ML20135A948
| ML20135A948 | |
| Person / Time | |
|---|---|
| Site: | Prairie Island  |
| Issue date: | 02/28/1997 |
| From: | Lesko J WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20135A931 | List: |
| References | |
| CAA-97-042, CAA-97-42, NUDOCS 9702280027 | |
| Download: ML20135A948 (66) | |
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Northern States Power Prairie Island l Units 1 and 2 Spent Fuel Rack Criticality Analysis Using Soluble l Boron Credit February 1997 J. R. Lesko W. D. Newmyer )
J. J. Huang l T. R.Wathey l R.N. Milanova l K. R. Robinson S. K. Kapil Prepared :
J. R/Lesko Criticality Services Team Leader
' Verified: d &. 1 W. D. Mewm/er r Criticality Sen es am Approved: / - /
(/ !/
jM. W. Fect9au, Manager l
Core Analyisis A Westinghouse Commerical Nuclear Fuel Division
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9702280027 970221 PDR ADOCK0500g2
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1 Table of Contents 1 1.0 Introduction............................................................................................................I l 1.I De si gn Desc ri p ti on. . . .. . . .. . . . . . . . . . . . . . . . .. .. . . . . . . .. ... . . . . . . .. . . . ... . . . . . . . . . .................2 l 1.2 Design Criteria. . .. . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................2 2.0 A n a ly t i c a l M e t h o d s .. ..... ...... ........................ .. .................................. ........................ 3 3.0 Criticality A nalysis of All Cell Storage ................................................................. 4 3.I No S ol ubl e Boron 9 5 /9 5 K g. . . . . e. . . . . . . . . . . . . . . . . .. . . . ... . . .... . . . . .. . . . . . .. . . . . . .. . . .. . . . . .. . .. . . . . 4 3.2 Soluble Boron Credit Keg Calculations....... . ..... . ... .. . ...........................6 3.3 Burnup and Decay Time Reactivity Equivalencing................ ............................... . 8 4.0 Criticality Analysis of 3x3 Checkerboard Storage ..............................................11 ;
4.1 No Soluble Boron 95/95 Ke gCalculations.. ... . ..............................................I1 l 4.2 Soluble Boron Credit K ge Calculations ................ . ......... . ........... ....... .................. I 3 4.3 Reactivity Equivalencing ......... ...... .. .. ........... ......................................I5 4.3.1 Burnup and Decay Time Reactivity Equivalencing.... ......... . .. . . . . . . . . 15 1 4.3.2 Gadolinium Credit Reactivity Equivalencing............... .... .............. .. .. .....17 i
5.0 Disc ussio n o f Post ulated Acciden ts........................................................................ 20 ;
6.0 So l u ble Bo ro n C redit S u m m a ry ............................................................................ 2 2 7.0 Storage Configuration Interface and Miscellaneous Requirements.................. 23 l 8.0 S u m m a ry o f C ri ticali ty Res ul t s ............................................................................. 2 4 i B i b li o g ra p h y .......... ................ ............ .......... .................................... ........................ 61 1
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Prairie Island Spent Fuel Racks i 1
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l List of Tables l l
Table 1. Fuel Parameters Employed in the Criticality Analysis .............. ........ ...... .............. 25 '
Table 2. Prairie Island All Cell Storage No Soluble Boron 95/95 K eg . ... ..... ....... ............. 26 ;
Table 3. Prairie Island All Cell Storage Soluble Boron Credit Ke g . ....... ....................... ... 27 !
Table 4. Prairie Island All Cell OFA Fuel Minimum Burnup Requirements.... . .... . . ........ 28 Table 5. Prairie Island All Cell STD Fuel Minimum Burnup Requiremer.ts ............. .... ..... 29 Table 6. Prairie Island 3x3 Checkerboard Storage No Soluble Boron 95/95 Ke g ........ .. .... 30 l
Table 7. Prairie Island 3x3 Checkerboard Storage Soluble Boren Credit Ke g ........... . ...... 31 Table 8. Gadolinium Credit Equivalent Enrichments for 3x3 Checkerboard......................... 32 ,
- Table 9. Prairie Island 3x3 Checkerboard OFA Minimum Bumup Requirements l (N o G A D C redi t ) . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Table 10. Prairie Island 3x3 Checkerboard STD Minimum Burnup Requirements (N o G A D C red i t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .
Table 11. Prairie Island 3x3 Checkerboard OFA 4 GAD Minimum Burnup Requirement ..... 35 Table 12. Prairie Island 3x3 Checkerboard OFA 8 GAD Minimum Burnup Requirement .. .. 36 .
Table 13. Prairie Island 3x3 Checkerboard OFA 12 GAD Minimum Burnup Requirement ... 37 Table 14. Prairie Island 3x3 Checkerboard OFA 16 or More GAD Minimum Burnup R eq u i re m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table 15. Prairie Island 3x3 Checkerboard STD 4 GAD Minimum Burnup Requirement.. .. 39 Tabie 16. Prairie Island 3x3 Checkerboard STD 8 GAD Minimum Burnup Requirement.... . 40 ;
i Table 17. Prairie Island 3x3 Checkerboard STD 12 GAD Minimum Burnup Requirement.... 41 Table 18. Prairie Island 3x3 Checkerboard STD 16 or More GAD Minimum Burnup R eq u i re m e n t . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .
Table 19. Summary of the Soluble Boron Credit Requirements .. ......................... .... .......... . 43 i
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Prairie Island Spent Fuel Racks ii i
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-List'of Figures i
- l. Figure 1. Prairie Island Spent Fuel Rack Layout ....................................... ...... .... .... ........,44 Figure 2. Prairie Island Spent Fuel Storage Cell Nominal Dimensions................. .... ........ 45 i Figure 3. Prairie Island All Cell OFA Storage Bumup Credit and Decay Time .
R eq u i re m e n t .. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 46 Figure 4. Prairie Island All Cell STD Storage Burnup Credit and Decay Time !
Req u i re m ent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 4 7 i L Figure 5. Prairie Island 3x3 Checkerboard Layout Requirement............... .......................... 48 l
' Figure 6. Prairie Island 3x3 Checkerboard OFA Storage Bumup Credit j and Decay Time Requirement (No GAD Credit) ............................... ................. 49 Figure 7. Prairie Island 3x3 Checkerboard STD Storage Burnup Credit -
and Decay Time Requirement (No GAD Credit) ........... ...................................... 50 :
Figure 8, Prairie Island 3x3 Checkerboard OFA 4 GAD Storage Burnup Credit !
and Decay Time Requirement ....... ....................................................................... 51 l Figure 9. Prairie Island 3x3 Checkerboard OFA 8 GAD Storage Bumup Credit i and Decay Time Requirement ..................................... . ... ...... ........................52 Figure 10. Prairie Island 3x3 Checkerboard OFA 12 GAD Storage Burnup Credit ,
and Decay Time Requirement . . . ..................... .... .................. ............................. 5 3 l Figure 11. Prairie Island 3x3 Checkerboard OFA 16 or More GAD Storage Bumup Credit f and Decay Time Requ irement .............. .... ............. ..... .......... ............................... 54 Figure 12. Prairie Island 3x3 Checkerboard STD 4 GAD Storage Burnup Credit ,
and Decay Time Requirement ................................................... ........................... 5 5 l Figure 13. Prairie Island 3x3 Checkerboard STD 8 GAD Storage Bumup Credit j and Decay Time Requirement ............... ................ ............................................... 5 6 l Figure 14. Prairie Island 3x3 Checkerboard STD 12 GAD Storage Burnup Credit and Decay Time Requirement .............................. ................... .... ... .......... . ..... 5 7 Figure 15. Prairie Island 3x3 Checkerboard STD 16 or More GAD Storage Burnup Credit and Decay Time Requirement ................................ .... ........ ........... ...................... 5 8 Figure 16. Gadolinium Rod Patterns within the Fuel Assembly........ .................................... 59 Figure 17. Prairie Island Interface Requirements...................... ........................................ .... 60 l
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Prairie Island Spent Fuel Racks iii i
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1.0 Introduction 1
This report presents the results of a criticality analysis of the Northern States Power Prairie Island i Units I and 2 spent fuel storage racks using credit for soluble boron in the spent fuel pool. The methodology employed here is contained in the topical report, " Westinghouse Spent Fuel Rack Criticality Analysis Methodology"W. !
The spent fuel storage rack design considered herein is an existing array of fuel racks, previously l qualified (2) (with Boraflex) for storage of various 14x14 fuel assembly types with maximum i
! enrichments up to 5.0 w/o 235 U. In this report, no credit is taken for the presence of Boraflex in I the racks. Two different storage configurations are currently allowed. The first configuration j l
allows fuel assemblies to be stored in a 2x2 checkerboard pattern of" burned" and " fresh" fuel assemblies with enrichments of 2.5 w/o 235 U (equivalent with burnup) and 5.0 w/o 235 U (no burnup), respectively. The second configuration allows storage of fuel assemblies in all storage .
cell locations (no checkerboard) if they satisfy a minimum burnup credit requirement as a l function of enrichment.
The Prairie Island spent fuel racks are reanalyzed to allow storage of all 14x14 fuel assemblies used at Prairie Island with nominal enrichments up to 4.95 w/o 2S U in all storage cell locations 1 using credit for checkerboard configurations and burnup credit. The analysis does not take any .
credit for the presence of the spent fuel rack Boraflex poison panels. Credit is taken for the !
presence of the integral absorber Gadolinium with 8 w/o Gd in the fuel and for the radioactive decay time of the spent fuel. The following storage configurations and enrichment limits are considered in this analysis:
All Cell Storage Storage of 14x14 assemblies in any cell location with nominal l Enrichment Limits enrichments no greater than 1.87 w/o 235 U for Westinghouse I 235 14x14 OFA fuel assemblies and 1.77 w/o U for Westinghouse l 14x14 STD and Exxon 14x14 fuel assemblies. Fuel assemblies with initial nominal enrichments greater than these must satisfy a minimum burnup and decay time requirement.
3x3 Checkerboard Storage of Westinghouse 14x14 OFA assemblies with nominal Enrichment Limits enrichments no greater than 4.95 w/o 235 U in the center of a 3x3 checkerboard. The surrounding fuel assemblies must have an initial nominal enrichment no greater than 1.30 w/o 235 U for I 235 Westinghouse 14x14 OFA fuel assemblies and 1.20 w/o U for Westinghouse 14x14 STD and Exxon 14x14 fuel assemblies. Fuel assemblies with initial nominal enrichments greater than these must satisfy a minimum burnup and decay time requirement. The surrounding enrichment limits are increased with Gadolinium
! credit in the center assembly.
i The soluble boron credit required for these storage configurations are 750 ppm for normal l conditions and 1300 ppm for accidents.
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Prairie Island Spent Fuel Racks
A L The. Prairie Island spent fuel rack analysis is based on maintaining K e g s 1.0 including l uncertainties and tolerances on a 95/95 basis without the presence of any soluble boron in the L storage pool (No Soluble Boron 95/95 Ke g conditions). Soluble boron credit is used to provide l safety margin by maintaining K eg s 0.95 including uncertainties, tolerances, and accident conditions in the presence of spent fuel pool soluble boron.
1.1 Design Description '
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- The Prairie Island spent fuel storage rack layout is depicted in Figure 1 on page 44 and the spent -
fuel rack storage cell is shown in Figure 2 on page 45. Nominal dimensions are provided on each j figure.
Fuel types being considered in the analyses include the Westinghouse 14x14 OFA design being l used in Prairie Island Units 1 and 2 and the Westinghouse 14x14 STD and Exxon 14x14 fuel ,
l assembly types previously used in the reactors and currently in storage in the Prairie Island spent i
! fuel pool. The Westinghouse 14x14 STD design bounds the reactivity of the 14x14 Exxon fuel l assemblies. The Westinghouse 14x14 OFA design is equivalent to the Westinghouse 14x14 Vantage Plus fuel type currently in use and is covered by this analysis.
l The fuel parameters relevant to this analysis are given in Table 1 on page 25. ,
1.2 Design Criteria i l Criticality of fuel a.csemblies in a fuel storage rack is prevented by the design of the rack which j limits fuel assembly interaction. This is done by fixing the minimum separation between fuel assemblies and inserting neutron poison between them. However, in this analysis no credit is taken for the presence of Boraflex panels in the racks.
In this report, the reactivity of the spent fuel rack is analyzed such that K eg remains less than 1.0 under No Soluble Boron 95/95 K eg conditions as defmed in Reference 1. To provide safety margin in the criticality analysis of the spent fuel racks, credit is taken for the soluble boron present in the Prairie. Island spent fuel pool. This parameter provides significant negative reactivity in the criticality analysis of the spent fuel rack and will be used here to offset the reactivity increase when ignoring the presence of the spent fuel rack Boraflex poison panels.
Soluble boron credit provides sufficient relaxation in the enrichment limits of the spent fuel racks to allow the racks to be used under checkerboarded conditions with no credit for the Boraflex poison panels. If some amount of Boraflex material is considered remaining, the reactivity of the spent fuel rack and the amount of soluble boron required to maintain K e gs 0. 95 will be reduced.
The design basis for preventing criticality outside the reactor is that, including uncertainties, there is a 95 percent probability at a 95 percent confidence level that the effective neutron multiplication factor, K eg, of the fuel rack array will be less than or equal to 0.95.
i Prairie Island Spent Fuel Racks 2 1
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l 2.0 Analytical Methods l l The criticality calculation method and cross-section values are verified by comparison with I
critical experiment data for fuel assemblies similar to those for which the racks are designed. This benchmarking data is sufficiently diverse to establish that the method bias and uncertainty will apply to rack conditions which include strong neutron absorbers, large water gaps, low moderator densities and spent fuel pool soluble boron.
The design method which insures the criticality safety of fuel assemblies in the fuel storage rack is described in detail in the Westinghouse Spent Fuel Rack Criticality Analysis Methodology topical reportW This report describes the computer codes, benchmarking, and methodology which are used to calculate the criticality safety limits presented in this report for Prairie Island.
As determined in the benchmarking in the topical report, the method bias using the described '
methodology of NITAWL-II, XSDRNPM-S and KENO-Va is 0.0077 AK with a 95 percent '
probability at a 95 percent confidence level standard deviation on the bias of 0.0030 AK. These values will be used throughout this report as needed.
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Prairie Island Spent Fuel Racks i i
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3.0 Criticality Analysis of All Cell Storage This section describes the analytical techniques and models employed to perform the criticality analysis and reactivity equivalencing evaluations for the Prairie Island spent fuel storage racks all cell enrichment limits using credit for soluble boron.
Section 3.1 describes the No Soluble Boron 95/95 Ke g KENO-Va calculations performed for the all cell storage configuration. Section 3.2 discusses the results of the spent fuel rack K eg soluble boron credit calculations. Finally, Section 3.3 presents the results of calculations performed to show the minimum burnup requirements for assemblies with higher initial enrichments above those determined in Section 3.1 including decay time credit.
3.1 No Soluble Boron 95/95 Ke g To determine the enrichment required to maintain Ke g s 1.0, KENO-Va is used to establish a nominal reference reactivity and PHOENIX-P is used to assess the effects of material and construction tolerance variations. A fmal 95/95 K egis developed by statistically combining the individual tolerance impacts with the calculational and methodology uncertainties and summing this term with the nominal KENO-Va reference reactivity. The equation for determining the final 95/95 K egis defmed in Reference 1.
The following assumptions are used to develop the No Soluble Boron 95/95 Ke g KENO-Va model for storage of fuel assemblies in the Prairie Island spent fuel storage racks:
- 1. The fuel assembly parameters relevant to the criticality analysis are based on the Westinghouse 14x14 OFA and 14x14 STD designs (see Table 1 on page 25 for fuel parameters). The Westinghouse 14x14 STD design bounds the reactivity of the 14x14 Exxon fuel assemblies.
- 2. Westinghouse 14x14 OFA and STD fuel assemblies contain uranium dioxide at a nominal ;
enrichment of 1.87 w/o 235 U and 1.77 w/o 235 U, respectively, over the entire length of each l rod. l
- 3. The fuel pellets are modeled assuming nominal values for theoretical density and dishing fraction.
- 4. No credit is taken for any natural or reduced enrichment axial blankets. This assumption l results in equivalent or conservative calculations of reactivity for all fuel assemblies used at Prairie Island including those with annular pellets at the fuel rod ends.
236 U in the fuel, nor is any credit taken for the buildup of
- 5. No credit is taken for any 234U or fission product poison material.
- 6. No credit is taken for any spacer grids or spacer sleeves.
- 7. No credit is taken for any burnable absorber in the fuel rods.
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- 8. No credit is taken for the presence of spent fuel rack Boraflex poison panels. The Boraflex volume is replaced with water. ;
l 9. The moderator is water with 0 ppm soluble boron at a temperature of 68'F. A water density of l 1.0 gm/cm3 is used.
- 10. The fuel assembly array is infinite in lateral (x and y) extent and finite in axial (vertical) extent with a 6 inch water region on the top and bottoin of the fuel in the axial direction or i conservatively modeled as infinite.
I1. All available storage cells are loaded with fuel assemblies.
With the above assumptions, the KENO-Va calculations of K eg under normal conditions resulted !
in a .K eg of 0.96914 and 0.96799 for both Westinghouse OFA and STD fuel assemblies, respectively, as shown in Table 2 on page 26.
Calculational and methodology biases must be considered in the final K,g summation prior to comparing against the 1.0 Ke g limit. The following biases are included: ,
Methodology: The benchmarking bias as determined for the Westinghouse KENO-Va methodology was considered. >
Water Temperature: A reactivity bias is applied to account for the effect of the normal range of spent fuel pool water temperatures (50*F to 150*F). !
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To evaluate the reactivity effects of possible variations in material characteristics and mechanical / construction dimensions, perturbation calculations are performed using PHOENIX-P.
For the Prairie Island spent fuel rack all cell enrichment storage configuration, UO2 material tolerances are considered along with construction tolerances related to the cell I.D., storage cell pitch, and stainless steel wall thickness. Uncertainties associated with calculation and methodology accuracy are also considered in the statistical summation of uncertainty components.
The following tolerance and uncertainty components are considered in the total uncertainty statistical summation:
235 235U Enrichment: The enrichment tolerance of 0.05 w/o U about the nominal reference 235 enrichments of 1.87 w/o 235U and 1.77 w/o U was considered.
UO 2Density: A i2.0% variation about the nominal reference theoretical density (the nominal reference values are listed in Table 1 on page 25) was considered.
Fuel Pellet Dishing: A variation in fuel pellet dishing fraction from 0.0% to 2.0% (the nominal ,
reference values are listed in Table 1 on page 25) was considered.
Storage Cell I.D.: The 0.10 inch tolerance about the nominal 8.27 inch reference cell I.D.was considered.
Storage Cell Pitch: The i0.06 inch tolerance about the nominal 9.50 inch reference cell pitch '
was considered.
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1 l Stainless Steel Thickness: The 10.01 inch tolerance about the nominal 0.09 inch reference stainless steel thickness for all rack structures was considered.
l Assembly Position: The KENO-Va reference reactivity calculation assumes fuel assemblies are symmetrically positioned within the storage cells. Conservative calculations show that an increase in reactivity can occur if the comers of four fuel assemblies are positioned together. ,
This reactivity increase was considered in the statistical summation of spent fuel rack ;
tolerances.
Calculation Uncertainty: The 95 percent probability /95 percent confidence level uncertainty on the KENO-Va nominal reference K eg was considered.
Methodology Uncertainty: The 95 percent probability /95 percent confidence uncertainty in the benchmarking bias as determined for the Westinghouse KENO-Va methodology was considered.
The 95/95 K eg for the Prairie Island spent fuel rack all cell storage configuration is developed by adding the temperature and methodology biases and the statistical sum ofindependent tolerances and uncertainties to the nominal KENO-Va reference reactivity. The summation is shown in Table.2 and results in a 95/95 Keg of 0.99947 and 0.99893 for Westinghouse OFA and STD fuel assembly types, respectively.
Since Keg is less than 1.0 for both fuel types, the Prairie Island spent fuel racks will remain subcritical when all cells are loaded with 1.87 w/o 235 U Westinghouse 14x14 OFA or 1.77 w/o 235 U Westinghouse 14x14 STD fuel assemblies and no soluble boron is present in the spent fuel pool water. In the next section, soluble boron credit will be used to provide safety margin by determining the amount of soluble boron required to maintain Ke g 5 0.95 including tolerances and uncertainties.
3.2 Soluble Boron Credit K eg Calculations To determine the amount of soluble boron required to maintain Ke gs 0.95, KENO-Va is used to establish a nominal reference reactivity and PHOENIX-P is used to assess the effects of material and construction tolerance variations. A final 95/95 Kegis developed by statistically combining the individual tolerance impacts with the calculational and methodology uncertainties and summing this term with the nominal KENO-Va reference reactivity.
The assumptions used to develop the nominal case KENO-Va model for soluble boron credit for all cell storage in the Prairie Island spent fuel racks are the same as those in Section 3.1 except for assumption 9 regarding the moderator soluble boron concentration. The moderator used is water with 200 ppm boron for both the Westinghouse OFA and STD fuel assembly types.
With the above assumptions, the KENO-Va calculation for the nominal case results in a Ke g of 0.90395 and 0.90823 for Westinghouse OFA and STD fuel assembly types, respectively, as shown in Table 3 on page 27.
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Calculational and methodology biases must be considered in the final Ke g summation prior to l
comparing against the 0.95 Ke glimit. The following biases are included:
Methodology: The benchmarking bias as determined for the Westinghouse KENO-Va l methodology was considered.
l Water Temperature: A reactivity bias is applied to account for the effect of the normal range i' of spent fuel pool water temperatures (50*F to 150*F).
To evaluate the reactivity effects of possible variations in material characteristics and mechanical / construction dimensions, PHOENIX-P perturbation calculations are performed. For l the Prairie Island spent fuel rack all cell enrichment storage configuration, UO2 material tolerances are considered along with construction tolerances related to the cell 1.D., storage cell pitch, and stainless steel wall thickness. Uncertainties associated with calculation and q methodology accuracy are also considered in the statistical summation of uncertamty j components. ;
The following tolerance and uncertainty components are considered in the total uncertainty I statistical summation:
l 235 U Enrichment: The enrichment tolerance of 0.05 w/o 235 U about the nominal reference enrichments of 1.87 w/o 235 U and 1.77 w/o 235 U was considered. i 00 Density:
2 A i2.0% variation about the nominal reference theoretical density (the nominal reference values are listed in Table 1 on page 25) was considered.
Fuel Pellet Dishing: A variation in fuel pellet dishing fraction from 0.0% to 2.0% (the nominal reference values are listed in Table 1 on page 25) was considered.
Storage Cell I.D.: The 10.10 inch tolerance about the nominal 8.27 inch reference cell I.D.was considered. .
Storage Cell Pitch: The i0.06 inch tolerance about the nominal 9.50 inch reference cell pitch I was considered.
Stainless Steel Thickness: The 10.01 inch tolerance about the nominal 0.09 inch reference stainless steel thickness for all rack structures was considered.
Assembly Position: The KENO-Va reference reactivity calculation assumes fuel assemblies are symmetrically positioned within the storage cells. Conservative calculations show that an increase in reactivity can occur if the corners of four fuel assemblies are positioned together.
This reactivity increase was considered in the statistical summation of spent fuel rack tolerances.
Calculation Uncertainty: The 95 percent probability /95 percent confidence level uncertainty on the KENO-Va nominal reference Keg was considered.
Methodology Uncertainty: The 95 percent probability /95 percent confidence uncertainty in the benchmarking bias as determined for the Westinghouse KENO-Va methodology was considered.
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7 Prairie Island Spent Fuel Racks J
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- The 95/95 K eg for the Prairie Island spent fuel rack all cell storage configuration is developed by l adding the temperature and methodology biases and the statistical sum ofindependent tolerances !
and uncertainties to the nominal KENO-Va reference reactivity. The summation is shown in !
Table 3 and results in a 95/95 K,g of 0.93505 and 0.94070 for Westinghouse OFA and STD fuel l assembly types, respectively. i Since Keg is less than 0.95 including soluble boron credit and uncertainties at a 95/95 l probability / confidence level, the acceptance criteria for criticality is met for the all cell l enrichment storage of 14x14 fuel assemblies in the Prairie Island spent fuel racks. Storage of fuel !
assemblies with nominal enrichments up to 1.87 w/o 235 U and 1.77 w/o 235 U is acceptable for Westinghouse OFA or STD fuel assembly types, respectively, in all cells of the Prairie Island !
spent fuel racks including the presence of 200 ppm. l 3.3 Burnup and Decay Time Reactivity Equivalencing 235 Storage of fuel assemblies with enrichments higher than 1.87 w/o U and 1.77 w/o 235U for the l Westinghouse OFA and STD fuel types in the Prairie Island spent fuel rack all cell configuration is achievable by means of the concept of reactivity equivalencing. The concept of reactivity )
equivalencing is predicated upon the reactivity decrease associated with fuel depletion and the radioactive decay of the spent fuel isotopes within the fuel assemblies.
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For burnup credit, a series of reactivity calculations are performed to generate a set of enrichment-fuel assembly discharge burnup ordered pairs which all yield an equivalent K,gwhen stored in the spent fuel storage racks.
Figure 3 on page 46 and Figure 4 on page 47 show the constant Ke g contours as a function of j assembly average burnup, for different decay times, generated for the Prairie Island spent fuel rack all cell configuration. These curves represent combinations of fuel enrichment and discharge J
burnup which yield the same rack multiplication factor (K eg) as the rack loaded with 1.87 w/o 235 U fuel (at zero burnup) for Westinghouse OFA and STD fuel assemblies, 235U and 1.77 w/o respectively, in all cell locations.
Uncertainties associated with burnup credit include a reactivity uncertainty of 0.01 AK at 30,000 MWD /MTU applied linearly to the burnup credit requirement to account for calculational and depletion uncertainties and 4% on the calculated burnup to account for burnup measurement uncertainty. The amount of additional soluble boron needed to account for these uncertainties in the burnup requirement of Figure 3 and Figure 4 is 200 ppm and 250 ppm for the Westinghouse OFA and STD fuel assembly types, respectively. This is additional boron above the 200 ppm required for Westinghouse OFA and STD fuel assembly types, as calculated in Section 3.2. This results in a total soluble boron credit of 400 ppm and 450 ppm for the Westinghouse OFA and STD fuel assembly types, respectively.
8 Prairie Island Spent Fuel Racks
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Decay Time Credit is an extension of the Burnup Credit process which includes the time an ,
assembly has been discharged as a variable. This methodology gains additional margin in I l reactivity and reduces the minimum burnup requirements. Spent fuel decay time credit results from the radioactive decay of isotopes in the spent fuel to daughter isotopies, which results in l reduced reactivity. One of the major contributors is the decay of 24t Pu to 2 Am. In this report, credit is taken only for the decay of actinides. Decay of the fission products has the effect of further reducing the reactivity of the spent fuel.
In the decay time methodology reported here, the fission product isotopes are frozen at the concentrations existing at the time of discharge of the fuel (except I"Xe which is removed).
These calculations are performed at different discharge burnups. The actinide isotopes are allowed to decay based on their natural process. The loss in reactivity due to the radioactive decay of the spent fuel results in reducing the minimum bumup needed to meet the reactivity requirements. Thus for different decay times, a family of curves is generated which all yield the desired equivalent Ke g when stored in the spent fuel storage racks. In the decay time methodology the following assumptions are used in the models:
- 1. The fuel assemblies are modeled using the same criteria as Section 3.1.
- 2. Fuel is depleted using a conservatively high soluble boron letdown curve to enhance the buildup of plutonium making the fuel more reactive in the spent fuel storage racks.
Sensitivity studies have shown that spectrum effects are also conservative for the decay time calculation.
- 3. No credit for fission product isotopic decay is used.
- 4. Actinide only isotopes decay is used.
- 5. Nominal spent fuel rack configu:ation/ dimensions are used.
With the above assumptions, the calculation of the decay time burnup credit curves are found to be conservative for use in the spent fuel pool criticality analysis.
i It is important to recognize that the curves in Figure 3 and Figure 4 are based on calculations of constant rack reactivity. In this way, the environment of the storage rack and its influence on assembly reactivity is implicitly considered. For convenience, the data from Figure 3 and Figure 4 are also provided in Table 4 on page 28 and Table 5 on page 29. Use of linear interpolation l between the tabulated values is acceptable since the curves shown in Figure 3 and Figure 4 are I linear in between the tabulated points. l The effect of axial burnup distribution on assembly reactivity has been considered in the development of the Prairie Island burnup credit limit. Previous evaluations have been performed to quantify axial burnup reactivity effects and to confirm that the reactivity equivalencing j methodology described in Reference 1 results in calculations of conservative burnup credit limits. 1 The evaluations show that axial burnup effects can cause assembly reactivity to increase only at l 9
Prairie Island Spent Fuel Racks
burnup-enrichment combinations which are beyond those calculated for the Prairie Island burnup credit limit. Therefore, additional accounting of axial burnup distribution effects in the Prairie Island burnup credit limit is not necessary.
1
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10 Prairie Island Spent Fuel Racks 4
t l
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4.0 Criticality Analysis of 3x3 Checkerboard Storage This section describes the analytical techniques and models employed to perform the criticality analysis and reactivity equivalencing evaluations for the Prairie Island spent fuel storage racks 3x3 checkerboard storage enrichment limits using credit for soluble boron. The purpose of the 3x3 checkerboard storage configuration is to allow the most reactive fresh fuel to be stored in the Prairie Island spent fuel racks. The most reactive fresh fuel for Prairie Island has a nominal enrichment of 4.95 w/o 235 U in a Westinghouse 14x14 OFA fuel assembly.
Section 4.1 describes the No Soluble Boron 95/95 Ke g KENO-Va calculations performed for the 3x3 checkerboard storage configuration. Section 4.2 discusses the results of the spent fuel rack Keg soluble boron credit calculations. Finally, Section 4.3 presents the results of calculations performed to show the minimum burnup requirements for assemblies with higher initial enrichments above those determined in Section 4.1 including decay time and Gadolinium credit.
4.1 No Soluble Boron 95/95 Ke g Calculations To determine the enrichment required to maintain Ke g s; 1.0, KENO-Va is used to establish a nominal reference reactivity and PHOENIX-P is used to assess the effects of material and construction tolerance variations. A final 95/95 K egis developed by statistically combining the individual tolerance impacts with the calculational and methodology uncertainties and summing this term with the nominal KENO-Va reference reactivity. The equation for determining the final 95/95 Kegis defined in Reference 1.
The following assumptions are used to develop the No Soluble Boron 95/95 Ke g KENO-Va model for storage of fuel assemblies in the Prairie Island spent fuel storage rack: ;
i
- 1. The fuel assembly parameters relevant to the criticality analysis are based on the l Westinghouse 14x14 OFA and STD designs (see Table 1 on page 25 for fuel parameters). The i Westinghouse 14x14 STD design bounds the reactivity of the 14x14 Exxon fuel assemblies currently stored in the Prairie Island spent fuel pool.
- 2. Westinghouse 14x14 OFA fuel assemblies stored in the middle of the 3x3 checkerboard 235 contain uranium dioxide at a nominal enrichment of 4.95 w/o U over the entire length of each rod.
- 3. Westinghouse 14x14 OFA and STD fuel assemblies surrounding the center of the 3x3 235 checkerboard contain uranium dioxide at nominal enrichments of 1.30 w/o U and j 235 1.20 w/o U respectively, over the entire length of each rod.
- 4. The fuel pellets are modeled assuming nominal values for theoretical density and dishing fraction.
- 5. No credit is taken for any natural or reduced enrichment axial blankets. This assumption results in equivalent or conservative calculations of reactivity for all fuel assemblies used at Prairie Island including those with annular pellets at the fuel rod ends.
11 Prairie Island Spent Fuel Racks
236
- 6. No credit is taken for any 234 U or U in the fuel, nor is any credit taken for the buildup of fission product poison material. ;
- 7. No credit is taken for any spacer grids or spacer sleeves.
- 8. No credit is taken for any bumable absorber in the fuel rods. (Burnable absorber credit is calculated in Section 4.3)
- 9. No credit is taken for the presence of spent fuel rack Boraflex poison panels. The Boraflex volume is replaced with water. ;
l
- 10. The moderator is water with 0 ppm soluble boron at a temperature of 68'F. A water density of i l.0 gm/cm 3is used.
I 1. The fuel assembly array is infinite in lateral (x and y) extent and finite in axial (vertical) extent
! with a 6 inch water region on the top and bottom of the fuel in the axial direction or i conservatively modeled as infinite. ;
- 12. Storage cells are loaded with fuel assemblies in a 3x3 checkerboard pattern as shown in )
235 Figure 5 on page 48. The center of the 3x3 checkerboard is always a fresh 4.95 w/o U ;
Westinghouse OFA assembly. The surrounding assemblies are Westinghouse OFA or STD fuel assemblies with the specified enrichment limits. 1 With the above assumptions, the KENO-Va calculations of K eg under normal conditions resulted !
in a K ge of 0.96157 and 0.95918 for the both Westinghouse OFA and STD fuel assemblies respectively, as shown in Table 6 on page 30.
Calculational and methodology biases must be considered in the final Ke g summation prior to comparing against the 1.0 Ke glimit. The following biases are included:
Methodology: The benchmarking bias as determined for the Westinghouse KENO-Va methodology was considered.
Water Temperature: A reactivity bias is applied to account for the effect of the normal range of spent fuel pool water temperatures (50*F to 150*F).
To evaluate the reactivity effects of possible variations in material characteristics and mechanical / construction dimensions, PHOENIX-P perturbation calculations are performed. For the Prairie Island spent fuel rack 3x3 checkerboard storage configuration, UO2 material tolerances sre considered along with construction tolerances related to the cell 1.D., storage cell pitch, and stainless steel wall thickness. Uncertainties associated with calculation and methodology accura cy are also considered in the statistical summation of uncertainty components.
The 'ollowing tolerance and uncertainty components are considered in the total uncenainty statistical summation:
235 235U Enrichment: The enrichment tolerance of 10.05 w/o U about the nominal fresh 235 reference enrichment of 4.95 w/o 235U and nominal enrichments of 1.30 w/o U and 1.20 w/o 235U was considered.
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l 12 Prairie Island Spent Fuel Racks
i I
UO 2Density: A i2.0% variation about the nominal reference theoretical density (the nominal reference values are listed in Table 1 on page 25) was considered.
Fuel Pellet Dishing: A variation in fuel pellet dishing fraction from 0.0% to 2.0% (the nominal l reference values are listed in Table 1 on page 25) was considered.
Storage Cell I.D.: The 0.10 inch tolerance about the nominal 8.27 inch reference cell I.D.was considered.
Storage Cell Pitch: The 0.06 inch tolerance about the nominal 9.50 inch reference cell pitch I l was considered.
Stainless Steel Thickness: The 10.01 inch tolerance about the nominal 0.09 inch reference i stainless steel thickness for all rack structures was considered.
l Assembly Position: The KENO-Va reference reactivity calculation assumes fuel assemblies l are' symmetrically positioned within the storage cells. Conservative calculations show that an !
increase in reactivity can occur if the corners of four fuel assemblies are positioned together.
This reactivity increase is considered in the statistical summation of spent fuel rack tolerances.
Calculation Uncertainty: The 95 percent probability /95 percent confidence level uncertainty on the KENO-Va nominal reference Kegwas considered.
l Methodology Uncertainty: The 95 percent probability /95 percent confidence uncertainty in j the benchmarking bias as determined for the Westinghouse KENO-Va methodology was ]
considered. l The 95/95 K eg for the Prairie Island spent fuel rack 3x3 checkerboard storage configuration is developed by adding the calculational and methodology biases and the statistical sum of independent uncertainties to the nominal KENO-Va reference reactivity. The summation is shown in Table 6 and results in a 95/95 K eg of 0.99983 and 0.99944 for Westinghouse OFA and STD fuel assembly types, respectively.
Since K,g is less than 1.0 for all fuel types considered, the Prairie Island spent fuel racks will ~
remain suberitical when cells are loaded in a 3x3 checkerboard as specified in Figure 5 with a 235 4.95 w/o U Westinghouse OFA fuel assembl237 surrounded by any combination of !
1.30 w/o 235 U Westinghouse OFA or 1.20 w/o U Westinghouse STD fuel assemblies, respectively. In the next section, soluble boron credit will be used to provide safety margin by determining the amount of soluble boron required to maintain K eg 5 0.95 including tolerances and uncertainties.
4.2 Soluble Boron Credit Ke gCalculations l To determine the amount of soluble boron required to maintain Ke gs 0.95, KENO-Va is used to establish a nominal reference reactivity and PHOENIX-P is used to assess the effects of material and construction tolerance variations. A final 95/95 Kegis developed by statistically combining the individual tolerance impacts with the calculational and methodology uncertainties and l summing this term with the nominal KENO-Va reference reactivity.
l l
13 Prairie Island Spent Fuel Racks I
i The assumptions used to develop the nominal case KENO-Va model for soluble boron credit for 1 3x3 checkerboard cell storage in the Prairie Island spent fuel racks are the same as those in Section 4.1 except for assumption 10 regarding the moderator soluble boron concentration. The i moderator is water with 250 ppm or 300 ppm for the Westinghouse OFA and STD fuel assembly !
types, respectively.
With the above assumptions, the KENO-Va calculation for the nominal case results in a Ke g of ;
0.90802 and 0.89614 for Westinghouse OFA and STD fuel assembly types, respectively as shown !
- in Table 7 on page 31. {
Calculational and methodology biases must be considered in the final Ke g summation prior to comparing against the 0.95 Ke glimit. The following biases are included:
Methodology: The benchmarking bias as determined for the Westinghouse KENO-Va l methodology was considered.
Water Temperature: A reactivity bias is applied to account for the effect of the normal range of spent fuel pool water temperatures (50*F to 150*F).
To evaluate the reactivity effects of possible variations in material characteristics and l mechanical / construction dimensions, PHOENIX-P perturbation calculations are performed. For ;
the Prairie Island spent fuel rack 3x3 checkerboard storage configuration, UO2 material tolerances i are considered along with construction tolerances related to the cell I.D., storage cell pitch, and stainless steel wall thickness. Uncertainties associated with calculation and methodology accuracy are also considered in the statistical summation of uncertainty components.
The following tolerance and uncertainty components are considered in the total uncertainty statistical summation: i 235 235U Enrichment: The enrichment tolerance of 10.05 w/o U about the nominal fresh l 235 235 reference enrichment of 4.95 w/o U and nominal enrichments of 1.30 w/o U and 235 l 1.20 w/o U was considered. 1 UO 2Density: A 2.0% variation about the nominal reference theoretical density (the nominal I reference values are listed in Table 1 on page 25) was considered.
Fuel Pellet Dishing: A variation in fuel pellet dishing fraction from 0.0% to 2.0% (the nominal l reference values are listed in Table 1 on page 25) was considered. j Storage Cell I.D.: The 0.10 inch tolerance about the nominal 8.27 inch reference cell I.D.was considered. l Storage Cell Pitch: The 0.06 inch tolerance about the nominal 9.50 inch reference cell pitch l was considered. l Stainless Steel Thickness: The i0.01 inch tolerance about the nominal 0.09 inch reference stainless steel thickness for all rack structures was considered.
l l l
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i 14 Prairie Island Spent Fuel Racks
1 1
Assembly Position: The KENO-Va reference reactivity calculation assumes fuel assemblies are symmetrically positioned within the storage cells. Conservative calculations show that an increase in reactivity can occur if the corners of four fuel assemblies are positioned together.
This reactivity increase.is considered in the statistical summation of spent fuel rack tolerances.
Calculation Uncertainty: The 95 percent probability /95 percent confidence level uncertainty on the KENO-Va nominal reference K eg was considered.
Methodology Uncertainty: The 95 percent probability /95 percent confidence uncertainty in the benchmarking bias as determined for the Westinghouse KENO-Va methodology was considered.
The 95/95 K eg for the Prairie Island spent fuel rack 3x3 checkerboard storage configuration is developed by adding the calculational and methodology biases and the statistical sum of independent tolerances and uncertainties to the nominal KENO-Va reference reactivity. The summation is shown in Table 7 and results in a 95/95 Keg of 0.94134 and 0.93466 for Westinghouse OFA and STD fuel assembly types, respectively.
Since Keg is less than 0.95 including soluble boron credit and uncertainties at a 95/95 probability / confidence level, the acceptance criteria for criticality is met for the 3x3 checkerboard configuration storage of 14x14 fuel assemblies in the Prairie Island spent fuel racks when cells are 235 loaded in a 3x3 checkerboard with a 4.95 w/o U Westinghouse OFA fuel assembly surrounded by any combination of 1.30 w/o 235 U Westinghouse OFA or 1.20 w/o 235 U Westinghouse STD fuel assemblies, respectively, including the presence of soluble boron as specified above.
4.3 Reactivity Equivalencing Increased flexibility for storage of higher enrichment fuel assemblies is achievable using .
reactivity equivalencing. Reactivity equivalencing is predicated upon the reactivity decrease associated with fuel depletion, addition of Gadolinium burnable absorbers (GAD), and radioactive decay of the spent fuel.
4.3.1 Burnup and Decay Time Reactivity Equivalencing Storage of fuel assemblies with enrichments higher than 1.30 w/o 235U and 1.20 w/o 235U for the Westinghouse OFA and STD fuel types in the Prairie Island spent fuel rack 3x3 checkerboard configuration is achievable by means of the concept of reactivity equivalencing. The concept of reactivity equivalencing is predicated upon the reactivity decrease associated with fuel depletion and the radioactive decay of the spent fuel isotopes within the fuel assemblies.
For burnup credit, a series of reactivity calculations are performed to generate a set of enrichment-fuel assembly discharge burnup ordered pairs which all yield an equivalent K e gwhen stored in the spent fuel storage racks.
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i 15 Prairie Island Spent Fuel Racks
-l
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Figure 6 on page 49 and Figure 7 on page 50 shows the constant Ke g contours as a function of. )
l assembly average burnup, for different decay times, generated for the Prairie Island spent fuel rack' 3x3 checkerboard storage configuration. These curves represent combinations of fuel
{
enrichment and discharge burnup which yield the same rack multiplication factor (Ke g) as the rack loaded with 1.30 w/o 235 U or 1.20 w/o 235 U fuel (at zero bumup) for Westinghouse OFA and l STD fuel assemblies, respectively. ;
I Uncertainties associated with burnup credit include a reactivity uncertainty of 0.01 AK at l 30,000 MWD /MTU applied linearly to the burnup credit requirement to account for calculational !
l= and depletion uncertainties and 4% on the calculated bumup to account for burnup measurement !
l uncertainty. The amount of additional soluble boron needed to account for these uncertainties in l l the burnup requirement of Figure 6 and Figure 7 are 350 ppm for Westinghouse OFA.and l 450 ppm for Westinghouse STD fuel assembly types.' This is additional boron above the 250 ppm j
! and 300 ppm required for Westinghouse OFA and STD fuel assembly types, respectively, as !
! calculated in Section 4.2. This results in a total soluble boron credit of 600 ppm and 750 ppm for Westinghouse OFA and STD fuel assembly types, respectively.
l Decay Time Credit is an extension of the Bumup Credit process which includes the time an !
l assembly has been discharged as a variable. This methodology gains additional margin in !
L reactivity and reduces the minimum bumup requirements. Spent fuel decay time credit results i s, which results in !
l-from the radioactive decay of isotopes in the
' reduced reactivity. One of the major contributors is the decay of Pu to spent 43 fuel to daughter isotp' ' Am.!
l credit is taken only for the decay of actinides. Decay of the fission products has the effect of !'
L further reducing the reactivity of the spent fuel.
i j In the decay time methodology reported here, the fission product isotopes are frozen at the 135 concentrations existing at the time of discharge of the fuel (except Xe which is removed).
These calculations are performed at different discharge burnups. The actinide isotopes are l allowed to decay based on their natural process. The loss in reactivity due to the radioactive decay of the spent fuel results in reducing the minimum burnup needed to meet the reactivity requirements. Thus for different decay times, a family of curves is generated which all yield the '
desired equivalent K,g when stored in the spent fuel storage racks. In the decay. time methodology the following assumptions are used in the models:
l 1. The fuel assemblies are modeled using the same criteria as Section 4.1.
' Fuel is depleted using a conservatively high soluble boron letdown curve to enhance the buildup of plutonium making the fuel more reactive in the spent fuel storage racks.
Sensitivity studies have shown that spectrum effects are also conservative for the decay time
- calculation.
f 3. No credit for fission product isotopic decay is used.
- 4. Actinide only isotopes decay is used.
f
- 5. Nominal spent fuel rack configuration / dimensions used.
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16 Prairie Island Spent Fuel Racks l - . - . . - - . . - - . Y
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l
( With the above assumptions, the calculation of the decay time bumup credit curves are found to .
l be conservative for use in the spent fuel pool criticality analysis.
- It is important to recognize that the curves in Figure 6 and Figure 7 are based on calculations of constant rack reactivity. In this way, the environment of the storage rack and its influence on i assembly reactivity is implicitly considered. For convenience, the data from Figure 6 and Figure 7 are also provided in Table 9 on page 33 and Table 10 on page 34. Use of linear interpolation between the tabulated values is acceptable since the curves shown in Figure 6 and Figure 7 are linear in between the tabulated points.
l The effect of axial burnup distribution on assembly reactivity has been considered in the development of the Prairie Island burnup credit limit. Previous evaluations have been performed j to quantify axial bumup reactivity effects and to confirm that the reactivity equivalencing methodology described in Reference 1 results in calculations of conservative burnup credit limits. ;
Since the 3x3 checkerboard burnup curves exceed the bumup-enrichment combinations at which the axial bumup reactivity effect is positive, an axial burnup reactivity bias is included in the generation of the burnup credit curves. ;
4.3.2 Gadolinium Credit Resetivity Equivalencing ;
Storage of fuel assemblies with enrichments higher than 1.30 w/o 235 U and 1.20 w/o 235 U for the Westinghouse OFA and STD fuel types in the Prairie Island spent fuel rack 3x3 checkerboard ]
configuration is achievable by means of the concept of reactivity equivalencing. The concept of reactivity equivalencing is predicated upon the reactivity decrease associated with the presence of Gadolinium burnable absorbers (GAD). GAD rods consist of the Gadolinium isotope mixed within the UO 2fuel pellet. This neutron absorbing material is a non-removable part of the fuel i assembly once it is manufactured.
Gadolinium in the fuel is handled by modeling the effect of the presence of the absorber in a 3x3 checkerboard configuration and then determining the acceptable enrichment of the surrounding fuel to assure the criticality limit.
The credit for the presence of Gadolinium in the fuel assemblies is based on matching the reactivity of these assemblies to an " equivalent enrichment" of fresh assemblies, without any bumup or any Gadolinium. This " equivalent enrichment" is determined using PHOENIX-P and using the maximum reactivity of the Gadolinium bearing assemblies during their lifetime. The assemblies with "equivaleat, enrichment" are put in a 3x3 checkerboard configuration (described in Section 4.1) and the e'sichment for the assemblies surrounding the center location is determined so that the new 3x3 checkerboard configuration will still meet the reactivity limits.
235 Table 8 on page 32 shows the results for the placement of the 4.95 w/o U enrichment OFA assemblies with varying number of Gadolinium rods and the corresponding maximum permitted enrichment of the surrounding OFA and STD fuel.
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l 17 Prairie Island Spent Fuel Racks
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! The following assumptions are used for the GAD rod assemblies in the PHOENIX-P models:
- 1. The fuel assembly is modeled at its most reactive point in life. This includes the net effect of reactivity increase due to depletion of Gadolinium and loss of reactivity due to fuel l burnup.
l 2. The fuel assembly uses a homogenized 235 U loading corresponding to the Gadolinium rod length and blanket enrichment.
- 3. The Gadolinium loading used in the analysis is 8 w/o Gd with a 132 inch length.
- 4. The fuel pellets are modeled assuming conservative theoretical density and dishing fraction. ,
- 5. The Gadolinium loading is reduced by an amount which corresponds to the minimum poison length offered for the given fuel assembly type. For instance, a 144 inch fuel stack with a minimum poison length of 132 inches would result in a 8.33% Gadolinium loading reduction to conservatively model the minimum poison length for that fuel assembly type.
With the above assumptions, the calculation of the Gadolinium burnup credit curves are found to
. be conservative for use in the spent fuel pool criticality analysis.
From these configurations, Figure 8 on page 51 through Figure 15 on page 58 shows the constant Keg contour generated for the Prairie Island spent fuel rack 3x3 checkerboard storage configuration with the use of GAD. These curves represent combinations of fuel enrichment and discharge burnup which yield the same rack multiplication factor (K eg) as the rack loaded with the enrichments specified in Table 8 (at zero burnup) for Westinghouse OFA and STD fuel assemblies. When assemblies contain more than 16 GAD rods, the burnup curves for 16 GAD rods should be used. This is because maximum reactivity of the 16 GAD rod depletion is always higher than that of an assembly containing more Gadolinium rods. Once the Gadolinium is gone, the reactivity behavior is consistent with unpoisoned fuel depletions.
It is important to recognize that the curves in Figure 8 through Figure 15 are based on calculations l of constant rack reactivity. In this way, the environment of the storage rack and its influence on l assembly reactivity is implicitly considered. For convenience, the data from Figure 8 through Figure 15 are also provided in Table 1I on page 35 through Table 18 on page 42. Use oflinear interpolation between the tabulated values is acceptable since the curves shown in Figure 8 through Figure 15 are linear in between the tabulated points.
Uncertainties associated with Gadolinium credit include 3% for manufacturing and 10% for calculational uncertainties. The amount of additional soluble boron needed to account for these uncertainties in the burnup requirement of Figure 8 through Figure 15 is 150 ppm for Westinghouse OFA fuel assembly type since GAD is only in the center assembly location which ,
l is an OFA fuel assembly. This is additional boron above the 250 ppm and 300 ppm required for Westinghouse OFA and STD fuel assembly types, respectively, as calculated in Section 4.2. This results in a total soluble boron credit of 400 ppm and 450 ppm for Westinghouse OFA and STD 18 Prairie Island Spent Fuel Racks i
~
i 1
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i I
fuel assembly types, respectively. The Gadolinium boron concentrations are bounded by the burnup credit boron concentration for reactivity equivalencing. The Gadolinium boron concentration is not additive since each is calculated using an independent integral method.
The Gadolinium rod patterns used in this analysis are shown in Figure 16 on page 59.
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Prairie Island Spent Fuel Racks 19
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5.0 Discussion of Postulated Accidents i
l Most accident conditions will not result in an increase in Kg of the rack. Examples are: j l
Fuel assembly drop The rack structure pertinent for criticality is not excessively deformed on top of rack and the dropred assembly which comes to rest horizontally on top of the rack har su!!icient water separating it from the active fuel height of i stored assem'> lies to preclude neutronic interaction.
1 Fuel assembly drop Design of the spent fuel racks is such that it precludes the insertion of a between rack fuel assembly in these locations.
modules or between rack modules and spent fuel pool wall i
However, two accidents can be postulated for each storage configuration which would increase :
reactivity beyond the analyzed condition. The first postulated accident would be a loss of fuel pool cooling system and the second would be a mistoad of an assembly into a cell for which the restrictions on location, enrichment, burnup, decay time, or Gadolinium credit are not satisfied.
For the loss of fuel pool cooling system accident, calculations were performed for both all cell storage and 3x3 checkerboard storage to show the reactivity increase caused by a rise in the Prairie Island spent fuel pool water temperature from 150*F to 240*F. The reactivity increase for all cell storage is 0.01729 AK and 0.00835 AK for Westinghouse OFA and STD fuel assembly types, respectively. The reactivity increase for 3x3 checkerboard storage is 0.00661 AK and 0.00691 AK for Westinghouse OFA and STD fuel assembly types, respectively. The Westinghouse OFA and STD fuel assembly types conservatively bound the Exxon fuel assembly types.
For the mistoad assembly accident, calculations were performed for both all cell storage and 3x3 235 checkerboard storage to show the largest reactivity increase caused by a 4.95 w/o U Westinghouse OFA fuel assembly misplaced into a storage cell. The reactivity increase caused by misplacing a fuel assembly in the storage cell will bound the reactivity increase caused by placing a ibel assembly into the cask loading area. This is because in the cask loading area only two faces J the assembly has interaction with other assemblies and in tbe storage cell all four faces of the ssembly have interaction with other assemblies. The largest reactivity increase for all cell storage is 0.05201 AK and 0.05166 AK for Westinghouse OFA and STD fuel assembly types, respectively. The largest reactivity increase for 3x3 checkerboard storage is 0.05200 AK and 0.05891 AK for Westinghouse OFA and STD fuel assembly types, respectively. The Westinghouse OFA and STD fuel assembly types conservatively bound the Exxon fuel assembly types.
l Prairie Island Spent Fuel Racks 20 l
l
l l For an occurrence of the above postulated accident condition, the double contingency principle of l ANSI /ANS 8.1-1983 can be applied. This states that one is not required to assume two unlikely, independent, concurrent events to ensure protection against a criticality accident. Thus, for these postulated accident conditions, the presence of additional soluble boron in the storage pool water (above the concentration required for normal conditions and reactivity equivalencing) can be assumed as a realistic initial condition since not assuming its presence would be a second unlikely event.
The reactivity change due to the presence of soluble boron in the Prairie Island spent fuel pool has been calculated with PHOENIX-P for the all cell storage and the 3x3 checkerboard storage. The l
additional amount of soluble boron needed for accident conditions is shown below:
Soluble Boron Total Soluble Storage Fuel Assembly Reactivity Required for Boron Required Configuration Type Increase (AK) Accidents (ppm) (ppm)
All Cell W - OFA 0.05201 300 700 l Storage W - STD 0.05166 350 800 l
)
3x3 W - OFA 0.05200 400 1000 j Checkerboard W - STD 0.05891 550 1300 '
Storage Based on the above discussion, should a loss of spent fuel pool cooling accident or a fuel ;
assembly mistoad occur in the Prairie Island spent fuel racks, Kg will be maintained less than or equal to 0.95 due to the presence of at least 1300 ppm of soluble boron in the spent fuel pool water.
Table 19 shows a maximum of 750 ppm soluble boron without accidents assures the reactivity requirements of all fuel types and storage conngurations considered here. Soluble boron concentration of 1300 ppm, similarly meets the requirements with the consideration of accidents discussed above. The limiting accident is found to be the mistoading of a single assembly in the pool. If the single assembly misload accident can be eliminated from consideration through spent fuel pool verification and administrative controls, the loss of cooling is the limiting accident.
Total soluble boron credit required with the inclusion ofloss of pool water cooling is 900 ppm.
l 21 Prairie Island Spent Fuel Racks
6.0 Soluble Boron Credit Summary :
Spent fuel pool soluble boron has been used in this criticality analysis to offset storage rack and
! fuel assembly tolerances, calculational uncertainties, oncertainty associated with bumup credit :
and the reactivity increase caused by postulated accident conditions. The total soluble boron concentration required to be maintained in the spent fuel pool is a summation of each of these i components. Table 19 on mye 43 summarizes the storage configurations, fuel types and corresponding soluble bor ,ri tit requirements.
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l 22 Prairie Island Spent Fuel Racks
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l 7.0 Storage Configuration Interface and Miscellaneous Requirements The Prairie Island spent fuel pool is composed of single type of rack. The spent fuel pool areas have been analyzed for all cell storage, where all cells share the same storage requirements and limits, and a 3x3 checkerboard storage, where neighboring cells have different requirements and limits.
The following interface requirements are applicable for the Prairie Island storage cells:
All Cell Storage Next to The boundary between all cell storage and 3x3 checkerboard can 3x3 Checkerboard be either separated by a vacant row of cells or the interface must be configured such that the first row of carryover uses the lower enrichment of the 3x3 checkerboard fuel assemblies. Figure 17 on page 60 illustrates the canyover configuration.
Open Water Cells The all cell and 3x3 checkerboard configurations have been analyzed with every location containing a fuel assembly. In any location of the spent fuel pool, an open water cell is pennitted to replace a fuel assembly since the water cell will not cause any increase in reactivity in the spent fuel pool.
Neutron Source in a Cell The placement of a neutron source in the spent fuel pool will not cause any increase in reactivity in the spent fuel pool because the source displaces water which reduces reactivity.
Prairie Island Spent Fuel Racks 23
8.0 Summary of Criticality Results ,
1 For the storage of fuel assemblies in the spent fuel storage racks, the acceptance criteria for criticality requires the effective neutron multiplicatien tactor, Kg, to be less than or equal to 0.95, including uncertainties. This report shows that the acceptance criteria for criticality is met for the Prairie Island spent fuel racks for the storage of 14x14 fuel assemblies under both normal and accident conditions with soluble boron credit, credit for the presence of the integral absorber Gadolinium in the fuel, credit for the radioactive decay time of the spent fuel, and no credit for the spent fuel rack Boranex poison panels and the following storage configurations and enrichment limits: .
All Cell Storage Storage of 14x14 assemblies in any cell location with nominal 235 Enrichment Limits enrichments no greater than 1.87 w/o U for Westinghouse 235 14x14 OFA fuel assemblies and 1.77 w/o U for Westinghouse 14x14 STD and Exxon 14x14 fuel assemblies. Fuel assemblies with initial nominal enrichments greater than these must satisfy the minimum bumup requirement and decay time shown in Figure 3 and Figure 4.
Storage of Westinghouse 14x14 0FA assemblies with nominal l 3x3 Checkerboard 235 Enrichment Limits enrichments no greater than 4.95 w/o U in the center of a 3x3 checkerboard. The surrounding fuel assemblies must have an 235 initial nominal enrichment no greater than 1.30 w/o U for 235 Westinghouse 14x14 OFA fuel assemblies and 1.20 w/o U for l Westinghouse 14x14 STD and other Exxon fuel assemblies. With i Gadolinium credit, surrounding enrichments limits are increased j as shown in Table 8. Fuel assemblies with initial nominal enrichments greater than these must satisfy the minimum bumup requirement and decay time shown in Figure 6 through Figure 15.
The soluble boron credit required for these storage configurations are 750 ppm for nermal conditions and 1300 ppm for accidents.
l The analytical methods employed herein conform with ANSI N18.2-1973, " Nuclear Safety Criteria for the Design of Stationary Pressurized Water Reactor Plants," Section 5.7 Fuel Handling System; ANSI 57.2-1983, " Design Objectives for LWR Spent Fuel Storage Facilities at Nuclear Power Stations," Section 6.4.2; ANSI N16.9-1975, " Validation of Calculational Methods l for Nuclear Criticality Safety"; and the NRC Standard Review Plan, Section 9.1.2, " Spent Fuel Storage".
24 Prairie Island Spent Fuel Racks l
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l . Table 1. Fuel Parameters Employed in the Criticality Analysis Westinghouse Westinghouse I Parameter 14x14 OFA 14x14 STD i' Number of Fuel Rods per Assembly 179 179 i l Rod Zirc.4 Clad O.D. (inch) 0.400 0.422 i Clad Thickness (inch) 0.0243 0.0243 Fuel Pellet 0.D.(inch) 0.3444 0.3659 Fuel Pellet Density (% of Theoretical) 95 95 Fuel Pellet Dishing Factor (%) 1.1926 1.1870 Rod Pitch (inch) 0.556 0.556 i
Number of Zire Guide Tubes 16 16 Guide Tube O.D. (inch) 0.526 0.539 Guide Tube Thickness (inch) 0.0170 0.0170 Number ofInstrument Tubes 1 I i i
Instrument Tube O.D. (inch) 0.399 0.422 Instrument Tube Thickness (inch) 0.0235 0.0240 l
i l
i I
l
\
1 25 Prairie Island Spent Fuel Racks l
? !
l l
i Table 2. Pralrie Island All Cell Storage No Soluble Boron 95/95 K,g ,
i W - OFA W - STD Nominal KENO-Va Reference Reactivity: 0.96914 0.96799 i Calculational & Methodology Biases:
Methodology (Benchmark) Bias 0.00770 0.00770 i Pool Temperature Bias (50*F - 150*F) 0.00588 0.00663 l TOTAL Bias 0.01358 0.01433 1 Tolerances & Uncertainties:
235 UO2Enrichment Tolerance (i0.05 w/o U) 0.00870 0.00901 ,
UO2Density Tolerance (t2%) 0.00365 0.00336 l 1
Fuel Pellet Dishing Variation (0 to 2%) 0.00190 0.00174 j Cell Inner Diameter (i0.10 inch) 0.00079 0.00102 Cell Pitch ( 0.06 inch) 0.00733 0.00743 !
Cell Wall Thickness (i0.01 inch) 0.00765 0.00792 Asymmetric Assembly Position 0.00766 0.00672 j Methodology Bias Uncertainty (95/95) 0.00300 0.00300 ,
1 Calculational Uncertainty (95/95) 0.00272 0.00271 TOTAL Uncertainty (statistical) 0.01675 0.01661 l
l l
Final K,n Including Uncertainties & Tolerances: 0.99947 0.99893 .
I i
1 l
l Prairie Island Spent Fuel Racks 26 l
! i
! l l
l l ,
Table 3. Prairie Island All Cell Storage Soluble Boron Credit K,g l W - OFA W - STD l l Nominal KENO-Va Reference Reactivity: 0.90395 0.90823 l Calculational & Methodology Biases:
l Methodology (Benchmark) Bias 0.00770 0.00770 l Pool Temperature Bias (50*F - 150*F) 0.00600 0.00668 l TOTAL Bias 0.01370 0.01438 Tolerances & Uncertainties 235 l UO2Enrichment Tolerance (10.05 w/o U) 0.00880 0.00909 UO2Density Tolerance (i2%) 0.00415 0.00378 j Fuel Pellet Dishing Variation (0 to 2%) 0.00221 0.00198 Cell Inner Diameter (i0.10 inch) 0.00022 0.00039 Cell Pitch (i0.06 inch) 0.00757 0.00776 l 1
Cell Wall Thickness ( 0.01 inch) 0.00561 0.00588 l l
Asymmetric Assembly Position 0.00992 0.01075 i Methodology Bias Uncertainty (95/95) 0.00300 0.00300 Calculational Uncertainty (95/95) 0.00262 0.00266 ;
I TOTAL Uncertainty (statistical) 0.01740 0.01809 Final K,g Including Uncertainties & Tolerances: 0.93505 0.94070 4
l Prairie Island Spent Fuel Racks 27
o D Decay Time (years) y Enn.chment c
y 0 1 2 3 4 5 6 7 8 9 19 12 14 16 18 28 F H
$ 1.87 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 m
gr
(/)
3 2.00 2377 2367 2357 2348 2339 2331 2324 2317 2311 2304 2298 2286 2274 2265 2257 2247 ."
E m y 2.20 4995 4957 4923 4891 4861 4832 4805 4780 4757 4737 4718 4686 4653 4614 4577 4571 k:2. '
e.
N 2.40 7521 7456 7397 7342 7289 7240 7193 7150 7110 7076 7045 6990 6934 6870 6808 6799 1 M 1 7 2.60 9964 9670 9786 9707 % 33 9562 9496 94 B79 9329 9285 9206 9128 9041 F956 8938 $
CL 2.80 12330 12207 12097 18995 11899 11807 11722 11643 11570 11505 1I446 l1342 11242 11133 11029 10998 h
13878 13781 13692 136l1 13538 13407 13284 13156 13036 12987 n
m 3.00 14625 14474 14338 14212 14094 13982 _
3.20 16856 16677 16515 16365 16225 16094 15971 15857 15752 15655 15567 15410 15264 15118 14983 I4914 3.40 19029 18823 18635 18462 18301 18150 18009 17878 17757 17645 17542 17358 17189 17027 16878 16788 9 N
3.60 21151 20918 20706 20510 20328 20158 20000 19852 19716 19589 19471 19260 19069 18891 18730 18617 3
=
3.30 23229 22970 22734 22517 .22315 22126 21951 21787 21635 21493 21362 21124 20912 20719 20545 20410 E.
E c
4.00 25269 24986 24727 24488 24267 2406l 23869 23690 23523 23367 23222 22959 22726 22517 22331 22175 g cc 4.20 27278 26972 26691 26432 26193 25970 25762 25569 25388 25218 25060 24773 24520 242 % 24096 23922 2
- s 4.40 29262 28934 28634 28357 28100 27861 27638 27430 27236 27054 26883 26574 26302 26062 25848 25658 $
x 4.6e 31229 30881 30562 30268 29995 29741 29504 29283 29076 28882 28701 28372 2808l 27823 27594 27394 y E.
4.80 33184 32818 32483 32173 31886 31618 31368 3tl34 30915 30711 30520 30173 29866 29589 29342 29136 Q E
4.95 34647 34268 33923 33603 33306 33028 32768 32525 32298 32087 31890 31532 31213 30921 30658 30453 @
a I:d
-- - ~~ ... . . __ . .. ..
- t3 Enrichment #8NI"' D'"")
h O
.-. O I 2 3 4 5 6 7 8 9 to 12 64 16 18 20 m
~ H 1.77 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.
e ,
f/)
3 2.00 4195 4170 4144 4121 4102 4086 4072 4058 4043 4026 4007 3971 3949 3955 3970 3907 ?
- e E 6145 6546 6504 M64 M26 6389 6321 6267 6230 6201
- T1 2.29 6890 6819 6753 6694 6640 6591 $_
C =
O.-=
8747 8692 8594 8508 8432 8365 8308 y 2.40 9493 9377 9274 9180 9093 0 13 8939 8870 8807 ,
E E 10793 10677 10567 IM67 IM03 g 18358 11257 11163 11076 10997 10924 }
7 2.60 12009 11853 11713 11585 l1467
- m. -
2.80 14446 14251 14076 13917 13769 13631 IPc5 13387 13279 13180 13088 12926 12780 12640 12512 12436 g
- 3.00 16810 16578 16370 16180 160M 15841 15689 TAs t 542ts 15302 15193 14999 14824 14657 14504 14413 h
- =
I 3.20 19107 18840 18601 18382 18179 17991 17817 17655 17506 17369 17243 17018 16815 16624 IM49 16339 q ,
e 1 21343 21044 20774 20528 20300 20088 19892 9710 19542 19387 19244 18988 18759 18545 18351 18221 9 3.40 m '
e 3.60 23526 231 % 22847 22624 22372 22139 21922 21721 21535 21362 21203 20917 20662 20428 20217 20064 h
=
24148 23912
- 23693 23489 23300 23125 22809 22530 22277 22050 21875 E-3.80 25660 25301 24976 24678 24403 E ;
e 4.00 27753 27367 27016 26694 26398 26123 25868 25631 25411 25207 25016 24672 24369 24098 23856 23659 3 '
tz 29024 28680 28363 28069 27797 27543 27307 27087 26882 26511 26186 25897 25641 25422 m .
4.2e 29811 29399
=
4.40 31840 3I4M 31006 30Mt 30305 29993 29703 29434 29182 28948 28729 28333 27986 27679 27407 27170 $
x 4.6e 33847 33 N 32969 32584 32229 31900 3I594 31309 31043 30795 30563 30143 29775 29450 29162 28910 y E.
4.se 35818 35357 34919 34515 34143 33797 33475 33175 32895 32634 32390 31948 31560 312f6 30910 30646 y B .
4.95 37324 36828 36376 35959 35574 35216 34882 34571 34281 34011 33758 33302 32900 32540 32219 31950 $
2 VJ D
Table 6. Prairie Island 3x3 Checkerboard Storage No Soluble Boron 95/95 Ke rr W - OFA W - STD Nominal KENO-Va Reference Reactivity: 0.96157 0.95918 Calculational & Methodology Biases:
l Methodology (Benchmark) Bias 0.00770 0.00770 Pool Temperature Bias (50*F - 150*F) 0.00416 0.00474 TOTAL Bias 0.01186 0.01244 Tolerances & Uncertainties:
235 UO 2Enrichment Tolerance (10.05 w/o U) 0.01332 0.01420 UO2DensityTolerance(i2%) 0.00404 0.00374 Fuel Pellet Dishing Variation (0 to 2%) 0.00214 0.00198 CellInner Diameter (i0.10 inch) 0.00039 0.00056 Cell Pitch ( 0.06 inch) 0.00649 0.00653 Cell Wall Thickness ( 0.01 inch) 0.00703 0.00723 Asymmetric Assembly Position 0.01985 0.02113 Calculational Uncertainty (95/95) 0.00195 0.00195 Methodology Bias Uncenainty (95/95) 0.00300 0.00300 TOTAL Uncertainty (statistical) 0.02640 0.02782 I
Final K ert ncluding Uncertainties & Tolerances: 0.99983 0.99944 Prairie Island Spent Fuel Racks 30
Table 7. Prairie Island 3x3 Checkerboard Storage Soluble Boron Credit K,g !
- W - OFA W - STD Nominal KENO-Va Reference Reactivity
- 0.90802 0.89614 Calculational & Methodology Biases:
Methodology (Benchmark) Bias 0.00770 0.00770 Pool Temperature Bias (50*F - 150'F) 0.00434 0.00481 TOTAL Bias 0.01204 0.01251 l Tolerances & Uncertainties:
235 UO2Enrichment Tolerance ( 0.05 w/o U) 0.01312 0.01390 UO2Density Tolerance (i2%) 0.00455 0.00427 Fuel Pellet Dishing Variation (0 to 2%) 0.00246 0.00229 CellInner Diameter (i0.10 inch) 0.00023 0.00019 Cell Pitch (10.06 inch) 0.00670 0.00683 ,
Cell Wall Thickness ( 0.01 inch) 0.00470 0.00455 Asymmetric Assembly Position 0.01320 0.01949 Calculational Uncertainty (95/95) 0.00188 0.00191 Methodology Bias Uncertainty (95/95) 0.00300 0.00300 TOTAL Uncenainty (statistical) 0.02128 0.02601 .
1 i
Final K,g Including Uncertainties & Tolerances: 0.94134 0.93466 I
l l
Prairie Island Spent Fuel Racks ' 31 l
Table 8. Gadolinium Credit Equivalent Enrichments for 3x3 Checkerboard
' Enrichment and Fuel Center Assembly Fuel Type Number of Gad Rods and Enrichment in Center Assembly "" "E
- 5 4.95 w/o OFA 0 1.30 w/o OFA 4 1.44 w/o OFA 8 1.58 w/o OFA l
+
12 1.65 w/o OFA l 4
16 or more 1.72 w/o OFA 0 1.20 w/o STD 4 1.34 w/o STD !
8 1.46 w/o STD 12 1.54 w/o STD 16 or more 1.62 w/o STD
}
32 Prairie Island Spent Fuel Racks
m e.
- 2.
h Decay Time (years) d Er Enrichment E e I 4 5 6 7 8 9 10 12 14 16 18 20 a 2 3 m
I.30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a e.
13706 13558 13423 13298 13076 12881 12705 12549 12430
[ 2.00 15184 14908 14660 14435 14229 14040 13866 y t
!!L 15890 14862
{ 2.20 18088 17770 17483 17222 16983 16763 16560 16372 16199 16040 15892 15629 15398 15005
[
n .
R- 20887 20532 20211 19918 19649 19401 19171 18959 18763 18581 18483 18113 17849 17611 17398 17233 ta >
rn 2.40 b
2.60 23591 23203 22851 22530 22234 21960 21706 21472 21254 2l053 20867 20533 20239 19972 19733 19550 (")
?
2.90 26207 25789 25410 25063 24743 24447 24171 23916 23680 23461 23258 22894 22572 22278 22014 21815 g%
ea 3.00 28743 28298 27895 27526 27184 26867 26572 26299 26045 25810 25592 25200 24853 -24534 24246 24034 C) {
>m 31207 30738 30314 29924 29563 29228 28915 28625 28356 28106 27874 27458 27087 26744 26434 26210 U'A 3.20 Oo 3.40 33606 33116 32673 32265 31887 3I535 31207 30901 30617 30354 30111 29672 29279 28914 28582 '28349
- ]
3.60 35948 35440 34979 34556 34162 33795 33452 33133 32836 32561 32306 31846 31433 31047 30696 30453 h E
- 3.90 38243 37717 37241 36803 36395 36014 35658 35326 35017 34731 34466 33987 33555 33150 32779 32529 E C
E 39013 38593 38199 37831 37487 37167 36870 36595 36099 35650 35225 34837 34579 g 4.00 40496 39955 39465 C
4.20 42717 42161 41658 41194 40761 40356 39976 39621 39290 38984 38700 381E6 37721 37279 36874 36609 3 C
T 43352 42907 42490 42099 4l734 41394 41078 40785 40255 39774 39316 38895 38622 g 4.40 44912 44343 43828 4.60 47091 46508 45981 45493 45037 44610 44208 43832 43482 43157 42856 42310 41814 4340 40w)5 40623 g 4.90 49261 48665 48124 47625 47158 46720 46308 45922 45562 45228 44918 44357 43845 43357 42W)8 42617 g E
4.95 50887 50280 49730 49222 48747 48300 47880 47487 47120 46779 46462 45888 45366 44867 44408 44110 g ,
L
- _ _ _ . . _ - . _ _ _ _ _ _ _____.-_______.__._,_._____._.-_____.______m_________m. _ _ _ _ _ _ _ _ _ --_______ -_ - _ _- , - - . . - . , e -e - - -
t
- U h.
a.
O d Decay Time (years) =
y F Enrichment ,E S e 1 2 3 4 5 6 7 8 9 le 12 14 16 18 20
.C C/)
l.20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $
=
15750 15601 15238
[ 2.90 20043 19540 19081 18671 18308 17985 17693 17424 17171 16929 16699 16281 15956 g 2.29 23074 22533 22042 21600 21203 20846 20520 20220 19940 19676 19428 18980 18615 18343 18122 17792 h a
2.40 26011 25433 24910 24438 24010 23620 23263 22934 22629 22344 22078 21600 211 % 20867 20587 20277 h 23328 22997 22698 a
2.60 28860 28246 27692 27190 26732 26313 25928 25572 25243 24937 24653 24145 23706 g llr 2.86 31625 30977 30393 29863 29378 28931 28519 28139 27787 27462 2716l 26622 26151 25730 25357 25060 ^$
2r oe 3.90 34312 33631 33019 32462 31951 31479 31043 30410 30267 29923 29606 29038 28537 28079 27669 27370 C) g'-
29936 U'
3.28 36925 36213 35575 34993 34458 33 % 3 33504 33080 32689 32327 31994 31398 30868 30378 2 % 32 g O
5 r/)
3.49 39469 38729 38066 37461 36944 36388 35909 35466 35056 34679 34331 33708 33152 32633 32163 31850 *H 9: e 3.60 41950 41184 40498 39873 392 % 38760 38263 37802 37376 36984 36622 35975 35395 34848 34351 34031 y a
3.88 44372 43583 42877 42233 41638 41086 40571 40094 3 % 53 39247 38873 38203 37601 37028 36505 36180 E c
45931 45208 44548 43938 43369 42839 42347 41893 41474 41089 40400 39777 39178 38628 38302 4.99 46741 03 m
4.20 49061 48234 47497 46823 46199 45616 45072 44567 44100 43671 43276 42571 41928 41302 40722 40402 g a
42792 42485 4.40 51338 50896 49748 49065 48429 47833 47276 46759 46281 45842 45441 44722 44061 43404 N
50632 5o026 49457 48928 4a440 47994 47587 46860 46182 45490 44840 44557 4.6e 53576 52724 51 % 9 51278 w
52815 52199 51619 51079 50583 50132 49721 48990 48296 47565 46869 46622 4.80 55780 54922 54164 53468 4.95 57414 56554 557 % 55099 54442 53819 53232 52685 52184 51729 51317 50585 49880 491I6 48381 48171 g r
_ _ . _ _ _ _ . _ . _ _ . _ . _ . _ . _ _ _ _ _ _ - - . . _ _ _ . _ . _ . _ _ . . _ _ _ _ . _ _ _ - . _ _ - _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ . -_m .- , _ . . , - , . _ _ . .-w- . - - - ,- , --e --- -
m H D Decav ~
Time (years) j: Enrichment 7 8 9 12 14 16 18 20 8
y 8 I 2 3 4 5 6 le ,
m
- 0
$ I.44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . .g a
w 3 2.00 1I271 11107 10958 10822 10697 10583 IM78 10381 10292 10209 10133 9996 9877 9770 9676 9601 W n W
[ 2.20 14117 13906 13714 13538 13377 13229 13093 12%8 12852 12744 12644 12464 12308 12172 12053 11947 E ao b u 2.44 16862 16608 16377 16166 15972 15794 15630 15479 15338 15208 15086 14867 14677 14512 14367 14235 a 50 ea m
2.60 19512 19221 139." 18713 18489 18284 18094 17919 17756 176M 17463 17209 16988 16794 16624 16472 U n
2 80 22076 21751 21455 21184 20935 20704 20491 20294 20110 19940 19781 19496 19245 19024 18827 18660 [
R-3.90 24561 24206 23883 23587 23314 2306l 22827 22609 22407 22219 22045 21731 21454 21205 20983 20803 @
if 3.20 26975 26593 26246 25927 25633 25360 25t06 24870 24651 24448 24259 23919 23617 23342 23095 22906 $
3.40 29325 28919 28551 28212 27899 27607 27335 27083 26848 26631 26429 26065 25740 25440 25169 24972 O ws 27504 27209 27(X)6 31618 31191 30804 3M48 30117 29808 29520 29252 29003 28773 28559 28174 27828 g 3.60 O
3.30 33863 33417 33012 32640 32293 31 % 9 31666 31384 31122 30879 30654 30249 29883 29537 29220 29012 >
C 4.Ge 36067 35603 35183 34796 34434 34096 33779 33484 33209 32955 32720 32296 31981 31544 31207 30993 3 g- .
~
4.20 38237 37757 37323 36921 36546 36195 35865 35557 35271 35006 34761 34319 33917 33530 33174 32954 g c
38635 38271 37929 37609 37312 37037 36783 36323 359M 35499 35126 34N98 3 4.40 40382 39886 39438 39023 on 40707 40330 39976 39646 39338 39053 38789 38312 37877 37456 37068 36830 j 4.6e 42508 41998 41535 41107
=
39405 39005 38754 9
44099 43622 43181 42768 42379 42014 41672 48354 41059 40786 40291 39840 4.80 44623 Na .
4.95 46207 45672 45184 44733 44310 43912 43539 43189 42863 42561 42280 41772 41308 40865 40458 40194 j W
e i E .
E
~
m t/m
m D Decay Time (years) H j: Enrichment e-p 9 I 2 3 4 5 6 7 8 9 le 12 14 16 18 2e
[u W
$ 1.58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h w Q 3 2.90 7975 7891 7816 7747 7683 7623 7567 7515 7468 7425 7386 7316 7251 7184 7121 7093 T +
n W y 2.20 10736 10606 IM88 103S0 10280 10188 10102 10023 9950 9883 9821 9709 9609 9516 9430 9372 E a
- 3 2.44 13404 13231 13074 12930 12798 12676 12563 12458 12361 12271 12188 12038 18906 11786 11679 18595 A a W
(**
14309 14146 14001 13871 13764 7 2.60 15984 15773 15580 154M 15242 15093 14954 14826 14707 145 % 14494 n
2.80 18484 18238 18013 17808 17619 17444 17282 17132 16992 16862 16742 16524 16333 16163 16011 15884 e 4
3.88 20910 20632 20379 20147 19933 19735 19551 19380 19222 19074 18937 18690 18472 18277 18tM 17960 $
if 3.20 23269 22 % 2 22683 22427 22190 2197I 21767 21577 21401 21237 21084 20809 20567 20349 20153 19995 %
3.40 25567 25235 24932 24654 243 % 24157 23934 23727 23534 23355 23189 22888 22622 22381 221M 21993 O "r1 24378 24i41 23959 3.68 27812 27455 27131 26833 26556 26299 26059 25835 25627 25434 25254 24930 24642 on O
3.88 30009 2%31 29287 28970 '28676 28402 28145 27907 27684 27478 27286 26940 26631 26346 26088 25897 >
C 4.90 32166 31768 31406 31072 30761 30471 30200 29946 29711 29492 29289 28922 28593 28287 28009 27811 3 E.
4.20 34289 33872 33493 33144 32817 32512 32227 31960 31712 31481 31268 30882 30514 30208 29910 29705 g a
33692 33451 33227 32822 32456 32111 31794 31583 I 4.40 36385 35951 35556 35191 34850 34531 34232 33952 CIS c
4.60 3846I 38009 37599 37219 36864 36532 36220 35928 35657 35405 35171 34749 34365 34001 33667 33449 y a
36265 35883 35532 35308 39235 38866 38521 38196 37893 37610 37348 37105 36666 4.80 40523 40054 3 % 28 N 4.9s 42065 4 583 41146 40741 40363 40008 3 % 74 39362 39072 38802 38552 38100 37687 37292 36929 36699 #,
e E
i w .E.
O i
- C l
@, Decay Time (years) d 3-G Enrichment iit e
[;;* O l. 2 3 4 5 6 7 8 9 10 12 14 16' 18 20 -
[ .
S. 1.65 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Q
m e.
3 2.00 6505 6449 6401 6357 6314 6273 6234 6198 6165 6137 6112 6069 6024 5%7 5909 5909 "!.
P. 2
[ 2.20 9221 9121 9032 8950 8874 8803 8737 8675 8619 8567 8520 8435 8357 8281 8210 8171 y G :ls 2.40 11847 18707 1:580 11464 11357 11257 11165 11080 11001 10927 10859 10736 10628 10531 10443 10372 7 2.60 14389 14212 14051 13903 13767 13641 13525 13417 13316 13222 13135 12977 12840 12720 12614 12517
- r 2.80 16854 16643 16450 16273 16110 15959 15820 15691 iS570 15458 15353 15163 14998 14854 14728 146tl E W
3.00 19248 19005 18783 18579 18392 18218 18057 17907 17768 17638 17517 17298 17107 16939 16790 16657 2
3.20 21577 21305 21056 20828 20617 20422 20241 20072 19915 19769 19633 19387 19170 18978 18806 18661 at 3.40 23848 23548 23276 23025 22793 22577 22376 22190 22016 21855 21705 21434 21194 20977 20782 20627 i 3.60 26066 25742 25446 25175 24923 24688 24469 24266 24077 23901 23738 23444 23t81 22940 22722 22560 g 27284 27013 26761 26525 26305 26102 25913 25737 25422 25138 24873 24632 24463 o
y 3 80 28238 27890 27575 C
4.00 30370 30001 29666 29357 29069 28800 28548 28314 28096 27895 27708 27371 27067 26780 26518 26343 g 5'
4.20 32469 12079 31726 31400 31096 30812 30545 30297 30066 29852 29655 29298 28975 28667 28384 28203 g e
4.40 34540 34131 33761 33420 33100 32801 32521 32259 32016 31790 31582 31206 30864 30537 30237 30tM7 5 tz 36163 35777 35420 35086 34773 34480 34205 33950 33714 33495 33100 32741 32397 32082 31882 .,
4.60 36590 =
c 35629 35399 34985 34609 34251 33924 33710 't:5 4.80 38625 38181 37779 3740) 37060 36734 3t428 36142 35876 W
4.95 40145 39689 39275 38892 38535 38200 37885 3759: 37317 37061 36824 36395 36007 35641 35306 35079 .E e
X 5
e 5
w E
~
u
~c 13 5: a i
o y Decay Time (years)
- E Er Enrichment ~
a *
- o. O I 2 3 4 5 6 7 8 9 IS 12 14 16 18 2e .
M 'U I.72 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 E
[
n 2.00 5 24 5090 5061 5034 5007 4981 4956 4933 4912 4894 4879 4853 4823 4782 4740 4748 se m
2.28 7799 7725 7659 7598 7541 7487 7436 7389 7347 7308 7273 7211 7152 7087 7025 7008 m A
9840 9707 9648 9595 M99 Mil 9322 9240 9200 tN,a 2.46 10386 10274 10174 10082 9996 9915 9771 240 12892 12745 12612 12490 12377 12271 12173 12082 11998 11921 11849 11721 11605 li494 11393 11330 h a
2Ae 15323 15143 14979 14829 14690 14560 14440 14329 14225 14130 14M2 13883 13740 13607 13456 13403
{
3.90 17684 17473 17281 171M 16941 16789 16648 16517 16395 16282 16178 15990 15822 15667 15527 15425 j 3.29 19982 19742 19523 19322 19135 18962 18801 18651 18512 18383 18263 18M7 17855 17679 17521 17401 k,"
BC 3.40 22223 21956 21712 21487 21279 21086 20906 20738 20582 20438 20303 20061 19845 19649 19472 19336 340 24413 24120 23852 23606 23378 23165 22967 22783 22611 22452 223M 22036 21798 21581 21386 2i235 [
3A0 26558 26240 25951 25684 25437 25206 24993 24791 24604 24431 24269 23978 23719 23482 23269 25tM 3 4.99 28663 28323 28013 27727 27462 27214 26983 26767 26567 26380 262 % 25892 25613 25357 25125 24944 O
30735 30374 30045 29741 29458 20195 28948 28718 285M 28305 28119 27784 27485 27210 26 % I 26774 4.29 32052 31731 31433 31154 30893 30649 30422 30211 30015 29660 29342 29048 28781 28585 4.49 32789 32399 4.6. mm mm m 40 3n04 um n097 n822 32565 32326 32im 3i897 3iS24 3ii88 30875 30590 30387 g a
4.se 36813 36395 36015 35664 35D6 35029 34742 34473 34222 33989 33773 33382 33029 32697 32394 32186 g N
36475 36178 35900 35642 35401 35178 34775 34410 34064 33748 3353t. m 4.95 38314 37883 37491 37130 36792
.a u
00
- C
@, Decay Time (years) H g- Enrichment g
- 0 1 2 3 4 5 6 7 8 9 le 12 14 16 18 20
- 2 N @
$ IJ4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .g a
m 3 2.90 14876 14559 I4277 14022 13789 13575 13379 1320i 13040 12894 12762 12529 12318 12112 11924 It833 4' a F y 2.2e i7900 i7528 17:98 ,,9 i6625 is372 16:40 is928 15735 is560 1540: isi20 i4865 i46i7 i4390 i4276 E 2-y 2.40 20805 20385 20011 4672 19360 19073 18809 18566 18344 18 42 17957 17631 17337 17053 16793 16653 8L W
7 2.64 23601 23137 22724 22349 22004 21686 21392 21I21 20873 20646 20439 20070 19739 19424 19136 18 % 9 n
22442 22078 2i735 21425 2:228 2.se 26296 25795 25347 24939 24563 24217 238 % 2360i 23329 23079 22850
[
w 3.00 28900 28366 27886 27448 27046 26674 26330 26012 25718 25448 25199 24754 24359 23993 23664 23437 $
X 3.2. 3i422 30859 3035i 29887 29460 29065 28699 2836i 28048 27758 2749i 270i2 26589 26202 25856 25 00 g 86 3.40 33872 33283 32750 32262 31812 313 % 31011 30654 30324 30017 29733 29223 28773 28368 28006 27722 e
3.68 36258 35M7 35090 34581 34III 33677 33274 32900 32553 3223I 31931 31392 309I8 30495 30t19 29809 A C
3.se 38590 37958 3738: 36852 36364 35913 35494 35104 34742 34405 34092 33526 33029 32589 32198 3t866 >
C 4.se 40877 40226 3%31 39084 38579 38112 37678 37274 36898 36548 36221 35631 35113 34655 34249 33898 $
E.
4.2e 43:28 42459 4i848 4:285 407w 40282 39834 394:6 39027 38
- 4 38326 377:3 37i75 36698 36275 359io 5 m
E 4.40 45353 44667 44039 43462 42927 42430 41968 4:538 41136 4076l 40412 39779 39221 38724 38281 37907 g a
4.68 47560 46857 46215 45623 4M)75 44564 44089 43645 43231 42845 42486 41835 41258 40737 40271 39894 3 C
- O 49759 49038 48382 47777 47215 46691 46202 45745 45319 44923 44554 43887 43292 42744 42249 41877 g 4.30 51408 50673 49393 48821 48287 47787 47320 46885 4M81 46105 45428 44818 44247 43728 43365 4.95 M.1007
- r e
E w .E
~ _ _ - - _ - . - - - _ . _ _ _ _ _ _ - _ _ _ . . . _ _ - . _ _ _ .- --
}
m
@, Decay Time (years) H
- g. Enrichment g 9 Ie 14 16 18 29 8
- 9 1 2 3 4 5 6 7 8 12 .
i EL m :
p "
$ 1.46 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h m ;:
3 2.00 11272 11075 10907 10753 10607 IM68 10338 10221 10119 10033 9960 9837 9702 9516 9327 9374 W R .W
[ 2.20 14225 13970 13747 13544 13354 13175 13010 12859 12724 12605 12501 12322 12143 11932 11727 11718
{
S
- c 2.40 17062 16754 I6482 16235 16005 15791 15592 15410 15246 15098 14966 14736 14517 14282 14058 14001
- g W
N b 16828 16569 16326 16228 7 240 19791 19436 19121 18834 18569 18322 18093 17883 17691 17518 17361 17084 n
- 22422 22023 21671 21349 2105l 20775 20589 20283 20067 19870 19690 19372 19082 18798 18536 18404 2.80 lR" ^
24529 24141 23787 2346l 23158 22877 22618 22379 22161 21 % I 21605 21284 20976 20695 20532 Q 3.99 24 % 3 25804 25477 25174 24893 24635 24397 24178 23788 23438 23107 22806 226t8 m j 3.20 27424 26957 26539 26157 29814 293I8 28872 28465 28080 27740 27416 27116 26839 26584 26348 25927 25550 25197 24877 24666 3.40 e
311,20 30720 30322 29953 2%I1 29293 28999 28727 28476 28026 27624 27250 26911 26680 ge 340 32142 31150 O
3.80 34418 33872 33380 32929 32512 32124 31764 31430 31120 30833 30568 30092 29666 29271 28915 28665 > i 4.00 36650 36083 35570 35100 34664 34260 33884 31534 33209 32909 32630 32128 31681 31267 30894 30626 3 Er
~
4.29 38848 38261 37729 37240 36788 36368 35976 356l2 35273 349%9 34667 34142 33673 33241 32853 32567 g l c
37670 37318 36990 36686 36137 35647 35200 34798 34492 E 4.48 41020 4N14 398M 39358 38890 38454 38048 llIll c
4.69 i 43176 42552 41984 41461 40977 40526 401 % 39714 39349 39009 38692 38119 37610 37148 36734 36407 g a
40691 40093 39565 39090 38666 38315 4.80 45325 44683 44096 43557 41057 42592 42158 41752 41374 41021 A '
45128 44617 44140 43696 43280 42892 42528 42188 41572 41029 40547 40117 39745 j 4.95 46938 46281 45681 w
e B
E u -
O r
_ _ . _ _ _ _ _ _ . _ . _ . . _ _ . _ _ _ _ .- _m _ _ _ . _m___ _._____m.__ _ _ . _ _ _ _ . _ _ _ _ __..m . .-----.-w-_v - , - , - , - , ,1,- ,-...,w. - . . . -.-~v.. ---v- y ,. ,-
c
@. Enrichment Decay Time (years) #
cr
- 3. -
o 16 20 a
- 0 I 2 3 4 5 6 7 8 9 10 12 14 is T.L q 1.54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 h m a 3m 2.00 9193 9059 8946 8842 8742 8646 8556 8474 8403 8343 8294 8212 8117 7979 7837 7884 E a
- T1 2.20 12080 18887 11720 11567 11424 11288 lil61 11045 10942 10851 10773 10638 10501 10334 10168 10172 r.,
C g O 5 13843 13682 13535 13403 13284 13180 12997 12821 12625 12436 12402 12-x 2.40 14857 14611 14395 14899 14015 Ga to F 240 17533 17238 16979 16743 16523 16388 16 27 15951 15792 15648 15519 15292 15080 14857 14646 14577 b n
v 2.80 20114 19777 19479 19206 18954 18719 18500 18299 18115 17948 17797 17529 17284 17035 16803 16703 g W
3.00 22611 22236 21902 21597 21315 21053 20809 20584 20378 20190 20018 19714 19436 19lM 18911 18783 $
II 24622 24256 23922 23613 23326 23060 22813 22586 22378 22188 21849 21543 21247 20975 20822 %
3.20 25031 CL 3.40 27383 26943 26549 26188 25855 25545 25258 24991 24746 24520 24312 23942 23608 23291 23001 22823 h
e 28403 28M 7 27717 27410 27125 26862 26620 263 % 25996 25637 25299 24992 24792 .-a 340 29675 29208 28787 tJ 30979 30573 301 % 29847 29522 29220 28941 28683 28444 28016 27634 27277 26953 26732 3.80 31915 31423 C
32705 32239 31942 31600 31283 30988 30716 30463 30008 29603 29228 28889 28647 y 4.00 34113 33598 33132 -
3
~~
35253 34806 34393 34009 33651 33319 33010 32723 32457 38977 31550 31158 30805 30542 4.20 36276 35740 B m
4.40 38413 37856 37350 36885 36454 36054 35681 35334 35011 34711 34431 33927 33478 33071 32705 32421 E to 38946 38499 38083 376 % 37335 36998 36685 36392 35863 35394 34972 34595 34289 %
4.60 40531 39955 39430
=
4J10 42641 42045 41500 40999 40535 40lM 39702 39327 38977 38649 38344 37790 37301 36866 36478 36148 $
x 4.95 44222 43611 43052 42537 42060 41617 41204 40819 4M 58 40121 39805 39232 38729 38284 37890 37541 2 s.
2 E
s =
_ _ _ . . - . _ _ _ . _ - _ _ _ _ _ _ . . _ _ _ _ _ _ _ _ _ . _ _ _ . _ . _ _ _ _ _ _ . . _ . _ _ _ . _ . _ _ _ . . . _ _ _ _ _ . _ _ _ _ m_ _ _ _ . . _ . - _ - _ %--- - ~ ~ .
i m
E 5: .H n m E Enrichment Decay Time (years) y E e 1 2 3 4 5 6 7 8 9 to 12 14 16 18 2e 00 ,
c.
W *C 3 1.62 0 0 0 0 0 0 0 0 0 0 0 -0 0 0 0 0 $
g a
6815 6775 6739 6677 6616 6541 6468 6468 * >
7029 6969 6913 6862
[ 2.se 7316 7231 7158 7091 _
lC. >
9 I 2.20 10131 9990 9866 9753 9648 9549 9458 9373 9297 9228 9167 9060 8958 8848 8742 87t7 $
PO
= m.
2.4e 12844 12651 12481 12326 12182 12048 11923 11809 Il7M 11610 l1524 l1374 18235 11092 10957 10906 y w
13ml 2.60 15462 15223 15010 14816 14636 14470 14315 14173 14M3 13924 13816 13625 13451 13278 13117 Q
a 2.88 17993 17711 17459 17230 17018 16822 16640 16472 16317 16176 16047 15818 15611 15411 15227 15125 r 3.00 20443 20123 19836 19574 19333 19109 18902 18710 18534 18372 18223 17958 17720 17495 17290 17162 ye#8 i c
20697 20516 20348 20049 19782 19534 19310 19157 A 21587 21338 21107 20894 3.2e 22821 22466 22147 21856
[ m-EH ,
3.40 25134 24748 24399 24080 23787 23515 23263 23029 22813 22613 22428 22097 21803 21534 21292 21115 $c i 3.64 27390 26975 26599 26255 25938 25645 25373 25120 24886 24670 24468 24107 23787 23498 23239 23039 [
t 3.90 29595 29154 28753 28386 28047 27734 27444 27174 26923 26690 26473 26083 25739 2543I 25157 24934 3 ,
R l 27337 27048 268M 4.se 31758 31292 30868 30479 30121 29789 29481 29194 28928 28679 28448 28031 27664 O
33397 32951 32542 32165 31815 31490 31188 30906 30643 30398 29955 29566 29222 28987 28654 4.2e 33886
. i 4.40 35986 35475 35004 34581 34185 33818 33478 33160 32864 32587 32328 31860 31450 31088 30768 30487 :::
E 4.69 38067 37535 37W8 36601 36188 35805 35448 35116 34805 34515 34244 33752 33321 32942 32605 32308 f
E I
386io 38180 37780 37408 37061 3673: 36433 36150 35636 35i84 34786 34433 34:22 m 4.se 40i34 3958i 39076 a >
40593 40114 3 % 70 39258 38875 38516 38182 37869 37576 37045 36379 36166 35800 354X0 E 4.95 41681 41113 =
'O t
Table 19. Summary of the Soluble Boron Credit Requirements Total Total Solub!e Soluble Soluble Soluble Boron Soluble Boron Boron Boron Boron Fuel Required for Required for Storage Credit Required Credit Assembly Tolerances / Reactivity Configurat on Required for Required Type Uncertainties Equivalencing Without Accidents With (ppm) (ppm)
Accidents (ppm) Accidents (ppm) (ppm)
All Cell W - OFA 200 200 400 300 700 Storage W - STD 200 250 450 350 800 3x3 W - OFA 250 350 600 400 1000 Checkerboard W - STD 300 450 750 550 1300 Storage Prairie Island Spent Fuel Racks 43 1
. - . . . - . . - . - . . . _ _ - . = . . . . - - - . . . . . . . . - - _ . . - - - . ... . . - ..-. -
e w
a et 1
e
/ Lf N #N -
c,
~
~ . .
= . ,
= .
- . . . E i i
= .
. y n l
.T f G
I i
l
.
= .
3 o
I lY
- wy t
E M 7
. . . g il Figure 1. Prairie Island Spent Fuel Rack Layout I
l l
l Prairie Island Spent Fuel Racks 44 l
i I
L
l 4
1 4
4 4
\
' - - i....-_.
y 1
8.20" -
J O.752=
t
- s .u-l t
O 1 i - - -
"'- - - - .<.z.-_,.
f CELT. CENTER TO CENTER f 9.5" l -]
~
I 0.090" Inner caelns 0.125" Absorber 0.024" Outer casing r
Figure 2. Prairie Island Spent Fuel Storage Cell Nominal Dimensions 4
45 Prairie Island Spent Fuel Fr.cks
40000 0 y. r, 35000
/
/, 5 Years
/ /, 10 Years
///j 15 Years 3 / ////
20 Years P 30000 /////
s O / ////
/////
~ / ////
/////
a 25000
//
- ' /f/#
- f/ff
///#
D 20000 /4W 9 /f//
g m /47 m /f//
< /M
~ 15000 ifff i
0 /A V '
k ///
M \
10000 i
A V i B !
s I f
5000 f
[
l 0 /
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o) ;
Figure 3. Prairie Island All Cell OFA Storage Burnup Credit and Decay Time Requirement l
l l
l Prairie Island Spent Fuel Racks 46 i
i l 40000 i ,
0 Years
/
j j s Years 35000 ! !- 10 Years
! ! ! 15 Years
/ /// 20 Years
^ / / ///
o / ////
,g 30000 s
) / ///
O / ////
/ ////
~ / fJ//
/ ////
a 25000 / //f/
u
//f//
/ ////
$ //fB
/ ////
h 20000 f/f//
g ///#
w //f//
m
- i///
< ///#
15000 //M
$ /Hf k gy FF 10000 M l
/F \
f F
5000 f
) 1 i
/
1 0 /
1.0 2.0 3.0 4.0 5.O Initial U-235 Enrichment (w/o) 4 Figure 4. Prairie Island All Cell STD Storage Burnup Credit and Decay Time Requirement Prairie Island Spent Fuel Racks 47 i
E E E E E E i
E E E Fresh Fuel: Must be less than or equal to nominal 4.95 w/o 235 U Bumed Fuel: Must satisfy the minimum burnup requirements of Figure 6 to 15 depending on number of GAD rods in fresh fuel Figure 5. Prairie Island 3x3 Checkerboard Layout Requirement
)
l Prairie Island spent Fuel Racks 48 l
(
s l
l ?
55000 ,
, 0 Years f
50000 '
j j 5 Years f l
/ / 10 Years !
f f j ,
/ / fs is Years 45000 / fj f, 20 Years ,
^
/ / / //
/ / /// .
f / / ///
sx 40000
/ ////
/ / /// ,
/ f///
/ ///
4
/ ,//// i
/ / ///
35000 / ///s '
i a / / ///
3 c
/ / /// .
f // ///
I / m
$ 30000 / //f/
i ///r H
> / /J//
f) /JF
,Q ' 'N m 25000 O / //if W / ////
- / ////
A /////
J m/
s 20000 ///N o f//// '
y ///ff
% ///f 3 15000 / f/2
/) W
//J iM 10000 fj ' _.
r T 5000 I
) ,
a 1
0 1 1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 6. Prairie Island 3x3 Checkerboard OFA Storage Burnup Credit and Decay Time Requirement (No GAD Credit) l 49 Prairie Island Spent Fuel Racks
i I
I 60000 0 Years
, 5 Years l / //
50000 '
/ / // 20 Years
! / ///
f / / ///
ka / ////
40000 / ////
/ ////
5 / //H
! /.6/
m / //H h 30000
/ /8/
/ /U/
-Q y / ////
m / //#
l$ 20000 /N#
l
~ //#/
/M/
HK
///
10000
/F W
J l
0 [
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 7. Prairie Island 3x3 Checkerboard STD Storage Burnup Credit l
and Decay Time Requirement (No GAD Credit) i Prairie Island Spent Fuel Racks 50
i 60000 50000
> 0 Years
> 5 Years
(
Q
- a > 10 Years i
$ 40000 2 $! NSN
~ ///f '
? ///#
B //>%' i 8 //,@'
>' 3 00 0 0
//& '
w /Hf E //4'
//M'
- 3 20000
/%V i w //f '
///
lN M ;
10000 I
/
0 /
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 8. Prairie Island 3x3 Checkerboard OFA 4 GAD Storage Burnup Credit and Decay Time Requirement 51 Prairie Island Spent Fuel Racks
50000 45000
> 0 Years
/ > 5 Years
^
40000 # # 10 Years
- ' 15 Years h 'I' // 20 Years
.E / ////
s / //'
o 35000 // ///
M / / ///
E
~
f////
g / ////
' H#
5 C 30000 / ////
4 / ////
/ ///)
$ / ////
' "'/
H> 25000 / ////
)o
/////
/ ////
in //f//
$ 20000 , ,(,,j
' V a //AV m ////)
o ///r
~ ,,((#
15000 _
HB hv
/A '
10000 g
[
f H
I l 5000
/
[
/
/ i 0 / l 1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 9. Prairie Island 3x3 Checkerboard OFA 8 GAD Storage Burnup Credit and Decay Time Requirement Prairie Island Spent Fuel Racks 52 J
I 4
45000
/ 0 Years !
400b0 /
/ / 5 Years
! 10 Years I
! ! 15 Years I
/// /> 20 Years j
^
35000 / / ///
f / / /// l
- El
% /////
O / ///)
///N
$ 30000
- / ////
a /////
c / ////
C f//H
/ //#
mc 25000 ///H \
}
/////
y ///H \
m g /N//
IN#
a> 20000 /Hf/
m m /f/f 4 /MF a H/E
$ 15000 'T aa w />V
//E f
Af 10000 F
[
f J
5000 f 1
)
/
0 /
1.0 2.0 '3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 10. Prairie Island 3x3 Checkerboard OFA 12 GAD Storage Burnup Credit and Decay Time Requirement Prairie Island Spent Fuel Racks 53
45000 40000 j 0 Years j j $ Years
/ // 10 Years !
^
D 35000 f /fj 15 Years-20 Years 7 777j
% / ////
O / f)//
/ //#
b'30000
~ jf/f/
/ / 7//
a p /.f///
C / /f//
/ /M
$ 25000 en /////
////f D f////
/f/if Qe 20000 /#/ '
m ///F m //f// \
4 //M 1 a /iff
$ 15000 fji[
//F M
/P i 10000 jf M
W f
I 5000 j
/
/
/
- 0 /
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 11. Prairie Island 3x3 Checkerboard OFA 16 or More GAD Storage Burnup Credit and Decay Time Requirement 54 Prairie Island Spent Fuel Racks
60000 50000
/
[ j 5 Years
- / /, 10 year.
@ / //j is years Y**
& / //,7 a
40000
/ ////
/ ////
a / /bV
$ / /49 e / /4V m
3 30000
/ //9 Q
!/N/
/!N/
///// .
////)
20000
!MY w hVf
/ff
///
/N 10000
!M lA 1 ,
I 1
0 [
1.0 2.0 3.0 40 5.O Initial U-235 Enrichment (w/o)
Figure 12. Prairie Island 3x3 Checkerboard STD 4 GAD Storage Burnup Credit and Decay Time Requirement Prairie Island Spent Fuel Racks 55
- _. . . _ . < s . _ ._, -.. _ - . . = . . - - . , = . __
I 50000
, 0 Years
/
45000 / j 5 Years l f /
l / / j 10-Years
/ / /. 15 Years I
l / I 20 years '
l ~
40000 / / / //
O / / ///
H / / ///
k
- i ////
/ / ///
35000 / r///
t l ~
/ / /// \
f fi//
g / / ///
P "
C 30000 / / /// j k / / /// ,
$ / / /// l
/ //// <
"' l H>' 25000 ) //// !
)o
/ f///
/////
m / /)ff A 20000 ) .'/ ///
p ,
///M o f//// ,
p //M '
N '##
15000 //AV
/f/1
/M )
. r/n 10000 fj f ;
v I r
A 5000 [
J K
I l 0 1 1.0 2.0 3.0 4.0 5.0 ,
Initial U-235 Enrichment (w/o) l Figure 13. Prairie Island 3x3 Checkerboard STD 8 GAD Storage Burnup Credit and Decay Time Requirement i
l l
Prairie Island Spent Fuel Racks 56
o y..,,
45000 ,
/
5 Years j
/ f. 10 v ar.
40000 / '
[ jj 15 Years f,
, , ,, 20 years
/ f//f
/ / /-//
^
O 35000 f f///
/ / /Y/
% / / ///
) ) ///
/ / ///
~
- 30000 / A///
/ / ///
a p /////
C / ////
/////
$ 25000 co / ////
/ //// ~
N / / f//
i f///
Qo 20000 /////
m ///V m /////
- ///f/
a ///E
$ 15000 //f
///A w /Hf f/M HH 10000 g[
H B
E 5000 I
[
I J
0 /
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 14. Prairie Island 3x3 Checkerboard STD 12 GAD Storage Burnup Credit and Decay Time Requirement l
l l
Prairie Island Spent Fuel Racks 57
{
I i
45000 0 Years j
g 40000 7 j 5 Years
/ / 10 Years j f j 15 Years 7 jr gj 20 Years f j ffj '
3 35000 / / //f y J / /f/
s / / /H O / / ///
y / / ///
_ 30000 / ) ///
4
/ ////
/////
$ / //// \
u (////
0 25000 / ////
i
/ //H
~
> / //// \
/ ///f
$o 20000 /////
M / f/jY
//f//
$ //M
//f//
Q //M o 15000 Ct.
//M
//M fff ,
/AV
'/#
10000 AV
/E E
F 5000 I
f f
I 0 /
1.0 2.0 3.0 4.0 5.0 Initial U-235 Enrichment (w/o)
Figure 15. Prairie Island 3x3 Checkerboard STD 16 or More GAD Storage Burnup Credit and Decay Time Requirement Prairie Island Spent Fuel Racks 58
1 1
D D D O O O!O C CIC DD D D 000000jo00100100 O O OO.OIOOQiOOOOO OQOOOOlo.eO'OOIOOO D QO'Q' OUCOOOOOOOOQ COOOOOOOOOOgQQ ,
0000100'e000 0000 000 OOO!eOOO CiOOO '
O0000000000000 000000~O0000!O00 00Q00000 000000
,D5 01000000 0 91000 OOOOOOOO O70DOOO OgO!OOOOOOO e!OOO 000'9000010001000 OOO!eO OO 000 010 eO :
000000 0010 00000 00001001000 00000 l OQ000000000000 OO 000010 0000000 :
DOOOOOOOO OOOOO OOO.OOOO OQ-QQQ.QO l 0000000000 0000 0000000000000D l 000000100000000 0000004lO0 0000 O O OO 00010000 0000 0000000101000000 !
4 GAD 8 GAD 000000000100000 0000010'00010000 0 OOOO90000iGO000 O OOO 9iOOOO!OOO9 0 OOOO'O00OOO000O OOOOO00OOOOOOO 000000!9000 0000 Q000009 0000000 O.9OOOOOOOOOO OO 0b00000000OOOO OOOOOOOO OOO'OOO OOOOOOOO OOOOO6 OOOlOOOO00 0 9OOO OOOOOOO00 09.000 OOO!OO OOOOO!OOOO OO OOOOO OOO OIOOO l Q000 00000 0000-0 0Q00 00000 0005D l O4000000000000 DWOOOOOOOOOO90 D00000000000Q0 00000000000000 DOOOOOOOOOOOOD 00000000000000 OOOO9OOOOOOOOO 09O09OOO019 OO9O !
00000000000000 0000000 0010 0000 l 12 GAD 16 GAD OOOO000OO1000oO 09O09OOOO'SOOGD OOO0000OOOOOOO OO0 9OOleOOO<GOOO 09OOOOiOOO00O9O D Fuel Rod O000OOiOO OO00OO DDO1QOOOOOOOfOOO Q GuideTube OO O'OO OOO!OOOlOOO OOOOOO OOiOOOOOO 09000000000000 M GAD Rod DOOeOOO gO OOO OO 00000000000000 090090000.0 0109'0 OlOOOOOO OOIO OiOOD 20 GAD Figure 16. Gadolinium Rod Patterns within the Fuel Assembly Prairie Island Spent Fuel Racks 59
i i
i Interface L L L 1MA l lE BRIER l
i ElERE i I I I i
j y(!w!;!. Fresh Fuel: Must be less than or equal to nominal l ::
MMI 4.95 w/o 235 U
l 1 Burned Fuel from the 3x3 Checkerboard Configuration I
Burned Fuel from All Cell Configuration l l
. 1 i l 1
1 Figure 17. Prairie Island Interface Requirements 1
4 i
i Prairie Island Spent Fuel Racks 60 l
I
?
l Bibliography ;
i
- 1. Newmyer, W.D., Westinghouse Spent Fuel Rack Criticality Analysis Methodology, WCAP-14416-NP-A, November 1995. !
- 2. Newmyer, W.D., Criticality Analysis ofthe Prairie Island Units 1 & 2 Fresh and Spent Fuel l Racks, February 1993. 1 i
I t
r .
1 >
I i !
i l
r i
f l
l l
l l
t I
l Prairie Island Spent Fuel Racks 61 l