of flow, I               3)  Flow area of the fuel assembly per total cross-sectional area of the assembly, I               4)  ~ystem pressure,
: 5)  Difference between average fuel temperature and moderator tempera-I                   ture as a function of relative power density.
I               The feedback calculation is performed tn the following manner.
an initial estimate of the fuel and moderator temperatures is made for each First, I coolant channel.      Based on this estimate and the function tables supplied, the FL.AJ.'1E3 code calculates the K-infinity and the migration area for each node. T~ese I parameters are then used to calculate the power density in each node.        This power distribution is used to compute new fuel and moderator temperatures for I each channel.      In turn, the new fuel and moderator temperatures are used to I                                        3-15 I

I I  calculate new K-infinities and migration areas for another power distribution I  calculation. This process.is continued until the power density for each node in the Nth iteration differs from the power density in the N-l~h iteration by I  less than the specified convergence criterion.
I  3.4  Xenon Concentration Calculation The Vepco FL1'..ME Model represents the xenon reactivity effect as a I  functional dependence of the basic Kmon xenon concentration (refer to Section 3.2.1.1). The xenon and iodine concentrations at each node ate calculated I  using the parameters described in Section 3.2.1.3 and the assumption of I  constant flux and power throughout the duration of a time/burnup step.
Wfth the assumption of constant power and flux, the differential equations I which describe the dependence of xenon and iodine concentration are solved by integration over the time step interval, tt.
I           The nodal iodine concentration, Ii(t) (atoms/barn-cm), is cal-culated with Equation 3.1:
I I
(3.1)
I where I
I              Ai, Yli are given in Section 3.2.1.3, p      = core power (watts),
core 3
V      = core volume (cm),
core
'I               Si = relative power density at node i, AI  = decay constant of Iodine-135.
I
 *I                                      3-16

I I
I           The nodal xenon.concentration, Xi(t) (atoms/barn-cm), is cal-culated with Equation 3.2:
I
                                                       - I i (t-6t)J
* exp (-A I 6t)
I I
I                                                                           (3. 2)
I                          Xe where     G2 =Ax+ oai(t-6t)*Gl, I             Xe oai Xe
                  = oa 2 i*SIGMi = t?ermal microscopic absorption cross .section I                                 of Xenon-135 (barns),
AX = decay constant of Xenon-135, I                  Xe YXi, oa 2 i' SIGMi are given in Section 3.2.1.3, and other para-meters are as previously defined for Equation 3.1.
.I I
I I
I I
I I

I
:I
                        *sEC.TION, 4*-'- **cALCULATIONAL TECHNIQUES I 4.1    Power Distribution Normalization The FLAME3 code provides two means by which the predicted power I distribution may be normalized to the results of either measurements or I another calculational model (e.g., Vepco PDQ07 Discrete Model).
normalization factors which may be used are 1) leakage parameters (radial The two I and/or axi?l albedoes) and 2) migration area multipliers.
For FLAME3 calculations, all the nodes modeled are inside the I core. The presence of the reflector is represented by leakage parameters (albedoes) which may be input for peripheral nodes.
I             The migration area multiplier is intended to correct a limitation I in the FLARE neutron source option.           This limitation arises from the inability of the FLARE option to account for spectral effects in assemblies containing I burnable poison or control rods.           The result of this limitation is that the power may be somewhat underpredicted in these assemblies.           The migration I area multiplier may also be used to "fine-tune" the radial power. distribution
 *1 of interior located assemblies that do not necessarily contain burnable poison.
I 4.1.1    Radial Power Distribution The radial power distribution calculated with the Vepco FLAME Model I is normalized to the radial power distribution calculated with the Vepco I PDQ07 Discrete Model.       This normalization is       generally accomplished by using a combination of radial albedoes and migration area multipliers.             Radial
*I  albedoes are chosen so that the desired in-out power sharing and peripheral powers are given by the FLAME3 code.           The migration area multipliers are I used* to "!ine* tune"* the* radial -power *distribution at ii:i.terior assembly locations.
I I                                                4-1

I I           The radial power distribution is normalized for two sets of condi-I tions. The first set of conditions consists of cycle depletion calculations where normalization is performed for the all rods out (ARO), hot full power I (HFP) condition. The design objective is to maintain less than a 5% dif-ference between the assemblywise radial powers computed by the Vepco FLAME I and PDQ07 Discrete Models throughout each cycle. The reason for this 5%
I limit is to insure that acceptable burnup distributions will be calculated during depletion. For "short" (e.g., annual) cycles in which relatively I little  fresh BP is used, the normalization factors for beginning of cycle (BOC) generally yield acceptable radial power dis*tributions throughout the I cycle. However for "long" cycles (i.e., 18 month.cycles) which contain large numbers  of fresh fuel assemblies and BP rods, it is necessary to I renormalize the in-out power sharing (i~e., change radial albedoes) at I approximately the middle of cycle (MOC) to maintain acceptable agreement in radial power distribution.
I           The second set of conditions at which the radial power distribution is normalized is BOC, HZP with control banks C and D inserted in the core. The I                                                                2 primary purpose for this normalization is to find the proper M multiplier for control rodded assemblies. For cases at less than full power and with I control rods inserted, the radial albedoes for HFP, ARO provide acceptable I peripheral powers so that changing the peripheral albedoes at HZP is usually not required. The acceptance criterion of 5% difference between the Vepco I FLAME and PDQ07 Discrete Models is relaxed for rodded cases in which no depletion is required (e.g., HZP and HFP rod worths), because variations in I radial power distribution have been demonstrated to have little affect on the axial information calculated.with the FLAME model.(ll)
I I                                     4-2 I

I I
I 4.1.2   Axial Power Distribution I            Normalizatjon of the axial power distribution calculated by the FLAME model is required only for zero or part power cas~s of annual cycles containing little fresh BP. In these cases, a generic value of I  the axial albedo gives close agreement between measured and calculated axial power distributions for HZP. For part power situations, the* axial I albedo is taken to be a percentage of the HZP value.
I 4.2   Differential and Integral Control Rod Worths as a Function of Bank Position Differential and integral control rod worths are calculated I with the Vepco FLAME Model in two steps. First, a series of cases is run with the FLAME3    code in which all reactor parameters are held constant I except for the position of the rod bank(s) whose worth is to be determined.
For example*, if the differential and integral worths of control bank D I are required, the following set of cases is analyzed:
: 1)   all rods out
: 2)   D bank inserted in the top node of the appropriate assemblies I            3)   D bank inserted in the top 2 nodes of the appropriate assemblies n+l)   D bank inserted in the top n nodes of the appropriate I                   assemblies last)   D 'bank fully inserted into the core.
I The change in core reactivity resulting from each movement of the rod bank(s)
I is a direct measure of the control.-rod bank(s) differential worth. The second step in the process of calculating bank worths is normalization to results I from the Vepco PDQ07 Discrete Model. The discrete model is the production calculational model for determining total integral control rod worths.       There-I I                                        4-3

I I
:1 fore, a normalization factor is applied to the results obtained with the I FLAME3 code to assure that the total integral worth predicted by the Vepco FLAME Model is the same as that predicted by the Vepco PDQ07 Discrete Model.
I           Based on the methodology outlined above, the following equations are used to.compute the rod worths:
I           Differential Worth at                                          (4.1)
Node 'i' (pcm/step)   =
I                                     ko   ki Integral Worth at                    105 xN (4.2)
I           Node I i I (pcm)      =   ko X ki X
ko = eigenvalue given by FLAME3 for the control bank out, I where i
k = eigenvalue given by FLAME3 for the control bank inserted in the 1th node, SPN = number of steps of control rod movement per node, I           N*= total integral worth from Vepco PDQ07 Discrete Model divided by total integral worth from Vepco FLAME Model.
I I
I I
I I
I I                                      4-4

I I                               SECTION 5 - RESULTS 5.1  Introduc.tiQn I           The purpose of this section is to demonstrate the predictive I capability of the Vepco FLAME Model for calculations of axial power dis-tributions, axial offsets, and differential and integral control rod I worths. As explained in the previous section, the radial power distribution calculated with the Vepco FLAME Model is normalized to a 2-D (x, y) dis-I crete power distribution calculated with the Vepco PDQ07 Discrete Model I prior to initiating axially dependent calculations. Therefore, this section presents 1) typical radial power distribution comparisons between the Vepco I FLAME Model (after normalization) and the PDQ07 Discrete Model, and 2) comparisons to measured data taken at the Surry Nuclear Power Stations for I axial power distribution, axial offset, and differential and integral rod worths. The specific types of results compared are presented in Table 5-1.
I 5.2  Radial Power Distribution I           As discussed in Section 4.1.1, radial power distributions calculated I with the Vepco FL.Af,fE Model are normalized to 2-D (x, y) discrete model power distributions calculated at the ARO, HFP condition as a function of I burnup. The power distribution comparisons given in Figures 5-1 through 5-4 for Surry 1, Cycle 1 and in Figures 5-5 through 5-8 for Surry 1, I Cycle 4 are representative of the agreement obtained between the Vepco FLAME Model (after normalization) and the Vepco PDQ07 Discrete Model.
I           Normally, it is desirable to maintain the assemblywise agreement I
11 in radial power distribution to less than a 5% difference, but this       administra-tive" limit is usually relaxed if -violations only occur infrequently in a I small number of fuel assemblies. The reason for this limit is to ensure that the accumulated assemblywise burnup obtained during a cycle depletion will be I acceptable. This limit may also be relaxed for power distributions associated 5-1 I

I I with non-depletion types of calculations (e.g., rod worths), since it has I beeri demonstrated to have little impact based on sensitivity studies.    (11)
I 5.3   Axial Power Distribution Axial power distribution and axial offset comparisons between II the Vepco FLAME Model and measurements are presented in this section for core conditions ranging from beginning-of-cycle (BOC) to end-of-cycle I (EOC) at hot zero power (HZP) and hot full power (HFP).
,I            In general, the Vepco Flame Model predictions attempted to simulate the actual core conditions in terms of power level, core burnup, I and control rod position. However, for reasons of increased calcula-tional efficiency, the Vepco FLAME Model does not explicitly represent I the effect of spacer grids, nor can the control rod position be exactly specified (due to the limitations of the axial mesh spacing). However, I the accuracy that is compromised for the increased calculational effi-I ciency is not significant.
Representative axial power distribution comparisons are presented I for Surry 1, Cycle 1, Surry 2, Cycle 3, Surry 1, Cycle 4 and Surry 2, Cycle 4. Figures 5-9 and 5-10 give the Surry 1, Cycle 1 core average I axial power distribution at BOC, HZP. for D-Bank partially inserted and near fully *inserted, respectively. The axial power distribution of an I individual assembly (B-8) containing a partially insert'ed control rod I (same core conditions as for Figure 5-10) is provided in Figure 5-11.
Surry 2, Cycle 3_axial power distribution comparisons are presented in I Figures 5-12 and 5-13 at BOC, HZP conditions for ARO and D-bank inserted.
Additionally, comparisons at HFP, ARO at approximately BOC, MOC, and EOC I conditions are ,given in Figures 5-14 through 5-16. Similar comparisons for Surry 1 and 2 Cycles 4 are provided in Figures 5-17 through 5-20and I 5-21 through 5-23, respectively. Measured and predicted axial I                                     5-2

I
:1    offset comparisons are also indicated on Figures 5-9 through 5-23, I    as appropriate.
*1    5.4   Differential And Integral Rod Worths Results of the Vepco FLAME Model predictions and startup physics I    measurements for differential and integral control rod bank worths for the first four cycles of Surry Units No. 1 and 2 are presented in this I    section. It should be noted that Surry 2, Cycle 1 results are not given, since they are essentially identical to Surry 1, Cycle 1.
I               Figures 5-24 through 5-27 provide the Surry 1, Cycle 1 indivi-I    dual differential *and integral bank worths for Banks D through A, respec-tively. Also worths for Banks D through B moving in 100 step overlap are I    given in Figure 5-28. For Cycles 2 and 3 of both Surry Units 1 and 2, only banks D and C control rod worths were measured during startup physics I    testing. These results for Surry 1, Cycle 2 and Surry 2, Cycle 3 are 1*   compared to Vepco FLAME Model predictions in Figures 5~29 through 5-32.
* Measurements taken for Banks D through A during the startup of Surry 1, I    Cycle 4 are compared with Vepco FLAME Model predictions in Figures 5-33 through 5-36 and in Figure 5-37 for the 100 step overlap mode. Similar I    comparisons for Surry 2, Cycle 4 are displayed in Figures 5-38 through 5-42.
I I
I I
I                                        5-3 I

I                                TABLE 5-1

==SUMMARY==
OF COMPARISONS I
Reactor Condition At                            Reference To I Type of Comparison     Which Comparision Is Made Radial P*ower Distribution Figure I                        Unit Unit 1,
1, Cycle Cycle 1,
1, HZP, ARO, HFP, ARO, BOC BOC 5-1 5-2 Unit 1, Cycle  1, HFP, ARO,     MOC                   5-3 I                        Unit 1, Cycle  1, HFP, ARO,     EOC                   5-4 5-5 Unit 1, Cycle  4, HZP,   ARO,   BOC I                        Unit Unit Unit 1,
1, 1,
Cycle Cycle Cycle 4,
4, 4,
HFP, HFP, HFP, ARO,
                                                  '.ARO, ARO, BOC MOC EOC 5-6 5-7 5-8 I AxiaLPower Distribution Unit 1, Cycle 1, HZP, D@,204, 70 HWD/Mru              5-9 I                        Unit 1, Cycle 1, HZP, D@ 26, 70 MWD/MTU Unit 1, Cycle 1, HZP, D@ 26, 70 MWD/MTU Assembly B-8 5-10 5-11 I                        Unit Unit 2,
2, Cycle Cycle 3,
3,
                                           *HZP, HZP, D@ 202, 0 MWD/MTU Din, 0 MWD/MTU 5-12 5-13 Unit 2, Cycle  3,  HFP,  D@ 219, 150 MWD/MTU          5-14 I                        Unit Unit 2,
2, Cycle Cycle 3,
3, HFP, HFP, D@,221, 3920 MWD/MTU ARO, 7740 MWD/MTU 5-15 5-16 Unit 1, Cycle  4,  HZP,   D@  220,  0 MWD/MTU         5-17 I                        Unit Unit 1,
1, Cycle Cycle 4,
4, HFP, HFP, D@
D@
215, 206, 150 MWD/MTU 7715 MWD/MTU 5-18 5-19 Unit 1, Cycle  4,  HFP,   D@  220,  12585 MWD/MTU     5-20 I                        Unit 2, Cycle 4, HZP, ARO, 0 MWD/MTU Unit 2, Cycle 4, HFP, ARO, 204 MWD/MTU 5-21 5-22 Unit 2, Cycle 4, HFP, D@ 210, 6986 MWD/MTU            5-23 I Differential and Integral Rod Worths I                        Unit 1, Cycle 1, HZP, BOC, Unit 1, Cycle 1, HZP, BOC, Unit 1, Cycle 1, HZP, BOC, D-Bank C-Bank B-Bank 5-24 5-25 5-26 I                        Unit 1, Cycle 1, HZP, BOC, Unit 1, Cycle 1, HZP, BOC, in 100 step overlap mode A-Bank B through D 5-27 5-28 I                        Unit 1, Cycle 2, HZP, BOC, D-Bank Unit 1, Cycle 2, HZP, BOC, C-Bank 5-29 5-30 I                        Unit 2, Cycle 3, HZP, BOC, D-Bank Unit 2, Cycle 3, HZP, BOC, C-Bank 5-31 5-32 Unit 1, Cycle  4,  HZP,   BOC,  D-Bank                5-33 I                        Unit Unit Unit 1,
1, 1,
Cycle Cycle Cycle 4,
4, 4,
HZP, HZP, HZP, BOC, BOC, BOC, C-Bank B-Bank A-Bank 5-34 5-35 5-36 I                                   5-4

I                                 TABLE 5-1

==SUMMARY==
OF COMPARISONS (Cont~nued)
I Reactor Condition At                 Reference To I Type of Comparison     Which Comparison is Made Differential and Integral Rod Worths (cont.)
Figures I                        Unit 1, Cycle 4, HZP, BOC, A through D in 100 step overlap mode 5-37 I                        Unit 2, Cycle 4, HZP, BOC, Unit 2, Cycle 4, HZP, BOC, D-Bank C-Bank 5-38 5-39 Unit 2, Cycle 4, HZP, BOC, B-Bank          5-40 I                        Unit 2, Cycle 4, HZP, BOC, Unit 2, Cycle 4, HZP, BOC, in 100 step overlap mode A-Bank A through D 5-41 5-42 I
I I
I I
I I
I I
I I
I                                5-5 I

ii                                                       FIGURE 5-1
*I.
I I      .
                    . 08        09     * *10 RADIAL POWER DISTRIBUTION COMPARISON
                                           .. FOR SURRY l *, CY CLE 1, HZP , ARO, BOC 11         12          13     14 15 I,
I.
r H
1.158.
1.1895
                 +2. 7
* Iii '.
DDDDDD 1.243       1.144 J
1.2971     1.1708
                 +4.4 1:I                        +2.3
  \ *1 I ;
1 K
1.134 1.1550
                 +1.9 1.214 1.2563
                            +3.5 1.098
                                     -1.1098
                                      +1.1 DODD ___
1.197      1.097 DOD 1.143        . 0. 998
: 1. 2279    .l!.1031  1.1640         0.9896
                +2.6      . +0.6      +1.8           -0.8 D
1.084       1.154     1.019          0.990        0.774 M
1.0748      1.1630    1.0027         0.9941       0.7630
                -0.8       .+0.8      -1.6           +0.4         +1.4 1.144       1.047     1.047        . o. 943       0.626 N   1.1342      1. 0208  1.0525          0.9230       0.6109
                -0.9        -2.5     +0.5            -2.1         -2.4             -
0.995       1.103    0.975           0.625 p   0.9809      1. 0929  0.9580          0.6108
                -1.4       -0.9      -1. 7           -2.3 0.872      0.657 R   o. 8564 . 0.6445
                -1.8       -1.9 I.; :
PDQ07 I ~-
FLAME
                                          ~%
I. ~-
   .. ~
5-6 I

I                                                                   FIGURE 5-2 RADIAL POWER DISTRIBUTION COMPARISON I                                        FOR SURRY 1 , CYCLE 1 , HFP , . ARO, BOC I           08          09            10                    11            12   13 14 15 I  H 1.1641 1.1699 H-0 .5    '
I DDDDDD
: 1. 2425       1.1519 J   1.2630        1.1558 I    +1.6
                    +o.3
                               ~-u~~~*DDDDI
                      \
:1 K 1.1417 1.1434 1.2158 1.2323 .
     +o.2           +1.4 I
I L
1.1982
: 1. 2092 1.1057 1.1015
                                                                  .-0D D -
                                                      ~_i_:~_~_:~_-
D i------'-------
      +o.9          -0.4       ...+o_i_J_:_~_~..........
1.0878        1.1522.        1.0276               0.998l.
                           *"*                                         0.793T 1.0751        1.1539'        1.0143 . L0113                     0.7988
      -1.2          +o.l          -1.3 .              +L3.            _+o.6     .
1.1322        1.0413 1.0212 1.0356 1.0499
                                                    ====
                                                      . 0-.9393
: 0. 935.5 0.-6414 0.6442 1.1226    I*
      -0.8          -1.9          +1.4                -0.4            +o.4 0.9835        1.0783.        0.9578               0.6270 0.9767        1.0696         0.-9453 . 0.6293 .
      -0.7          -0.8          -1.3 .              +o.4
____,,,I.__.____. :::=======:::..':::!=====-.i 0.8605        0.6526 0.6553 .
I R   0.8537
      -0.8          +o.4 I
* PDQ07 I                                 *FLAME I                                                                      5-7 I

I                                                              FIGURE 5-3 I                                         RADIAL POWER DISTRIBUTION COUPARISON FOR SURRY 1, CYCLE 1, HFP, ARO, MOC I            08          09           10                  11         12     13   14 15 I  H 1.1290 1.1330
        +o.4 I
DDDDDD
: 1. 2249      1.1273 .
J
: 1. 2288      1.1320
.I      +o.3        +o.4 I
I DODD 1.1248       1.2186        1..1155 1.1301     . 1.,2238       1.1219 K                              +Q,'6
        +o.5        +o.4
*.1 I
L 1.2095 1.2149
        +o.4 1.1115 1.1174
                    +o.5.
1.1901 1... 1956
                                   +o.5 l.0646DDD 1..0710
                                                  +o.6 I            1r           !I                              '
I  M
: 1. 0920 1.0961 1.177 3 1.1801 1.0639' 1.0647
                                   +0.1
* 1..0772 L:0859
                                                  +o*.8 0.8549 0.8639'
                                                                 +1.1
        +o.4        +0.2 I       1.1295 '     1. 0332'      1.0649        . 0.9825        0.6601 I N    1.1271
        -0.2*
1.0323 .
                    -0.1 1.0733' . 0.9630' . 0.6571
                                   +0.8           -2.0 .         -0.5 I p 0.9288
: 0. 9309
        +0.2
: 1. 0140
: o. 9963 .
                    -1. 7 t  0.8825 0.8747
                                   -0. 9      .
o ... 6152 0.6070
                                                  -0.9 I      0.7427       0.5884 I      0.7348 R -1.1 0.5865
                    -0.3 I
 *I                              @l     LAME
                                             ~
I I                                                                5-8
* FIGURE 5-4 RADIAL POWER DISTRIBUTION c*oMPARISON FOR SURRY 1, CYCLE 1, HFP, .ARO, EOC 08          09            10               11            12        13 14 15 1.0613 .
: 1. 0585 *,
     -0. 3 .
DDDDDD 1.1635         1. 0659 1.1636         1.0626'
     +a.a           -0.3
                     \              ..
DODD
: 1. 0695        1.1722      1.-0757 1.0659         1.1710      1. 0714
     -0.3 *         -0.1        -0.4
.1                                  ..
i.-1782 .
DOD 1.1761         1. 0763                     1.0650 I    1.1745 L -0.1
: 1. 0720
                    -0.4 1.1749
                                -o:~3
* 1.0621
                                               -0.3 .
I I
M  1. 0717 1.0681
     -0.3 II 1.1723 1.1692
                    -0.3 11 1.0660 1.0581
                                -0.l I1   ..
1~i216 1.1193J*
                                                +0.1     *
                                                               . 0~9005 ...
                                                             --o-*.-as_9_4_*
                                                               +1.2 LJ        .,.
1.1391         1. 0354      1.10(}3 . .1.-0346             0.6880 I N  1.1389
     -0.0
: 1. 0346
                    -0.1 1.1064
                                +0.6 1.-0166
                                               -1.7 0.6947
                                                               +1..d I p 0.9363 0.9494 .
1.0323
: 1. 0257 0.-8856 0.8871 0-.6351 0.-6388
     +1.4           -0.6        +o.2           +o.6 I
     ~
0.6005 I R  0.7560
     +2.0 0.6155
                    +2.5 I
PDQ07 I                               FLAME 6.%
I 5-9 I

I                                                                FIGURE 5-5 RADIAL POWER DISTRIBUTION COMPARISON I                                             F.OR .SURRY 1; CYCLE 4, HZP, ARO, BOC I             08 09           10               11          12      13   14    15 I   H 0.783
: o. 7635
         -2.5 '
I, I
J 1.039*
1.0722
         +3.2
_ _ ..____.1;~~
2 DDDDDD I K ~i;fi1               ;)~;4 ~;~!11 DD DD
:   L -~-i-~_!~_  9 1
t_:;_i_i__. : t: ~:j:~:
3 9
                                                    .._t_:;_i_6__, D DD LJ*
11              11            1 1 I   M 1.113 1.0890
                     't' 1.
1.078 0606
* L153 1.15 39 1,108*
1.1145 1.029
: 1. 0 391
         -2.2            -1.6           +o.l           +o.6          +1.0 I        0.954        I  l. 208         1.078         .1.030         0.689 N    0.9242       "J.:*             1.0577         1.0339        0.6967 I       -3.1          [3.1 1702
                                        -1.9           +o.4          +1.0 I  p
        -1.075 1.0302 1.091 1.1194 0.967 0.9837 0.634 0.6421                        ., .
         "'."4.2         +2.6           +1. 7          +1.3 I     ----
0.810           0.627
                              }.
0.8057          0.6268 I R
         -0.5            -0.0 1
I I
I                                                                  5-10 I

I                                                                 FIGURE 5-6 I                                            RADIAL POWER DISTRIBUTION.COMPARISON
_.FOR SURRY 1, CYCLE 4, HFP, ARO, BOC
-I          08           09           1Q                 11 .           12   13    14 15
*I  H 0.820 0.8139  '
       -0.7 I  J  1.067 1.0962
      +2.7 1.io8 1.1489
                      +3.7 DDDDDD 0.930 0.9300 0.0 r~.040
: 1. 0616
                      +2.1
: 1. 093 ..
1.-097
: 1. 0737
                                    -2.1         DODD~
DOD 1.037                        1.071           1.132" 1.0347          1.1097        1. 0785         1.1194*
      -0.2            +1.5          +o.7            -1.1 Ir                               .
t~i~ LJ
                  !I            l1                               *j I 1.103 M
            ----'~~81._~_;;_!_~6_.. ,.
: 1. 0886
      -1.3 .                                     '--~~-*~_[_;7_*__,
N 0.954 0.9419           :i!~o i: ~:~4 "i: ~~r2 ,--~-:-;~-l-2---.
I    -1.3 3 *6        -1. 7            -0
* 3 .          +1. 7 I
I p i.082 1.0394
      -3_._9_ _ _~
[l  093 .
1:1087
                      +1.4 .
0.976 0.9839
                                   +o*.8 0.652 0.6656
                                                    +2.1 I R 0.837 0.8379
      +o.l J
G::~~4 IJ1.1
 *1
                                   -PDQ07 I                                 FLAME I                                                                    5-11 I

I                                                     FIGURE 5-7 RADIAL POWER DISTRIBUTION COMPARISON I                                     FOR SURRY 1, CYCLE 4, HFP, ARO, MOC 08
* 09           10              11                13      14 1.5
: 0. 937
: o. 9228,
      -1.5 11.198 1.233 1.1850    I 1. 2102
      -2.9      I
     ----         ~LO II         - 11           11            I I LJ 1.085       1.103         1.106         1.06T        0.938 M                                          1.0890       0.9728
: 1. 0793     1.1046        1.1332
      -0.5        +0.1         +2.5           +2.1.        +3. 7 0.877 '     1.069         1.070       . 1.001        0.662 N  0. 8779     1. 0868       1. 0641       1.0087       0.6742
.I    +O.l        +1.7          -0.6          +o.8         +1.8 I p 0-~913 0.9004
      -1.4 0.979
: o. 9940
                  +1.5 0.868 0.8812
                                +1.5 0.613 0.6169
                                              +o.6
     -;~II o.;~~2 0.567 o.5640
       +o:o      ~-
PDQ07 FLAME                 '
11%
5-12

I                                                                FIGURE 5-8 I                                                RADIAL POWER DISTRIBUTION COMPARISON FPR SURRY 1, CYCLE 4, HFP, ARO, EOC I                    08           09         10             11         12      13     14 15 I      H 0.908 0.8966
                 -1.3 '
I                               1.132**
DDDDDD 1.179 J         J..1291        1.1400 I                -4.2           +0.7
                                \
I DODD 1..037         1.227      1.140 K         1. 0136"       1.1757     1.1028
                 -2. 3 .        -4.2       -3."3 .
I DOD 1.231          1.225      1.214        1.100 L         1.1708         1.2222     1.1638       1.0939*
I                -4.9           -0.2       --4.1        -0.6 Ii          !I           11            !
I     M 1.078
                 ;L.0678 .
                 -0.9 1.137 1.1179
                                -1. 7 1.100.
: 1. 0981
                                           -0.2 1.083 I&deg;. 0838
                                                        +o.l 0.934 0.9584
                                                                     +2.6 u  .
* I               0.878          1.054      1.096        1.021        0.669 I     N 0.8793
                 +o.l 1.0604
                                +o.6 1.0789
                                           -1.6 1.031_9
                                                        +1.1 0.6932
                                                                     +3.'6 I      p 0.899 0.9220
                 +2.6 0.982 1.0189
                                +3.8 0.858 0.8905
                                           +3.8 0.621 0.6490
                                                        +4.5 I               0.696          0.573 I     R 0.7454
                 +7.*l
                               *0.6171
                                +7.7 I
PDQ07 I                                          FLAME
                                             !).%
1-. ir:~".*:,.*
5-13 I

FLAME(x) MEASURED(&#xa2;)
Burnup(MWD/MTU)         0         70
             -     Power(%)
D Bank Position Axial Offset(%)
0 203
                                          -2.0 0
204
                                                     -8.4 n
0 l'1 CD
                                                                                                                               ~
ID t1 Ill 1-tiOQ 0     fl)
Ii
* Cl.I   it i:: ....
t1 Ill
                                                                                                                 ~~
                                                                                                          ~~~
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ltj
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                                                                                                         ,.             ID          i::
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3:
0
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                .                                                                                                      n 0
a:                                                                                                             ,El
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LO                                                                                                        0 i:s
             "'0
* 0 0
             ~o::t.-:o::o~----:ir:::-:------:i:--:-:----,-"""'""'.'---,-----,------r----.----
20 .oo   40.00     so.oo      eo.oo   100.00    120.00    1~0.00   -1so.oo AXIAL POSITION IN INCHES

in r--
          .... Bumup(MWD/MTU)
FLAME(x) 70 MEASURED (0) 70 Power(%)              3            3 D Bank. Position     29           26 0
I.I)
Axial Offset(%)      -3 ..4       -6.0*
n 0
11 11)
                                                                                                            ~
11) 11 Ill      I OQ I-to CD I
0
                                                                                                ',   ~~
                                                                                                 . i:: Ill
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0 3:   0                                                                                        ..      o' 0                                                                                                     i::
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     ~                                                                                                    ::s
         *w Csl 0
0 0
            *.;-----.----~-----,.-----,------.-----
          &deg;o .oo    20.00      40.00       60.00      ao.oo  100.00 120.00     140.00 160.00 AXIAL POSITION IN.INCHES

lJ) r--.
FLAME(x)   MEASURED((>)
Burnup(MWD/MTU)      70          70 Power(%)              3           3 D Ban~ Posit ion     29          26 0
II) g;,-
(Jl (1)
                                                                                                                  ~
                                                                                                                 ~
in N
b:I I
en co
                                                                                                             ~ ~
                                                                                                           ~     I-'*
II) 0                                                                              l:Il I-' I-'
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                       "-+-----.------.----,------.------.----..------------,
                   . &deg;o. 00   20.00      40.00      60.00      ao.oo   100.00 120.00 140.00 160.00 AXIAL POSITION IN INCHES L_ _ _ _

----~~--~----~------                                                 *.':
l/)
['
FLAME(X)   MEASURED((>)
Burnup(MWD/MTU)      0           0 Power(%)             0           4 D Bank*Position    203         202 0      Axial Offset(%)     21. 3       18.2 ln C")
0 t1 ID
                                                                                                              ~
lJ)                                                                                            ID N                                                                                              t1 Ill OQ C/l ID
                                                                                                        ~     P>
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Ill 0                                                                                       N    I-'
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               ~-00      2.0. 00   40.00      so.oo      eo.oo  100.00    120.00 140.00 *160.00 AXIAL POSITION IN INCHES

-     ll!J .... -             -*     -       . . . 1111!1   ~        -    -    -       -    -   -*- -                        -        -
1/)
r--
FLAME(x)   MEASURED(<))
Bumup(MWD/MTU)         0           0 Power(%)               4           4 D Bank Position        0           0 Axial Offset(%)       23.6        23. 0 0
                 \I)
(")
0 ti ID
                                                                                                                       ~
ID
                ...                                                                                                    ti Ill (lQ en ID i=
0
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Ill 0                                                                                        N ..
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                  .                                                                                                 ~.
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                     -L---------.,-----...------,-----,i-----,-----,-----,
                &deg;o .oo     20.00       40.00      *60.00      eo.oo    1.00.00  120.00   140&deg;00 160.00 AXIAL POSITION IN INCHES

-     9J      ., -* -* :-' .. -                           -      -    -      ... * -   -      -     -  -                  -        -
U) r--
                   -        Burnup(MWD/MTU)
FLAME(x) 158 MEASURED (0) 158 Power(%)              100        100 0        D Bank Position       218        219 U)
                   -        Axial Offset(%)        -3.0        0.1
(")
0 Ii CD 1./)                                                                                               ~
N
                     .                                                                                                CD
                   -                                                                                           C OQ C/J CD Ii Ill 3~     Ill 0
                                                                                                              .N I-'
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0 0
0 9J-L---------.----......,....----,------,----,------.-----,
                        ,DO   20.00      40,00     60,00     80,00    100.00    120.00 140,00   160,00 AXIAL POSITION IN INCHES

- -      .,,     -   .............               .,     ....         (. .\ -   ..     - - - - *1111111                --     -
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            -      Burnup(MWD/MTU)
FLAME(X) 3290 MEASURED((>)
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                                                                      *I

                                \
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FLAME(x)   MEASURED(<))
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- - ., .. - ........ - -1 ........ ,_. ....... *- -
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-     - -** -) . . . . . . . . . . 9" ......~. . . . . . {. ., . . . . . . -                                        --
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Power(%)
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ID    Axial Offset(%)        -7.8      '1-1. 5
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                                                                         /
ID
          -    Burn up (MWD/MTU)
FLAME(x) 7715 MEASURED (0) 7715 Power(%)               100         100 D Bank Position        203         206 0
            . Axial Offset(%)         -7.1        -4.4 II)
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ID l"'"
FLAME(x)  MEASURED (0)
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* 160.00 AXIAL POSITION IN INCHES L

                                    ,       )         ,          (        ,         ,                         :'
FLAME(X)  MEASURED(O)
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LI)   Axial Offset(%)        23.5      21. 9 n
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- - ...... -/ - ............ - ... -;' - - .... -
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           -        Bum up (MWD/MTU)
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D Bank Position FLAME(x) MEASURED( )
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                      ' /

I I                                                    FIGURE 5-24 I.                                        Control Rod Worth Comparison for Surry .1, Cycle 1, BOC, HZP, D Bank I
16                                                                                                                         1600 I                    1-*               ~~
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I 0                                                                                                                             0 I              0                    40                   80 BANK POSITION (STEPS) .
120                 160          200           228 I
5-29 I
I

FIGURE 5-25 Control Rod Worth Comparison for Surry 1, Cycle 1, BOC,
* HZP, C Bank 14                                                                                                                 '-~
1400
                                                                                                                              'ct I
                                                  --.,..j.
                           ~-                                                                                               -     -  .... . FI.,.A?1E
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                                                                         !~ _:;
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                                                                                                                              .;.__ MEASURED 12                                                                                                                                                              1200
                                                                                                                         , 11 *1-.*rr_,1*1,~*1!r:c~---:-r,
                               ~                     .
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L.                                                                                                                                                              200 0                                                                                                                                                                 0 0                  40                               80                                120               160                          200              228 BANK POSITION (STEPS) 5-30

FIGURE 5-26 Control Rod Worth Comparison for Surry 1, ~ycle 1, BOC, HZP, B Bank 22                                                                                                                  2200
                                                   .:~
20                                                                                       **,*1;:... L.::L+/-L~.       2000
                                                                                             - - - FLA}{E
                                                                                             --MEASURED
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: o.                        40                                                 120    160                  200 228 BANK POSITION (STEPS) 5-31

.,                                                                     FIGURE 5-27 I                                                          Control Rod Worth Comparison for Surry 1, Cycle 1, BOC, HZP, A Bank I
I           15 i..,....:
                 ~                  -~                   ~  ,:
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                                                                                                                                --MEASURED 1200
                                                    ~
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I                                                                               5-32

I I                                    Figure 5-28 Control Rod Worth Comparison for Surry 1, Cycle 1, BOC, I                        HZP; B'anks B - D moving in 100 Step Overlap I
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I 5-33 I

I FIGURE* 5-29 I
.I                                                               Control Rod Worth Comparison for Surry 1, Cycle 2, BOC, I                                                                                    HZP, D Bank I            12 Qe+W'i3i51~*i/i"fi:&#xa5;,":.;;;:;'!'? ...=;_ !"?::?>>.#: i='.9.'IJldf'    51'5i!f,i1$plfu<!1Xl:jl;;,+,' ;q ili "!'i*:*fi$t4A#l4\ll}411, f' lt_-f!I&'-' ilfM31lif?t:"'1",5:llt:i&sect;j@!4: .aI,200 I
I            10 I
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I                                                                        BANK POSITION (STEPS)
I                                                                                               5-34 I

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                                                                   ~
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0 N.
N 00                                         ....          ....N N   +'-            Cl\       00    0 0   0              0         0     0             0 0 0   0              0         0     0             0 INTEGRAL WORTH (PCM)

-----------~---~---
DIFFERENTIAL WORTH (PCM/STEP) 0
             ~
0
(')
Hi 0 0 ::,
t1 rt b:1                                                                 t1 00                                                        CJl.O 0                                                  ::i::  i;   I-'
        ~                                                                           ttj ttj                                                                 ~       H 0                                                      .~~          p.. Ci)
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 -...J  0                                                       Ill         rt      VI z                                                       ::, n       P'       I I-'                                                ;,;" I-'            w
       ,-... N                                                         CD   C')     N C/J  0                                                              0 t-'l                                                           wS trJ                                                           ..   'cl ttj                                                                 Ill C/J                                                            b:1 t1
       '-'                                                             0 I-'*
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                                                                      . 0 I-'
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             &deg;'
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N 00 I-' I-' I-A N                               0   N   w
                     ~                         00  0   0   0 0 0            &deg;'0          0 0 0 0            0            0   0   0   0 INTEGRAL WORTH (PCM)

DIFFERENTIAL WORTH (PCM/STEP) 1--'             1--'
0               N                                         (X)                0                N
           .i:-
0 C"l Hi 0 0     ::i (X)                                                                                                               t;    rt 0                                                                                                                       t; td                                                                                                                     en o i:: 1--'
t;
      ~                                                                                                              ::i:: ~ :,;l         >rj N             O      I-'-
1-'d                                                                                                           1-'d          i:;l. (lq V,
0                                                                                                             .        1--'         i::
I  C/l                                                                                                                   ..     :i:::  t; w   H                                                                                                               t::;I        0      Cl) 00  H    1--'                                                                                                              C"l t; H     N                                                                                                         td    '<     rt V, 0    0                                                                                                         Ill     n ::t          I z                                                                                                              ~~C"lw
     ,-..                                                                                                                          0      w C/l                                                                                                                    .i:-  s H                                                                                                                     ..    'd tx:1                                                                                                                         Ill 1-'d                                                                                                                    td t; en                                                                                                                     0     I-'*
     "',.J                                                                                                                   C"l   en
                                                                                                                            .      0 1--'                                                                                                                     ~
0
           &deg;'
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:::; -~~mi::!.tilimt:mc~~m==**i:::i:ii:i&m~a~;at+/-t:::t:m;la2mat:m:l--':!it.z:::,,,.ti:s;;:;;mmi..iil--'
OO                   N             .i:-,           &deg;'           00                  0                N O             O               O            O                   O                0 0               O             O               O            O                   O                0 INTEGRAL WORTH (PCM)

DIFFERENTIAL WORTH (PCM/STEP) b:I
    ~
1-"d 0
C/l V,  H I  H vJ  H
 \0 0 z
C/l H
    -t:xJ 1-"d en l'.J    .i:,.           0\         OJ 0       0               0          0 0 0       0               O*         0 INTEGRAL WORTH (PCM)

- - - - - -* - - - - - - - - - - - - -1.
DIFFERENTIAL WORTH (PCM/STEP)
I-'          N N
(")
t-t, 0 0 ::,
ti rt.
ti C/l 0 t,:J                                                  ~     ......
p::: ti t
          ~
N~ O "d          ~ t-rj p.. I-'*
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H                                               t,:J (") ti (D I    H                                               cu '<       rt
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H                                               ::in::rV1 0                                                     :,;' I-'           I
          @                                                     (D    (")    uJ
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          ~                                                     0 I-'*
Cl)                                                         rn
         '-"                                                   .n     0 I-'    I-' N
                 .p,.         ())            N          0 0            0              0      0
                                                    &deg;'  0 0 0            0              0      0   0 INTEGR.i\L WORTH (PCM)

I I
I                           Figure 5-36 Control Rod Worth Comparison for Surry 1, Cycle 4, BOC, I                         HZP, A Bank I
2000 I         20 I
16.
I ,..,
p.,
r:i::I I -c E-l tll p.,
   ~
12                                                                1200 I  ~
0 l:3:
   ~
I  H E-l 8                                                                 800 r:i::I I  r:,:..
r:,:..
H A
I I                                     ' .. -, -*-.
:*=:: l:: : ;
I :
                                                          - . ~. -
:*: : L :::
0                                                                   0.
I             0 40     80           120                           160 200 228 BANK POSITION (STEPS)
I I                               5-41 I
I

I Figure 5-37 I           Control Rod Worth Comparison for Surry 1, Cycle 4, BOC, HZP, Banks A - D moving in 100 Step Overlap I
I                      INTEGRAL WORTH (PCM)
                                                                                                                        ~
                                                                                                                         ~
a:I i:'l 0  0              0                       0                       0                              0                    A I 0 0
  '&deg; 0
co
     ..::I" 0
                    '&deg; M
0
                                            ..::I" N
0 N
                                                                    ,-f
                                                                                         -t*-....
co N
                                                    ---, ~-+-'* -- "
                                                                         -~-      ...
                                                                             -.j::=.
N I                                                                ::..,.
                                                              .:.ii'{:-.--~
                                                                                         ---   -~':/J-
                                                                                       --*-* 71--
r-
                                                                                                                   ~
                                                                                                                    ~
ct1 i:'l 0
_,::J*                           '&deg;
                                                                                                                        ,-f I                                                    .*.
                                                                                    - *!J::=
II-*
                                                                                       ---~ -~
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co
                                          --                                                                       N N
I                      ... f.~"
                      --:~---
_: ~+2-
                                                                                                              ~
                                                                                                               ~
0 co ct1 0 I
i:'l
                                                                                                                   '&deg;
       * ~ ~ - - - - @ :.:~
                                                                                                                   ,-f i:'l 0   U)
Pa co             r,::i I
N              E-l N              tll 0         '-'
                                                                                                       ~
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H
                                                                                                          ~
I           *-    - --1=:1i'-:_
                                   ~i:~:)."~
                         ----r~-1==-JI/.:,, *-
                                  '"':'J!:;f*
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i:'l 0
                                                                                                              '&deg;
                                                                                                              ,-f 0
E-l H
tr.I 0
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                        ----+-----,~:'/~~  -.
I                                                                                      --~
                                                                * - - ...:...:..t::-:::l=-
                                                                      -l-.L--             -  L-----
co N
N 0
co
                                                                                                                              ~
i:'l I                                                                     -     -- - -- ----!--
1:-:=-. * --~:~-~
                                                   ..__cl--:::j:::=1=;:::'--:= ~ :[
0
                                                                                                       '&deg;..-l l::::::::t=             0 I                                                                                   _*'- ::i::.::::
0 co I
I  0 N  '&deg;
      ,-f co                                                      0 0
I I                                       5-42 I

I I
I                                                                   Figure 5-38 Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, HZP, D Bank I
I       12                                        -.                                                                                                            1200 I            *~-**
                     --~.
                     ~
                                                                                                                                   ,,gf*
                                        ~
1000 I       10 8
                             ***If,,
b:+/-
                                                                                                  - - - FIMrE
                                                                                                   --MEASURED
                                        '::   < Tll'J _:__.'
                                                        . !\ .
I        8                                                                                                                                                       800 I -
r:i..
a
  &#xb5;:l
  ~
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::.:     R;:.1: l< 1::                   :1                                                                                                                          r:i..
I u r:i..
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  ~
6                                                                                                                                                       600
:::c:
t 0
:s:
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  ,-:i 1-+,ri--!--                                                               *--
                                                                              ++:,:..:..~*
                                                                                                                                                                       ~c.,
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  ~                                                                                                                                                                     z I  z                                                                                                                                                              400
                                                                                                                            ~~---~'7,.'
4                                                                                                                                                              H
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2                                                                                                                                                        200
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             *~-v-=-*
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           ~-,;,t:5::,;:,:H   -4"i:*xis:-:l"M -3,~,a ei-:; pg I ti@ :ii.,*:.;                                                                                       0 I          0                              40                   80                 120 BANK POSITION (STEPS) 160                     200                            228 I
5-43 I
I

I I
I Figure 5-39 I                                                            Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, HZP, C Bank I
I        10 ~ - _                                                                                                                                    . 1000 I                            '     ...             >  '  I 1- '
I 8                                                                                                      ;,.;... _- _     . FLAME               800
  ,-..                                                          ,- ~7.-                                          ---MEASURED I
p.,
r"1
  -E-1                                                  *rt~*~b~:,3-:
* ti)
:u:.::
                                                     * ...       *~i-~-~-                                                                                   g e
I -p.,    6 600
                                                                                                                                                             ~
   ~
0
  &                                       ,,      r-.*:                                                                                                     :::c I ~
H 4
: H-*.
* II--
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E-1                                                                                                                                                   400  ~
z I ~
r"1
  ~
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A I         2
                                                                                                           . -~'S.-
                                                                                                                            .....                       200
            . *:::::::;:J;:+ ;-:-I . ::I                                                                 .. ': -f~--~-r *~-
I             *---'-'-'-~1
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               ~II"-'
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I         0 0                             40                           80                            120 160                  200       228 0
I                                                                     BANK POSITION (STEPS)
I                                                                                      5-44 I
I

I I
Figure 5-40 I                                                        Control Rod Worth Comparison for Surry 2, Cycle 4, BO.C, HZP, B Bank I
18                                                                                                                                                                     1800 I
:-;-.                                                                                                      - * . +-----.---
                   *---~
I        16              ....____.=t:=?
                                            ~
c..:-=-~
:j::c_                                                                                                                1600 I
1----l---
                                                                                                                      ,rr, 14                                                                                                      Iii 1400 I
::\l==l':\.=:/:=
: l\=i:::;::\:c=l l=l
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                                                                                                                  * - - - - FLAME
                                                                                                                    - - MEASURED I
I
                                                      --:_1\~~
    ~ 12                                             *-:r:::\--::f.::=+/-:*                                                                                                        1200
   -E-1 tf.l
    ~              -
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                   ~- I 1=t-=.:1.f=4~
I _ ___. .* * - . . *   . t=r.
:\:=-l~......._-
                                                                    -\-l----r:=-.....:.;c..\.                                                                                    1000 p.,
I g
   ~
    ~                                                                                                                                               _...:.....:...._+--,;-
                                                                                                                                                           *.:..~:
I H
E-1        ;*, -=--1=-=-7-;J-.::..Jf                                                                                                                                                ~
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                                                                               ---1~4~
8  ~~----*.
800 I  ~
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l=J-==-1 I~~+----
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                                                                                                            --~**=-.               -~-:=--                                            ~
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I          6 l'--'-!C.
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I 4    :
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400 I          2                                                                                                                                                                      200 I          0 mrt~alttciEt.~~
0
                                        ****"-,~--
40                            80                      120                 160                       200                        228 0
I                                                                     BANK POSITION (STEPS) 5-45 I

I I                                                    Control Rod Worth Comparison Figure 5-41 for Surry 2, Cycle 4, BOC, I                                                                           HZP, A Bank I        17                                               :J.
1700 I        16  ,----~                                                                                                                           1600 I  ==t=t=I =:i*'\
                                                     *~
I        14                                                                                                                                   1400 I
             ~~t~~'~
                                                     ~.:\~];.
:::::::e: ~,./--                                                               -'.
                                                                                                          . --.,-.---~-~-,.~~i~-
12                                                   1\'1~-oQj.'  -_- -_ -1                                                          1200 I -p..
r,a
                                                                    ~
                                                           .''1~--=tl=n ~
g I -a E:-1 Cf.l p..
rn i''t--4'-
:QJ~
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1000 p..
::i:::
                                                                                                                                                   ~
0
::i::                                                                                                                                           ::.:
I  ~
0 H
8 H
800 ~
c.,
r,a
   <                                                                                                                                               t I  H E:-1
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                                       =-*
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I  r:r..
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6
                                 .,c'!-J4Jt~*                                                                              _------4___.__      600 l-        -_t ..                                                                                 --+--
f----t-- - ' .
I         4
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                                   --1 n
                                              ...                                                                                              400
               ~=+/-=-- ,=!=:_
I         2
            ,~ ~---,1J::;::!:::~
             '=l=~=J:~ci:-:
::-:--::J:_ :')l'--.r.,.:::r:.                                                                                                  200 I
I         0 0                             40                           80                 120                     160    200              228 0
I                                                                  BAi.'TI< POSITION (STEPS)
I                                                                         5-46 I

I Figure 5-42*
I                              Control Rod Worth Comparison for Surry 2, Cycle 4, BOC, I                                HZP, Banks A - D moving in 100 Step Overlap
.1                                                                                                                                                               ~
                                                                                                                                                                   ~
INTEGRAL WORTH (PCM)                                                                                                  i::Q I           0 0
0 u,
0 0
0
                                 ..;;t 0
0 0
('I")
0 0
0 N
0 0
0 r-i 0                      A co N
                                                                                                     .-,.          *-*.:::i*.:;;...,,,,c:'                       N I                                                                                                                  ~~,*--=*'.
                                                                                                 ':... ;::: __ ._____ ;_;J.
                                                                                                                                                          ~
i::
                                                                                                 . ;"t-$.;         -~~=fl=                                   Ill i::Q 0
I                                                                                          _r::;;~
f-::ll
                                                                                                                             -*-- ~==-*
0
                                                                                                                                                                 '&deg; r-i
                                                                                                                            ,,_                           co
                                                                                 =~-
I N
                                                                                   *~                                                                     N
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                                                                  *-:-      *I co
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                                                                                                                                                    '&deg; r-i H
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I ;:--
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                                                                                                                                                                      ~
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                  ~    :.,....y. *: -:~ _.:.: __ _; ":-~-
                  ~-. --='E
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s==             .-t=::: **=!=-                                       '&deg; r-i I  *--:_ -
:~~~~fl:~*-=-~ =
:--::t-- _:i;:_.:: :-~1'::.::- ..:-== ... .:. ~ : -*==:
:-=~---
                                                                                       . ~~--===t=-
                                                                                                                    --r-*
                                                                                                       . -- -=::' _-:c- ::::.t:::
                                                                                                                                   ~-=.:
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    . -- ~~::___ ,:::+:-                ---- - ~ .           f'~---- - ~ - ~ - -- - - - , -                         --~- ----
I 0
   .:~~; ~~% ~:::p/.~ ..::.:;._. ~~:, :;i= &sect;~~~ :~==: == .:_:t-:::;                                                                           co
:=*:-:1 ~r~ =ct~:?;: .:.=~::T:. =:=:L.t= -1=:~t==~~;t.:.~==~ ::~_'I.:.'= \:ii__:
I  :tj~~~=:~~::~=~~~~itl 0                    \0                    N                            CO                         ...;t                       0 0
N                    r-i                   r-i I                                (d~LS/w:Jd) HJ.~O~ 'IVILN~~~~Ia I                                                                            5-47 I
J

I Section 6 - Summary and Conclusions I
I           The Vepco FLAME Model is operational at Vepco for the purpose of performing three-dimensional reactor physics analyses and supporting I  the evaluation of core performance. The model consists of the FLAME3 code with the NULIF, PDQ07, FLAFIT, EDITQAR, PICCOLO, and FLMSHUFL codes I  being used to provide either input or data manipulation. The accuracy I  of the Vepco FLAME Model has been established through extensive com.,...
parision of calculations with measurements from the Surry Units No. 1 I  and 2 over eight cycles of operation. The results of these comparisions indicate that tq_e Vepco FLAME Model (which includes normalization to the Vepco I  PDQ07 Disc~ete Model) provides the*capability to predict axial peating factors and axial power distributions as well as differential and* int_egral* control I  rod worths. The comparisions also indicate an acceptable capability to I  predict axial offset trends as a function of changing reactor core con-ditions.
I           Verification, as well as improvements to the Vepco FLAME Model, will continue to be made as more experience is obtained through the I  application of the model to the. units at* the Sur*ry and North Anna Nuclear I  Power Stations.
I I
I I
I                                      6-1 I.

I I                       SECTION 7 - REFERENCES I  1. W. A. Wittkopf, et. al., "NULIF - Neutron Spectrum Generator, Few Group Constant Calculator, and Fuel Depletion Code," BAW-10115, June 1976 (Babcock and Wilcox).
I  2. H. H. Hassan, et. al., "Babcock and Wilcox Version of PDQ07 -
User's Manual," BAW-10117P, December 1975 (Babcock and Wilcox).
I  3. C. W. Mays and M. Furtney, "FLAME3 - A Three-Dimensional Nodal Code for Calculating Core Reactivity and Power Distributions,"
BAW-10124A, August 1976 (Babcock and Wilcox).
I  4. Private correspondence from the Babcock and Wilcox Company to the Virginia Electric and Power Company dated February 3, 1971, and I     October 6, 1971.
: 5. C. B. Franklin, "EDITQAR and PICCOLO - Auxiliary Fortran Computer Codes for Use with FLAME3," NFE Technical Report No. 27, April I     1977 (Virginia Electric and Power Co.).
: 6. W. C. Beck, "FLMSHUFL - An Auxiliary Fortran Computer Code for Use I     with FLAME3," NFE Technical Report No. 55, October 1977 (Virginia Electric and Power Co.).
: 7. M. L. Smith, "The PDQ07 Discrete Model," VEP-FRD-19, July 1976 I     (Virginia Electric and Power Co.).
: 8. Final Safety Analysis Report - Surry Power Station Units 1 and 2, I     Virginia Electric and Power Company, December 1969.
: 9. D. L. Delp, et. al., "FLARE - A Three ....Dimensional Boiling Water Reactor Simulator," GEAP-4598, July 1964 (General Electric).
I 10. C. B. Franklin, "Sensitivity Study of K-Infinity Multipliers for Depleted BP for the FLAME Model," NFE Calculational Note PM-g, I     July 1978 *(Virginia Electric and Power Co.).
: 11. W. c. Beck, "Sensitivity of Control Rod Worth Shapes to Variation in Radial Power Distribution," NFE Calculational Note PM-3, July I     1978 (Virginia Electric and Power Co.).
I I
I I
I                                   7-1}}