ML18087A119

Enclosure 3 - APR1400-Z-A-NR-14011-NP, Rev. 2, Criticality Analysis of New and Spent Fuel Storage Racks.

ML18087A119
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Issue date:	01/31/2018
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MKD/NW-18-0039L APR1400-Z-A-NR-14011-NP, Rev. 2
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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Criticality Analysis of New and Spent Fuel Storage Racks Revision 2 Non-Proprietary January 2018 Copyright 2018 Korea Electric Power Corporation &

Korea Hydro & Nuclear Power Co., LTD.

All Rights Reserved KEPCO & KHNP

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 REVISION HISTORY Rev. Date Page Description Nov.

0 All First Issue 2014 Feb.

1 All Page numbering, list of tables, and list of figures updates.

2017 In response Rev.1 to RAI 90-7939, Question 09.01.01-1, revised Feb. 34, 43, 51, 52, 1 Sections 3.4.3, 3.5.1, 3.5.3 and Table 3.4-7 to clarify the BUC 2017 53, 54, 55 methodology.

In response Rev.1 to RAI 179-8190, Question 09.01.01-16, the loading curve was regenerated based on target keff of 0.998 with Feb. 57, 82, 83, 1 additional margin. Section 3.5.4, Tables 3.5-25, 3.5-26 and Figures 2017 88~90 3.5-5, 3.5-6, 3.5-7 were revised to incorporate the regenerated loading curve.

Feb. In response to RAI 179-8190, Question 09.01.01-17, revised the 1 114 2017 B-10 areal densities to the design values in Section 5.3.

In response Rev.1 to RAI 179-8190, Question 09.01.01-21, Feb. 10, 14, 18 1 Sections 2.4.2, 2.4.3, 2.5, Tables 2.4-2, 2.5-2, and Figures 2.4-2, 2017 19, 20, 22 2.4-3 were revised to incorporate the accident analysis.

In response Rev.2 to RAI 179-8190, Question 09.01.01-23, Sections 2.4.3(previously 2.4.2), 2.5, Tables 2.1-1, 2.4-3, 2.4-4, Feb. 3, 10~12, 15, 1 2.5-1, and Figures 2.4-2, 2.4-3, 2.5-1 were revised to incorporate 2017 16, 18~21, 23 the additional sensitivity results considering the storage pit concrete.

In response Rev.2 to RAI 179-8190, Question 09.01.01-25, Feb. 3, 10~12, 15, Sections 2.4.3(previously 2.4.2), 2.5, Tables 2.1-1, 2.4-3, 2.4-4, 1

2017 16, 18~21, 23 2.5-1, and Figures 2.4-2, 2.4-3, 2.5-1 were revised to incorporate the additional sensitivity results considering the tolerances.

In response Rev.1 to RAI 179-8190, Question 09.01.01-26, revised Feb.

1 5, 27, 60 the Figure 2.1-1 to clarify dimensions and corrected the incorrect 2017 dimensions in the Tables 3.1-3 and 3.5-3.

In response to RAI 179-8191, Question 09.01.01-3, revised the Feb. 2, 5, 7, 33, 1 Sections 2.1, 3.4, 3.5, 3.6, Figures 2.1-1, 2.1-3, 3.4-5, 3.4-6, 3.5-8, 2017 49~51, 91~94 3.5-9, 3.6-1 to include adequately detailed descriptions.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 REVISION HISTORY (Cont.)

Rev. Date Page Description 25, 26, 29, 35, In response Rev.1 to RAI 179-8191, Question 09.01.01-4, revised 36, 40, 43, 44, the Sections 3.2, 3.4, 3.5, 4.1~4.3, Tables 3.1-1, 3.1-2, 3.4-4, 3.4-54, 57, 64, 65, 7, 3.4-8, 3.5-7, 3.5-8, 3.5-22~3.5-26, 4.1-1, 4.2-2, 4.3-2~4.3-4, and Feb.

1 79~83, 88~90, Figures 3.5-5~3.5-7, 4.1-2, 4.3-3. The inconsistency of the applied 2017 95, 96, 98, 99, design values of NAP were corrected and the criticality analysis 101, 103~105, was revised to incorporate the design values of NAP with revised 107~110, 113 assumptions.

In response Rev.1 to RAI 179-8191, Question 09.01.01-5, revised Feb.

1 34 the Section 3.4.2 to clarify the conservatism of the applied 2017 assumptions.

In response to RAI 179-8191, Question 09.01.01-6, replaced the Feb.

1 46, 47 Figures 3.4-2, 3.4-3 with high resolution Figures to clarify the 2017 analysis models.

In response to RAI 179-8191, Question 09.01.01-10, revised Feb. 32, 52, 55, 56, 1 Sections 3.3, 3.5, and Table 3.5-12 to clarify the burnup record 2017 69 method and information.

In response to RAI 179-8191, Question 09.01.01-11, revised Feb.

1 49, 91, 93, 94 Section 3.6, and Figures 3.4-5, 3.5-8, 3.6-1 to correct misstated 2017 gap dimensions and provide detailed design information.

Jan. Description about the Thermal Conductivity Degradation (TCD) 2 51 2018 effect on fuel burnup.

This document was prepared for the design certification application to the U.S. Nuclear Regulatory Commission and contains technological information that constitutes intellectual U

property of Korea Hydro & Nuclear Power Co., Ltd..

Copying, using, or distributing the information in this document in whole or in part is permitted only to the U.S.

Nuclear Regulatory Commission and its contractors for the purpose of reviewing design certification application materials. Other uses are strictly prohibited without the written permission of Korea Electric Power Corporation and Korea Hydro & Nuclear Power Co., Ltd.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 ABSTRACT This report presents the criticality and depletion calculation methodology that is used for the design of the new and spent fuel storage racks of the APR1400 design. The contents of this document include acceptance criteria, the description of the fuel storage racks, the computer codes, the criticality analysis of new and spent fuel storage racks, the accident analysis, and the limitations of analysis.

The new fuel storage racks provide onsite storage capacity of 112 new fuel assemblies corresponding to one (1) refueling batch plus additional margin. The spent fuel storage pit is made up of region I and region II. The fresh or partially burnt fuel assemblies are stored in region I which has a storage capacity for one (1) full core, one (1) refueling batch, and five (5) damaged fuels. Region I storage area is designed to accommodate fuel assemblies with initial enrichment up to 5.0 weight percent U-235. Region II has a storage capacity of spent fuel assemblies generated during plant operation of twenty (20) years at full power in case of an 18-month fuel cycle. Spent fuel storage racks are capable of receiving 1,792 fuel assemblies.

The SCALE 6.1.2 code package is used for the depletion and criticality calculations. Among the modules of the SCALE 6.1.2 code package, the TRITON module is used for generating cross section libraries and the ORIGEN-ARP is used for depletion calculations with cross section libraries generated using the TRITON module. The CSAS5 module with KENO-V.a is used for the criticality calculation using the isotopic content from the depletion calculation. The ENDF/B-VII 238-group library is used for the depletion and criticality calculations.

The depletion and criticality calculations are performed to evaluate criticality safety of new and spent fuel storage racks. The biases and uncertainties by the calculation methods and variations of design parameters are analyzed and the results are included to calculated keff. The postulated accident analyses such as a dropped fuel assembly, a misloaded fuel assembly and a boron dilution accident are also performed.

All the effective neutron multiplication factors for new and spent fuel storage racks meet the acceptance criteria of the 10 CFR 50.68 described as below under normal and accident conditions with some limitations on fuel, operation and spent fuel pool.

The acceptance criteria of the new fuel storage racks are such that keff including all biases and uncertainties does not exceed 0.95 with full density unborated water and 0.98 with optimum moderation in the new fuel storage racks, at a 95 percent probability and 95 percent confidence level. For spent fuel storage racks, the credit is taken for soluble boron so that the keff including all biases and uncertainties does not exceed 0.95 with borated water, at a 95 percent probability and 95 percent confidence level, and remains below 1.00 with full density unborated water, at a 95 percent probability and 95 percent confidence level.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TABLE OF CONTENTS 1 INTRODUCTION .................................................................................................. 1 2 CRITICALITY ANALYSIS OF NEW FUEL STORAGE RACK .................................. 2 2.1 Design Input Data ........................................................................................................................... 2 2.2 Key Assumptions ............................................................................................................................ 8 2.3 Design Method................................................................................................................................ 9 2.4 Criticality Analysis for New Fuel Storage Rack ............................................................................ 10 2.5 Results .......................................................................................................................................... 20 3 CRITICALITY ANALYSIS OF SPENT FUEL STORAGE RACK ............................. 24 3.1 Design Input Data ......................................................................................................................... 24 3.2 Key Assumptions .......................................................................................................................... 29 3.3 Design Method.............................................................................................................................. 31 3.4 Criticality Analysis for Spent Fuel Pool Region I .......................................................................... 33 3.5 Criticality Analysis for Spent Fuel Pool Region II ......................................................................... 51 3.6 Interface Between Regions .......................................................................................................... 93 4 ACCIDENT ANALYSIS ........................................................................................ 95 4.1 Dropped Fresh Fuel Assembly ..................................................................................................... 95 4.2 Misloaded Fresh Fuel Assembly................................................................................................... 99 4.3 Boron Dilution Accident .............................................................................................................. 103 5 LIMITATIONS OF ANALYSIS ............................................................................ 114 5.1 Fuel Limitations ........................................................................................................................... 114 5.2 Operational Limitations ............................................................................................................... 114 5.3 Spent Fuel Pool Limitations ........................................................................................................ 114 6 CONCLUSIONS ................................................................................................ 115 7 REFERENCES .................................................................................................. 116 KEPCO & KHNP v

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 LIST OF TABLES Table 2.1-1 Design Input Data of Fuel Assembly and New Fuel Storage Rack ..................................... 3 Table 2.1-2 Composition Ratio of Constituent Nuclide for Calculation Model ........................................ 4 Table 2.4-1 Calculated Nominal keff of the NFR .................................................................................... 13 Table 2.4-2 Calculation Results of keff for a Dropped Fuel Assembly Accident .................................... 14 Table 2.4-3 Tolerance Uncertainty for Optimum Moderation Condition ................................................ 15 Table 2.4-4 Tolerance Uncertainty for Fully Flooded Condition ............................................................ 16 Table 2.5-1 Evaluation Results of keff for Various Water Densities ....................................................... 21 Table 2.5-2 Evaluation Results of keff for a Dropped Fuel Assembly Accident ..................................... 22 Table 3.1-1 Design Data for Spent Fuel Pool Region I ......................................................................... 25 Table 3.1-2 Design Data for Spent Fuel Pool Region II ........................................................................ 26 Table 3.1-3 Fuel Assembly Design and Operating Data ....................................................................... 27 Table 3.2-1 Considered Nuclides in the Criticality Calculation ............................................................. 30 Table 3.4-1 keff without Bias and Uncertainty for Spent Fuel Pool Region I ......................................... 37 Table 3.4-2 Benchmark Calculation Bias and Bias Uncertainty as a Function of Enrichment ............. 38 Table 3.4-3 Benchmark Calculation Bias and Bias Uncertainty Area of Applicability ........................... 39 Table 3.4-4 Uncertainty due to Mechanical Tolerances ........................................................................ 40 Table 3.4-5 Uncertainty due to Fuel Assembly Position in the Cell ...................................................... 41 Table 3.4-6 Bias due to Cooling Water Temperature ............................................................................ 42 Table 3.4-7 Summary of Bias and Uncertainty for Spent Fuel Pool Region I ....................................... 43 Table 3.4-8 Summary of keff with Bias and Uncertainty for Spent Fuel Pool Region I .......................... 44 Table 3.5-1 Bounding Value of Reactor Parameters for the Depletion Calculation .............................. 58 Table 3.5-2 Sensitivity Analysis for Power Level .................................................................................. 59 Table 3.5-3 Parameters for Generated ORIGEN-ARP Libraries of PLUS7 16x16 Fuel Assembly ...... 60 Table 3.5-4 Burnup Values of Cross Section Sets ................................................................................ 61 Table 3.5-5 keff without Bias and Uncertainty for Spent Fuel Pool Region II ........................................ 62 Table 3.5-6 Monte Carlo Standard Deviation for keff Calculation .......................................................... 63 Table 3.5-7 Mechanical Tolerances ...................................................................................................... 64 Table 3.5-8 Uncertainty due to Mechanical Tolerance .......................................................................... 65 Table 3.5-9 Bias for Minor Actinides and Fission Products .................................................................. 66 Table 3.5-10 Bias for Pool Cooling Water Temperature ......................................................................... 67 Table 3.5-11 Uncertainty due to Eccentric Fuel Assembly Positioning .................................................. 68 Table 3.5-12 Uncertainty due to Reactor Burnup Record ....................................................................... 69 Table 3.5-13 Depletion Uncertainty ........................................................................................................ 70 Table 3.5-14 Bounding Axial Burnup Profile ........................................................................................... 71 KEPCO & KHNP vi

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-15 keff Calculated with Bounding Axial Burnup Distribution (Non-Blanketed) ......................... 72 Table 3.5-16 keff Calculated with Flat Burnup Distribution (Non-Blanketed) ........................................... 73 Table 3.5-17 Reactivity difference between Flat and Axial Burnup Distribution (Non-Blanketed) .......... 74 Table 3.5-18 keff Calculated with Bounding Axial Burnup Distribution (Blanketed) ................................. 75 Table 3.5-19 keff Calculated with Flat Burnup Distribution (Blanketed) ................................................... 76 Table 3.5-20 Reactivity difference between Flat and Axial Burnup Distribution (Blanketed) .................. 77 Table 3.5-21 Total Bias for Spent Fuel Pool Region II ............................................................................ 78 Table 3.5-22 Total Uncertainty for Spent Fuel Pool Region II................................................................. 79 Table 3.5-23 Total Bias and Uncertainty for Spent Fuel Pool Region II ................................................. 80 Table 3.5-24 keff with Bias and Uncertainty for Spent Fuel Pool Region II ............................................. 81 Table 3.5-25 Minimum Burnup Calculated with Raw Fitting Equation .................................................... 82 Table 3.5-26 Minimum Burnup versus Enrichment for Raw Fitting and Adjusted Fitting ....................... 83 Table 4.1-1 Criticality Analysis Results for Dropped Fuel Assembly Accident...................................... 96 Table 4.2-1 Number Densities of Nuclide in the Spent Fuel ............................................................... 100 Table 4.2-2 Criticality Analysis Results for Misloaded Fuel Assembly Accident ................................. 101 Table 4.3-1 Number Densities of Nuclide in the Spent Fuel ............................................................... 106 Table 4.3-2 Analysis Results of Boron Dilution Accident in the Region I ............................................ 107 Table 4.3-3 Analysis Results of Boron Dilution Accident in the Region II ........................................... 108 TS Table 4.3-4 Critical Time Values for Boron Dilution from [ ] within the SFP ....... 109 KEPCO & KHNP vii

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 LIST OF FIGURES Figure 2.1-1 Top View of Criticality Calculation Model for the NFR ......................................................... 5 Figure 2.1-2 Front View of Criticality Calculation Model for the NFR ....................................................... 6 Figure 2.1-3 Elevation of New Fuel Storage Rack ................................................................................... 7 Figure 2.4-1 Criticality Calculation Model for the NFR in a New Fuel Storage Pit ................................. 17 Figure 2.4-2 Criticality Calculation Model for a Dropped Fuel Assembly Accident (Contact) ................ 18 Figure 2.4-3 Criticality Calculation Model for a Dropped Fuel Assembly Accident (Centered) ............. 19 Figure 2.5-1 Effective Multiplication Factors of NFR according to Water Density Changes .................. 23 Figure 3.1-1 Arrays and Dimensions of Spent Fuel Pool Regions I and II ........................................... 28 Figure 3.4-1 Reference Model of Spent Fuel Pool Region I .................................................................. 45 Figure 3.4-2 Model for Gap Effect of Spent Fuel Pool Region I............................................................. 46 Figure 3.4-3 Model for Damaged Fuel Storage Cells of Spent Fuel Pool Region I ............................... 47 Figure 3.4-4 Model for Eccentric Position of Fuel Assembly in Spent Fuel Pool Region I .................... 48 Figure 3.4-5 Top View of the Spent Fuel Storage Racks in the Region I ............................................... 49 Figure 3.4-6 Side View of the Spent Fuel Storage Racks in the Region I ............................................. 50 Figure 3.5-1 Symmetric Depletion Calculation Model for the PLUS7 16x16 Fuel Assembly ................. 84 Figure 3.5-2 Cross Section View of KENO-V.a Model for 2x2 Array of Fuel Rack in Region II ............. 85 Figure 3.5-3 3-D View of KENO-V.a Model for 2x2 Array of Fuel Rack in Region II .............................. 86 Figure 3.5-4 Model for Eccentric Position of Fuel Assemblies in Spent Fuel Pool Region II ................. 87 Figure 3.5-5 Burnup versus k eff with Fitting Equations ........................................................................... 88 Figure 3.5-6 Minimum Burnup versus Enrichment with Raw Fitting and Adjusted Fitting ..................... 89 Figure 3.5-7 Minimum Burnup versus Enrichment Curve ...................................................................... 90 Figure 3.5-8 Top View of the Spent Fuel Storage Racks in the Region II .............................................. 91 Figure 3.5-9 Side View of the Spent Fuel Storage Racks in the Region II ............................................ 92 Figure 3.6-1 Spent Fuel Storage Rack Interfaces .................................................................................. 94 Figure 4.1-1 Accident Analysis Model for the Dropped Fresh Fuel Assembly ....................................... 97 Figure 4.1-2 keff versus Boron Concentration Curves for Dropped Fuel Accident and Misloaded Fresh Fuel Accident ........................................................................................................... 98 Figure 4.2-1 Accident Analysis Model for Misloaded Fresh Fuel Assembly ........................................ 102 Figure 4.3-1 Analysis Model of Boron Dilution Accident in the Region I ...............................................111 Figure 4.3-2 Analysis Model of Boron Dilution Accident in the Region II ............................................. 112 Figure 4.3-3 keff versus Boron Concentration Curves for Boron Dilution Accident............................... 113 KEPCO & KHNP viii

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 ACRONYMS AND ABBREVIATIONS 2-D two dimensional 3-D three dimensional AFG average energy group of neutrons causing fission EALF energy of average lethargy causing fission ENDF evaluated nuclear data file FA fuel assembly G/T guide tube GWd gigawatt days HTC Haut Taux de Combustion I.D. inner diameter keff effective neutron multiplication factor LCO limiting conditions for operation TM METAMIC trademark of Metamic, LLC MTU metric ton uranium MWt megawatts thermal NFR new fuel storage rack NFSP new fuel storage pit O.D. outer diameter PWR pressurized water reactor SFP spent fuel pool SFR spent fuel storage rack SS stainless steel wt% weight percent KEPCO & KHNP ix

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 1 INTRODUCTION This report documents the criticality safety analysis of the new fuel storage rack (NFR) and the spent fuel storage rack (SFR) of the APR1400 design. This report includes the acceptance criteria, the description of the fuel storage racks, computer codes, the criticality analysis of new and spent fuel storage racks, the accident analysis, and limitations of analysis.

The acceptance criteria and relevant guidance for the criticality safety evaluation for new and spent fuel storage racks are as follows: 10 CFR 50 Appendix A, General Design Criterion (GDC) 62 (Reference 1),

10 CFR Part 50.68 (Reference 2), NRC guidance (Reference 3), and NUREG/CR-6698 (Reference 4).

The 10 CFR Part 50.68 (b) items (2) and (3) for new fuel storage racks and item (4) for spent fuel storage racks are applied as the criticality safety design criteria.

Chapter 2 and 3 denote the criticality analysis for new and spent fuel storage racks, respectively. Chapter 4 describes the accident analysis for a dropped fuel assembly, a misloaded fuel assembly and a boron dilution accident. Chapter 5 describes the limitations of analysis, and Chapter 6 provides the conclusions.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 2 CRITICALITY ANALYSIS OF NEW FUEL STORAGE RACK 2.1 Design Input Data New fuel assemblies are stored in the NFR in a dry fuel storage pit. The NFR consists of 2 racks, each of which has 7x8 cells array, so a total of 112 new fuel assemblies can be stored in the NFR. Figure 2.1-1 and Figure 2.1-2 show the top and front view of the NFR calculation model, and Figure 2.1-3 provides the elevation of NFR. As shown in the Figures the racks are designed to be located in the new fuel storage pit (NFSP) surrounded by concrete walls. To set up boundaries of SCALE model, 30 cm thickness of concrete is assumed to build bounding walls in side and bottom. Concrete with 30 cm thickness is enough to take account of back scattering effect of neutrons from the wall to the NFR.

The design input data for the criticality calculation for the NFR are summarized in Table 2.1-1 and the composition ratio of constituent nuclides for the SCALE model is shown in Table 2.1-2.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.1-1 Design Input Data of Fuel Assembly and New Fuel Storage Rack Description Design Data Fuel type TS Pellet enrichment (wt%)

3 Pellet theoretical density (g/cm )

3 Pellet stack density (g/cm )

Pellet diameter (cm)

Material of fuel clad Inner diameter of fuel clad (cm)

Fuel Outer diameter of fuel clad (cm)

Assembly Material of guide tube Inner diameter of guide tube (cm)

Outer diameter of guide tube (cm)

Fuel rod pitch (cm)

Fuel assembly pitch (cm)

Fuel assembly active length (cm)

Material of rack cell Thickness of rack cell (cm)

New Fuel Inner dimension of rack cell (cm)

Storage Rack Cell pitch (cm)

Cell array KEPCO & KHNP 3

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.1-2 Composition Ratio of Constituent Nuclide for Calculation Model Composition Ratio [wt%]

Nuclide UO2 Pellet ZIRLO SS-304 Concrete TS KEPCO & KHNP 4

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 2.1-1 Top View of Criticality Calculation Model for the NFR KEPCO & KHNP 5

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 2.1-2 Front View of Criticality Calculation Model for the NFR KEPCO & KHNP 6

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 2.1-3 Elevation of New Fuel Storage Rack KEPCO & KHNP 7

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 2.2 Key Assumptions For a normal condition of new fuel storage rack (NFR), the effective multiplication factor for the fuel rack system is very low since the fuel assemblies are stored in dry environment. Therefore, the criticality evaluation for the NFR is performed for the postulated accident situations such as a mist environment, which provides an optimum moderation condition, and an immersion in pure water with the maximum density.

The key assumptions applied for the criticality analysis of the NFR are as follows:

a. The design maximum enrichment of 5.0 wt% is applied to all the UO2 fuel rods in the NFR,

b. There is no zoning of enrichment and no burnable poison rod in the fuel assembly (all fuel rods have the same maximum enrichment in the fuel assembly),

c. Axial blankets in the fuel rod are not considered for conservatism (the same maximum enrichment is assumed along the entire axial length of the effective fuel region),

d. The structural materials in the upper and lower parts of fuel rod such as plenum, spring, end caps, etc., and the grids in the fuel assembly are assumed as water,

e. The structural materials beyond the effective fuel length area in the NFR are ignored and replaced by water, and

f. The temperature of a fuel assembly, a rack structure, and water are assumed as room temperature.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 2.3 Design Method The CSAS5 module in the SCALE 6.1.2 code system (Reference 5) is used to calculate the effective neutron multiplication factor (keff) for the NFR with immersion in pure water and optimum moderation conditions. The v7-238 cross section library based on ENDF/B-VII (Reference 6) is used for CSAS5 module calculations.

Calculated result of criticality analysis should reflect the bias and bias uncertainty obtained from benchmark calculations based on the criticality experiments. Moreover, additional uncertainties which account for the variations of design parameters and mechanical tolerances of the NFR and fuel assembly should be included in the criticality analysis result. To take account of the bias and uncertainties, keff is evaluated from the following expression:

keff = k(calc) + k(bias) + k(uncert) where:

keff = effective neutron multiplication factor, k(calc) = calculated nominal keff, k(bias) .= sum of biases determined from critical benchmark comparisons, and k(uncert) = statistical summation of all tolerance and uncertainty components (square root of the sum of the squares).

The bias and bias uncertainty due to the criticality code are provided in Reference 7 and the uncertainties due to variations of design parameters and mechanical tolerances are calculated through the sensitivity analyses for the dimensional and material tolerances of the NFR and fuel assembly.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 2.4 Criticality Analysis for New Fuel Storage Rack 2.4.1 Criticality Calculation The criticality analyses for the NFR consider waters with an optimum moderation condition and the maximum densities, therefore criticality calculations are performed for water densities ranged from 0.01 3 3 g/cm to 1.0 g/cm to determine the maximum keff for an optimum moderation condition. The criticality calculation model including NFSP is shown in Figure 2.4-1.

The calculation results are presented in Table 2.4-1 as the calculated nominal keff with corresponding water densities. The nominal keff values in the Table 2.4-1 do not contain any bias or uncertainties.

2.4.2 Criticality Calculation for a Dropped Fuel Assembly Accident For one of postulated accident conditions, a fresh fuel assembly is assumed to be dropped and positioned in the space between the fuel racks in dry air environment. The dropped fuel assembly accident evaluation considers the fully loaded NFR model with a dropped fresh 5.0 wt% fuel assembly between the fuel racks. Two sub-cases are considered. Subcase 1 is for a dropped fuel assembly face adjacent to the one of rack cells as its closest proximity and subcase 2 is for a dropped fuel assembly being centered in the space between the fuel racks. The criticality calculation models for a dropped fuel assembly cases are shown in Figures 2.4-2 and 2.4-3.

The calculation results are presented in Table 2.4-2 with the keff for normal dry condition of NFR system.

The keff values in the Table 2.4-2 do not contain any bias or uncertainties.

2.4.3 Bias and Uncertainty The bias and uncertainties by the calculation methods and variations of design parameters are estimated from the following items:

a. Bias and bias uncertainty of a criticality calculation method,

b. Statistical uncertainty of the Monte Carlo calculation, and

c. Uncertainty due to tolerances or variations in the design parameters.

The basis of bias and uncertainty items and their corresponding values considered for the criticality analysis of the NFR are described in below.

(1) Bias and bias uncertainty of a criticality calculation method Bias and bias uncertainty are evaluated to validate the criticality analysis methodology through the benchmark calculations based on the criticality experiments (Reference 7).

TS

a. Bias: [ ]

TS

b. Bias uncertainty: [ ]

(2) Statistical uncertainty of the Monte Carlo calculation TS

a. Optimum moderation (2) : [ ]

TS

b. Moderation by full density water (2) : [ ]

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Statistical uncertainties of the criticality calculation for the optimum moderation condition and fully flooded condition are provided in Tables 2.4-3 and 2.4-4, respectively.

(3) Uncertainty due to tolerances or variations in the design parameters To evaluate uncertainties due to the tolerances in the mechanical and material specifications of the fuel and rack structures, sensitivity analyses are performed for the fuel rack cell in various conditions including the dimensional and material tolerances of the structure. Items in the sensitivity analysis for the criticality uncertainty evaluation are as follows:

TS

a. U-235 enrichment: [ ] ,

TS

b. UO2 pellet stack density: [ ] ,

TS

c. UO2 pellet diameter: [ ] ,

TS

d. Fuel rod pitch: [ ] ,

TS

e. Fuel clad outer diameter: [ ] ,

TS

f. Guide tube outer diameter: [ ] ,

TS

g. Fuel assembly position in fuel rack cell: [ ] ,

TS

h. NFR cell pitch: [ ] , and TS

i. NFR cell thickness: [ ] .

The uncertainty analyses are performed for the finite array model including NFSP as shown in Figure 2.4-

1. The calculation results for the uncertainty analysis due to the tolerances or variations in the design parameters are summarized in Tables 2.4-3 and 2.4-4. To determine the reactivity difference (ki) associated with a specific manufacturing tolerance, the keff calculated for the reference model is compared to that for the model with an individual tolerance. The ki due to a tolerance is then calculated as follows:

TS The resultant uncertainty due to tolerances or variations in the design parameters which is calculated as square root of the sum of the squares of individual ki is presented in the last row of Tables 2.4-3 and 2.4-4.

The evaluated total bias and uncertainty (kNFR ) for optimum moderation and fully flooded conditions, which include bias for the criticality analysis of the NFR is determined as follows:

TS

[ ]

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS

[ ]

TS For conservatism, a total uncertainty of [ ] will be applied to obtain final criticality analysis results for new fuel rack storage system.

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Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.4-1 Calculated Nominal keff of the NFR Water Density 3 Calculated Nominal keff Standard Deviation ()

[g/cm ]

TS Note:

Bias and uncertainty are not included.

KEPCO & KHNP 13

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.4-2 Calculation Results of keff for a Dropped Fuel Assembly Accident Case keff Standard Deviation (1)

TS Normal condition Subcase 1 accident (Contact)

Subcase 2 accident (Centered)

Note:

Bias and uncertainty are not included KEPCO & KHNP 14

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.4-3 Tolerance Uncertainty for Optimum Moderation Condition Effective Multiplication Factor Individual Uncertainty Input Parameter (ki )

ki TS Notes:

TS

1) [ ]

2) Square root of the sum of the squares ( =i(k i )2 ). Negative uncertainties are not included in the resultant uncertainty.

KEPCO & KHNP 15

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.4-4 Tolerance Uncertainty for Fully Flooded Condition 1)

Effective Multiplication Factor Individual Uncertainty Input Parameter (ki )

ki TS Notes:

TS

1) [ ]

2) Square root of the sum of the squares ( =i(k i )2 ). Negative uncertainties are not included in the resultant uncertainty.

KEPCO & KHNP 16

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Fuel Assembly NFR Cell Concrete Water Figure 2.4-1 Criticality Calculation Model for the NFR in a New Fuel Storage Pit KEPCO & KHNP 17

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Figure 2.4-2 Criticality Calculation Model for a Dropped Fuel Assembly Accident (Contact)

KEPCO & KHNP 18

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Figure 2.4-3 Criticality Calculation Model for a Dropped Fuel Assembly Accident (Centered)

KEPCO & KHNP 19

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 2.5 Results The criticality analysis for the NFR with 5.0 wt% enrichment of the PLUS7 fuel is performed by using SCALE 6.1.2 code. Table 2.5-1 and Figure 2.5-1 show the evaluated effective neutron multiplication factors according to various water densities. The evaluated results for the criticality analysis include the evaluated total bias and uncertainty (kNFR). An optimum moderation condition occurs at water density of TS

[ ] . Table 2.5-2 shows the evaluated keff for postulated accident cases of a dropped fuel assembly in the space between fuel racks.

The evaluated effective neutron multiplication factors for the NFR have the additional margin due to the conservative assumptions for the criticality analysis as follows:

- The design maximum enrichment of 5.0 wt% is applied to all the UO2 fuel rods in the NFR,

- Miscellaneous structures such as grid, spring, end caps, etc., are not included in the calculation model,

- Burnable absorber rods in fuel assembly or axial blankets in fuel rod are not considered in the calculation model, and

- Zoning to alleviate the power peak in the fuel assembly is not considered and all fuel rods are assumed to have the same maximum enrichment.

As a conclusion, the evaluated effective neutron multiplication factors for the NFR satisfy the acceptance criteria as follows:

Description keff Acceptance criteria keff for flooded by pure water TS 0.95 keff for optimum moderation 0.98 KEPCO & KHNP 20

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.5-1 Evaluation Results of keff for Various Water Densities Water Density Effective Multiplication 3 1)

[g/cm ] Factor (keff) 0.01 TS 0.03 0.05 0.10 0.13 0.14 0.15 0.16 0.17 0.18 0.20 0.30 0.40 0.60 0.80 1.00 Note:

1) Total uncertainty (kNFR =[ ]TS) is included.

KEPCO & KHNP 21

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 2.5-2 Evaluation Results of keff for a Dropped Fuel Assembly Accident 1)

Effective Multiplication Factor Case (keff)

Subcase 1 accident TS (Contact)

Subcase 2 accident (Centered)

Note:

1) Total uncertainty (kNFR =[ ]TS) is included.

KEPCO & KHNP 22

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 2.5-1 Effective Multiplication Factors of the NFR according to Water Density Changes KEPCO & KHNP 23

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3 CRITICALITY ANALYSIS OF SPENT FUEL STORAGE RACK 3.1 Design Input Data The spent fuel storage pit of the ARP1400 design is made up of region I and region II. The fresh or partially burnt fuel assemblies are stored in region I which has a storage capacity for one (1) full core, one (1) refueling batch, and five (5) damaged fuel assemblies. Region I storage area is designed to accommodate fuel assemblies with initial enrichment up to 5.0 wt% U-235. Region II has a storage capacity of spent fuel assemblies generated during plant operation of twenty (20) years at full power in case of an 18-month fuel cycle. Spent fuel storage racks are capable of receiving 1,792 fuel assemblies TS and the center-to-center spaces between adjacent fuel assemblies are designed to be [ ] and TS

[ ] for region I and II, respectively, to maintain subcriticality.

The design input data for a criticality analysis of spent fuel storage rack are shown in Tables 3.1-1, 3.1-2, and Figure 3.1-1. The fuel assembly (PLUS7) design data and the operating data are listed in Table 3.1-3.

KEPCO & KHNP 24

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.1-1 Design Data for Spent Fuel Pool Region I Parameters Value Storage cell TS Material Thickness Cell pitch Inner dimension Neutron absorber Material Boron concentration (minimum)

Thickness Width Length Sheath Material Thickness Damaged fuel storage cell Material Thickness Cell pitch Inner dimension Canister Material Thickness Inner dimension KEPCO & KHNP 25

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.1-2 Design Data for Spent Fuel Pool Region II Parameters Value Storage cell TS Material Thickness Cell pitch Inner dimension Neutron absorber Material Boron concentration (minimum)

Thickness Width Length Sheath Material Thickness KEPCO & KHNP 26

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.1-3 Fuel Assembly Design and Operating Data Parameters Value Assembly lattice TS Model Enrichments (maximum)

No. rods per assembly No. water holes Rod pitch Assembly pitch Fuel rod data Fuel density Pellet diameter Clad material Clad inner diameter Clad outer diameter Fuel temperature (expected)

Clad temperature Guide tube data Inner diameter Outer diameter material Moderator data Average density (expected)

Average boron concentration (expected)

Moderator temperature (expected)

Power level (expected)

KEPCO & KHNP 27

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.1-1 Arrays and Dimensions of Spent Fuel Pool Regions I and II KEPCO & KHNP 28

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.2 Key Assumptions Key assumptions for the conservative criticality calculation of spent fuel storage rack are as follows:

a. KENO-V.a model for spent fuel pool region I assumes an infinite array of one normal fuel storage cell using all reflective conditions,

b. KENO-V.a model for spent fuel pool region II assumes an infinite array of 2x2 storage cells with periodic boundary conditions for sides and reflective conditions for top and bottom, TS

c. KENO-V.a model assumes [ ] of water above and below the active fuel length,

d. The assemblies are assumed as non-blanketed assemblies for conservatism (see Subsection 3.5.3.9.4),

e. Fuel rod cladding and guide tube cladding are only considered as structural material within the active fuel length, 3

f. Water density of 1.0 g/cm is used for conservatism (see Subsections 3.4.3.5 and 3.5.3.5),

g. Soluble boron is not considered in normal conditions,

h. No burnable absorber rod is considered for conservatism,

i. No zoning around guide tube is considered for conservatism,

j. 12 actinides and 16 fission products recommended in ISG-8 (Reference 8) are considered for spent fuel pool region II. Recommended 28 nuclides are presented in Table 3.2-1, and TS

k. A neutron absorber plate is assumed to have [ ] of the minimum B-10 areal density for conservatism.

Key assumptions for the conservative depletion calculation of spent fuel storage rack are as follows:

TS

a. The maximum fuel temperature, [ ] , is used, TS

b. The maximum fuel density, [ ] , is used, TS

c. The maximum moderator temperature, [ ] , is used, TS

d. The maximum cycle average soluble boron concentration, [ ] , is used, TS

e. The maximum power level, [ ] , is used,

f. No decay time is considered after the fuel assembly is depleted for conservatism,

g. No burnable poison rod is considered for conservatism,

h. No zoning around guide tube is considered for conservatism,

i. The uniform axial power distribution is assumed and the end effect is considered as a bias, and

j. No burnup credit is considered for spent fuel pool region I.

KEPCO & KHNP 29

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.2-1 Considered Nuclides in the Criticality Calculation (Reference 8)

Recommended set of nuclides for actinide-only burnup credit U-234 U-235 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-141 Recommended set of additional nuclides for actinide and fission product burnup credit Mo-95 Tc-99 Ru-101 Rh-103 Ag-109 Cs-133 Sm-147 Sm-149 Sm-150 Sm-151 Sm-152 Nd-143 Nd-145 Eu-151 Eu-153 Gd-155 U-236 Am-243 Np-237 KEPCO & KHNP 30

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.3 Design Method Design methods of the criticality analysis for spent fuel storage rack are described in following Subsections.

3.3.1 Criticality Calculation Criticality calculations are performed using the CSAS5/KENO-V.a sequence with the ENDF/B-VII 238-energy-group library. The isotopic contents of burned fuel are generated by the depletion calculation discussed in following Subsections.

3.3.2 Depletion Calculation The depletion calculations are performed using the ORIGEN-ARP with cross section libraries which are pre-generated by the TRITON-NEWT.

3.3.2.1 ORIGEN-ARP calculation The ORIGEN-ARP is a depletion analysis sequence of SCALE 6.1.2 to perform point-depletion calculations with the ORIGEN-S code using problem-dependent cross sections. Problem-dependent cross section libraries are generated using the ARP (Automatic Rapid Processing) module using an interpolation algorithm that operates on pre-generated libraries created for a range of fuel properties and operating conditions.

3.3.2.2 TRITON-NEWT calculation TRITON-NEWT calculation is used to generate cross section libraries for PLUS7 16x16 fuel assembly.

The procedures to generate ORIGEN-ARP cross section libraries by TRITON-NEWT method are described in below.

The first step is to construct a physics model of the fuel lattice of the reactor assembly under consideration. For a given initial fuel enrichment, a TRITON depletion calculation is performed using 2 dimensional depletion analysis sequence of SCALE 6.1.2. TRITON uses an explicit 2-D representation of the fuel assembly using the NEWT discrete ordinates transport code.

The depletion calculation sequences are used to simulate irradiation and depletion of the fuel over the required irradiation history. A burnup analysis is performed using a series of time intervals. During the simulation, cross sections that are representative of the mid-point of each burnup step are created and saved in the library by the depletion sequence.

Each set of burnup-dependent cross sections is stored within the single library, and is accessed sequentially by its position in the library. Position 1 contains fresh-fuel cross sections and the other positions contain cross section sets which correspond to burnup levels characterizing the midpoint of each burnup step in the depletion sequence calculation.

For fuels with multiple enrichment values, the above procedure is repeated for the multiple enrichment values. Cross section changes with enrichment are generally represented using 0.5 wt% increments (1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5 and 6.0 wt% of U-235).

KEPCO & KHNP 31

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.3.3 Bias and Uncertainty Calculation For spent fuel pool region I, the bias and uncertainties by the calculation methods and variations of design parameters are estimated from the following items:

a. Bias and bias uncertainty of the criticality calculation method,

b. Statistical uncertainty of the Monte Carlo calculation,

c. Uncertainty due to tolerances or variations in the design parameters,

d. Uncertainty due to eccentric fuel assembly positioning, and

e. Bias due to pool cooling water temperature.

For spent fuel pool region II, the bias and uncertainties by the calculation methods, variations of design parameters and the depletion calculation are estimated from the following items:

a. Bias and bias uncertainty of a the criticality calculation method,

b. Statistical uncertainty of the Monte Carlo calculation,

c. Uncertainty due to tolerances or variations in the design parameters,

d. Uncertainty due to eccentric fuel assembly positioning,

e. Bias due to pool cooling water temperature,

f. Bias due to axial burnup distribution (end effect),

g. Bias due to minor actinides and fission products,

h. Uncertainty due to reactor burnup record, and

i. Uncertainty due to the depletion calculation.

3.3.4 Calculation of the Loading Curve for Spent Fuel Pool Region II The loading curve of spent fuel pool region II is a function of burnup versus enrichment to meet the minimum burnup requirement for each initial enrichment satisfying the target keff. The curve is produced targeting keff less than 1.0 with consideration of all the biases and uncertainties associated with the analyses.

KEPCO & KHNP 32

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.4 Criticality Analysis for Spent Fuel Pool Region I Spent fuel pool region I is designed to accommodate damaged fuel assemblies and fuel assemblies with initial enrichment up to 5.0 wt% U-235. The damaged fuel assemblies are stored in the canister which is located in the damaged fuel storage cell. Fresh or partially burnt fuel assemblies are stored in the normal fuel storage cell. Therefore, the criticality analysis is conducted to evaluate criticality safety of both normal fuel storage cell and damaged fuel storage cell.

Figures 3.4-5 and 3.4-6 provide the top and side views of SFP region I. As can be seen from the Figure 3.4-5, four neutron absorber plates are attached to the four faces of each fuel storage cell in the SFP region I. So, all cells along the outer walls of the racks have a neutron absorber plate facing the outer wall or other racks.

Design data for fuel storage cell of SFP region I are provided in Figures 3.4-5, 3.4-6 and Table 3.1-1, and information of rack interfaces within and between the SFP regions are provide in Subsection 3.6.

3.4.1 Normal Fuel Storage Cell The criticality calculation model for normal fuel storage cell is modeled as an infinite array of one normal fuel storage cell with reflective boundary conditions on all sides as shown in Figure 3.4-1. The design input data for the criticality analysis are as follows:

a. Cross section library: ENDF/B-VII based 238 multi-group library,

b. Material composition, TS

- Fuel pellet: Fresh 5.0 wt% U-235 with density of [ ] ,

- Cladding: ZIRLO, 3

- Cooling water: non-borated pure water with density of 1.0 g/cm ,

TM TS

- Neutron absorber: METAMIC with B-10 areal density of [ ] ,

- Structural material: SS-304,

- Pool wall: Concrete,

c. Fuel assembly geometric data: See detailed data in Table 3.1-3,

d. Normal fuel storage cell geometric data: See detailed data in Table 3.1-1, TS

e. KENO-V.a model assumes [ ] of water above and below the active fuel length, and

f. Reflective boundary conditions are applied for all sides of the calculation model.

To evaluate the gap effect between racks on criticality, sensitive analyses are performed for the gap between racks ranged from 0 mm to 60 mm. Figure 3.4-2 shows the model for a gap effect with 0 mm gap between racks. The effective neutron multiplication factors and the statistical Monte Carlo calculation uncertainties are shown in Table 3.4-1.

3.4.2 Damaged Fuel Storage Cell Criticality The damaged fuel is stored in a canister which is located in the damaged fuel storage cell, so the size of damaged fuel storage cell is a little bigger than the normal fuel storage cell. The damaged fuel storage cell is made with the same material as normal fuel storage cell.

The criticality calculation model for damaged fuel storage cells is modeled as a 6x8 array as shown in Figure 3.4-3. A 6x8 array consists of five damaged fuel storage cells and 43 normal storage cells. The design input data for criticality analysis are almost the same as those of the normal fuel storage cell KEPCO & KHNP 33

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 criticality analysis, except for the geometric data (See detailed data in Table 3.1-1).

For the purpose of conservatism, the damaged fuel assemblies are modeled under the following assumptions.

a. Unburned new fuel with initial enrichment of 5.0wt%, and

b. All gaps between the pellet and the cladding are assumed to be flooded by water.

The effective neutron multiplication factor and the statistical Monte Carlo calculation uncertainty for the damaged fuel storage cell are shown in Table 3.4-1.

3.4.3 Bias and Uncertainty Calculations As discussed in Subsection 3.3.3, the bias and uncertainties for criticality analysis of spent fuel pool region I are following items:

a. Bias and bias uncertainty of the criticality calculation method,

b. Statistical uncertainty of the Monte Carlo calculation,

c. Uncertainty due to tolerances or variations in the design parameters,

d. Uncertainty due to eccentric fuel assembly positioning, and

e. Bias due to pool cooling water temperature.

To estimate the reactivity difference (ki) associated with a specific disturbed condition, the keff for the reference model is compared to the keff for the individual disturbed condition.

The analyses of the bias and uncertainties are described in the following Subsections.

3.4.3.1 Bias and Bias Uncertainty due to Methodology The bias and bias uncertainty of the criticality calculation method are evaluated to validate the criticality analysis methodology through the benchmark calculations based on the criticality experiments (Reference 7). As a result of trend analysis discussed in Reference 7, only enrichment showed a statistically significant trend. Table 3.4-2 provides the 95/95 bias and bias uncertainty developed in Reference 7. Table 3.4-7 provides the value used in the criticality analysis, which doubled the bias uncertainty provided in Table 3.4-2 for the purpose of conservatism. Table 3.4-3 shows the area of applicability for the bias and bias uncertainty.

3.4.3.2 Uncertainty due to Monte Carlo Calculation Statistical uncertainties due to Monte Carlo calculations are listed in Table 3.4-1.

3.4.3.3 Uncertainties due to Mechanical Tolerances The uncertainties due to mechanical tolerances of the fuel assembly and the rack are summarized in Table 3.4-4. And the detailed assessments are described in the following Subsections.

3.4.3.3.1 Fuel Assembly The uncertainties due to mechanical tolerances for the fuel assembly including a fuel pellet enrichment, a fuel pellet stack density, a fuel pellet diameter, a fuel cladding diameter, a fuel rod pitch, and a guide tube cladding diameter are evaluated. Table 3.4-4 shows the uncertainties due to mechanical tolerances of fuel assembly:

KEPCO & KHNP 34

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS

a. Maximum fuel enrichment: [ ] ,

TS

b. Maximum fuel pellet stack density: [ ] ,

TS

c. Maximum fuel pellet outer diameter: [ ] ,

TS

d. Maximum fuel cladding inner diameter: [ ] ,

TS

e. Minimum fuel cladding outer diameter: [ ] ,

TS

f. Minimum fuel rod pitch: [ ] ,

TS

g. Maximum fuel rod pitch: [ ] , and TS

h. Minimum guide tube cladding outer diameter: [ ] .

3.4.3.3.2 Racks The uncertainties due to mechanical tolerances about the rack including a cell pitch, a cell wall thickness, and a sheath thickness are assessed. The uncertainties due to mechanical tolerances about the thickness and width of neutron absorber plates (NAP) are also evaluated and provided in Table 3.4-4. The uncertainty due to tolerance of the NAP length will not be evaluated, because the NAP length applied to TS the criticality analysis is assumed to be identical to the active fuel length ([ ] ) which is shorter TS than the minimum length of NAP ([ ] ).

Table 3.4-4 shows the uncertainties due to mechanical tolerances of the racks:

TS

a. Minimum cell pitch: [ ] ,

TS

b. Minimum cell wall thickness: [ ] ,

TS

c. Maximum cell wall thickness: [ ] ,

TS

d. Minimum sheath thickness: [ ] ,

TS

e. Maximum sheath thickness: [ ] ,

TS

f. Minimum neutron absorber thickness: [ ] , and TS

g. Minimum neutron absorber width: [ ] .

3.4.3.4 Uncertainty due to Eccentric Fuel Assembly Positioning The uncertainty due to fuel assembly positioning in the cell is evaluated. Figure 3.4-4 shows the eccentric position of fuel assembly and the evaluation results are shown in Table 3.4-5. The effective neutron multiplication factor of the eccentric fuel assembly positioning model is less than that of normal positioning model as shown in Table 3.4-5. So the uncertainty of fuel assembly positioning is not included in the total uncertainty.

3.4.3.5 Bias due to Pool Cooling Water Temperature The bias due to the temperature of cooling water in the pool is assessed. The evaluation results are listed in Table 3.4-6 and show that the pool has a negative moderator coefficient, i.e., k eff at the lower temperature is higher than those at the higher temperatures. Therefore, the bias due to cooling water density is not included in the total bias.

KEPCO & KHNP 35

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.4.4 Results of Criticality Analysis of Spent Fuel Pool Region I The criticality analysis for spent fuel pool region I with 5.0 wt% U-235 enrichment of PLUS7 fuel is performed by using SCALE 6.1.2 code. Table 3.4-7 shows the summary of bias and uncertainty. Table 3.4-8 shows the evaluated effective neutron multiplication factors including total bias and uncertainty. The evaluated effective neutron multiplication factors for spent fuel pool region I have additional margin due to the conservative assumptions included in the input parameters for the criticality analysis as follows:

a. The design maximum enrichment of 5.0 wt% is applied to all the UO2 fuel rods in the spent fuel pool region I,

b. Miscellaneous structures such as grid, spring, end caps, etc., are not included in the calculation model,

c. Burnable absorber rods in fuel assembly or axial blankets in fuel rod are not considered in the calculation model, and

d. Zoning to alleviate the power peak in the fuel assembly is not considered and all fuel rods are assumed to have the same maximum enrichment.

The acceptance criteria of the spent fuel storage racks with soluble boron credit are as follows:

a. The keff value, including all biases and uncertainties, must not exceed 0.95 with borated water, at a 95 percent probability, 95 percent confidence level, and

b. The keff value, including all biases and uncertainties, less than 1.00 with full density unborated water, at a 95 percent probability and 95 percent confidence level.

TS The keff for the normal fuel storage cell is [ ] without applying soluble boron and the keff for the TS damaged fuel storage cells is [ ] without applying soluble boron. Therefore, the spent fuel pool region I satisfies criticality safety criteria since the keff for both normal and damaged fuel storage cells are less than the regulatory limit as follows:

Acceptance criteria Acceptance criteria Description keff (with soluble boron) (without soluble boron)

Keff for the Normal Fuel Storage Cell TS 0.95 < 1.00 Keff for the Damaged Fuel Storage Cell KEPCO & KHNP 36

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-1 keff without Bias and Uncertainty for Spent Fuel Pool Region I Monte Carlo Calculation Calculation Model Calculated keff Uncertainty ()

Normal Condition TS Distance between Racks 00 mm 12 mm 24 mm 36 mm 48 mm 60 mm Including Damaged Cell KEPCO & KHNP 37

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-2 Benchmark Calculation Bias and Bias Uncertainty as a Function of Enrichment (Reference 7)

Enrichment Bias Bias (wt% U-235) Uncertainty 1.0 TS 1.4 Fresh Fuel, with Absorber 1.6 or 1.8 Combined Fresh and Spent Fuel, 2.0 with Absorber 2.4 2.5 3.0 3.4 3.5 4.0 4.5

5.0 Notes

TS

1) Biases for enrichments greater than or equal to [ ] have been replaced with the un-trended bias which is higher than the trended bias for those enrichments,

2) Linear interpolation is available between points, and

3) Negative sign - in front of the bias is the convention, indicating that the bias should be added to the calculated keff values.

KEPCO & KHNP 38

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-3 Benchmark Calculation Bias and Bias Uncertainty Area of Applicability (Reference 7)

Range Parameter Combined Fresh and Spent Fuel, Fresh Fuel, with Absorber with Absorber Fissionable Material TS Isotopic Composition of Fuel 1)

(wt% U-235)

Physical Form of Fuel Moderation Material Reflector Material Structural Material Absorber Material Physical Form of Absorbers Soluble Boron Concentration (ppm) 2 B-10 Areal Density (g/cm )

Geometry Pin Pitch (cm)

EALF AFG Note:

1) The HTC experiments contained mixed oxide (UO2/PuO2) fuel designed to represent spent UO2 fuel.

Therefore this validation suite is valid for fresh and spent UO2 fuel but not for mixed oxide systems.

KEPCO & KHNP 39

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-4 Uncertainty due to Mechanical Tolerances 1)

Design Parameter Nominal Tolerance Applied Value keff ki Normal - TS Rack in Min. Cell Pitch Region I Min. Cell Wall Thick.

Max. Cell Wall Thick.

Min. Sheath Thick.

Max. Sheath Thick.

Neutron Min. Thick Absorber Plate Min. Width Fuel Max. Fuel Enrichment Assembly Max. Fuel Pellet Density Max. Fuel Pellet O.D.

Max. Fuel Clad I.D.

Min. Fuel Clad O.D.

Min. Fuel Rod Pitch Max. Fuel Rod Pitch Min. G/T Clad O.D.

TS 2)

Square root of the sum of the squares ktol = i (ki )2 [ ]

Notes:

TS

1) [ ] , and

2) Negative ki is not included in the ktol.

KEPCO & KHNP 40

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-5 Uncertainty due to Fuel Assembly Position in the Cell Model keff Normal TS Inward Outward KEPCO & KHNP 41

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-6 Bias due to Cooling Water Temperature Water Water o 3 keff Temperature ( C) Density (g/cm )

4 TS 30 45 55 65 80 95 KEPCO & KHNP 42

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-7 Summary of Bias and Uncertainty for Spent Fuel Pool Region I Parameter Value Type Benchmark Calculation Bias TS 1)

Benchmark Calculation Bias Uncertainty Mechanical Tolerance Uncertainty Monte Carlo Calculation Uncertainty (2)

- Normal Condition

- Distance between Racks 00 mm 12 mm 24 mm 36 mm 48 mm 60 mm

- Including Damaged Cell Note:

1) Doubled bias uncertainty provided in Table 3.4-2 is applied to the criticality analysis for the purpose of conservatism KEPCO & KHNP 43

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.4-8 Summary of keff with Bias and Uncertainty for Spent Fuel Pool Region I 1) keff with Bias and Total Bias and Parameter Uncertainty Uncertainty TS

- Normal Condition

- Distance between Racks 00 mm 12 mm 24 mm 36 mm 48 mm 60 mm

- Including Damaged Cell Note:

2

1) keff = kcal + kBias + (kUnc ) .

KEPCO & KHNP 44

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-1 Reference Model of Spent Fuel Pool Region I KEPCO & KHNP 45

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-2 Model for Gap Effect of Spent Fuel Pool Region I KEPCO & KHNP 46

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-3 Model for Damaged Fuel Storage Cells of Spent Fuel Pool Region I KEPCO & KHNP 47

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-4 Model for Eccentric Position of Fuel Assembly in Spent Fuel Pool Region I KEPCO & KHNP 48

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-5 Top View of the Spent Fuel Storage Racks in the Region I KEPCO & KHNP 49

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.4-6 Side View of the Spent Fuel Storage Racks in the Region I KEPCO & KHNP 50

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.5 Criticality Analysis for Spent Fuel Pool Region II The spent fuel pool region II is designed to accommodate the fuel assemblies with the minimum burnup which satisfies the criticality acceptance criteria. The criticality analysis is performed using the CSAS5/KENO-V.a sequence and the ORIGEN-ARP with cross section libraries generated using the TRITON and the ENDF/B-VII 238 energy group library.

In order to determine the loading curve, the criticality analyses are performed to find the minimum burnup which produced a keff less than 1.0 at the each initial enrichment of fuel assemblies.

Figures 3.5-8 and 3.5-9 provide the top and side views of SFP region II. As can be seen from the Figure 3.5-8, spent fuel storage racks in SFP region II are based on a high density rack design and at least one neutron absorber plate is placed between adjacent fuel assemblies to maintain sub-criticality.

Design data for fuel storage cells of SFP region II are provided in Figures 3.5-8, 3.5-9 and Table 3.1-2, and information for rack interfaces within and between the SFP regions are provided in Subsection 3.6.

3.5.1 Depletion Calculations As discussed in Subsection 3.3.2, the depletion calculations are performed using the ORIGEN-ARP with cross section libraries generated using the TRITON sequence. For the generation of the cross section libraries using the TRITON sequence, bounding reactor parameters described in the Subsection 3.5.1.1 are used. The isotopic concentrations are generated by the ORIGEN-ARP at each 2.25 GWd/MTU intervals from 0 to 72 GWd/MTU for the initial enrichments from 2.0 to 5.0 wt% U-235 with 0.5 wt%

increments of U-235 enrichment.

Zero cooling time is taken for conservatism so that the fuel assembly is not allowed to decay after depleted to a desired assembly-average burnup.

3.5.1.1 Bounding Reactor Parameters for the Depletion Calculation The bounding reactor parameters are used for the depletion calculation for conservatism. The reactor parameters are a fuel temperature, a fuel density, a moderator temperature, a soluble boron concentration and a power level as presented in Table 3.5-1.

a. Fuel temperature: Higher fuel temperature causes Doppler broadening and it results in increased plutonium production. Therefore, the maximum fuel temperature of [

TS

] is applied to the depletion calculations. The applied fuel temperature is higher than the maximum fuel temperature of TS

[ ] including Thermal Conductivity Degradation (TCD) effect.

TS KEPCO & KHNP 51

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS

b. Fuel density: To maximize fissile material, the maximum pellet density of [ ] was applied to the depletion calculations.

c. Moderator temperature: Higher moderator temperature causes less moderation and it results in energy spectrum hardening. Therefore, the maximum moderator temperature of [

TS

] is applied to the depletion calculations.

d. Soluble boron concentration: Higher soluble boron concentration causes energy spectrum hardening. Therefore, the maximum cycle average soluble boron concentration of [

TS

] was applied to the depletion calculations.

e. Power level: The sensitivity analysis is performed to identify the trend with respect to a power level, and it is found that there is no trend with respect to power level as shown in Table 3.5-2. So, the maximum power level corresponding to the maximum fuel temperature is used as a bounding reactor parameter.

f. Partial nuclide credit: The partial nuclide credit was taken for the purpose of conservatism. So only 28 nuclides presented in Table 3.2-1 are considered in criticality analysis.

By using the bounding reactor parameters for the depletion calculation, there is no need to add the additional uncertainty to the calculated nominal keff for the reactor operational conditions.

3.5.1.2 ORIGEN-ARP Calculation As discussed in Subsection 3.3.2.1, the ORIGEN-ARP code is used for the depletion calculation.

3.5.1.3 TRITON-NEWT Calculation The TRITON sequence is used to generate libraries for the PLUS7 16x16 fuel assembly. Figure 3.5-1 shows the depletion calculation model for the PLUS7 16x16 fuel assembly. The burnup steps of 3 GWd/MTU are generally adequate to represent the cross section variations with burnup in creating LWR fuel libraries (Reference 5). But, burnup steps of 2.25 GWd/MTU are used in this calculation for better accuracy. In this calculation, the maximum burnup is 72 GWd/MTU. 32 burnup steps are used with intervals of 2.25 GWd/MTU, and one library is generated for each steps. The library generated by this analysis contains 33 sets of cross sections, which are fresh fuel cross sections and 32 burnup-dependent cross sections. Summary of parameters for the depletion calculation are listed in Table 3.5-3. The burnup values corresponding to each set are listed in Table 3.5-4.

3.5.2 Criticality Calculations The KENO-V.a code with 238 multi-group library based on ENDF/B-VII is used for the criticality calculation. The criticality analysis model for the spent fuel pool region II is modeled as an infinite 2x2 array of the spent fuel storage cells as shown in Figures 3.5-2 (2D) and 3.5-3 (3D). The design data of the spent fuel pool region II and the fuel assembly are presented in Tables 3.1-2 and 3.1-3, respectively. The keff without bias and uncertainty and Monte Carlo standard deviations for keff calculation are summarized in Tables 3.5-5 and 3.5-6, respectively.

3.5.3 Bias and Uncertainty Calculations The bias and uncertainty related to the criticality calculations are as follows:

a. Bias and bias uncertainty due to methodology,

b. Uncertainty due to Monte Carlo calculation,

c. Uncertainty due to mechanical tolerances, KEPCO & KHNP 52

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2

d. Bias due to the credited minor actinides and fission products,

e. Bias due to Pool cooling water temperature, and

f. Uncertainty due to eccentric fuel assembly positioning.

And the bias and uncertainty related to the depletion calculations are as follows:

a. Reactor burnup record uncertainty,

b. Depletion uncertainty, and

c. Bias due to the axial power distribution.

The analysis results of the bias and uncertainty calculations are shown in the following Subsections.

3.5.3.1 Bias and Bias Uncertainty due to Methodology The bias and bias uncertainty of the criticality calculation method are evaluated to validate the criticality analysis methodology through the benchmark calculations based on the criticality experiments (Reference 7).

Two sets of benchmark cases are analyzed to perform trend analysis and to generate bias and bias uncertainties.

a. Fresh fuel with absorbers for region I, and

b. Fresh and depleted fuel (HTC) with absorbers for region II.

In both sets, the only statistically significant trend observed is related to enrichment. Bias and bias uncertainty due to the first set (fresh fuel only) is slightly higher than that due to the second set (with HTC).

Therefore, the first set of bias and bias uncertainty is used for both region I and region II calculations.

1)

Table 3.4-2 shows the bias and bias uncertainty as a function of enrichment and Table 3.4-3 shows the area of applicability for the bias and bias uncertainty.

3.5.3.2 Uncertainty due to Monte Carlo Calculation The statistical uncertainties due to the Monte Carlo calculation are presented in Table 3.5-6.

3.5.3.3 Uncertainty due to Mechanical Tolerances To evaluate uncertainties due to tolerances in the mechanical and material specifications of the fuel and rack structures, sensitivity analyses are performed with various parameters as shown in Table 3.5-7.

The uncertainty due to mechanical tolerances of the fuel assembly and the rack is summarized in Table 3.5-8. And the detailed assessments are described in the following Subsections.

3.5.3.3.1 Fuel Assembly The uncertainties due to mechanical tolerances for the fuel assembly including a fuel pellet enrichment, a fuel pellet diameter, a fuel cladding diameter, a fuel rod pitch, and a guide tube cladding diameter are evaluated. A bounding fuel pellet stack density is used in both the depletion calculations and the criticality

1) Doubled bias uncertainty provided in Table 3.4-2 is applied to the criticality analysis for the purpose of conservatism.

KEPCO & KHNP 53

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 analyses so that no tolerance calculation for density is needed.

Items in the sensitivity analysis for the criticality uncertainty evaluation are summarized as follows:

TS

a. The maximum fuel enrichment: [ ] ,

TS

b. The maximum fuel pellet outer diameter: [ ] ,

TS

c. The maximum fuel cladding inner diameter: [ ] ,

TS

d. The minimum fuel cladding outer diameter: [ ] ,

TS

e. The minimum fuel rod pitch: [ ] ,

TS

f. The maximum fuel rod pitch: [ ] , and TS

g. The minimum guide tube cladding outer diameter: [ ] .

3.5.3.3.2 Rack The uncertainties due to mechanical tolerances for the rack including a cell pitch, a cell wall thickness, and a sheath thickness are evaluated. The uncertainties due to mechanical tolerances about the thickness and width of neutron absorber plates (NAP) are also evaluated and provided in Table 3.5-8. The uncertainty due to tolerance of the NAP length will not be evaluated, because the NAP length applied to TS the criticality analysis is assumed to be identical to the active fuel length ([ ] ) which is shorter TS than the minimum length of NAP ([ ] ).

Items in the sensitivity analysis for the criticality uncertainty evaluation are summarized as follows:

TS

a. The minimum cell pitch: [ ] ,

TS

b. The minimum cell wall thickness: [ ] ,

TS

c. The maximum cell wall thickness: [ ] ,

TS

d. The minimum sheath thickness: [ ] ,

TS

e. The maximum sheath thickness: [ ] ,

TS

f. Minimum neutron absorber thickness: [ ] , and TS

g. Minimum neutron absorber width: [ ] .

3.5.3.4 Bias for Minor Actinide and Fission Product In order to analyze the bias for minor actinide and fission product, the sensitivity analysis is performed to assess the worth of the minor actinides and fission products. The reactivity differences are the worth of the minor actinides and fission products as summarized in Table 3.5-9. Table 3.5-9 shows that the credited minor actinide and fission product worth is no greater than 0.1 in keff. Although the worth TS TS

([ ] ) of [ ] is slightly over the limit, the excess worth is negligible.

As discussed in the NUREG/CR-7109 (Reference 9), one point five percent (1.5 %) of the worth of the minor actinides and fission products conservatively covers the bias due to these isotopes under the following rage of applicability:

a. Low enriched fuel (< 5.0 wt% U-235) with ENDF/B-VII cross section library,

b. Maximum burnup is 70 GWd/MTU, and

c. Total minor actinide and fission product nuclide worth does not exceed 0.1 in keff.

KEPCO & KHNP 54

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 So, 0.0015 is used as the bias for the minor actinides and fission products for all burnup and enrichment range.

3.5.3.5 Bias due to Pool Cooling Water Temperature The bias due to the pool cooling water temperature is assessed. The sensitivity analyses in the ranges of 3 3 water density from 0.962 g/cm to 1.0 g/cm are performed to evaluate the effect of pool cooling water o o temperature range of the spent fuel pool with water temperature from 4 C to 95 C.

The effective neutron multiplication factors of the disturbed models are less than those of reference model as shown in Table 3.5-10. So the bias due to cooling water density is not included in the total bias.

3.5.3.6 Uncertainty due to Eccentric Fuel Assembly Positioning The fuel assembly is assumed to be located in the center position of the cell for the reference model. But the fuel assembly could be located eccentrically in the cell. The uncertainty due to fuel assembly positioning in the rack cell is assessed. Figure 3.5-4 shows the model of the eccentric positioning of the fuel assembly. The fresh fuel has the highest reactivity at each enrichment value compared to the burned fuel, so the fresh fuel is used to evaluate the uncertainty due to the eccentric fuel assembly positioning.

The multiplication factor for the fuel assembly positioning model is less than that of the reference model as shown in Table 3.5-11. So the uncertainty of fuel assembly positioning is not included in the total uncertainty.

3.5.3.7 Uncertainty due to Reactor Burnup Record The reactor burnup record uncertainty is an uncertainty representing the deviation between the true burnup of a fuel assembly and the burnup based on the reactor record.

The fuel assembly burnup is generated by using the CECOR computer code. The CECOR computer code synthesizes a three-dimensional assembly and the peak pin power distributions using signals from fixed in-core detectors. When performing a CECOR calculation, snapshots are selected to be representative of a period of reactor operation. The information contained in the burnup record includes the number of assemblies, number of axial nodes, core average exposure and axial exposures for all assemblies.

The reactor burnup record uncertainty is typically less than 5 % based on NUREG/CR-6998 (Reference 10). Therefore, the reactivity difference due to the 5 % change in burnup is applied to the reactor burnup record uncertainty. The uncertainties due to the reactor burnup record are provided in Table 3.5-12.

3.5.3.8 Uncertainty due to Depletion To cover the uncertainty in the isotopic number densities generated during the depletion calculations, the depletion uncertainty provided in Kopps memo (Reference 11) is applied to the criticality analysis.

The depletion uncertainty is taken to be 5 % of the reactivity difference between the reactivity at the fresh fuel condition and the reactivity at the burned fuel condition. The depletion uncertainty is calculated by the following equation:

TS KEPCO & KHNP 55

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS The kfresh and kburned values are provided in Table 3.5-5, and fresh and burned values are provided in Table 3.5-6. The depletion uncertainties are provided in Table 3.5-13.

3.5.3.9 Bias due to Axial Power Distribution The reactivity difference between the effective neutron multiplication factors (keff) calculated with explicit representation of the axial burnup distribution and keff calculated assuming a uniform axial burnup distribution is referred to as the end effect. The end effect is shown to be dependent on many factors, including the axial burnup profile, a total accumulated burnup, a cooling time, an initial enrichment, an assembly design, and the isotopic concentrations.

In this calculation, the fuel assembly type is only the PLUS7 16x16 fuel assembly, assumed as non-blanketed fuel, 28 actinides and fission products are considered, and no decay time is credited. And calculations are performed with and without a bounding axial burnup profile, to assess the magnitude of the end effect which is applied as a bias.

3.5.3.9.1 Selection of Bounding Axial Burnup Profile For the axial power distribution, the uniform axial burnup is assumed and the end effect is considered as a bias. To quantify the end effect as a function of enrichment and burnup, a bounding axial burnup profile is selected by surveying 304 burnup profiles which cover all possible types of axial burnup distributions.

The significantly under-burned top nodes of the fuel assemblies are the most important to quantify the end effect. So the axial burnup profile having the smallest burnup of the top fuel region is chosen as a bounding axial burnup profile among the profiles. And then the original 26 non-uniform heights (nodes) are modified into the 18 non-uniform heights (nodes) by merging flat burnup regions in the middle of fuel rod as shown in Table 3.5-14.

3.5.3.9.2 Modeling of Axial Burnup Distribution The axial burnup profile has 18 nodes having different local burnups. The local powers for each node are assumed by multiplying a normalized burnup distribution by the assembly-averaged power as shown in Table 3.5-14.

3.5.3.9.3 End Effect of Non-Blanketed Fuel The fuel assemblies are assumed as non-blanketed fuel for conservatism. The keff calculated with explicit representation of the axial burnup distribution for the non-blanketed fuel is shown in Table 3.5-15, and keff calculated assuming flat axial burnup distribution for the non-blanketed fuel is shown in Table 3.5-16. And the reactivity difference between them is shown in Table 3.5-17, which is the end effect of non-blanketed fuel. Only positive end effects are applied as bias.

3.5.3.9.4 End Effect of Blanketed Fuel TS The PLUS7 16x16 fuel assembly has blankets ([ ] ) at the top and bottom end of the fuel rod. Calculations are performed to assess the magnitude of the blanket effect which is considered as an additional margin.

The keff calculated for a blanketed fuel with explicit representation of the axial burnup distribution is shown KEPCO & KHNP 56

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 in Table 3.5-18, and keff calculated for a blanketed fuel assuming flat distribution is shown in Table 3.5-19.

And the reactivity difference between them is shown in Table 3.5-20 which is the end effect of blanketed fuel. By comparing the end effect without blanket (Table 3.5-17) and with blanket (Table 3.5-20) shows TS that assuming fuel as a non-blanketed fuel gives margin up to [ ] in keff.

3.5.3.10 keff with Bias and Uncertainty All biases are directly added to determine the total bias. Total bias is the sum of all the biases due to the methodology, a minor actinide and fission product, and an axial power distribution. The total bias is summarized in Table 3.5-21.

All uncertainty values are statistically combined (the square root of the sum of the squares) to determine the total uncertainty. The uncertainties are due to the methodology, a Monte Carlo calculation, a mechanical tolerance, a reactor burnup record, and a depletion. The total uncertainty is summarized in Table 3.5-22. Total bias and uncertainty and the keff with bias and uncertainty are summarized in Tables 3.5-23 and 3.5-24, respectively.

3.5.4 Calculation of Minimum Burnup versus Enrichment Curve The minimum burnup versus enrichment curve is based on the keff with bias and uncertainty in Table 3.5-

24. The keff with bias and uncertainty is represented as graph in Figure 3.5-5 which shows the linear fitting TS equations for each enrichment value. Table 3.5-25 shows the minimum burnup for target [ ]

calculated by the fitting equations in Figure 3.5-5 for each enrichment value. And Figure 3.5-6 shows the minimum burnup versus enrichment curve based on Table 3.5-25. The 3rd degree polynomial is used to generate the fitting equation. Then, for conservatism the y-interception of the fitting equation is adjusted to TS be [ ] of the raw value. Table 3.5-26 shows the adjustment result and Figure 3.5-6 shows the adjusted fitting equation.

TS Figure 3.5-7 shows the final minimum burnup versus enrichment curve for spent fuel pool region II.

KEPCO & KHNP 57

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-1 Bounding Value of Reactor Parameters for the Depletion Calculation Bounding Reactor Parameters Value TS Maximum Fuel Temperature

- Peak fuel temperature at peak linear power TS assuming a maximum over power of [ ] :

TS

[ ]

TS

- Operational disturbance : [ ]

Maximum Fuel Density TS

- Nominal fuel stack density: [ ]

TS

- Tolerance of fuel stack density: [ ]

Maximum Moderator Temperature (Minimum moderator density)

TS

- Saturation temperature at [ ]

Maximum Cycle Average Soluble Boron Concentration

- Maximum cycle average soluble boron TS concentration: [ ]

TS

- Operational disturbance : [ ]

Maximum Power Level KEPCO & KHNP 58

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-2 Sensitivity Analysis for Power Level TS TS Reactivity difference between nominal power ([ ] ) case and max. power ([ ] )

case Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh - - - - - - - TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

TS The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 59

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-3 Parameters for Generated ORIGEN-ARP Libraries of PLUS7 16x16 Fuel Assembly Parameters Value Assembly lattice TS Model Enrichments No. rods per assembly No. water holes Rod pitch Assembly pitch Fuel rod data Fuel density (bounding)

Pellet diameter Clad material Clad inner diameter Clad outer diameter Fuel temperature (bounding)

Clad temperature Guide tube data Inner diameter Outer diameter Guide tube material Moderator data Average density (bounding)

Average boron concentration (bounding)

Moderator temperature (bounding)

Power level (bounding)

KEPCO & KHNP 60

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-4 Burnup Values of Cross Section Sets Set Burnup (MWd/MTU) 1 TS 2

3 4

5 6

7 8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Note:

These values represent the burnup of the 33 cross section sets retained in the final cross section library.

KEPCO & KHNP 61

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-5 keff without Bias and Uncertainty for Spent Fuel Pool Region II Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 KEPCO & KHNP 62

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-6 Monte Carlo Standard Deviation for keff Calculation Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 KEPCO & KHNP 63

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-7 Mechanical Tolerances Design parameter Nominal Tolerance Applied Value Rack in Min. cell pitch TS Region II Min. cell wall thick.

Max. cell wall thick.

Min. sheath thick.

Max. sheath thick.

Neutron Min. thick.

Absorber Plate Min. width Fuel Max. fuel enrichment Assembly Max. fuel pellet O.D.

Max. fuel clad I.D.

Min. fuel clad O.D.

Min. fuel rod pitch Max. fuel rod pitch Min. G/T clad O.D.

KEPCO & KHNP 64

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-8 Uncertainty due to Mechanical Tolerance keff for nominal and disturbed cases 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh fresh fresh fresh fresh fresh fresh Nominal TS Min. cell pitch Min. cell wall thick.

Rack Max. cell wall thick.

Min. sheath thick.

Max. sheath thick.

Min. thick.

NAP Min. width Max. fuel enrichment Max. fuel pellet O.D.

FA Max. fuel clad I.D.

Min. fuel clad O.D.

Min. fuel rod pitch Max. fuel rod pitch Min. G/T clad O.D.

1)

Reactivity difference between reference case and disturbed case 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh fresh fresh fresh fresh fresh fresh Min. cell pitch TS Min. cell wall thick.

Rack Max. cell wall thick.

Min. sheath thick.

Max. sheath thick.

Min. thick.

NAP Min. width Max. fuel enrichment Max. fuel pellet O.D.

FA Max. fuel clad I.D.

Min. fuel clad O.D.

Min. fuel rod pitch Max. fuel rod pitch Min. G/T clad O.D.

2)

Total uncertainty (ktol = i(ki )2 )

Notes:

TS

1) The reactivity differences are derived as follows: [ ] , and

2) The negative reactivity difference is not included to the total uncertainty for conservatism.

KEPCO & KHNP 65

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-9 Bias for Minor Actinides and Fission Products Worth of minor actinides and fission products 1)

Reactivity difference between major actinides-only and minor actinide and fission products Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

TS

1) The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 66

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-10 Bias for Pool Cooling Water Temperature keff for reference and possible water densities Water 2.0 2.5 3.0 3.5 4.0 4.5 5.0 3

Density (g/cm ) fresh fresh fresh fresh fresh fresh fresh TS Monte Carlo standard deviation () for keff calculation Water 2.0 2.5 3.0 3.5 4.0 4.5 5.0 3

Density (g/cm ) fresh fresh fresh fresh fresh fresh fresh TS 1)

Reactivity difference between reference case and disturbed case Water 2.0 2.5 3.0 3.5 4.0 4.5 5.0 3

Density (g/cm ) fresh fresh fresh fresh fresh fresh fresh TS Note:

TS

1) The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 67

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-11 Uncertainty due to Eccentric Fuel Assembly Positioning 4x4 infinite array and normal position (center) with all reflective conditions: reference cases Fresh fuel with enrichment (wt% U-235) keff and 2.0 2.5 3.0 3.5 4.0 4.5 5.0 keff TS 4x4 infinite array and eccentric position (inward) with all reflective conditions: disturbed cases Fresh fuel with enrichment (wt% U-235) keff and 2.0 2.5 3.0 3.5 4.0 4.5 5.0 keff TS 1)

Reactivity difference between the reference cases and the disturbed cases Reactivity Fresh fuel with enrichment (wt% U-235) difference 2.0 2.5 3.0 3.5 4.0 4.5 5.0 TS k

Note:

TS

1) The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 68

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-12 Uncertainty due to Reactor Burnup Record 1)

Reactivity difference between 5% less burned fuel and exactly burned fuel.

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

TS

1) The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 69

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-13 Depletion Uncertainty 1) 5 % of the reactivity difference between fresh fuel and burned fuel Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

TS

1) The reactivity differences are derived as follows: [ ] .

KEPCO & KHNP 70

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-14 Bounding Axial Burnup Profile Modified Node Axial Node Modified Modified node Local 1)

Node Height burnup Normalized length node normalized length power no. (%) (MWd/MTU) axial burnup (cm) no. axial burnup (cm) (MWt/MTU) 1 (top) TS 2

3 4

5 6

7 8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Note:

1) Percent of Axial height from the bottom of active fuel region.

KEPCO & KHNP 71

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-15 keff Calculated with Bounding Axial Burnup Distribution (Non-Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

1) This axial burnup distribution model is made with fuel rods divided into 18 nodes, and

2) The fuel assembly is assumed as a non-blanketed fuel.

KEPCO & KHNP 72

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-16 keff Calculated with Flat Burnup Distribution (Non-Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

1) This flat burnup distribution model is made with fuel rods divided into 18 nodes, and

2) The fuel assembly is assumed as a non-blanketed fuel.

KEPCO & KHNP 73

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-17 Reactivity difference between Flat and Axial Burnup Distribution (Non-Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

TS

1) The reactivity difference = [ ] , and

2) The fuel assembly is assumed as a non-blanketed fuel.

KEPCO & KHNP 74

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-18 keff Calculated with Bounding Axial Burnup Distribution (Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

1) This axial burnup distribution model is made with fuel rods divided into 18 nodes, and

2) The fuel assembly is modeled as a blanketed fuel.

KEPCO & KHNP 75

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-19 keff Calculated with Flat Burnup Distribution (Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

1) This flat burnup distribution model is made with fuel rods divided into 18 nodes, and

2) The fuel assembly is modeled as a blanketed fuel.

KEPCO & KHNP 76

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-20 Reactivity difference between Flat and Axial Burnup Distribution (Blanketed)

Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Notes:

TS

1) The reactivity difference = [ ] , and

2) The fuel assembly is modeled as a blanketed fuel.

KEPCO & KHNP 77

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-21 Total Bias for Spent Fuel Pool Region II Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

Total bias = kBias .

KEPCO & KHNP 78

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-22 Total Uncertainty for Spent Fuel Pool Region II Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

2 Total uncertainty = (kUnc ) .

KEPCO & KHNP 79

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-23 Total Bias and Uncertainty for Spent Fuel Pool Region II Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 Note:

2 Total bias and uncertainty = kBias + (kUnc ) .

KEPCO & KHNP 80

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-24 keff with Bias and Uncertainty for Spent Fuel Pool Region II Burnup Enrichment (wt% U-235)

GWd/MTU 2.0 2.5 3.0 3.5 4.0 4.5 5.0 fresh TS 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.00 29.25 31.50 33.75 36.00 38.25 40.50 42.75 45.00 47.25 49.50 51.75 KEPCO & KHNP 81

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-25 Minimum Burnup Calculated with Raw Fitting Equation Enrichment Raw Fitting Minimum Burnup (GWd/MTU)

TS wt% U-235 Equation when keff = [ ]

2.0 TS 2.5 3.0 3.5 4.0 4.5 5.0 Note:

x and y denote the burnup and keff, respectively.

KEPCO & KHNP 82

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Table 3.5-26 Minimum Burnup versus Enrichment for Raw Fitting and Adjusted Fitting Min. burnup for raw fitting Min. burnup for adjusted fitting Enrichment wt% U-235 TS 2.00 2.10 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 Notes:

1) The 3rd degree polynomial is used to generate fitting equation, and TS TS

2) The y interception of adjusted fitting ([ ] ) is assumed to be the [ ] of the raw fitting TS

([ ] ) for conservatism.

KEPCO & KHNP 83

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Note:

Reflective boundary conditions are applied on all sides.

Figure 3.5-1 Symmetric Depletion Calculation Model for the PLUS7 16x16 Fuel Assembly KEPCO & KHNP 84

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Cell Pitch:[ ]

Water Fuel Rod y

Sheath, Neutron Absorber Plate Cell Plate, TS x Thickness: [ ]

TS Width: [ ]

TS Inner Dimension: [ ]

TS Thickness: [ ]

TS Thickness: [ ]

Note:

x-y axis: periodic boundary conditions, z axis: reflective boundary conditions.

Figure 3.5-2 Cross Section View of KENO-V.a Model for 2x2 Array of Fuel Rack in Region II KEPCO & KHNP 85

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Sheath z

y Neutron Absorber Plate Fuel Rod Cell Plate Water Notes:

x-y axis: periodic boundary conditions, z axis: reflective boundary conditions.

Figure 3.5-3 3-D View of KENO-V.a Model for 2x2 Array of Fuel Rack in Region II KEPCO & KHNP 86

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 Figure 3.5-4 Model for Eccentric Position of Fuel Assemblies in Spent Fuel Pool Region II KEPCO & KHNP 87

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.5-5 Burnup versus keff with Fitting Equations KEPCO & KHNP 88

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.5-6 Minimum Burnup versus Enrichment with Raw Fitting and Adjusted Fitting KEPCO & KHNP 89

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.5-7 Minimum Burnup versus Enrichment Curve KEPCO & KHNP 90

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.5-8 Top View of the Spent Fuel Storage Racks in the Region II KEPCO & KHNP 91

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 TS Figure 3.5-9 Side View of the Spent Fuel Storage Racks in the Region II KEPCO & KHNP 92

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.2 3.6 Interface Between Regions 3.6.1 Interface within Each Region Gaps between racks in SFP are provided in Figure 3.6-1. Interface within region I is less reactive than the TS reference case for region I, because the gap between the racks in region I is [ ] , but the gap TS between the cells in region I (the reference case) is [ ] .

Interface within region II is also less reactive than the reference case for region II, because the gap TS between the racks in region II is [ ] , but the gap between the cells in region II (the reference case)

TS is [ ] .

3.6.2 Interface between Regions I and II Gaps between racks in SFP are provided in Figure 3.6-1. Interface between region I and region II is also predictable due to the same reason in Subsection 3.6.1, because the gap between region I and region II TS is at least [ ] . Furthermore, racks in region I have neutron absorber panel on the exterior of the rack, so there is no local increase in reactivity at the rack interface. There are sufficient neutron absorber panels among racks so that the maximum keff is much less than the limiting keff in region I or region II.

KEPCO & KHNP 93

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 TS Figure 3.6-1 Spent Fuel Storage Rack Interfaces KEPCO & KHNP 94

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 4 ACCIDENT ANALYSIS The following postulate accidents are considered in following Subsections:

a. Dropped fresh fuel assembly,

b. Misloaded fresh fuel assembly into incorrect storage rack location, and

c. Boron dilution accident.

4.1. Dropped Fresh Fuel Assembly During the placement of the fuel assemblies in the spent fuel storage rack, it is possible to drop the fuel assembly between concrete wall and racks. This postulate accident is analyzed under the most severe conditions such that the dropped fuel assembly lands just beside outer-most storage cell of region I and all storage cell are occupied by fresh fuel assemblies.

Figure 4.1-1 shows the accident analysis model of a dropped fresh fuel assembly. As shown in the figure, the analysis model consists of a dropped fresh fuel assembly, a concrete wall, fuel storage cells and fuel assemblies stored in the cells. Instead of modeling whole storage cells in the region I, 1x17 arrays of storage cells with reflective boundary condition are considered. Enrichment of a dropped fuel assembly and stored fuel assemblies is assumed as 5.0 wt%. It is assumed that the soluble boron concentration in TS the pool water is [ ] , which is the minimum boron concentration specified in technical specification LCO 3.7.15. Additional analyses are performed to find the minimum boron concentration which is sufficient to assure the regulatory limit (keff of 0.95).

The criticality analysis results of a dropped fuel accident are summarized in Table 4.1-1. Under the TS TS minimum boron concentration, [ ] , keff with bias and uncertainty is [ ] , much smaller than regulatory limit (keff of 0.95). It is shown that the keff reaches to 0.95 when boron concentration TS decreases to [ ] as demonstrated in Figure 4.1-2.

The criticality analysis information of dropped fresh fuel assembly is summarized as follows:

a. Enrichment of dropped fuel and stored fuel: 5.0 wt%,

TS

b. Distance between inner concrete wall and outer-most storage cell: [ ] ,

TS

c. Distance between dropped fuel assembly and stored fuel assembly: [ ] ,

TS

d. Soluble boron concentration: [ ] ,

TS

e. Thickness of concrete wall: [ ] ,

f. Boundary conditions:

+X, +Y, -Y, +Z and -Z directions: Reflective boundary condition,

-X direction: Vacuum boundary condition,

g. Design data of storage cell of SFP region I and fuel assemblies are presented in Tables 3.1-1 and 3.1-3, respectively, and

h. Bias and uncertainty discussed in Subsection 3.4.3 are applied to the critical analysis results.

KEPCO & KHNP 95

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.1-1 Criticality Analysis Results for Dropped Fuel Assembly Accident Boron Concentration Effective Multiplication 1)

[ppm] Factor (keff)

TS Note:

1) Bias and Uncertainty are included KEPCO & KHNP 96

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Figure 4.1-1 Accident Analysis Model for the Dropped Fresh Fuel Assembly KEPCO & KHNP 97

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 TS Figure 4.1-2 keff versus Boron Concentration Curves for Dropped Fuel Accident and Misloaded Fresh Fuel Accident KEPCO & KHNP 98

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 4.2. Misloaded Fresh Fuel Assembly The misloaded fresh fuel assembly accident is the case that a fresh fuel assembly is placed into region II storage cell intended for spent fuel assemblies. The most severe case is that misloaded fresh fuel assembly is being surrounded by the most reactive fuel allowed in region II.

As illustrated in Figure 4.2-1, the analysis model for misloaded fresh fuel assembly accident consists of 2x2 arrays of storage cell with periodic boundary conditions on all four sides. The 2x2 arrays of storage cell are occupied by a misloaded fresh fuel assembly and three spent fuel assemblies. The enrichment of fresh fuel assembly is assumed as 5.0 wt% and the burnup and the initial enrichment of the spent fuel TS stored in the region II are assumed [ ] , respectively. The nuclide densities of spent fuel assembly are obtained from the depletion calculation and presented in Table 4.2-1. This assumption is conservative because the acceptable minimum burnup for initial enrichment of [

TS

] as discussed in Subsection 3.5.4. The soluble boron concentration is assumed as TS

[ ] , which is the same as Subsection 4.1. Additional analyses are performed to find the minimum boron concentration which is sufficient to assure the regulatory limit (keff of 0.95).

The criticality analysis results of a misloaded fresh fuel accident are summarized in Table 4.2-2. Under the TS TS boron concentration of [ ] , keff with bias and uncertainty is [ ] , much smaller than regulatory limit as dropped fuel accident case. It is shown that the keff reaches to regulatory limit when TS boron concentration decreases to [ ] as demonstrated in Figure 4.1-2.

The criticality analysis information of the misloaded fresh fuel assembly accident is summarized as follows:

a. Enrichment of misloaded fuel: 5.0 wt%,

TS

b. Initial Enrichment of spent fuel stored in the region II: [ ] ,

TS

c. Burnup of spent fuel stored in the region II: [ ] ,

TS

d. Soluble boron concentration: [ ] ,

TS

e. Thickness of concrete wall: [ ] ,

f. Boundary conditions:

X, Y axis: Periodic boundary condition, Z axis: Reflective boundary condition,

g. Design data of storage cell of region II is presented in Table 3.1-2, and

h. Bias and uncertainty discussed in Subsection 3.5.3 are applied to the critical analysis results.

KEPCO & KHNP 99

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.2-1 Number Densities of Nuclide in the Spent Fuel TS TS (Initial enrichment: [ ] , Burnup: [ ] )

Number Density Nuclide

[atoms/cm-barn]

U-234 TS U-235 U-236 U-238 Np-237 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 Am-243 Mo-95 Tc-99 Ru-101 Rh-103 Ag-109 Cs-133 Nd-143 Nd-145 Sm-147 Sm-149 Sm-150 Sm-151 Sm-152 Eu-151 Eu-153 Gd-155 O-16 KEPCO & KHNP 100

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.2-2 Criticality Analysis Results for Misloaded Fuel Assembly Accident Boron Concentration Effective Multiplication 1)

[ppm] Factor (keff)

TS Note:

1) Bias and Uncertainty are included KEPCO & KHNP 101

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Figure 4.2-1 Accident Analysis Model for Misloaded Fresh Fuel Assembly KEPCO & KHNP 102

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 4.3. Boron Dilution Accident 4.3.1 Minimum Soluble Boron Concentration The soluble boron concentration is the important factor for the critical safety since it is utilized to control the reactivity of spent fuel in the pool. Therefore, a boron dilution accident is one of the most severe accidents in the view of criticality safety.

The analysis model of a boron dilution accident for region I is illustrated in Figure 4.3-1. The model consists of 2x2 arrays of region I storage cell with reflective boundary conditions. The 2x2 arrays of storage cell are occupied by the fresh fuel assembly and its initial enrichment is assumed as 5.0 wt% for conservatism.

Figure 4.3-2 shows the analysis model of a boron dilution accident for region II. The model consists of 2x2 arrays of region II storage cell with periodic boundary conditions. The 2x2 arrays of storage cell are occupied by spent fuel assemblies. The burnup and the initial enrichment of the spent fuel stored in the TS region II are assumed as [ ] , respectively. The burnup of [

TS

] is conservative assumption since the acceptable minimum burnup for initial enrichment of TS

[ ] . The nuclide number densities of spent fuel are obtained from the depletion calculation and presented in Table 4.3-1.

The criticality analysis results of boron dilution accident for region I and region II are summarized in Tables 4.3-2 and 4.3-3, respectively. As demonstrated in Figure 4.3-3, keff of region I doesnt exceed regulatory limit even though boron concentration is 0 ppm. In case of region II, the minimum boron concentration to TS assure the regulatory limit is [ ] as shown in Figure 4.3-3.

The criticality analysis information of boron dilution accident is summarized as follows:

For region I

a. Enrichment of fresh fuel: 5.0 wt%,

b. Boundary conditions:

All axis: Reflective boundary condition,

c. Design data of storage cell of region I and fuel assemblies are presented in Tables 3.1-1 and 3.1-3, respectively, and

d. Bias and uncertainty discussed in Subsection 3.4.3 are applied to the critical analysis results.

For region II TS

a. Initial Enrichment of spent fuel stored in the region II: [ ] ,

TS

b. Burnup of spent fuel stored in the region II: [ ] ,

c. Boundary conditions:

X, Y axis: Periodic boundary condition, Z axis: Reflective boundary condition,

d. Design data of storage cell of region II is presented in Table 3.1-2, and

e. Bias and uncertainty discussed in Subsection 3.5.3 are applied to the critical analysis results.

KEPCO & KHNP 103

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 4.3.2 Evaluation of Boron Dilution Accidents in the Spent Fuel Pool This Subsection provides analyses of potential boron dilution accidents if credit for soluble boron is taken for demonstrating spent fuel storage rack subcriticality for the APR1400 spent fuel pool (SFP) design.

There are various systems within the SFP vicinity which contain unborated water and under accident conditions could potentially result in some degree of boron dilution for the SFP. Based on the systems and the associated maximum unborated water flow rates of such postulated unborated water addition, the amount of time takes for the postulated maximum flows considered to dilute the boron concentration to the TS prescribed limit of [ ] can be calculated. This calculation utilizes the following boron dilution equation.

TS For the conservative calculation of the boron dilution time in SFP, instead of utilizing the normal (operating)

TS concentration of boron in the SFP of [ ] and the normal operation volume of SFP of TS

[ ] , the boron concentration and the SFP volume listed above are utilized.

Utilizing the equation, the SFP input data, the above conservative assumptions, and the maximum unborated water flow rates, the time required to dilute the SFP from a boron concentration of [

TS TS

] to a boron concentration of [ ] is calculated. Additionally, utilizing the volumetric flow rate of unborated water and the SFP volume at the high level alarm set point, the time to SFP high level alarm TS and the required time values for boron dilution to [ ] after SFP high level alarm are also calculated.

TS In this evaluation, the SFP volume at the high level alarm set point is [ ] . The results of these calculations are provided in Table 4.3-4.

As a result of this evaluation, it is concluded that an event which would result in the dilution of the SFP TS boron concentration from [ ] is not a credible event. This conclusion is supported by all of the followings.

TS

- In order to dilute the SFP from a boron concentration of [ ] resulting in a TS keff of 0.95, a substantial amount of water (greater than [ ] ) is needed. Since such a large water volume turnover is required, a SFP dilution event would be readily detected by plant personnel via high level alarms, or by normal operator rounds through the SFP area.

KEPCO & KHNP 104

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1

- The requirement of the minimum soluble boron concentration to assure the keff is less than 0.95 TS TS was set to [ ] . This is far less than the normal operating conditions of [ ] . In the case of a boron dilution event, the calculated dilution times in Table 4.3-4 are long enough to allow corrective actions to be made and to disrupt the dilution event.

- The existence of high level alarms in the main control room would be readily detected by plant personnel. As provided in Table 4.3-4, the sufficient time after SFP high level alarm is available to respond to a dilution event.

From the evaluation of boron dilution accidents in the spent fuel pool, it is confirmed that the design criteria 10 CFR 50.68 are met and that subcriticality is maintained.

KEPCO & KHNP 105

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.3-1 Number Densities of Nuclide in the Spent Fuel TS TS (Initial enrichment: [ ] , Burnup: [ ] )

Number Density Nuclide

[atoms/cm-barn]

U-234 TS U-235 U-236 U-238 Np-237 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 Am-243 Mo-95 Tc-99 Ru-101 Rh-103 Ag-109 Cs-133 Nd-143 Nd-145 Sm-147 Sm-149 Sm-150 Sm-151 Sm-152 Eu-151 Eu-153 Gd-155 O-16 KEPCO & KHNP 106

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.3-2 Analysis Results of Boron Dilution Accident in the Region I Boron Concentration Effective Multiplication 1)

[ppm] Factor (keff)

TS Note:

1) Bias and Uncertainty are included.

KEPCO & KHNP 107

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Table 4.3-3 Analysis Results of Boron Dilution Accident in the Region II Boron Concentration Effective Multiplication 1)

[ppm] Factor (keff)

TS Note:

1) Bias and uncertainty are included.

KEPCO & KHNP 108

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 TS Table 4.3-4 Critical Time Values for Boron Dilution from [ ] within the SFP Time to [

Volumetric Time to Time to High TS TS ] after SFP Component Flow Rate [ ] Level Alarm Dilution Event Details High Level Alarm (gpm) (min) (min)

(min)

TS Component Cooling Water Makeup Pumps Spent Fuel Pool Makeup Water Lines Spent Fuel Pool Spray Lines Spent Fuel Pool Cooling Heat Exchangers KEPCO & KHNP 109

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 TS Table 4.3-4 Critical Time Values for Boron Dilution from [ ] within the SFP (Cont.)

Time to [

Volumetric Time to Time to High TS TS ] after SFP Component Flow Rate [ ] Level Alarm Dilution Event Details High Level Alarm (gpm) (min) (min)

(min)

TS Demineralized Water Transfer Pumps Fire Protection 2.5" Line Fire Protection 1.5" Line Generic System Leakage KEPCO & KHNP 110

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Figure 4.3-1 Analysis Model of Boron Dilution Accident in the Region I KEPCO & KHNP 111

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 Figure 4.3-2 Analysis Model of Boron Dilution Accident in the Region II KEPCO & KHNP 112

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 TS Figure 4.3-3 keff versus Boron Concentration Curves for Boron Dilution Accident KEPCO & KHNP 113

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 5 LIMITATIONS OF ANALYSIS The APR1400 design is an advanced PWR design that is functionally similar to existing plants. The following design input data to this analysis will be checked in order to ensure compliance with the criticality safety design basis.

5.1 Fuel Limitations

1. This analysis is applicable to the PLUS7 16x16 fuel design.

TS

2. The initial stack density shall be less than [ ] of the theoretical TS density of uranium dioxide ([ ] ).

5.2 Operational Limitations

1. The cycle averaged soluble boron concentration for all fuel assemblies shall be less than TS

[ ] .

2. Fuel assemblies that do not meet operational limits and assumptions will be specifically evaluated and classified following the same methodology used in this report.

5.3 Spent Fuel Pool Limitations TM

1. An areal density of each neutron absorber material (METAMIC ) shall be greater than or TS equal to [ ] for spent fuel pool region I.

TM

2. An areal density of each neutron absorber material (METAMIC ) shall be greater than or TS equal to [ ] for spent fuel pool region II.

TS

3. The center to center spacing of region I shall be greater than or equal to [ ] and TS the center to center spacing of region II shall be greater than or equal to [ ] .

KEPCO & KHNP 114

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 6 CONCLUSIONS The effective neutron multiplication factors, keff, are calculated for the new and spent fuel storage racks of the APR1400 design. The analysis covers both a normal and accident conditions. The proper set of bias and uncertainty is applied for each case in order to assure the conservatism in the analysis.

From the evaluation results described in Chapter 2 (NFR), Chapter 3 (SFR), and Chapter 4 (accident analyses), it is confirmed that the design criteria are met and the subcriticality is maintained in the new and spent fuel storage racks.

KEPCO & KHNP 115

Non-Proprietary Criticality Analysis of NFR and SFR APR1400-Z-A-NR-14011-NP, Rev.1 7 REFERENCES

1. 10 CFR 50, Appendix A, GDC 62, Prevention of Criticality in Fuel Storage and Handing, U.S.

Nuclear Regulatory Commission.

2. 10 CFR 50.68, Criticality Accident Requirements, U.S. Nuclear Regulatory Commission, November 1998.

3. DSS-ISG-2010-01, Staff Guidance Regarding the Nuclear Criticality Safety Analysis for Spent Fuel Pools, U.S. Nuclear Regulatory Commission, October 2011.

4. NUREG/CR-6698, Guide for Validation of Nuclear Criticality Safety Calculational Methodology, U.S. Nuclear Regulatory Commission, January 2001.

5. ORNL/TM-2005/39, Scale: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, Version 6.1, ORNL, June 2011.

6. Nuclear Data Sheets, 107(12), 2931-3059, ENDF/B-VII.0 Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology, Chadwick et al, December 2006.

7. WCAP-17889-P, "Validation of SCALE 6.1.2 with 238-Group ENDF/B-VII.0 Cross Section Library for APR1400 Design Certificate," WEC, June 2014.

8. Interim Staff Guidance-8, "Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transportation and Storage Casks," U.S. Nuclear Regulatory Commission, September 2012.

9. NUREG/CR-7109, An Approach for Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses - Criticality (keff) predictions, U,S. Nuclear Regulatory Commission, April 2012.

10. NUREG/CR-6998, Review of Information for Spent Nuclear Fuel Burnup Confirmation, U,S.

Nuclear Regulatory Commission, June 2009.

11. NRC memorandum, Guidance on the Regulatory Requirements for Criticality Analysis of Fuel Storage at Light-Water Reactor Power Plants, U.S. Nuclear Regulatory Commission, August 1998.

KEPCO & KHNP 116